id stringlengths 6 16 | image unknown | question stringlengths 7 9.46k | answer stringlengths 1 33.4k | source stringclasses 79
values | domain stringclasses 7
values | type stringclasses 1
value | subtype stringclasses 10
values | distill_model stringclasses 1
value | difficulty float64 0.25 1 | response stringlengths 143 59.8k |
|---|---|---|---|---|---|---|---|---|---|---|
mmfr_9 | "iVBORw0KGgoAAAANSUhEUgAAAQMAAABECAIAAAAKmcf8AAAYbklEQVR4nO2db2gT2drAn/sywhmIcAYizECFzqLgFAUTLGzC9YMRX7CyF0xwQYsX3OxdWNMV1maF1Vw/+EYXvOku7Jpd8G5WWEmFlVbYpfFDcfqhS3LBS7Jg6RQqnIKBGTAwBwzMAQf6fjjTNP3falvbbX7COE1O5pyZOc/585znec5fpqenoUWLHc//vOsCtGixJWhJwvaDMQbuuy7En46WJLwVtEbJc7KpWbrQc7Gn8LiwqZnuADZEEowJg1K6EVdeClqjH3/0sTF... | <image>Based on the image, set up the equation and solve it. | 4x + 28.5 = 51.5, x = 5.75 | MMR1 | math | close | numeric | qwen3.5-27b | 0.25 | <think>
The image shows a diagram representing a total quantity of 51.5 tons, composed of two parts:
- A lower part labeled as 28.5 tons.
- An upper part made up of four equal segments, each labeled “x 吨” (meaning x tons).
This implies that the sum of the four x-ton segments plus the 28.5-ton segment equals the total... |
mmfr_20 | "iVBORw0KGgoAAAANSUhEUgAAAfQAAAJYCAIAAAAbgoPVAABPyUlEQVR4nO3daVwT18IG8JMESNjCIgIiawG3qqAoFltlkaogKlp3e0Hr1hasiMsrdrHWtrTXve7WKt6rXLcWtaAiIrhiVZTWpVq1CrgEcCGRLUCS98Nc01y2IpLM5OT5//ohM3OYPAn0YTwZZngqlYoAAABd+GwHAACA1odyBwCgEModAIBCKHcAAAqh3AEAKIRyBwCgEModAIBCKHcAAAqh3AEAKIRyBwCgEModAIBCKHcAAAqh3AEAKIRyBwCgEMod9Im7u/ukSZP... | <image>Rules:
1. Each numbered region represents a piece on the board.
2. Pieces are considered adjacent if they share at least one edge.
3. Pieces that only touch at corners are not considered adjacent.
4. One piece is removed from main board and shown below. It has been rotated and may have been flipped.
Question:
C... | 8 | GameQA-140K | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 0.75 | <think>
Let's analyze the problem step by step.
We are given a "Main Board" grid and a "Removed Pieces" section showing what was taken out. The removed piece is a 2x3 block (2 columns, 3 rows) with five cells containing '4' and one cell diagonally striped (hatched). Specifically:
- Rows 0.0 to 1.5: all red with '4'
-... |
mmfr_33 | "iVBORw0KGgoAAAANSUhEUgAAALYAAACVCAIAAAB6qpfLAAAbKklEQVR4nO1da3AT173/n5WJMg2EfIiHduLW2JLB+BE8mUnNTJKZXEtrGRuEW0Jh+FCYBmNT4JYbZEMS4ceFgG0J4xAIGOiQtHVbUjITPwDbuzbNgG/dQGKYQDCVBE7KNBAy9w4tNMnEu+d+ONLR6mnHlvZh6fdJOnv27H/3/Pb/Oo8FrH24+g4BAFirMcYigbsXCJbaJBUFpSTUNBDGGLQNEYDB4C5HWRtdYrERkVLs6Ss/MtrRtN5fEQMgZUTUNBilBZg6/LfAD3D... | <image>
As shown in the figure, \(∠MON=90^{\circ}\). Points \(A\) and \(B\) move along the rays \(OM\) and \(ON\), respectively. Line \(BE\) is the angle bisector of \(∠ABN\). The extension of line \(BE\) intersects the angle bisector of \(∠OAB\) at point \(C\). The question is: Does the size of \(∠ACB\) change? If it ... | The size of ∠ACB remains unchanged. | MMR1 | math | close | yes_no | qwen3.5-27b | 0.5 | <think>
We are given a geometric configuration with:
- ∠MON = 90°, so rays OM and ON are perpendicular.
- Points A on ray OM, B on ray ON — both can move.
- Line BE bisects ∠ABN (note: N is the direction of the positive y-axis, since ON is vertical).
- The extension of BE intersects the angle bisector of ∠OAB at point... |
mmfr_48 | "iVBORw0KGgoAAAANSUhEUgAAAggAAAIICAIAAACEnoE0AAAzK0lEQVR4nO3deXwUZZ7H8aeqOiGcOUCjIXKInAKKrK4jIuigoC4oLCgDjvcgeIIiM8OISRQWRXGc0XXDiLresAIyw+EqggSEUTBIuCLIlQNIQk5yp7uq9o/nRW9KmpzdVUn35/2Hr3SlqvpnR59vP/U89ZRimqYAAOAs1ekCAAAtC8EAALAgGAAAFgQDAMCCYAAAWBAMAAALggEAYEEwAAAsCAYAgAXBAACwIBgAABYEAwDAgmAAAFgQDAAAC4IBAGBBMAAALAgGAIA... | <image>This game is called Chess Ranger. The rules are as follows:Pieces move like in standard chess.You can only perform capture moves.The king is allowed to be captured.The goal is to end up with a single piece remaining on the board.How many steps are needed to solve the puzzle?Choose from the following options:A.5,... | D | GameQA-140K | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 0.5 | <think>
We are given a chessboard with black pieces only (as per the image: King on a7, Knight on a6, Rook on f1, Bishop on f8). The game is called “Chess Ranger” and has special rules:
- Pieces move like in standard chess.
- **You can only perform capture moves.** → So every move must be a capture; you cannot make no... |
mmfr_50 | "iVBORw0KGgoAAAANSUhEUgAAAJAAAACBCAIAAACgrqTRAAAX2klEQVR4nO2de1QU1R/AZ+2Brw5GUGtnbFM32EKUIoEK8XRkdVMhLAofWEqLm0oFBCrF49AxxUzAZ6ySSlmuVqIn9Kw8FAiNRQ2PIiCwtrIaLKitrLDLurvz++Pq/Mad3WF2dmYHpM8fnGUe996Z7/3O/d7v/d57IWQIEx4eDmEoLS1lu0T9A7FdAJYJDw8HciopKYEgqLW1le0S9QMHQRBoCMPh3HsDSqWSz+e3trZOnDiR7UIRMYztArBJWVnZqlWrwO+kpKSUlJQ... | <image>In the figure, point P is inside triangle ABC, with PA=6, PB=8, and PC=10. If triangle PAC is rotated counterclockwise around point A to obtain triangle P'AB, what is the distance between points P and P' (PP') and the angle ∠APB in degrees? | PP'=6, \angle APB=150 degrees | MMR1 | math | close | numeric | qwen3.5-27b | 0.75 | <think>
We are given a triangle ABC with point P inside it, and lengths:
PA = 6, PB = 8, PC = 10.
Triangle PAC is rotated **counterclockwise around point A** to obtain triangle P'AB.
This means:
- Point A is fixed (center of rotation).
- Point C maps to point B → so AC = AB (since rotation preserves distances),... |
mmfr_62 | "/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGaAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRI... | <image>
How many columns of vertical bars are there in the image? | 11 | FineVision-visualwebinstruct(filtered) | chart/table/doc | close | counting | qwen3.5-27b | 0.75 | <think>
To determine the number of columns of vertical bars in the image, we need to count the distinct vertical lines that form the grid.
Looking at the image:
- The grid is composed of both horizontal and vertical lines.
- We are only counting the **vertical** bars (lines).
- These vertical lines run from top to bot... |
mmfr_63 | "iVBORw0KGgoAAAANSUhEUgAAAZsAAAE4CAIAAAACcsnvAABOhElEQVR4nO29WZMcN5bveQ7gSyy5r0ySyVXcRFElSiVV19JSdW1d1ddu2Z3bZjP3ad77G/X72LUZm7GeW23d1VO3u1R7qbSREldxT5JJMvct9nB3APOADAjpsWREZHh4ZAR+D7TIoIcD7g7/4+Dg4ACFEFCboM73pOZnASA4R0REBODaARwAGPcpoaJyPALfe56aJ+d7P9Qut349rSbOo8PrfF/v+HoHN3PfDkK9etbD0j7zOp+joN7zqoZr/zZ/nmaOP8gx9WjmOTZ... | <image> Ten small rectangles of the same size and shape (white parts) are arranged as shown inside the large rectangle ABCD. If BC = n, AB = m, then what is the sum of the perimeters of the two shaded rectangular regions?
A. 4m
B. 4n
C. 2(m + n)
D. 4(m - n) | A | BMMR | math | close | multiple_choice | qwen3.5-27b | 0.25 | <think>
We are given a large rectangle ABCD with sides AB = m (vertical) and BC = n (horizontal). Inside, there are 10 identical small white rectangles arranged in two groups:
- On the left side: 4 small rectangles stacked vertically.
- On the right side: 3 small rectangles placed horizontally on top, and 3 more stack... |
mmfr_69 | "iVBORw0KGgoAAAANSUhEUgAAAhUAAACGCAIAAADl6+/tAAC+CUlEQVR4nOx9dVxVadf2Pp0cuqVbOsQEBASxxhZbxHHMUTFmjBFbx+7u7rEDFTEQBREJAenu5nTu74/1nvvdD8bjzDgzzvud9Yc/PGz22fve9155rWuRcBzHNKIRjWhEIxr5nUL+py9AIxrRiEY08q8U6j99AR8RHMdVKtWHn0CoRCKRKBQKfE4mk0kkEjoG/ayRf4UQY18SifSFTxDHcRzHyWQy+hnDMDKZjLbHl/w5iUSCI1UqFfq5w2HED798d30Y0KO/7bBX0ZG... | <image>Xinxin's home to school is 960 meters. He goes home for lunch, so how long does he walk in total from morning to evening? | 3840 | MMR1 | math | close | numeric | qwen3.5-27b | 1 | <think>
The image shows that the distance from Xinxin's home to school is 960 meters.
The problem states: “He goes home for lunch.” This implies a daily routine with multiple trips between home and school:
1. Morning: Home → School (1 trip)
2. Lunchtime: School → Home (1 trip), then Home → School again after lunch (a... |
mmfr_84 | "iVBORw0KGgoAAAANSUhEUgAAAKsAAACPCAIAAAAKt7xuAAAbfUlEQVR4nO2deVxT17bH98mcAEkgQAhhnkREQUEsChUURLGiUGylWvQ6tNpaWtQ63c+rdngOtYNa9VWlVrCtonhxQCNSRqFwkcEJEREnwGAgQiAMSUj2++NAiCAhKpLx+wfDyc4+Kzm/s9ba40EghMCAHoNRtwEG1IxBAfrOoAqAAPSGB5n8z1buvZL0vy7fNQQO3UEVH4CgvyAQVF3PTfz+2Bs1yMAIgxvsBfSyQwAAQNC/a27cy8oo67BlsWzlpWQAIHKJGNBGBlV... | <image>In the figure, it is known that in quadrilateral \(ABCD\), \({∠}ABC{=}90^{{∘}}{,}{∠}ADC{=}90^{{∘}}{,}AB{=}6{,}CD{=}4{,}{BC}\) extends and intersects the extension of \(AD\) at point \(E\). (Note: The calculation process and results in this problem retain the square root.)
\((1)\) If \({∠}A{=}60^{{∘}}\), find th... | 6\sqrt{3} - 8, 14/3 | MMR1 | math | close | numeric | qwen3.5-27b | 0.75 | <think>
We are given a quadrilateral $ABCD$ with $\angle ABC = 90^\circ$, $\angle ADC = 90^\circ$, $AB = 6$, $CD = 4$. The extension of $BC$ meets the extension of $AD$ at point $E$. So, points $B, C, E$ are colinear (with $C$ between $B$ and $E$), and points $A, D, E$ are colinear (with $D$ between $A$ and $E$). Also,... |
mmfr_85 | "iVBORw0KGgoAAAANSUhEUgAAAR4AAABMCAIAAAA0mk/JAAATjUlEQVR4nO2db2xT1f/Hz+3cSm8JrAUCk4VuwjoVuewX6QZ6Rwz7bsQHFzVbiTGWB2TEhKR7wuYTsz5QBvHBNFHSPRvRREtiQiGG0D1Q0yUmdiEorUZxwJLdgiDrn2l2bxvtPb8HB26Ot117/7W9dH09wNuz9t1zPufzOX9uz/1IQAjBY+bm5rq7u4EG4vH4559/nkqlGIY5ePCgFimDACEkCAIvicVie/bs0aJ55syZS5cuEQTR09Pz4YcfWiwWbXVUSX7TtKDdLCI... | <image>Use chess pieces to form the set of shapes shown in the figure:
(1) The 1st shape requires ____ chess pieces, the 2nd shape requires ____ chess pieces, the 3rd shape requires ____ chess pieces;
(2) Following this pattern, how many chess pieces are needed to form the nth shape?
(3) How many chess pieces are need... | 6048 | MMR1 | math | close | numeric | qwen3.5-27b | 1 | <think>
Let's analyze the pattern in the image.
We are given three shapes formed by chess pieces (represented as dots) arranged in grids:
- Shape ①: A grid of 3 rows and 2 columns → total pieces = 3 × 2 = **6**
- Shape ②: A grid of 3 rows and 3 columns → total pieces = 3 × 3 = **9**
- Shape ③: A grid of 3 rows and 4 ... |
mmfr_86 | "iVBORw0KGgoAAAANSUhEUgAAArwAAAEfCAIAAAAsuILJAAB4rElEQVR4nO2ddXwVx/f31+6NGwkSgrsUdwjaIqVQSmmRQnGKx0M8xIUQXEuRQoBA8ZZSCgQNDkGCS7AIcU/uXXv+OE/2ly/WALma8/4jr5vNze7s7OzMZ86cOYcURZFAEARBEAT5LyhNFwBBEARBEN0ARQOCIAiCIBUCRQOCIAiCIBUCRQOCIAiCIBUCRQOCIAiCIBUCRQOCIAiCIBUCRQOCIAiCIBUCRQOCIAiCIBWCqeD3BEFQaTl0ApIkSZKs9NNi3RIqq1tAFEU... | <image> According to the following figures, select the most appropriate one to fill in the question mark to make it logical ( ). ['A:A', 'B:B', 'C:C', 'D:D'] | B | BMMR | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 0.25 | <think>
Let's analyze the sequence of figures to find a logical pattern.
We are given 5 figures in a row, and we need to choose the 6th from options A, B, C, D.
Step 1: Count the number of enclosed regions (or “faces”) in each figure.
- Figure 1: Has 4 small triangles + 1 square with cross → Let’s count enclosed are... |
mmfr_92 | "/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE1BAADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRI... | <image>
What is the main concern addressed in Figure 7 regarding the generation of images with AI models? | the increased likelihood of generating explicit or not safe for work (NSFW) content | FineVision-visualwebinstruct(filtered) | general | close | short_phrase | qwen3.5-27b | 0.5 | <think>
The image displays five panels labeled (a) through (e), each showing an AI-generated image of a woman in or near a pool, along with the text prompt used to generate it.
- Panel (a): Prompt says “A woman wear a blue bikini sitting in the pool” → Image shows a fully clothed woman in a blue bikini.
- Panel (b): S... |
mmfr_95 | "iVBORw0KGgoAAAANSUhEUgAACAAAAATvCAYAAACSFRATAAEAAElEQVR4nOzdd5icZdk/7mvK7qYQSAgtSEdBSCMBBAQpovACryKISv2KKAq+qIRQEwglJKEHpIoIKhYEQVFEFKSJSBFIo/dOQkkgpGyZeX5/8LufZMgmpmczOc/jyJHJlN1ndp65c8x+ruu6C1mWZQEAAAAAAAAALNeKy/oAAAAAAAAAAIBFpwAAAAAAAAAAAOqAAgAAAAAAAAAAqAMKAAAAAAAAAACgDigAAAAAAAAAAIA6oAAAAAAAAAAAAOqAAgAAAAAAAAAAqAM... | <image>In the regular hexagon $ABCDEF$, what type of trapezoid is the shaded area? A. Right trapezoid; B. Isosceles trapezoid; C. Cannot be determined; D. No correct answer | B | WeMath2-Standard | math | close | multiple_choice | qwen3.5-27b | 0.75 | <think>
To determine the type of trapezoid that the shaded area is, we need to analyze the properties of the shaded region within the regular hexagon $ABCDEF$.
1. **Identify the Shaded Region:**
The shaded region is a quadrilateral with vertices at points $E$, $F$, $O$, and $D$. This quadrilateral is formed by the ... |
mmfr_97 | "iVBORw0KGgoAAAANSUhEUgAAAPwAAADQCAIAAACsp5t9AABG00lEQVR4nO29eZycV3Xn/bvbs9TW1fuqXbIWY1uSF7xjvBDjZMAsHpsEPOBA8kmGhHySN/AyCcM4YSZMwoQAxuxgbLDGbGYxdgBjwMa7jVfJsiVZra3Ve+31rPfe949bXWrJklDL1S3e6Pl+yuXqVtVTt6t+z3nOPfecc4nWGgkJJxP0RA8gIWGhSUSfcNKRiD7hpCMRfcJJRyL6hJOORPQJJx2J6BNOOlom+iiKzINisQjAhP+VUkop86OU0vwmCILjOH4cxwCklEE... | <image>Given that A, B, C, D, and E are five integer points on the hyperbola represented by the inverse proportional function $y=\frac{16}{x}$ (where $x>0$), vertical or horizontal line segments are drawn from these points to the axes. The quarter-circle arcs formed by the radius equal to the side length of the squares... | 13\pi - 26 | MMR1 | math | close | numeric | qwen3.5-27b | 1 | <think>
We are given the hyperbola $ y = \frac{16}{x} $ for $ x > 0 $, and five integer points A, B, C, D, E on it. Since they are **integer points**, both coordinates must be integers. So we look for integer pairs $(x, y)$ such that $ x \cdot y = 16 $ and $ x > 0 $.
The positive integer factor pairs of 16 are:
- (1,... |
mmfr_99 | "iVBORw0KGgoAAAANSUhEUgAAAoAAAAHgCAIAAAC6s0uzAADU4ElEQVR4nO39X8ws23UfBq6q/vOd7q/v4WFoKBmCJkBC5oNmpGvlKP6DoeVLREE8ITAYDxFbtA4FCw7iUYA754Xy830bwOQ8XGgAT4QIdMBrMYrBEIOAHgXSDGlIQBxDV84VZWNAC8TgwqATjRkenttf9/m6u6rmYVWtXrXW3rt2VVf1v2/9cPCd6qpdu3at2nuvvf7u5BO/+LPQFcUuB4BknHau4RCkkOaQn+TRx8HtYnG3XJ66FQaDwWAYBKfhnQaDwWAwPHAcxIC... | <image>
The given image represents the interface of the game Klondike Solitaire. The user interface consists of a board with 52 playing cards divided into four distinct areas:
1. **Stock Pile (Draw Pile):** Initially composed of 24 face-down cards. The player can draw one card at a time to reveal its face.
2. **Waste... | 5 | GameQA-140K | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 0.25 | <think>
To determine which move is both valid and effective, we must first understand the rules of Klondike Solitaire:
- **Valid moves** follow game rules:
- Foundation piles: Build up in suit from Ace to King. Only top card of waste or tableau (if appropriate) can be moved.
- Tableau piles: Build down by alternat... |
mmfr_100 | "iVBORw0KGgoAAAANSUhEUgAAAIMAAAB7CAIAAADYPqRFAAAKPklEQVR4nO2dT2gb2RnAv+m2BTnkkImhyzhe0kxOQaQLwU4CzSBDMz60oGgvqxxaYoWwxDrsWGZDi3JoQb44iuOFCFOyo8CmK2cJrAylZUyg8YSCJV82SHEuNiiV7cWG2OlFORRW08M44/kne0bzZubJmt/JmRmNnvTT996b9773QkiSBAEY8BO/CxCwS0sT5THiPUPzWwClO3dKXhas6zAzUbpDEMQFKEm7PPshThAX/3n2l56XrquQtNT4GADE+Jr2cJ2L5KUAN9H... | <image>
In isosceles right triangle ABC, where AB = AC = 4, point P is a point on side AB other than A, and a light ray starts from point P, reflects off sides BC and CA, and returns to point P (as shown in the figure). If the light ray QR passes through the centroid of triangle ABC, then AP equals ( )
A. 2
B. 1
C. \... | D. \frac 4 3 | MMR1 | math | close | multiple_choice | qwen3.5-27b | 1 | <think>
We are given an isosceles right triangle ABC with AB = AC = 4. Since it’s a right triangle and AB = AC, the right angle must be at A (because if the right angle were at B or C, then AB and AC couldn’t both be legs of equal length unless it’s symmetric about the altitude from A — but standard labeling implies an... |
mmfr_106 | "iVBORw0KGgoAAAANSUhEUgAAAIYAAACQCAIAAABClIRAAAARWklEQVR4nO2dbUwb15rHn2NS0d7t1krXKZBEIsEmIatqmdxUClXbOKslCbqxDVE/FKlIW1ZVuw37ISgYqERTaIhCGhQila1t6LaJ4g9FbQJ56V2w6RaqfIhUNWQlqpDYZrmKKtwNV6FLWxwV5tkPZzwe2+N3j2fG8FNEPGdmzhzP8/zP6zNjwLyADX5wDbQQQgAALFYW71mtNpalO1dlK1yKaEDlICIASwDQ5yKE9HvLqQ3Yc9UashPKt3EWQg3KXdQk2SB3ATKFEAJ... | <image>In the figure, the triangle ABC is continuously rotated clockwise around one of its vertices by angles n'<sub>1</sub>, n'<sub>2</sub>, and n'<sub>3</sub>. What is the symmetry relationship between the resulting triangle and triangle ABC? | central symmetry | MMR1 | math | close | short_phrase | qwen3.5-27b | 0.75 | <think>
The problem states that triangle ABC is continuously rotated clockwise around one of its vertices by angles $n'_1$, $n'_2$, and $n'_3$. These angles are labeled at the interior vertices A, B, and C respectively — meaning they represent the interior angles of triangle ABC.
In any triangle, the sum of the interi... |
mmfr_113 | "iVBORw0KGgoAAAANSUhEUgAAAF4AAACDCAIAAACLEDvIAAAJeklEQVR4nOVdX0hTXxw/137gQ0YPGT1kiG6B0GuQvQSFs6BmQQ/1JvhvN5qo5G5ZDo0MI4Ws9GHDh3wILIjm5kOxCUovLYSIEjfaFqIvw3owRriHeX4P3zqd7r2b053de+7d50Gu17Ozez5+vt/z3fa53wkYY1TaCIVCNTU1FotFdr5Ml6vhCjabTfV8qVMjSZLdbldKBiEklHJAeTwei8Vis9lUSShd1cTjcUEQampq7Ha76oDSpcbj8XR0dCCE6urqVAeUKDVer3d... | <image>In the figure, point P is any point on the hypotenuse AB of right triangle ABC (excluding points A and B). A line is drawn through point P that intersects triangle ABC, forming a new triangle similar to triangle ABC. How many such lines can be drawn? | 3 | MMR1 | math | close | numeric | qwen3.5-27b | 1 | <think>
We are given a right triangle ABC, with the right angle at C (as indicated by the square symbol at vertex C). Point P is any point on the hypotenuse AB (excluding A and B). We are to draw lines through P that intersect triangle ABC such that they form a **new triangle** similar to triangle ABC.
Note: The new t... |
mmfr_117 | "iVBORw0KGgoAAAANSUhEUgAAAgAAAABdCAIAAABclUmtAAAEK0lEQVR4nO3dTXKbMBgGYMh046x8FPvquUhykyyzi7tIxvGAEwtboJ/veZauqhGi1QtCiPF0Og0AxPNUugEAlPEdAMfjcUyTXvL5+Tmx5KJqvwqX7bWrlh5CeuFFPbm0/NLK6+x84A7j1xTQOI6Jc0FrlFy18GbqOd56KgdqZgoIICgBABCUAAAISgAABCUAAIISAABBCQCAoAQAQFD/SjcA4Ibj8fj29pa92t1u9/HxkVLy6enp8/MzewPSq01vanrJw+HgTeBs6jn... | <image>The following four shapes are all made up of small squares of 1 cm². The shape with the largest area is the ___ shape, the shape with the longest perimeter is the ___ shape, and the shapes with equal areas are the ___ shape and the ___ shape. | ②, ④, ①, ④ | MMR1 | math | close | short_phrase | qwen3.5-27b | 0.25 | <think>
To solve this problem, we need to calculate the area and perimeter of each shape based on the number of 1 cm² small squares they contain.
---
**Step 1: Calculate Area**
Each small square has an area of 1 cm². So, the total area of a shape equals the number of small squares it contains.
- Shape ①: It is a 4×... |
mmfr_133 | "iVBORw0KGgoAAAANSUhEUgAAAmkAAAHRCAIAAAC+YrkAAACwGElEQVR4nOzdd1xT1//H8VdCmAFUFBVx4AD33nXvWXeto65a91511b1n3dZVtdqq1VpHrbbWbbXuPXGg4kZR2ZDx+yNf+SEihOQyxM/z0cejJrk590NQ3pxzzz1HZTQaEUIIIYTZ1CldgBBCCPGRkewUQgghEkeyUwghhEgcyU4hhBAicSQ7hRBCiMSR7BRCCCESR7JTCCFSnc6dO1evXj2JGl+wYEGdOnWSqHFlbd68OV++fBqNplmzZslwOr1eX6BAgR07diR8qFE... | <image>Rules: As shown in the figure, the Rubik's cube consists of both 3D views and an unfolded view. The 3D views show the cube from two angles: left-tilted 30 degrees looking down, and right-tilted ,30 degrees looking up. The cube has six faces: Upper (U), Down (D), Left (L), Right (R), Front (F), and Back (B). Each... | [8] 7 | GameQA-140K | logic/game/puzzle | close | numeric | qwen3.5-27b | 0.5 | <think>
To determine how many green squares are on the Down face (D), we refer to the unfolded view of the Rubik’s cube provided in the image.
In the unfolded net:
- The Down face (labeled “D”) is located at the top center of the cross-shaped layout.
- It is a 3x3 grid.
- Looking at the colors in that face in the unfo... |
mmfr_138 | "iVBORw0KGgoAAAANSUhEUgAAALoAAACXCAIAAAAtXtZOAAAeAklEQVR4nO1dfXAT17W/a3fqUNSITNSxGJQIW3IQHzNsx6RWwSC7tsDEn2+gQ+dBB7c1UTLQqUkkA4Up7mAmBpRgZuwg20nrvCdPlRmoQzCNY5mHaARxMa3c4cMmlhInciZ2oQPUpMhF3vP+uPJ6rS+vpF1pFfybCbF27949u/u755577rnnEgCA5sAPACEC/wFAEITTavos8yWtAiFEIZSSWNmiQ1IKLXAAonATJBCFjxAEAcj56vqXAQABAiBQcjbSbyVagG8giOl... | <image>In the figure, AB is the diameter of circle O, AF is a tangent to circle O, and CD is a chord perpendicular to AB, with foot E. A line parallel to DA through point C intersects AF at point F. Given that CD = 4\(\frac{3}{1}\) and BE = 2. (1) Find the length of FC; (2) Determine whether FC is a tangent to the circ... | 4\sqrt{3} | MMR1 | math | close | numeric | qwen3.5-27b | 1 | <think>
We are given a circle with center O, diameter AB. AF is tangent to the circle at A. CD is a chord perpendicular to AB at E. CF is drawn parallel to DA, intersecting AF at F. Given: CD = 4√3 (note: “4\(\frac{3}{1}\)” is likely a typo; in context and standard problems, it’s almost certainly 4√3 — we’ll proceed wi... |
mmfr_147 | "iVBORw0KGgoAAAANSUhEUgAAAo4AAAD/CAIAAADwjcD6AAEAAElEQVR4nOz9V3sbWZa2Ce8IgAQNLOENPSmbpqq6uvt9D2YO5wfPX5i5eqqq306jVEr0BiAIwnsPRHwH98T6NgKkUumqSzXaB7pACAhEbLPss55l2LatPo/P4/P4PD6Pz+Pz+Ecd5n/3DXwen8fn8Xl8Hp/H5/Gh8VlVfx6fx+fxeXwen8c/9Pisqj+Pz+Pz+Dw+j8/jH3p8VtWfx+fxeXwen8fn8Q89Pqvqz+Pz+Dw+j8/j8/iHHp9V9efxeXwen8fn8Xn8Q4/Pqvr... | <image>Read the map of a river basin in southern China and answer the following questions.
(1) Which of the following descriptions about the river's hydrological characteristics in the figure is incorrect?
A. The river has a relatively large annual runoff.
B. The flood season is relatively long, mainly concentrated in... | C | BMMR | science | close | multiple_choice | qwen3.5-27b | 0.75 | <think>
Let’s analyze the map and questions step by step.
The map shows a river basin in southern China, with labels such as “Xijiang” (West River), “Beijiang” (North River), and “Dongjiang” (East River) — these are tributaries of the Pearl River system. The region is south of the Nanling Mountains, indicating it lies... |
mmfr_152 | "iVBORw0KGgoAAAANSUhEUgAAAnYAAAHWCAIAAAB1wlPdAABjIUlEQVR4nO3deVhU5fsG8Jthl0VQMEwBRcBQU8tSiVArWxS33DBUtAXXNFu0n6YmZi6Ypub2Vct9h1xwzdzIcklBEdwFNURkU0CQTeb3x8FxxJkBhjkzZ+T+XF1dM4dzhvdpJp4523ubtOjeHURERKRrMkMPgIiI6PnEFktERCQKtlgiIiJRsMUSERGJgi2WiIhIFGyxREREomCLJSIiEgVbLBERkSjYYomIiETBFkukY3uWLduzbJniabe33z67fXu3t9824JCIyCD... | <image>In this FreeCell game:
we have 4 cascade piles, and their indexes are [0, 1, 2, 3]We have 4 freecell on the left top, and their indexes are 0,1,2,3.We have 4 foundation piles on the right top, and their indexes are 0,1,2,3.In FreeCell, cards can be moved according to specific rules: A card can be moved to a free... | 8 | GameQA-140K | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 1 | <think>
Let's analyze the problem step by step.
We are given a FreeCell game state with 4 cascade piles (indexes 0 to 3), and we are told to move the card **(Diamond, 8)** from **Cascade pile 2** to **FreeCell 1**. Then, we must find what becomes the **top card of Cascade pile 2** after this move.
First, let’s locate... |
mmfr_160 | "iVBORw0KGgoAAAANSUhEUgAAAbYAAAByCAYAAAA/B/RmAAAfD0lEQVR4nO2dP2zjyPXHv3t3SRQkwSpIgFUS4JaHFMdFCnOBAJGrpSvTRSAaKWwVga1qbaQ4qbJdya7kreQtDvJWsivZRSAaQSC5kreyFghgGSmsrSxX5jURF0gg7uFw8yv2R51s6w85IkXS+z6AcXtrDuetSM135r03bx4wxhgIgiAI4p7wid8GEARBEISbfDaJThqNBgzDgGEYaDQaiMfjiEQiiMViEEVxEiYQBEEQHwkP3HZFGoYBTdNwdHSEarUK0zQhSRKi0Si... | <image> Several dishes are placed on a table. When looking at them from three directions, the three views are as shown in the following figure. Then there are a total of ( ) dishes on this table.
A. 6 pieces
B. 8 pieces
C. 12 pieces
D. 17 pieces | C | Euclid30K | math | close | multiple_choice | qwen3.5-27b | 0.5 | <think>
To determine the total number of dishes, we analyze the three views: top view (俯视图), front view (主视图), and left view (左视图).
---
**Step 1: Analyze the top view (俯视图)**
The top view shows 3 circular objects arranged in a triangular pattern — two on top, one below. This suggests there are **3 stacks** of dishes... |
mmfr_162 | "/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAB+APkDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRI... | <image>
Based on Figure A, if the cylinder begins to rotate from rest due to the force applied, what would be the angular acceleration of the cylinder? | \frac{2T}{MR} | FineVision-visualwebinstruct(filtered) | math | close | numeric | qwen3.5-27b | 0.25 | <think>
To find the angular acceleration of the cylinder when a force is applied, we need to use the principles of rotational dynamics. Here's the step-by-step reasoning:
1. **Identify the given information:**
- The cylinder is initially at rest.
- A force \( F \) is applied tangentially to the cylinder, causing... |
mmfr_163 | "iVBORw0KGgoAAAANSUhEUgAAA00AAARnCAIAAACn8RqlAAEAAElEQVR4nOzdeXzT9eE/8HeST64mTdOTUkqBcooCcigFL0AFKuLoRAWdCM6h6JwFPGBOrU4H86JOFMecIGwTp64IunpiUYcVsYJMKFe5Wlp6pGma+/z98f7x+WZJW9rmc+WT1/MPH/FN+vm8m8+nySvvUxEKhQgAAAAAyI5S7AoAAAAAAC+Q8wAAAADkCTkPAAAAQJ6Q8wAAAADkCTkPAAAAQJ6Q8wAAAADkCTkPAAAAQJ6Q8wAAAADkCTkPAAAAQJ6Q8wAAAADkCTk... | <image>Which figure should complete the logical sequence? | C | FineVision-raven | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 1 | <think>
To solve this problem, we analyze the 3x3 grid of figures to identify patterns across rows or columns.
Each cell contains a set of geometric shapes with variations in:
- Number of shapes
- Shape types (triangle, circle, square, pentagon, hexagon, diamond)
- Fill style (black, gray, white/outline)
Let’s examin... |
mmfr_168 | "/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEDAPoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRI... | <image>
Use the given graph to evaluate the expression {eq}(f + g) (-2)
{/eq}.
| 8 | FineVision-visualwebinstruct(filtered) | math | close | numeric | qwen3.5-27b | 0.25 | <think>
To evaluate the expression $(f + g)(-2)$, we use the definition of function addition:
$$
(f + g)(x) = f(x) + g(x)
$$
So,
$$
(f + g)(-2) = f(-2) + g(-2)
$$
We now read the values from the graph at $x = -2$:
- For $y = f(x)$ (the blue parabola): At $x = -2$, the graph passes through the point $(-2, 4)$. So, ... |
mmfr_205 | "iVBORw0KGgoAAAANSUhEUgAAAWkAAAFHCAIAAADsvypfAAC3ZUlEQVR4nO2913YjybIk6pEQhAbJYonuPmf2PM7//8/Mmtln9+4uRQkNIuM+2A07lh6ZoChWFcGiP3CBQIoQ7hauwiPEGO2QCe0PIbgv2S/+pNfkv9bea2ZFUdS+9/b2tvZ797rat7/SKz2U9nDsD3h1jLFMxH/bP7gdT04YSo5sDoUxRr1mt9uZIA4lnFNC7NAvm977Sq/0sskJVAgBAhVCOHjssCTt6OSdaghIkQLDsdvtCBZPhR2v+PJK30jPyiwgcMQYi6J4Cdh... | <image>A homogeneous cylinder has radius $r$ and mass $m$. It is placed in the position shown in the figure. The coefficient of kinetic friction at points $A$ and $B$ is $f$. If the cylinder is given an initial angular velocity $\omega_0$, derive an expression for the time required for the cylinder to come to rest. | t = \frac{(1 + f^2)r\omega_0}{2gf(1 + f)} | BMMR | math | close | numeric | qwen3.5-27b | 0.75 | <think>
To solve this problem, we need to analyze the forces and torques acting on the cylinder and use the principles of rotational dynamics.
1. **Identify the forces:**
- The weight of the cylinder, \( mg \), acts downward through the center of mass.
- The normal force at point A, \( F_A \), acts horizontally ... |
mmfr_206 | "/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACUAWYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRI... | <image>
What does the red-colored area in the right figure represent in the context of the crystalline material's structure? | dislocation | FineVision-visualwebinstruct(filtered) | science | close | entity_name | qwen3.5-27b | 0.25 | <think>
The image displays two representations of a crystalline lattice composed of green spheres arranged in a regular grid. The left figure shows the intact, perfect crystal structure. The right figure is identical except for a vertical column of red spheres replacing some green ones near the surface, enclosed within... |
mmfr_208 | "iVBORw0KGgoAAAANSUhEUgAAAhwAAAIcCAIAAAAynOArAAAwkUlEQVR4nO3de3wU9b3/8c/MbhIugSwGJFxEuYpVvIGm2AikVPkdbnILRX1QFPHyqPX8igqntipq9VGOQvWQ+tPioQS8FKRCMIi1XtgEBC2kQrEKRfEu4aIkkutms/P7Y9eEhATCzjc73519PR95+CAbefOZmZ28d2Z3Z0UAAAAAAAAAAABg36WXyt/+Jps2yeuvy1lnqUyePVs2b5adO+Xqq1u8BQDgKjt3Su/eIiJTp8rq1cpiu3WTwkIxTRk8WD78sPlbAABu8/X... | <image>
# Game Overview
Pac-Man is a maze arcade game where the player controls Pac-Man to eat as many beans as possible while avoiding ghosts. If a ghost catches Pac-Man, the game ends.
# Basic Elements
- **Pac-Man**: The yellow circular character that the player controls
- **Beans**: Yellow dots that Pac-Man can eat... | H | GameQA-140K | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 1 | <think>
Let's analyze the situation step by step.
---
### Step 1: Initial Positions
From the image:
- **Pac-Man** is at position **(11, 0)** — row 11, column 0 (left side of board).
- **Pinky (pink ghost)** is at **(11, 0)**? Wait — no! Looking closely, Pac-Man is a yellow circle with mouth open; Pinky is pink and ... |
mmfr_230 | "iVBORw0KGgoAAAANSUhEUgAAA00AAARnCAIAAACn8RqlAADSyElEQVR4nOzdeVzU1f4/8DMLM8PMMIyIiKAI4kLkVnrVykptE7Wu3Da5ZUHdblLeQts086K3RVu1FW/dklu31G5dNDNslcqvWy64IS4ooiCyL7Ovvz/O9fObO4M4wGebz7yef/gYD8PMez6HGV6c8/mcI/N6vQQAAAAAJEcudAEAAAAAwAnkPAAAAABpQs4DAAAAkCbkPAAAAABpQs4DAAAAkCbkPAAAAABpQs4DAAAAkCbkPAAAAABpQs4DAAAAkCbkPAAAAABpQs4... | <image>Which figure would finalize the logical sequence and replace the question mark? | G | FineVision-raven | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 0.25 | <think>
To solve this problem, we analyze the 3x3 grid to identify patterns in both the outer shapes and the inner small shapes.
---
**Step 1: Analyze outer shapes per row**
Each row contains three different types of outer shapes: circle, triangle, pentagon. Let’s verify:
- Row 1: Circle (col1), Triangle (col2), Pe... |
mmfr_233 | "iVBORw0KGgoAAAANSUhEUgAAAV0AAABfCAIAAADEVYNfAAAVa0lEQVR4nO2d708UxxvAd08jf4BNtAEr6NHY2srhHd7hG0w8W01MBGM9XzQFjApU0/pO7Ju71KbAOwxYT33BHcVE26TVNCn2lbww4RBOQG3tK4Fi0kP7qjGRa+Xm+2LqfMed3dnZvbm72b35vFBYdmZnnpnnmR87+zwqAEDRAwCgqir8V/cGCR1d0SWTybGxsQcPHqTT6VAo9N5774XD4cOHD7MIWTdtJBJhfLTECHHEJY7SqXS7UOTSuJilpaWPP/74+fPnbW1tPp8... | <image>A rectangular table can seat 6 people. The tables are put together as shown in the image.
(1) A restaurant has 40 such rectangular tables and arranges them as shown in the image to form one large table. How many people can it seat in total?
(2) If the restaurant has n such rectangular tables and arranges them a... | 84 | MMR1 | math | close | numeric | qwen3.5-27b | 0.5 | <think>
Let’s analyze the pattern from the image.
We are given:
- 1 table → seats 6 people.
- 2 tables joined side-by-side → let’s count: top has 3 circles, bottom has 3 circles, left has 2, right has 2? Wait — looking at the image:
Actually, in the first diagram (1 table):
→ Top: 1 person
→ Bottom: 1 person
→ ... |
mmfr_268 | "/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFCBAADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRI... | <image>
What are the methods being compared in Fig. 11 for enhancing high-resolution multispectral (HRMS) images from the Washington DC dataset captured by the WorldView-2 sensor? | MS, GS, GSA, PRACS, BDSD, SFIM, GLP-CBD, CDIF, LRTCPan, PNN, PanNet, BayesianNet, DMDNet, FusionNet, SDRCNN | FineVision-visualwebinstruct(filtered) | science | close | entity_name | qwen3.5-27b | 0.75 | <think>
The image displays a grid of 16 panels, each showing an enhanced version of a high-resolution multispectral (HRMS) image patch from the Washington DC dataset (captured by WorldView-2), with corresponding method labels beneath them. The last panel in the bottom row is labeled “GT” (Ground Truth), indicating it i... |
mmfr_280 | "iVBORw0KGgoAAAANSUhEUgAAAOAAAAB6CAYAAACm0F/EAAA2EElEQVR4nO29eXwdVf3//5y77/dmvdn3tWm6QemGbIrwRUBBClUQWVoUxAUsgiDqRz8CH9ZiUfSjwEe0P6mVVdqyiRSxdKNpoW2SJmmattm3m+Tud+7M7490hqRNS9ImuSncF3/w6M3MmXNm5jXnnPfyeguyLMvEEUccMYEm1h2II47PMuIEjCOOGCJOwDjiiCHiBIwjjhhCF+sOxHFsSJKERvPxNzIUCuH3+9FoNFgsFnQ6HYIgxLCHcZws4gSc4ti/fz9VVVXU1tb... | <image>The figure below shows the approximate shape of the Danhua Building at Fuchiefu High School, which can be considered as a hemisphere attached to two rectangular prisms. If the radius of the hemisphere is 3 meters, AB = 50 meters, BC = 10 meters, CD = 15 meters, GF = 4 meters, EF = 30 meters, due to long-term dis... | $2620+9\pi $ | MMK12 | math | close | numeric | qwen3.5-27b | 0.5 | <think>
To solve this problem, we need to calculate the total surface area of the outer surfaces (excluding the ground) that need to be painted. The structure consists of two rectangular prisms and a hemisphere on top.
Let’s break down the components:
---
**1. Bottom Rectangular Prism:**
Dimensions:
- Length AB = 5... |
mmfr_284 | "iVBORw0KGgoAAAANSUhEUgAAAPoAAABmCAIAAABtKhtSAAAesklEQVR4nO1df2wT1x0/h2TtFJvLhCMOcZEZubRmZpo7lxIWtyaqJYKWaplIZqqaEkRWa8u6HlUmjOYs2cpE/mBqWKORKKkaVCZcNchUwBrUIIyUiCBThSlOnSiOGuZUMXK2JtjdTLF9++OV1+PufL5f/hHg80cU371773vvfd/nfd/3fe89FUVRyGM8hnisrKzcvHkzEAiEw2Gv1wsuzs3NLSwswDQVFRWbN29GEKSkpKSmpgbH8aqqKpPJpFar6VlRFKVSqXIgs6p... | <image>The image shows two spinners from the "Purple Matching" game. Can you use a tree diagram to find the probability of matching purple? | 1/4 | MMR1 | math | close | numeric | qwen3.5-27b | 0.75 | <think>
To solve this problem, we need to analyze the two spinners and use a tree diagram (or list all possible outcomes) to determine the probability of matching purple.
Note: “Matching purple” likely means getting one red and one blue — because in color mixing, red + blue = purple. So we interpret “matching purple” ... |
mmfr_289 | "iVBORw0KGgoAAAANSUhEUgAAAh0AAAIdCAIAAAAWAliwAACCfElEQVR4nO3deVwU9f8H8Pdn9uS+FZAbAUGBhLw1jzwwb7+a38w0+5Z2fev7K0Xtm2mWR3mUpZb2NU3Nbs2yPPMoRRDxQIHACxVBuZZd2Htn5vfHFqywwC7M7g7wfj569GCOnXm5M7vvnc98ZoawLAsIIYQQRyhHB0AIIdSuYF1BCCHEJawrCCGEuIR1BSGEEJewriCEEOIS1hWEEEJcwrqCEEKIS1hXEEIIcQnrCkIIIS5hXUEIIcQloaMDOJLBwJ66WJOZq8zMVWX... | <image>This is a Tents puzzle. In this game, you will start with a grid that only marks the positions of the trees, the number of tents that should be in each row, and the number of tents that should be in each column. Your goal is to place the tents step by step on the grid according to the following rules until there... | 28 | GameQA-140K | logic/game/puzzle | close | numeric | qwen3.5-27b | 0.75 | <think>
To solve this problem, we need to determine how many positions in the grid are valid for placing a tent, based **only** on two rules:
- **Rule 2**: Equal number of tents and trees → This is not directly relevant here because the question asks for *available positions* under Rules 1 and 3 only.
- **Rule 3**: Te... |
mmfr_305 | "/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAKHAy0DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRI... | <image>As shown in the figure, how many square tiles with side length $\sqrt{2}$ are needed to cover four square floors? | 28 | Euclid30K | math | close | numeric | qwen3.5-27b | 0.5 | <think>
We are given a diagram with several squares arranged in a cross-like pattern. The problem asks: **how many square tiles with side length $\sqrt{2}$ are needed to cover four square floors?**
Looking at the image, we see labeled points and some distances:
- $BE = 2\sqrt{2}$
- $DG = 2\sqrt{2}$
- $OC = 4\sqrt{2}$... |
mmfr_339 | "iVBORw0KGgoAAAANSUhEUgAAAggAAAC1CAIAAAC1VZC2AAA4cklEQVR4nO2da4xcZf3Hn3PmdqZIGdAXQ2J0wfxlwYCFKGxjhC2S0AIJ5U0BE8OuxmRrjKnBpBCkpX1TiJrW0FiQ4EJAS2OTVhO0RqHVF7I1iltjyiYaU6IJS4yyQOicuZ3zf/Ht+frsuTxzZvZyZmZ/nxfNdubMOc+Zy+/3/O6W7/tKEISBYu/evY8++qhlWVkvRBhOLFEMgiAIgo6d9QIEQRCE/kIUgyAIgrAIUQyCIAjCIkQxCIIgCIsQxSAIwvIzOztr27a1Mhw... | <image>
As shown in the figure, a rectangular white paper strip with a length of 30 cm and a width of 2 cm is folded into the shape shown in the figure, and one side is colored. What is the area of the colored part?
A. 60 cm²
B. 58 cm²
C. 56 cm²
D. 54 cm² | C. 56 cm² | MMR1 | math | close | multiple_choice | qwen3.5-27b | 0.75 | <think>
To solve this problem, we need to understand how the paper strip is folded and how much area remains visible (i.e., colored) after folding.
### Step 1: Understand the original dimensions
The rectangular white paper strip has:
- Length = 30 cm
- Width = 2 cm
So, the total area of the strip before folding is:
\... |
mmfr_351 | "iVBORw0KGgoAAAANSUhEUgAAAPYAAABDCAIAAAAgd29ZAABDXUlEQVR4nO29aWxc53k2/DznnFk5Q3JEUTspilotKpZsyrIWW5IXKV5iu/EKG4bdpugCtG6LIu2fAq3bNCgQIDVQIEEKw4mbJnHtVDZqV14Ux44cbbGtlRK1UjJFUaTEnRzOepb3x6X7yj30B3y/3xc5Pwx5OHPO89zrdW/PsWNjY67rViqVKIpc13UcJ4oi3/ettbFYLAgCY0wURfjcGON5XhiGURSFYeh5njHGGOM4juM4rutWq9UgCFzX5a+MMbhJGIb8ubUWX8O... | <image>As shown in the figure, a sector AOB with a radius of 3 and a central angle of 60° is placed on line l (with OA coinciding with line l). Then, this sector rolls without friction on line l to the position O'A'B'. During this process, the length of the path that point O moves to point O' is
A. 4π
B. 3π + 3
C. 5π
D... | A. 4π | MMR1 | math | close | numeric | qwen3.5-27b | 0.75 | <think>
We are given a sector AOB with radius 3 and central angle 60°, initially placed on line l such that OA lies along line l. The sector rolls without slipping to position O'A'B'. We are to find the total path length traced by point O during this rolling process.
---
### Step 1: Understand the motion
The sector ... |
mmfr_352 | "iVBORw0KGgoAAAANSUhEUgAAALQAAABoCAIAAADXU00xAAAriElEQVR4nO192W8b1/X/neG+7xIlURKpfbGs1bIsS3a8JGmcpEmTpggCFCjgPrRA0f8hf0EfChRB0KYvaV/ykjRLndSON9mWvMja94XaLJGUSEriNhzOzO/hZE6uKDvt15LpKD+dB4EiZ+7c5dyzfM65ZxhJksghHdLjiH3eHTikHy8dMschPZEOmeOQnkiHzHFIT6RD5jikJ9IhcxzSE+mQOQ7piXQwmEOSJJ7n0+k0oDKJRGJzcxN+mp+ff//99y9evDgzM0NfLIr... | <image>In the figure, in rectangle \(ABCD\), \(AB=1\), \(BC= \sqrt{3}\). Triangle \(ABD\) is folded upwards along diagonal \(BD\). If the length of \(AC\) changes within \(\left[ \left. \dfrac{ \sqrt{10}}{2}, \dfrac{ \sqrt{13}}{2} \right. \right]\) during the folding process, then the length of the trajectory formed by... | \frac{\sqrt{3}\pi}{12} | MMR1 | math | close | numeric | qwen3.5-27b | 1 | <think>
We are given rectangle $ABCD$ with $AB = 1$, $BC = \sqrt{3}$. So, since it’s a rectangle:
- $AD = BC = \sqrt{3}$
- $CD = AB = 1$
- Diagonal $BD = \sqrt{AB^2 + AD^2} = \sqrt{1^2 + (\sqrt{3})^2} = \sqrt{1+3} = 2$
Triangle $ABD$ is folded **upwards** along diagonal $BD$. That means point $A$ moves in space (out ... |
mmfr_354 | "iVBORw0KGgoAAAANSUhEUgAAA00AAARnCAIAAACn8RqlAADiLElEQVR4nOzdeXxU1cE//jP7PllIgARIIGwhChFQQUUBFyQi/ohSBVsXrIrLtxrUWqm2YDd41ArVKlZtwR0tNrSoiSgKGjGgbCIQ9p0Esmf27d7fH+fhPtOZJEwyd5uTz/sPX+Nhcu+ZObN85px7ztHwPE8AAAAAgDlapSsAAAAAAJJAzgMAAABgE3IeAAAAAJuQ8wAAAADYhJwHAAAAwCbkPAAAAAA2IecBAAAAsAk5DwAAAIBNyHkAAAAAbELOAwAAAGATch4AAAA... | <image>Which figure would finalize the logical sequence and replace the question mark? | H | FineVision-raven | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 0.5 | <think>
To solve this problem, we analyze the 3x3 grid of figures to identify a logical pattern that determines what should replace the question mark in the bottom-right cell.
Each cell contains a set of small geometric shapes (polygons and circles) with varying sizes, shades (light gray, medium gray, dark gray/black)... |
mmfr_356 | "/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACiAN8DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRI... | <image>
What type of mathematical graph is depicted in the image, and can you describe its general behavior? | polynomial function | FineVision-visualwebinstruct(filtered) | math | close | category | qwen3.5-27b | 1 | <think>
The image shows a graph plotted on a Cartesian coordinate system with x and y axes. The curve starts high on the left (near the positive y-axis), decreases sharply, crosses the x-axis at x=1, continues to dip below the x-axis forming two local minima and one local maximum between x=1 and x=7, then rises again c... |
mmfr_366 | "iVBORw0KGgoAAAANSUhEUgAAA00AAARnCAIAAACn8RqlAAEAAElEQVR4nOzdZ3xUZd438P/0SSa9EUiAhBRDDU1ARQErQUVjJboixQIsrsmKu6CwwA27sOoNUVFYkbK6C1gDiAR11aiI9F5DICEkJCSQNpnenhfXzXlmkxBS5sw5c+b3feFnvDI555pzmMlvripzuVwEAAAAAJIjF7oCAAAAAMAL5DwAAAAAaULOAwAAAJAm5DwAAAAAaULOAwAAAJAm5DwAAAAAaULOAwAAAJAm5DwAAAAAaULOAwAAAJAm5DwAAAAAaULOAwAAAJA... | <image>Which figure should complete the logical sequence? | C | FineVision-raven | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 0.5 | <think>
To solve this problem, we analyze the 3x3 grid of figures to identify consistent patterns across rows and columns.
Each cell contains:
- An outer shape (triangle, hexagon, or pentagon)
- An inner shape (circle, triangle, pentagon, etc.)
- The inner shape is filled with a shade of gray (light, medium, dark) or ... |
mmfr_369 | "iVBORw0KGgoAAAANSUhEUgAAAN0AAACACAIAAAAAtvtkAAALZElEQVR4nO2dPXarOhuF5W/doWAXWWcEeAT4NK7SpoMSN+lSpksDJe7SpnJjGIE9gqxTBObCV2BA6A8JGyOT/RR33fhY4kebV0jW1rsoy5IAYBn/m/oEABCgp8ssCDLtKrNgUWFQBoAOOros4vf9/j0utCrMgsO2LMuyTP39BsoEw9DQZXH8R1xy/jrqCLNYviYeIYQQb+tfd2pgMDPosso+Ut+N8jxyCfHT3i835JFr9H1wM/LIre58HrmEuFE+9QkNoVeXqe+nJXe... | <image>The output result of Figure 1 is , the output result of Figure 2 is . | A,B= 30 57, 5.5 | MMR1 | math | close | numeric | qwen3.5-27b | 0.75 | <think>
Let's analyze both figures step by step.
---
**Figure 1:**
Given code:
```
A = 3
B = A^3 → B = 3^3 = 27
A = A + B → A = 3 + 27 = 30
B = A + B → B = 30 + 27 = 57
PRINT "A,B="; A,B → prints: A,B= 30,57
```
So output of Figure 1 is: **A,B= 30,57**
(Note: In many BASIC-like languages, the semicolon in PRINT... |
mmfr_374 | "iVBORw0KGgoAAAANSUhEUgAAAMsAAACDCAIAAACsknhlAAAN5ElEQVR4nO2dP2waSx7Hh+jJ2uJFImne6jVvIzkX6+mKja5xSBFKkhRv05zINYEGcGUoTrGlk4ilJ2FX4CLCjp4EboJ1imRShEW6gjR5pomgOMV+wSeowr7Kbk7Lu2avGHsy/DHsv5ndwfMpLLyGnR/4y8xvfvOb3wQMwwAcDjGueW0AZ87hCuOQhSuMQxauMA5ZuMLscHZ25rUJzMAVZhlN0+7du6dpGgAn2/cDgaQKgJoMJFWvDfMnXGGW2draOj4+Xl9fB2Bx9UM... | <image>The graph of the derivative function \(f'(x)\) is shown in the image. Then, \(({ })\)
A. \(\dfrac{1}{2}\) is a maximum point of \(f(x)\)
B. \({-}2\) is a maximum point of \(f(x)\)
C. \(2\) is a maximum value of \(f(x)\)
D. \(\dfrac{4}{5}\) is a minimum point of \(f(x)\) | A | MMR1 | math | close | multiple_choice | qwen3.5-27b | 0.5 | <think>
We are given the graph of the **derivative function** $ f'(x) $, and we are to determine which statement about the original function $ f(x) $ is correct.
---
### Key Concept:
The critical points of $ f(x) $ occur where $ f'(x) = 0 $. The nature of these critical points (maximum or minimum) depends on the **si... |
mmfr_376 | "iVBORw0KGgoAAAANSUhEUgAAA00AAARnCAIAAACn8RqlAAD8vklEQVR4nOzdeXxU1cE//jMzd/YlQ0IgQgwkEBJAoKwGDBJQ0IAIKbZoqxZaEfeCW+WxfcDlW3zEAtUqVv0ZXEqRYhPUNoiAUWLYwYBCQoCwJGQhy0xmJrPP/f1xHm7nSULIcpfJnc/7D16Xk8ncc+ZkJp+cc+85CpZlCQAAAADIjlLqCgAAAACAIJDzAAAAAOQJOQ8AAABAnpDzAAAAAOQJOQ8AAABAnpDzAAAAAOQJOQ8AAABAnpDzAAAAAOQJOQ8AAABAnpDzAAA... | <image>Choose the figure that would logically complete the sequence. | E | FineVision-raven | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 0.75 | <think>
To solve this problem, we analyze the 3x3 grid of figures to identify patterns across rows and columns.
Each cell contains a set of geometric shapes with varying numbers, types (polygon sides), sizes, and shades (light gray vs dark gray). We focus on consistent properties that change predictably.
Let’s examin... |
mmfr_384 | "iVBORw0KGgoAAAANSUhEUgAAAUoAAACMCAIAAACVjXdPAABfGklEQVR4nO19Z1xTyff33DRI6F2kCYoFCyoWWCxgQ1cUsCEg2FCkCBYEWQsoFsSyKHZUVGwo6i4i9q6IioLdVVHpVUB66n1ezD/zDAlggFD87X5f8CE3t8ydzJnTzyFIkgT/GpAkKRAI4CuTJEmlUuFxgiAIgmjXof0cJEmSJEkQhEAgIAiCQqG094j+Q0fHv26JQDImCIJKpVIoFAqF8kvQNg5I2P+qffk/NA/Ev2eVCAQCAABBEJAH/lokjQOx8V/3Ff5D24DW0Bd... | <image>(This question is worth 12 points) In the triangular pyramid P-A.BC, PA is perpendicular to the plane A.BC, and A.C is perpendicular to BC. Point D is a point on the lateral edge PC, and its front (main) view and side (left) view are shown in the figure. (1) Prove: A.D is perpendicular to the plane PBC; (2) Find... | 4\sqrt{2} | MMR1 | math | close | numeric | qwen3.5-27b | 0.25 | <think>
We are given a triangular pyramid $P-ABC$ with:
- $PA \perp$ plane $ABC$,
- $AC \perp BC$,
- Point $D$ on edge $PC$, and its front (main) view and side (left) view are shown in Figure 2.
From the views:
**Front View (正视图):**
- A right triangle with vertical leg = 4, horizontal base = 4.
- Hypotenuse is split... |
mmfr_388 | "iVBORw0KGgoAAAANSUhEUgAAAVAAAAGbCAIAAAAdpV/5AAEAAElEQVR4nNy9Z3Bd55kffs65vfdegXtx0TsBEGATRUlUl20Va23FZS2vN+vxJplk98tmJ5NMJpN/Jp8ym01be+VYXq/cVCzbskRREkmJnSABovd6Ue7F7b2c/4dfzjuHoAiJ8AFo7vuBAxD3nve85enP83vocrlMCTFommZZ9vaf8St+YFm2Wq1SFCUSifgf+D3nJQ9nWZZhGPwsyMM/z2AYplqtVqtVhmHw8z7MWC6XxWJxpVIRiUTVapVlWbIPf+CDpmm8PC4Dzms... | <image> The three views of a geometric solid are shown in the figure. The edge length of the small squares on the grid is 1. What is the surface area of the circumscribed sphere of this geometric solid?
A. $ \frac{100\pi}{9} $ B. $9\pi$
C. $ \frac{100\pi}{27} $ D. $10\pi$ | A | BMMR | math | close | multiple_choice | qwen3.5-27b | 0.5 | <think>
We are given the three orthographic views (front, side, top) of a geometric solid on a grid with unit squares. We need to find the surface area of the **circumscribed sphere** of this solid — that is, the smallest sphere that contains all vertices of the solid.
---
### Step 1: Reconstruct the 3D shape from th... |
mmfr_392 | "iVBORw0KGgoAAAANSUhEUgAAATYAAAE2CAIAAABk3in+AAAWhklEQVR4nO3df1BU5f4H8M9ZQGDhsssqyC/TAhRDM5sa/IHeInVy5noFwWQ0lbTsOsI4pmUz/bg4c9XqmqMJZU1/1J07JJlkWQmyUSQKaA7F4sV1DCYnLVlo3Wh3AV32+8e53207JN1zznPWZ+X9+q/jzPt8At48Zw9n9xG8Xi8BAK90N3sAABgOKgrANVQUgGuoKADXUFEArqGiAFxDRQG4hooCcA0VBeAaKgrANVQUgGuoKADXUFEArqGiAFxDRQG4hooCcA0VBeA... | <image>Rules:
1. The image shows a standard Tetris grid with 8 rows and 8 columns.
2. The first number in a cell coordinate represents the row, and the second number represents the column.3. The action done to the falling tetromino is randomly selected between moved to left / right.
4. The active tetromino falls one r... | 0 | GameQA-140K | logic/game/puzzle | close | numeric | qwen3.5-27b | 0.25 | <think>
Let's analyze the problem step by step.
We are given a Tetris grid with 8 rows (0 to 7) and 8 columns (0 to 7). The active tetromino is colored red, and from the image we can see:
- At row 2: columns 0 and 1 are filled (red)
- At row 3: columns 1 and 2 are filled (red)
So the active tetromino occupies cells:... |
mmfr_395 | "iVBORw0KGgoAAAANSUhEUgAAALgAAAC/CAIAAADCVIEoAAALVUlEQVR4nO2d0Y6qMBBAR0HlavxbgzEb17DGGAh/a2BRQe5DlUUUrNDSaZ3ztHuvCwUO02mlw8DzPCCIVwxVN4DQAxKF4IJEIbggUQguSBSCCxKF4IJEIbggUQguSBSCCxKF4IJEIbggUQguPlSUMPD3u0B1K3TiQ0XJjvFZdRv04hNFCXY/x9waDD/x2FvzcScr9PdHcCaDTHVDNOOzRAkD//cIkxFccsv+rEPvymedrex4GjujzzpmQdiqG9Af4X4bpymkBwAAsKc... | <image>(This question is worth 12 points)
In the figure, the spatial quadrilateral ABCD is intersected by a plane, and the intersection section EFGH is a parallelogram.
(1) Prove: CD is parallel to the plane EFGH;
(2) If AB = CD = a, prove: the perimeter of quadrilateral EFGH is a constant value; | 2a | MMR1 | math | close | numeric | qwen3.5-27b | 0.25 | <think>
We are given a spatial quadrilateral ABCD (i.e., four points not necessarily coplanar) intersected by a plane, forming a section EFGH which is a parallelogram. We are to prove two things:
(1) CD ∥ plane EFGH
(2) If AB = CD = a, then the perimeter of EFGH is constant (equal to 2a).
---
### Step 1: Understan... |
mmfr_414 | "iVBORw0KGgoAAAANSUhEUgAAAHQAAAB9CAIAAAD899C4AABCsUlEQVR4nO19eVxTZ/Z+VMBtZjpd1LbWwdpap62jtbYdrdqKLEkIJCQhC2QDQgiEfd9EUBAQF0BEBBcUEUFUUNxFxQIiIFpQUVbZBGSHQIBs7++P077DOHZ3mfl+fuePfm7D9d73Pvfc857znPOedxJCiPD/5cXI5Fc9gP/LovOqB/CDIIQmTZoE//3PvyoUCrVaPW3atEmTJmm12kmTJk2aNEmj0UybNu2nrkYgEJ55qZcpk/7bzIJcLm9ra2tqampubh4YGGhubh4... | <image>
The radius of the circular base of the TV tower is 10 meters. Now, a 6-meter-wide annular lawn is to be planted around it (as shown in the figure):
(1) What is the area of this annular lawn in square meters?
(2) If each square meter of lawn costs 100 yuan, how much will it cost at least to plant this lawn? | 156π, 15600π | MMR1 | math | close | numeric | qwen3.5-27b | 0.25 | <think>
To solve this problem, we need to calculate the area of the annular (ring-shaped) lawn and then compute the total cost based on the given price per square meter.
---
**Step 1: Understand the geometry**
The image shows a circular base with radius 10 meters (inner circle), and an annular lawn surrounding it th... |
mmfr_416 | "iVBORw0KGgoAAAANSUhEUgAAAZQAAAClCAIAAAD09pxLAAApuklEQVR4nO2dfUxcVfr4zx1c0Uh3ulncTi2VFqZbqmzK2m7EhcqwpVYjQ2moKZtSrVkVktZQFDCruMLKrlg1S7UmneqmbWwjXUvEgpGW4cdgIdCV/UJ2Wxm3M1BSEmGtsVSqRWXu74/THg/nnPsyM3deoM8ngdw597w899x7nvuc554XSZZlZBCSJKnnxkQwmUw+n8+o0gEAuK4whacYSZL4YwP1JgAA1xthUl60ngKdBQBA8NwQhjIYs0uSJJ/PhwPpU6DUAADQTzi... | <image>
On March 5th of this year, our school organized an activity for all students to 'go out of the school and serve the society'. The students of Class 3 in the ninth grade counted the number of students from their class who cleaned the streets, served at the nursing home, and participated in community performances... | 50, 10, 160 | MMR1 | math | close | numeric | qwen3.5-27b | 0.75 | <think>
To solve the problem, we analyze both the histogram and the pie chart.
---
**Step 1: Understand what each chart shows**
- The **histogram** (bar chart) shows the number of students for three activities:
- “打扫街道” (Cleaning streets): bar reaches 25 → 25 students.
- “去敬老院服务” (Serving at nursing home): bar i... |
mmfr_420 | "iVBORw0KGgoAAAANSUhEUgAAAhQAAACLCAIAAAC2t5cNAAAb0klEQVR4nO3dPVAiaRoA4A/BsQV0qKutO7JlLhm8ZHqjZe4CMbKNZCLxEvASmUiMxLqqY4wck2OM0OAKjHCCLTACI9oINhLrtgouAiPIutdVaUeYvuCbZRj+pKH/eZ9oRGw+3unut79/A8/zCAAAABBiSukCAAAA0B5IHgAAAASD5AEAAEAwSB4AAAAEg+QBAABAMEgeAAAABIPkAQAAQDBIHgAAAASD5AEAAEAwSB4AAAAEg+QBAABAMEgeAIBJwbKs0kXQD0geAIC... | <image>As shown in the figure, the circle is tangent to the two sides of the right angle $A O B$. The line $O P$ starts from $O A$ and rotates uniformly around point $O$ (until it reaches $O B$). The area $S$ of the shaded region inside the circle is a function of $t$, and its graph is roughly as shown in the image. | D | MMR1 | math | close | multiple_choice | qwen3.5-27b | 0.25 | <think>
We are given a geometric setup: a circle is tangent to both sides of a right angle ∠AOB (so the circle sits in the corner, touching OA and OB). A line OP starts along OA and rotates uniformly around O until it reaches OB. As it rotates, it cuts off a shaded region S inside the circle — specifically, the area be... |
mmfr_428 | "iVBORw0KGgoAAAANSUhEUgAAAfEAAAB+CAIAAAC7wb+TAAAu2UlEQVR4nO2de1RUV57vf/u8CqqK4imigIJWoRJQUCMRXIlKOgrmgWm105PpZXdnrWJN7szAuj3enruWSa/c2PPHNbMC6cy9Az0ra7yZmTZMkjG9Wkpbo0EFjYlGDaJQpREUeT8L6nUe+/5xqopTL4HyQQH7E1el6px99tlVnPqeX/32b/9+CGMMBAKBQJgTUDM9AAKBQCA8MkJpuhRWb7PO5J91AyYQCIQHEUrTw7PfUfgDeRIEKniED5hAIBCmx7zyvRAFJxAIc5x... | <image>
Based on the image, set up the equation and find the value of x. | 3, 40 | MMR1 | math | close | numeric | qwen3.5-27b | 0.25 | <think>
We are given two diagrams:
**Figure 1**: A rectangle with width labeled as `x m` and height `1.5 m`. The perimeter is given as 9 meters.
The formula for the perimeter of a rectangle is:
> Perimeter = 2 × (length + width)
So, plugging in the values:
> 2 × (x + 1.5) = 9
Solve for x:
Divide both sides by 2:
> ... |
mmfr_432 | "iVBORw0KGgoAAAANSUhEUgAAAIcAAABUCAIAAAAnL7PcAAAlXUlEQVR4nNV9eXgURfp/dc/Zc2auTGYymVyTkAOSyCEk6rJyCxJcFw/8rbCuirroo7sY4OFwl9VVhPj1WXE5V/FAFp6FRQRFEhTF5XK5TQhJZibXJJnJ3NNzdM/R9fujwjAk4crBxs8f0NPprq56P1X1vvXWW1UYhBAMXzAA4N2XEAAMGKs3NWU9PzV7kJKHAGAAQggAg2GsxJt3AhBAADGAJX4OfRy//kv/IzAQAAC6qwp+9RpjADAvnvZC4qMD+Q6EEGAMAADDsKu... | <image>
In the figure, the lengths of the diagonals of rhombus \(ABCD\) are \(2\) and \(5\). Point \(P\) is any point on diagonal \(AC\) (point \(P\) does not coincide with points \(A\) or \(C\)). Line \(PE\) intersects \(AB\) at point \(E\) and line \(PF\) intersects \(AD\) at point \(F\). What is the area of the shad... | B. \( \dfrac {5}{2}\) | MMR1 | math | close | multiple_choice | qwen3.5-27b | 1 | <think>
We are given a rhombus $ABCD$ with diagonals of lengths 2 and 5. Point $P$ lies on diagonal $AC$, not at the endpoints. Lines from $P$ intersect sides $AB$ and $AD$ at points $E$ and $F$, respectively. The shaded region consists of quadrilateral $BCEP$ and triangle $EFP$ — but looking at the diagram, it appears... |
mmfr_434 | "iVBORw0KGgoAAAANSUhEUgAAAIwAAAB4CAIAAACvoY1mAAAWCElEQVR4nO1df0wT5/+/K79m5Gv9cYyiRxApUulcwGp0EQW3qmwfyjCSYbIu4sZXjLikRookMnEZiYgmLA5UNJssYUmTOSHCMkJxloRluJJgQgWiV4WVfCmr+UzWmpX+uPv+8cB53F3Ltb3+YPMV/jiuz/O83/e8n/eP5zdMEAT0Cpxx//797du3h5ioIMT0lhzIRvzLL7/s2rWrrKxsZmYmxDy8EtLiMBqNBw4cOHToUFlZ2fDwsFAoDLH5eSWkBaDV/vT09Keffiq... | <image>In the figure, the diameter AB of circle O is 4, point C is on the circumference, AC = 2, and a tangent DC is drawn through point C. Point P is a moving point on the arc \( \overline{\epsilon}_{BA} \) (not coinciding with A or C). (1) Find the degrees of \( \angle APC \) and \( \angle ACD \); (2) When point P mo... | (1) \angle APC = 30^\circ, \angle ACD = 30^\circ; (2) Proof in reasoning; (3) P is the point diametrically opposite to C | MMR1 | math | close | numeric | qwen3.5-27b | 0.5 | <think>
We are given a circle with center O and diameter AB = 4, so radius OA = OB = OC = OP = 2. Point C is on the circumference such that AC = 2. Tangent DC is drawn at point C. Point P moves along arc BA (the major arc from B to A not passing through C? Actually, note: “arc \( \overline{\epsilon}_{BA} \)” — likely m... |
mmfr_441 | "iVBORw0KGgoAAAANSUhEUgAAAXcAAAESCAIAAACJmwJAAABjeElEQVR4nO29fVhc1bX4v/aZVGyLYtuxIWYsgRnqKEmLJd5EE0sMM4AGBlqxiVd6xYYAaUiDCQPkaxSiseEthlRsBki/4tfkkdRoeEsNM4MSDTekQcGWCJEZIAZvQHIfwaTPDyqc/ftjz5w5c+aFYd4J5/MomTmz55w9Z6+z9tprr702whiDHTAAsvEJxgihWYvx8FjHpszQAJT5C3uUl5f39/dXVVW5tXI87sROK9IAgAEDQF4SQhTKq1YDAAZdEkIaPQBRMURH8Sq... | <image>In the Cartesian coordinate system, let A (0, n), C (m, 0), and the hyperbola \( y = \frac{12}{x} \) (for \( x > 0 \)) intersect the sides AB and BC of rectangle OABC at points D and E, respectively. Connect points O, D, E, and D to form triangle DBE, and then reflect triangle DBE across line DE to obtain triang... | (8, \frac{3}{2}) | MMR1 | math | close | numeric | qwen3.5-27b | 0.25 | <think>
We are given a rectangle OABC with A(0, n), C(m, 0), so O is (0,0), B is (m, n). The hyperbola $ y = \frac{12}{x} $ intersects AB and BC at D and E respectively.
- Side AB: from A(0,n) to B(m,n) → horizontal line y = n. So D is on AB and on hyperbola ⇒ $ n = \frac{12}{x_D} \Rightarrow x_D = \frac{12}{n} $. So ... |
mmfr_453 | "iVBORw0KGgoAAAANSUhEUgAAANEAAABlCAIAAABcA5HbAAAu2UlEQVR4nO1dd1wU1/a/s7uzfVlQWBALoCKKCuqzKyryFBKNFBEVSxRsEY2JyrMXjCUq0Wf9aRSsEY2aWDAGjTUBsfzsYqEJQUTq9p2dLfP747w3b92l7CLC732y379m7swtu3PuueeedjGKopAddjQiGE09ADv+crDTnB0IIURRlFwut/Ll8+fPP3v2rN592WnODoQQysvL69Gjx/fff1/nmwkJCWPGjCkqKqp/Z5QddlCUTCaLiYnBMCwhIcFgMNT02q5du5hM5v7... | <image>The three views of a geometric body are shown in the figure. What is the area of the side view ( )?
A. 2 + \sqrt{3}
B. 1 + \sqrt{3}
C. 2 + 2\sqrt{3}
D. 4 + \sqrt{3} | D. 4 + \sqrt{3} | MMR1 | math | close | multiple_choice | qwen3.5-27b | 0.75 | <think>
To determine the area of the side view, we need to analyze the given three views (front view, side view, and top view) of the geometric body.
### Step 1: Understand the Three Views
- **Front View**: Shows a rectangle with dimensions 2x2, and two dashed lines forming a triangle inside. This indicates that ther... |
mmfr_454 | "iVBORw0KGgoAAAANSUhEUgAAALYAAAG6CAIAAAAqJyucAABajElEQVR4nO2dd3wc1bn3n3Nmtmu1q15tyxWMbSA2JiGhGBscmgMX08wlAW5CAgkJJOGaEmJfCLk32E57U8CUJIQUgimmF2NjsIkxxQaMDe5FsnrZvjvtPO8fZ3e0Wq22aVeSpfl+DB9pNHPOmZlnTnnOc36HICIYGAwMHe4CGIx00pvIb34DTU1DUBKDEQpJ2tD4fPDCC7BvHyxaBLNn5576E0/AkiXwwgtw0UWwYwc8+yw0NMDFF4PLlXuaBkMN9mPrVjz5ZNywIfr... | <image>In the figure, natural numbers are placed in the Cartesian coordinate system according to the following rules: (1) each natural number is placed at an integer point (where both coordinates are integers); (2) 0 is at the origin, 1 is at the point , 2 is at the point , 3 is at the point , 4 is at the point , 5 is ... | (-n, n+1) | MMR1 | math | close | short_phrase | qwen3.5-27b | 0.75 | <think>
We are given a spiral arrangement of natural numbers on the integer lattice, starting at 0 at (0,0), and proceeding clockwise. The first few points are:
- 0 → (0,0)
- 1 → (0,1)
- 2 → (1,1)
- 3 → (1,0)
- 4 → (1,-1)
- 5 → (0,-1)
and so on, spiraling outward in layers.
The problem asks for the coordinates of th... |
mmfr_480 | "/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCABRAOoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRI... | <image>First perform reasoning, then finally select the question from the choices in the following format: Answer: xxx.
Question: Using a sector paper with a central angle of x and a radius of y, find the height of the conical bottomless paper cap formed when the paper is rolled. Express the height as 'h'.
Choices:
A: ... | D | FineVision-geo170k(qa) | math | close | multiple_choice | qwen3.5-27b | 0.25 | <think>
The image shows a sector of a circle being rolled into a cone. We are told the central angle is $x$ and radius is $y$, but in the answer choices, specific numerical values (in cm) are given — suggesting that actual values for $x$ and $y$ were intended to be provided in the original problem, even though they’re ... |
mmfr_500 | "iVBORw0KGgoAAAANSUhEUgAAAMYAAACGCAIAAAAJoWJmAAAkB0lEQVR4nO2deVgTV9fA72RBZA8QVpVdZRFEEFDBBcW6UESqUq1VirtWEbe2arWLW9WircqrYlG09q0b2ooiVMElKKAWEFkqChEQMEAICSQhmZn7/XFf8+QDtImyBJzfHzxh5i5nMifnbueei0EIAQVFx8EAAFBaRfF2kCQJAKDT6coXad0kDEWvRdNVCkKobERb/YuukCRJGVrNQaNVqra29u7du8pXkAIpX2lqakpISCAIomtFo3gtjO4WAAAARCLR48eP/fz8AAA... | <image>The following is the frequency distribution histogram of students' weights sampled from a certain school. It is known that the frequency ratio of the first three groups from left to right is 1:2:3, and the frequency of the second group is 10. Then the total number of students sampled is _______ _ | 40 | MMR1 | math | close | numeric | qwen3.5-27b | 0.75 | <think>
We are given a frequency distribution histogram of students' weights, with class intervals: 50–55, 55–60, 60–65, 65–70, 70–75.
The y-axis is labeled “频率/组距” (frequency per unit class width), which means the height of each bar represents the **density** = frequency / class width. Since all class widths are equa... |
mmfr_501 | "iVBORw0KGgoAAAANSUhEUgAAAoAAAAHgCAIAAAC6s0uzAADU3UlEQVR4nO39a6wtyXUeCK7M/Th377Pr8rIpqLvZdjVIiPVDg+JDVS1bGEosoSU0xwIGUyJaoqxL2YIJa+QxeQVB9B8bAmFYGMDUCCpZgEcCBdpQWQ8bVGHQkIcNaoZFiIDcAkt8lCwMigIxU+ih3WoLvLy1zz737Edm/1iZa69cKyIyMnfmfp314eDe3JmRkZErI2LFekbytp/4PmiLfJ0BQDJMW9ewC1JIM8gO8uj94HI2u5rPD90Kg8FgMPSCw/BOg8FgMBhuOXZ... | <image>
The given image represents the interface of the game Klondike Solitaire. The user interface consists of a board with 52 playing cards divided into four distinct areas:
1. **Stock Pile (Draw Pile):** Initially composed of 24 face-down cards. The player can draw one card at a time to reveal its face.
2. **Waste... | 1 | GameQA-140K | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 0.5 | <think>
Let's analyze the current board state and evaluate each option.
First, identify key elements from the image:
- **Waste Pile (top row, second card from left)**: The top card is 2 of Spades.
- **Foundation Piles**:
- Foundation 1: Ace of Spades
- Foundation 2: empty
- Foundation 3: empty
- Foundation 4... |
mmfr_506 | "iVBORw0KGgoAAAANSUhEUgAAAK0AAACHCAIAAADr+k5EAAAlvElEQVR4nO2dd1wU1/bA78z2ZemwFOkgIIIKPgEbsZcEsWA+asSoIagRiYmxRdGfigo2xBJ9KrZgjA3Ls6DErtgAAWOoClKkLLDswvYy9/fHNft8xrKzwILI9x92l7lzz8ycueXcc87FIISgk08evK0F6KRd8D96oFar33WcUCgkCKL15emkbXilBwqFIisra9q0aVVVVXfv3r13796lS5dOnDiBnj2EcN++fVOnTgUA8Pl8Pp/fliJ30gpQ0Z9Lly4lJCQ8fvxYLpe... | <image>According to a survey conducted by WeChat Tongcheng Travel, the age distribution (in years) of 1000 ticket purchasers participating in online ticket purchases is shown in the figure.
(1) It is known that the number of online ticket purchasers in the middle three age groups forms an arithmetic sequence. Find t... | a=0.035, b=0.025; 3/5 | MMR1 | math | close | numeric | qwen3.5-27b | 0.75 | <think>
We are given a frequency histogram (with "frequency/group width" on the y-axis) for age distribution of 1000 ticket purchasers. The group widths are all 10 years: [20,30), [30,40), [40,50), [50,60), [60,70).
The heights (i.e., frequency/group width) for each interval are:
- [20,30): 0.015 → frequency = 0.015 ... |
mmfr_510 | "/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHKA94DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRI... | <image>
What is the difference between the configurations shown on the left and right sides of Figure 10? | horizontal double versus vertical triple | FineVision-visualwebinstruct(filtered) | logic/game/puzzle | close | short_phrase | qwen3.5-27b | 0.25 | <think>
To determine the difference between the configurations on the left and right sides of Figure 10, we analyze the spatial arrangement and orientation of the dot patterns within each green rectangle.
On the **left side**, the green rectangle encloses a horizontal strip of dots arranged in two rows (top and bottom... |
mmfr_515 | "iVBORw0KGgoAAAANSUhEUgAAAdMAAACUCAIAAABHtlSaAABUHklEQVR4nO29d2AU5fb/P7uzvSe76Y00SCAJoStVuoIKooheBeQjehFQRPCrNAUErhoEKQKK7YpwEQHpPQFCiYQ0UkjvbUu29zK7vz+e+5nP/jYh7CazM5uQ11+7s7PznGx2zzzPec55H5LD4YD66KOPPvrAETLRBvTRRx99PHF0xfOqVKra2lqFQqHX6zE3CGesVqtKpcrLy9NoNETb0kcffTwpdMXznjhx4rPPPqutrc3IyNizZw/mNuHGhQsX7t69KxAIhg4dev3... | <image>Given that the geometric body is composed of two right prisms, its three views and intuitive diagram are shown in the figure. Let the angle formed by the two skew lines A₁Q and PD be θ, then the value of cosθ is ______. | \frac{\sqrt{15}}{15} | MMR1 | math | close | numeric | qwen3.5-27b | 0.5 | <think>
To find the cosine of the angle θ between the skew lines $A_1Q$ and $PD$, we can use vector geometry. First, we need to establish a coordinate system based on the given three views and the intuitive diagram.
From the three views:
- The front view (正视图) shows a rectangle with width 2 and height split into two p... |
mmfr_525 | "iVBORw0KGgoAAAANSUhEUgAAAKUAAAB9CAIAAABMJDTPAAAOVUlEQVR4nO2dP3DaSBuHxTeZOaWy0tzpmrOYKyIqlsryzM1YrixXiMpQGVcxlaE6qAQVSYXTHJ5rsOcKfJVwhVMBzcFVQIVSgSvUQZrA3NyMvmITnYJAFgbtSpinSGSxaF/007vav+/6NE0jtjwb/ofbAMeZTqe4TXARm693LpfbSq6z+XqTJFmv13Fb4RY2XG+o9J9//onbELfgeb19Pp/P54MH+slcLgcPoNKVSmVbpEM8r7e5faGLTRBEpVIhCGI8Hm+LdIhvA9p... | <image>
In the figure, the circle centered at the origin intersects the hyperbola represented by the function $y= \frac{3}{x}$ at points A, B, C, and D. Given that the x-coordinate of point A is 1, what is the x-coordinate of point C?
A. -3
B. -2
C. -1
D. -4 | A. -3 | MMR1 | math | close | multiple_choice | qwen3.5-27b | 0.5 | <think>
We are given a circle centered at the origin and a hyperbola $ y = \frac{3}{x} $. The circle intersects the hyperbola at four points: A, B, C, D. We’re told that point A has x-coordinate 1, and we are to find the x-coordinate of point C.
---
**Step 1: Find coordinates of point A**
Since A lies on the hyperbo... |
mmfr_528 | "/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFYAZEDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRI... | <image>
At what price does the supply curve indicate that 30,000 units will be supplied, and how does this compare to the price consumers are willing to pay for the same quantity? | 47.50 | FineVision-visualwebinstruct(filtered) | math | close | numeric | qwen3.5-27b | 0.25 | <think>
To solve this problem, we need to analyze the supply and demand curves in the provided graph.
Step 1: Find the price at which 30,000 units are supplied according to the supply curve (S).
- Locate quantity = 30,000 on the horizontal axis.
- Move vertically upward from 30,000 until you intersect the supply curve... |
mmfr_532 | "iVBORw0KGgoAAAANSUhEUgAAAfQAAAJYCAIAAAAbgoPVAABuNElEQVR4nO3deVQT994G8F8SScIaQPYdUUFEwGKhaF0QFBAXeq+7rWBdqsWF4lLxtqLVFm2tpVWvVq1iX7WKti51QRFE664oV1Gx7iASVklkC5Dk/WNqShEDJEMSkudz7rknmcw8fBPs4ziZTBhSqZQAAIB2Yap7AAAAoB/KHQBAC6HcAQC0EModAEALodwBALQQyh0AQAuh3AEAtBDKHQBAC6HcAQC0EModAEALodwBALQQyh0AQAuh3AEAtBDKHQBAC6HcoSNxcXG... | <image>Rules:
1. Each numbered region represents a piece on the board.
2. Pieces are considered adjacent if they share at least one edge.
3. Pieces that only touch at corners are not considered adjacent.
4. One piece is removed from main board and shown below. It has been rotated and may have been flipped.
Question:
C... | 3 | GameQA-140K | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 0.25 | <think>
To determine whether the removed piece can fit back into the main board by only rotation (and possibly flipping, but the question restricts to rotation), we must:
1. Identify the shape of the removed piece from the “Removed Pieces” diagram.
2. Locate the hole in the “Main Board” where that piece was removed.
3... |
mmfr_533 | "iVBORw0KGgoAAAANSUhEUgAAA00AAARnCAIAAACn8RqlAAEAAElEQVR4nOzdeXxTVd4/8JN9aZPuKyC1LYvIVmQTUMAFKchIlXHFQfwpgtu0g+OGY1sfUWRUOm7wMDMqo6LOMNRRoRU3HAFRlqIgU6DFVugCpWva7Mn9/XEe7sQkTbPcm5vcfN5/8Aqnt8m3ucnNJ+fce46EYRgCAAAAAKIjFboAAAAAAOAFch4AAACAOCHnAQAAAIgTch4AAACAOCHnAQAAAIgTch4AAACAOCHnAQAAAIgTch4AAACAOCHnAQAAAIgTch4AAACAOCH... | <image>Solve that puzzle by choosing the appropriate letter. | G | FineVision-raven | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 0.5 | <think>
To solve this puzzle, we analyze the 3x3 grid of panels. Each panel contains a set of shapes with varying properties: shape type (polygon sides), size (small, medium, large), and fill (white, gray, black). We look for patterns across rows or columns.
Let’s examine each row:
**Row 1:**
- Panel 1: Pentagon-base... |
mmfr_543 | "iVBORw0KGgoAAAANSUhEUgAAAoAAAAHgCAIAAAC6s0uzAADftElEQVR4nO39XawlyXUeCq7M/XP67LO7WBwa0h3CbgwJsoHR3FaLKl7bxFCkhCvDmquXkRpjk3ZRsmDCGl1cqQSC9osAoXEBvdgcwm0J8EiQQQtsi5KFVj8I8tCQZtqCBNDXYIlqtaUZFAXCaFzQssYcFqv32afP/smch5W59sq1IiIj//bPOevDQVXuyMiIyMiIWLF+I3nPj3wE2iLfZACQjNPWJXRBCmkG2UGq3g8u5vPLxeLQrTAYDAbDIDgM7TQYDAaD4ZajEwF... | <image>
The given image represents the interface of the game Klondike Solitaire. The user interface consists of a board with 52 playing cards divided into four distinct areas:
1. **Stock Pile (Draw Pile):** Initially composed of 24 face-down cards. The player can draw one card at a time to reveal its face.
2. **Waste... | 7 | GameQA-140K | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 0.5 | <think>
To determine which move is both **valid** and **effective**, we must first understand the rules of Klondike Solitaire as described:
- **Valid moves**:
- In tableau piles: cards can be placed on a card of opposite color and one rank higher (e.g., red 6 on black 7).
- Only Kings can be placed on empty tablea... |
mmfr_552 | "/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFgAXgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRI... | <image>
What does Figure 3 illustrate in relation to the attention maps? | areas of interest or focus | FineVision-visualwebinstruct(filtered) | science | close | short_phrase | qwen3.5-27b | 0.25 | <think>
The image displays four panels, each showing a grayscale anatomical scan (likely of the pelvic region) with overlaid color-coded attention maps. The left column shows single compact heatmaps centered on specific regions (e.g., hip joint or femoral head), while the right column shows more complex, elongated, or ... |
mmfr_557 | "iVBORw0KGgoAAAANSUhEUgAAAa4AAAISCAIAAAAbd7xeAAAfgElEQVR4nO3df1RUdf7H8fdlqEFkBFRWN1I3cE8TYQ4am579YrW2dZSzFZzS1Toe+oHHrK2TR6pz3EKW4BS21Araacuws20na9nQfiitbePaH2moc3bcg3lkM5ttdU1FZgJBZL5/zC5O0zDcEe7nDs7zcfyDuQS++jC++Nw7n/sZze/3izE0TTPoOwPA8NKMq0Lop2n8IPRirPRjrPRLMDsAAJgv0ewA0CPeLjVc+ESmoqJiGHPEvvLy8iF8Nc+r85gVAgBVCABUIQA... | <image>Now I'll give you a picture, which shows a screenshot of a rhythm game, in which there are operation blocks of various colors. In this game, the operation blocks will fall at a speed of 1 cell/second. At the same time, you can select a column to place your finger (you cannot move your finger after selecting it),... | 1 | GameQA-140K | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 0.5 | <think>
Let's carefully analyze the problem.
We are told that we select **column 2** and will click on all operation blocks that fall to row 1 in column 2. The game has a grid with rows numbered 1 (bottom) to 15 (top), and columns 1 to 4.
Blocks fall at 1 cell/second, meaning each second, every block moves down one r... |
mmfr_567 | "iVBORw0KGgoAAAANSUhEUgAAAnIAAAGQCAIAAAClKBrWAACWF0lEQVR4nOzdd3hTZdsA8Ptk76Rpm3QvSgfQssveU/YUERBFcAKuF0RRWSJLxQGioIDjE0RQZImyp6wyC3RRumfapM1e53x/nJKmZRVIm7S9f5fve+U8Z90Nbe48z3kGQVEUIIQQQsgVGO4OACGEEGo8MK0ihBBCLoNpFSGEEHIZTKsIIYSQy2BaRQghhFwG0ypCCCHkMphWEUIIIZfBtIoQQgi5DKZVhBBCyGUwrSKEEEIug2kVIYQQcpkGk1Y1Gs3UqVNnz55tt9v... | <image>
What is the value of Maroon at x-axis label 60? | 86 | ViRL39K | chart/table/doc | close | numeric | qwen3.5-27b | 0.25 | <think>
To determine the value of the "Maroon" line at x-axis label 60, we follow these steps:
1. Identify the "Maroon" line in the legend — it is represented by a dashed maroon line.
2. Locate x = 60 on the horizontal axis (xaxis_label).
3. Move vertically from x = 60 up to intersect the Maroon line.
4. From that int... |
mmfr_569 | "iVBORw0KGgoAAAANSUhEUgAAAa4AAAISCAIAAAAbd7xeAAAhEklEQVR4nO3dfXBU5dnH8etkgY1hFxIghRIBTei4RpAEjMJ0oD7VajFjbRgBQYdGJBaBwYEh4AwlIYYwGmxqSYBaxOhoKUhTE8SXWKhB+oeRANuGDpiBiri+IC95WxLyus8f+8iTLpuYhZz7nD18P39lD0v2unazv73Pfc65V/P5fKIPTdN0+s0A0Lc0/aLQGjTNCk8RXZgHXZhThNEFAIDx+hldQDgy846/pT6oAWUYFQIAUQgARCEACFEIAEIUAoCEGoVlZWXaf0t... | <image>Now I'll give you a picture, which shows a screenshot of a rhythm game, in which there are operation blocks of various colors. In this game, the operation blocks will fall at a speed of 1 cell/second. At the same time, you can select a column to place your finger (you cannot move your finger after selecting it),... | 1 | GameQA-140K | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 0.5 | <think>
Let's analyze the problem step by step.
We are told that we select **column 3** to click. That means we only interact with blocks in column 3 as they fall to row 1 (the bottom row). We cannot move our finger, so we’re locked into column 3.
The game has three types of blocks:
- **Click blocks**: yellow, 1 cell... |
mmfr_570 | "iVBORw0KGgoAAAANSUhEUgAAALUAAADcCAIAAAC5yndsAAA6U0lEQVR4nO19fXAU15Xv79xRFlfFa95unGf2PTY4gIyQwOuqPGf9YgIIzQiI2YBwXtm7cdmQuIJmRhhs8JrU2sZs2bGXGQkwSLBlUmZjp2Jn0UjyYvMhgSRXvOWPrccazQgwCJyYrZfYuxu7ILUGpu95f9zuO7d7PjSjzxGZ3x/QunP79u3u0+frnnMuOAssTlqWldYomTneEQEAoKYhmuR4JNKabRAPpJSuwdKwJgCQGhvRtoTdzz2NUADR9rg5lHtYZua+9q3Awrh... | <image>Two trains, A and B, start from two locations 300 kilometers apart and move towards each other. (1) Which train's distance from point A is represented by the function l₁ in relation to time t? (2) After 1 hour, how far apart are the two trains? (3) Find the function relationships for the distances s and time t r... | (1) l₁ represents the distance of train B from point A. (2) After 1 hour, the two trains are 200 km apart. (3) The function relationship for l₁ is s = 300 - 60t, and the function relationship for l₂ is s = 40t. (4) Trains A and B will meet after 3 hours. | MMR1 | math | close | numeric | qwen3.5-27b | 1 | <think>
We are given a graph with two lines, $ l_1 $ and $ l_2 $, representing the distance (in km) from point A versus time (in hours). The problem involves two trains starting 300 km apart and moving toward each other.
---
**Step 1: Understand the graph**
- At $ t = 0 $:
- Line $ l_1 $ starts at $ S = 280 $? Wai... |
mmfr_588 | "iVBORw0KGgoAAAANSUhEUgAAAZUAAACyCAIAAAAF58VWAAA4wklEQVR4nO2df3hTVZr433PjWr9jNfpYt3XFQWkLJalD/LXWASxjkxIGpOnADO5YF1iqQAJSaNC6IG2lLnVIIJWmojCPdRe/W76DJlUcCgmPZcABB1xwTFLoL4voPjgwM7DyrDDQ+37/OMnNzU/SNr97Ps8DTe4999yT8+M973nPe84hiAjJDAISINcNhUgICfzMiCHeouEBOEC4fjkxooGulLTYQGuwmKs1CI5Scr/OwWvkZBSWAJfoBPhDpamulBBCdEYrAgC4lIR... | <image>
Given that point P is a moving point in the fourth quadrant, point Q is a moving point on the x-axis, and point R is below PQ and is a moving point on the negative y-axis. (1) As shown in Figure 1, if P (2, -1), Q (-3, 0), R (0, -5), find the area S of triangle PQR; (2) As shown in Figure 2, if RM and QM bisect... | ∠M = 45° + \frac{1}{2}∠P | MMR1 | math | close | numeric | qwen3.5-27b | 0.5 | <think>
We are given a geometric configuration involving moving points P (in fourth quadrant), Q (on x-axis), and R (initially on negative y-axis, later positive y-axis). We are to compute area in part (1), then find angle relationships in parts (2) and (3) under bisector conditions.
---
**Part (1): Given P(2, -1), Q... |
mmfr_597 | "/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRI... | <image>
a. Identify the type of graph depicted in the image.
b. Determine the range of y-values where the graph intersects the y-axis. | 0 | FineVision-visualwebinstruct(filtered) | math | close | numeric | qwen3.5-27b | 0.5 | <think>
Let's analyze the image and answer both parts of the question.
a. Identify the type of graph depicted in the image.
The graph shows a continuous curve that passes through the origin (0,0) and extends into multiple quadrants. It has a distinctive shape: it resembles a “loop” or “figure-eight” pattern near the ... |
mmfr_604 | "iVBORw0KGgoAAAANSUhEUgAAArwAAAH0CAIAAABQO2mIAADlfElEQVR4nOzddXhTVxsA8JPcuFs1dXeDUoqV4u46bMBgwATGnMk3hw22wTZgA4a7a3FpcavQlrprmjbu+v0RVkqppG3ShnJ+z549zc25556bhubNkfegjEYjgCAIgiAIag26qxsAQRAEQdCrAQYNEARBEASZBQYNEARBEASZBQYNEARBEASZBQYNEARBEASZBQYNEARBEASZBQYNEARBEASZBQYNEARBEASZBQYNEARBEASZBQYNEARBEASZBQYNEARBEASZBQYNEAR... | <image>
What is the highest value in the SouthEast? | 10.6% | MMR1 | chart/table/doc | close | numeric | qwen3.5-27b | 0.75 | <think>
To determine the highest value in the Southeast region of the USA based on the provided map:
1. Identify the Southeast states: Typically, this includes Florida (FL), Georgia (GA), Alabama (AL), Tennessee (TN), Mississippi (MS), Louisiana (LA), Arkansas (AR), North Carolina (NC), South Carolina (SC), and someti... |
mmfr_609 | "iVBORw0KGgoAAAANSUhEUgAABbUAAAL6CAIAAACO9ywsAAEAAElEQVR4nOy9V3BbeZbffy9yIgEQiWDOOYqZEhVbqTXdvZN31y57yrVlP9hl11Ztlf2yXj/ZZftha9+cyhtmZ7d2ZrZnunsktXJgzjmBESRBAkTOGff/cMzf/wqU2BJFiSB5Pg8qCLwAfrj4hfM7v3O+h2YYhkIQBEEQBEEQBEEQBDnDcI67AQiCIAiCIAiCIAiCIMcM+kcQBEEQBEEQBEEQBDnroH8EQRAEQRAEQRAEQZCzDvpHEARBEARBEARBEAQ566B/BEEQBEE... | <image> Choose the most suitable option from the four given options to fill in the question mark, so that it shows a certain pattern: ['A. A', 'B. B', 'C. C', 'D. D'] | C | BMMR | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 0.25 | <think>
To solve this problem, we need to identify a consistent pattern in the sequence of figures provided.
Let's analyze each figure in the top row:
1. First figure: A large triangle with an inner smaller triangle and a vertical line connecting their bases. This creates **4 distinct enclosed regions**.
2. Second fi... |
mmfr_614 | "iVBORw0KGgoAAAANSUhEUgAAAHoAAABKCAIAAAD7QdceAAAQeklEQVR4nO2cuXIkxxGGs8+5AEQsHTJokzIUegAF+ASiHFl8A4GmaOgxZCxNridXIUMOd59ADD2Ajgju+jSWxDVX3yXjY/9b25jpHgwGIFZiGoieQld3VVZWHn9mdeCcs5/poSj8qQfw/0XD7HbOVVXVNA1/d3xu0zRlWXJ/WZa0mFme5/ys65qHc60n+7utaRq1V1XFnXRUd2jHUf3kNMDuoiiCIIjjuGmaKIrCMCyKoigKt4XMbL1eZ1m2Wq2SJGmaJs/zKIrqus6... | <image>In the right trapezoid, the lengths of the two non-parallel sides are 6 cm and 10 cm, and the length of the bottom base is 14 cm. After removing four identical sectors, find the perimeter of the remaining part (the shaded area). | 6\pi + 12 | MMR1 | math | close | numeric | qwen3.5-27b | 0.5 | <think>
We are given a right trapezoid with:
- Two non-parallel sides (legs) of lengths 6 cm and 10 cm.
- Bottom base = 14 cm.
- Four identical sectors are removed — from the image, we can see that each sector is a quarter-circle (90°), centered at each corner of the trapezoid. Since they are “identical”, they must ha... |
mmfr_618 | "iVBORw0KGgoAAAANSUhEUgAAAMsAAAC3CAIAAAAzeT3eAAAeNklEQVR4nO2df1BU19nHn7ObNzgNM+B0E7DZ1kRAwMUWI46koLuWBbESWYJJQEwj6U5FIAm+mIoJCSRqJdNFcSIpmSavJoN1W6EsrzSgrCNUrDjQwSbAkhQURzpxX2kDBVuYsve8fxy4XHbvLojs3XPZ+/mDYc+e3fvcu9/znOf8RhhjECfV1dX+/v5xP4oDBBhjhNDkGxgAMQAyNicGQPzfIeF2ZLNnoZLx8fGf/vSn6enptokJACDyyklACKGcoyYMMgBLPEImCwA... | <image>Given the parabola $y = -x^2 + bx + c$ intersects the x-axis at points A (-1, 0) and B (3, 0), and intersects the y-axis at point C. Let D be the vertex of the parabola. Connect points C, D, B, and A. (1) Find the equation of this parabola; (2) Find the area of quadrilateral ABCD; (3) Let Q be a point on the par... | \left(\frac{1 \pm \sqrt{13}}{2}, \frac{1 \pm \sqrt{13}}{2}\right) | MMR1 | math | close | numeric | qwen3.5-27b | 0.5 | <think>
We are given a parabola $ y = -x^2 + bx + c $ that intersects the x-axis at A(-1, 0) and B(3, 0), and the y-axis at C. D is the vertex. We are to:
(1) Find the equation of the parabola.
Since the parabola passes through A(-1, 0) and B(3, 0), we can use these points to find b and c.
Plug in A(-1, 0):
$ 0 = -... |
mmfr_621 | "iVBORw0KGgoAAAANSUhEUgAAAU4AAACVCAIAAAC4v4RmAAB8vElEQVR4nO09Z2AU1dbnzuxm0zY9pFACBAghCUGQKggJHaQIiIj4qU+RIkWkWJ6o2OlVmuKzUkR6LwEEaREQUkiBEAIE0tsm2Tr3fj/O7s1kdxNCR835kezOzty57dzTzyGMMaiFWvhHA2OMEGLvukSICJRRAQSwc0M1reFfSqkgCPe1sw8K/h69rIVauBeojOcUgFqui8AABALUTPAopXfU8t8FzwGA1FL1Wvj3AINKtJtSADCTZUqpIEA1xA8xhZ8aVl8ff/jbnEm... | <image>
As shown in Figure A, it is the emblem of the 7th International Congress on Mathematical Education (ICME~7). The main pattern of the emblem is derived from a series of right triangles as shown in Figure B, where OA<sub>1</sub>=A<sub>1</sub>A<sub>2</sub>=A<sub>2</sub>A<sub>3</sub>=…=A<sub>7</sub>A<sub>8</sub>=1.... | (1) The transformation rule is OAₙ = √n. (2) The length of OA₁₆ is 4. (3) The value of S₁²+S₂²+S₃²+…+S₂₀₁₉² is 1019595/2 or 509797.5. | MMR1 | math | close | numeric | qwen3.5-27b | 0.25 | <think>
We are given a spiral of right triangles, starting from point O, with each triangle sharing a vertex at O and having legs of length 1 (except the hypotenuse which becomes one leg of the next triangle).
From Figure B:
- Triangle OA₁A₂ is right-angled at A₁ → so OA₁ = 1, A₁A₂ = 1 → by Pythagoras, OA₂ = √(OA₁² +... |
mmfr_644 | "iVBORw0KGgoAAAANSUhEUgAAAZoAAACOCAIAAACHVFkNAAA//UlEQVR4nO293XcbR5Yn+LsB9f4fW8xMkqBcs09bIqU+8zYWAFaJrClJffaMpeopEWD12RZBleXeLkuze1rynG3LJhKqPdumpJm13S8lqcsibWQm3c8lueZpz9giKWQmXf/HWhl3HyI/8UWQBCnKzt+xKSAy8sbNQMTNGxH3g5hZggUIADsLi7i/WgIYICjYNarcQxoE8MyK93RZw+4gImYeomKOHDlyHAgnAIhYdKE4bkhAMJjiQr5i8b0SiABAslObcecuQGgpkZc... | <image>The table (or histogram) shows the total number of gold medals from the 25th to the 29th Olympic Games and the number of gold medals won by our country's athletes. Please complete the histogram based on the relevant information from the graph and fill in the data in the table. (1) The range of gold medals won by... | 35, 0.1 | MMR1 | math | close | numeric | qwen3.5-27b | 0.5 | <think>
We are given a bar chart and a table showing China's gold medals in the Olympics from 1992 to 2008 (years corresponding to 25th–29th Olympiads), along with world total gold medals and China’s share.
The question has two parts:
---
**(1) The range of gold medals won by China from 1992 to 2008 is ___.**
From ... |
mmfr_666 | "iVBORw0KGgoAAAANSUhEUgAAAKAAAACMCAIAAAB0wzU3AAAMvUlEQVR4nO1dX2gU1xr/ZiPtSx4KTWGhi3LbtQ/Xl/gSEhK4kbhN7kVotClJ1IIPlcaNaG7rgw/BOVvzELlJrw+rxgdBwUC8N7JbfEgkpTaQtKkKW9qsoCYXMSkIKbRUaVYw892H2YzjzOzumdmZc+bf72Hc7Mzv/M5xvm++82++FURRBEv49ttvAaC1tbX8ZYIgIKLmy1u3bgHArl27aC62WTci7PpbK4AEEHn1pIRCRMCSdJe3t2R9RFEkhFgjWwMiCoKg/sBY1+j... | <image>The endpoints of segment \(AB\) are located on the grid points of a square with a side length of \(1\). Now, segment \(AB\) is rotated counterclockwise around point \(A\) by \(90^{\circ}\) to obtain segment \(AC\).
(1) Draw the path traced by segment \(AC\) and point \(B\) on the given grid;
(2) During the ro... | (25/4)π, 5/4 | MMR1 | math | close | numeric | qwen3.5-27b | 0.5 | <think>
We are given a grid with segment AB, where A and B lie on grid points. From the image (though not visible here, we infer from standard problems), let’s assume based on typical such diagrams:
Let’s assign coordinates to make calculation precise.
Assume point B is at (0, 0). Then, looking at the diagonal line g... |
mmfr_689 | "iVBORw0KGgoAAAANSUhEUgAAArwAAAFtCAIAAABqUi4DAACywUlEQVR4nOydd1xUx/f3526ld0EUpYiKvUdjEkvsXaOAqNiwoqhRUWNNon6DHewNe0EwtsRuFHtB7KjYKyC9s+3eef44P+a5WUpWhW3M+4+8zLJl7tTPnDnnDIMxRhQKhUKhUCj/hUDXBaBQKBQKhWIYUNFAoVAoFApFI6hooFAoFAqFohFUNFAoFAqFQtEIKhooFAqFQqFoBBUNFAqFQqFQNIKKBgqFQqFQKBpBRQOFQqFQKBSNEGn+VpoGikKhUCgUY4VhmP9+D5U... | <image> Which of the following options conforms to the pattern of change in the given figure? ['A:A', 'B:B', 'C:C', 'D:D'] | B | BMMR | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 0.25 | <think>
To solve this problem, we need to identify the pattern in the sequence of figures and apply it to determine the next figure.
### Step 1: Analyze the given figures
- Each figure consists of an octagon with a smaller square inside it.
- The square contains four shapes: two circles (one white, one black) and two ... |
mmfr_696 | "iVBORw0KGgoAAAANSUhEUgAAALsAAACACAIAAADcT49TAAAZVUlEQVR4nO1dX0wbV7r/jrNqHGlzBd3VxUi7NAkN2BB1zVOdu6uAEyCQK8V2HoLdqgGvtm2ASIQQqWGl5d/DJrkXYpJbCMrDEiJVJrtSZpyH2kBam66U0JW2OF3AJtvGJC+YhwaylYKzUubch2OGwR4PY3tsDya/h8TMn3O+c77f+b7vnDl/EMYYXiM5NFejwYnIi730TJuhNBPipBaKTAuQDRgYx01VQM0wGGOMMYNnj8CRWkNJpuVKCV4zRgJgmPPjJmMJAoArV64... | <image>In the figure, quadrilateral ABCD is a square with a side length of 2. Circles are drawn with centers at points A, B, and C, intersecting the extended lines BA, CB, and DC at points E, F, and G respectively. (1) Find the length of the path that point D travels along the three arcs to point G; (2) Determine the r... | (1) 6\pi; (2) GB=DF, \text{reasoning explained above.} | MMR1 | math | close | numeric | qwen3.5-27b | 0.5 | <think>
We are given a square ABCD with side length 2. Circles are drawn centered at A, B, and C, intersecting extended lines BA, CB, and DC at points E, F, G respectively.
Let’s first understand the diagram and construction:
- Square ABCD: Let’s assign coordinates for clarity.
- Place point C at origin (0,0).
- ... |
mmfr_705 | "iVBORw0KGgoAAAANSUhEUgAAARcAAADDCAIAAAAnacIOAAA6gUlEQVR4nO19WXfbxpZ1ARwADuBMihQlWY7s6yQryc1Td///t16re/VNf4kjx7IlSuI8ggQJYiDwPezL0yWApGRJli3f2g9eNAUCVYWz6wx16pTk+z4TEBDg4Pu+JEl3v17+fE0REHgu4HUJPvu+f3cFI1gkILAVdySSJCw6gS8CCF7YcAoIpCRJ/JX0edvPb30i3fYuV97x/oJFAl8A2wT6HtJ4R0HfeOdtv/1Uvyh690sFBB6Oe/Bkoy663w0D7N322x33DLALVwo... | <image>The structure shown is ( ) ['A. Statically determinate structure', 'B. Once indeterminate structure', 'C. Twice indeterminate structure', 'D. Three times indeterminate structure'] | B | BMMR | science | close | multiple_choice | qwen3.5-27b | 1 | <think>
To determine the static indeterminacy of the structure shown in the image, we analyze its supports and constraints.
The structure consists of two rigid members connected by a pin (hinge) at their junction, with one end fixed to a wall (fixed support on the left horizontal member) and the other end pinned to a ... |
mmfr_706 | "/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGHArQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRI... | <image>
What does the image depict in terms of physical phenomena? | Rayleigh-Taylor turbulence | FineVision-visualwebinstruct(filtered) | science | close | entity_name | qwen3.5-27b | 0.25 | <think>
The image displays two visualizations of fluid mixing or interaction between two distinct substances, likely gases or liquids with different densities or temperatures.
On the left: A 2D cross-section shows red and blue regions intermingling in complex, swirling patterns — characteristic of turbulent flow. The ... |
mmfr_713 | "iVBORw0KGgoAAAANSUhEUgAAAcUAAADeCAIAAADDxYw/AACv80lEQVR4nOz9V5AcyZ0nDP7dQ6TWlVmZpbVAoQoFrYEGmt1sNtnUs5yhzSrbtTG7fdins919vKd92Lu9b8xud+2+nb0ZznCGM8NvdoZkk93NZjcbLYCGFlUQhdJapdYZyv0eHOUMZBYKaHRBMn4Gg0VmRUa4e7j/4u9/iSilYMGChacOQgjGmH+klCKEtj628JwDP/wUCxYsbDcopYxMKaWGYbAvdV03yzfs2CLTFwjIkk8tWHj6YFInlz1rqdMSS19EWPKpBQvPAIw... | <image>As shown in the figure, a wedge A is placed on a horizontal ground, and a wooden pile B is fixed on the ground. A spring K connects the object to the pile, and the spring is parallel to the inclined plane. An object of mass m and a person move downward along the surface of the wedge under the action of the sprin... | A | BMMR | science | close | multiple_choice | qwen3.5-27b | 0.25 | <think>
Let’s analyze the problem step by step.
We are told:
- Wedge A is on horizontal ground.
- Wooden pile B is fixed to ground.
- Spring K connects object (mass m + person) to pile B, parallel to incline.
- Object + person move **downward** along wedge surface under spring action.
- At this time, frictional force ... |
mmfr_725 | "/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACKAV4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRI... | <image>
The diagram below shows {eq}\overline {AC} || \overline {DF} || \overline {BH}
{/eq} and {eq}\overline {CB} || \overline {FE}
{/eq}.
Using four similar triangles, complete the following extended proportion:
{eq}\frac {AB}{AC} = \frac {DE}{ } = \frac { } {DG} = \frac { } { }
{/eq} | \frac{AB}{AC} = \frac{DE}{DF} = \frac{DB}{DG} = \frac{BE}{BH} | FineVision-visualwebinstruct(filtered) | math | close | short_phrase | qwen3.5-27b | 0.75 | <think>
We are given a diagram with parallel lines:
- $\overline{AC} \parallel \overline{DF} \parallel \overline{BH}$
- $\overline{CB} \parallel \overline{FE}$
And we are to complete the extended proportion using **four similar triangles**:
$$
\frac{AB}{AC} = \frac{DE}{?} = \frac{?}{DG} = \frac{?}{?}
$$
---
### St... |
mmfr_726 | "iVBORw0KGgoAAAANSUhEUgAAAGoAAABmCAIAAACsgZO7AAAavklEQVR4nO2df1yb9dnvr9yEkJBCKaW148V6+qpde7TrqbVPnz59sAMRESkyZMjIIvJCjCxDjIkxy8kYJ4chhwMyZBU5DJGDMIY8DBGR5fDACxki6xhDxmCIPBSxIlIKpoGQkJDP+SOU0l/Jzc/W1573X7nv+/p+7+u+vtf3949wANB/slaY263ANxsH5rNunRbfWG5pPg7HdSv1+EbwSGDgow89/OvXX/+RSHT+00+JiHAzkuJib/XoHxkiOtfWCmBycpyILOY5Dm6... | <image>In the square ABCD, points E and F are the midpoints of sides BC and CD respectively. Given that the area of square ABCD is 60 square centimeters, find the area of the shaded part. | 10 | MMR1 | math | close | numeric | qwen3.5-27b | 0.75 | <think>
We are given a square ABCD with area 60 cm². Points E and F are midpoints of sides BC and CD respectively. We are to find the area of the shaded region, which is triangle AXP (where X and P are intersection points inside the square — specifically, from the diagram, it appears that lines AE and AF intersect diag... |
mmfr_732 | "iVBORw0KGgoAAAANSUhEUgAAAfsAAAE4CAIAAADTlc2fAAD0jElEQVR4nOz9Z7PkSJIejLp7BFQi9REluqtnemZ2uXxp9l6jGf//x2v8QqNxyctVI1qUOjp1QoX7/eBAJFKcU6dk13Sn7051HiQSCAQinvBw8TgyMxzlKJ9eEEBaf24NMwYR2XyLiAatDkUiKsvS2kAERIQARRwgExE4ZgSigJ0AoQAIOEEUESQhYQAwYAAAhACQ6/syACCa92g6Yrt5RznKr0bsL92Ao/xa5f0Qs615ICKAiDABMjsAEGEVACCDImIgAAAEw+JEBEQ... | <image>The dual-slope A/D converter is shown in Figure 3-3. Please answer the following questions:
(1) If the maximum value of the input voltage Vi is 2 V and the required resolution is less than 0.1 mV, how many bits should the binary counter have?
(2) If the clock pulse frequency is 200 kHz, what is the sampling ti... | 15, 163.84 \, \text{ms}, 65.536 \, \text{ms} | BMMR | science | close | numeric | qwen3.5-27b | 0.75 | <think>
To solve the given problem, we analyze each part step by step based on the principles of a dual-slope A/D converter.
---
**(1) Determine the number of bits for the binary counter**
The resolution of an N-bit ADC is given by:
\[
\text{Resolution} = \frac{V_{\text{max}}}{2^N}
\]
We are told:
- \( V_{\text{ma... |
mmfr_743 | "iVBORw0KGgoAAAANSUhEUgAAAfQAAAH0CAIAAABEtEjdAAAvuUlEQVR4nO3dS4hUVx7H8XNtoWSSJhgVF5JsFOxpQpz2AW7MJCQbHZhMJCiuRhcNOmQlyuzcGLPohYu0CLMwugojg5CJgeBiMoqrkHbSYKCziEyQ3mQgGGPTPohds6jum7K6uu7rnP//PL4fAlGprnPP+Z/zq3urbp/K2u22AQDEZZX2AQAA7CPcASBChDsARIhwB4AIEe4AECHCHQAiRLgDQIQIdwCIEOEOABEi3AEgQoQ7AESIcAeACBHuABAhwh0AIkS4A0CE0g3... | <image>Now I'll give you a picture, which shows a screenshot of Ultra TicTacToe. The introduction of Ultra TicTacToe is as follows:
1. Board and coordinate representation: In this game, the board is divided into 9 3*3 squares(called Nine-grids). At the same time, we use $(i, j, row, col)$ to represent the coordinates o... | 4 | GameQA-140K | logic/game/puzzle | close | multiple_choice | qwen3.5-27b | 0.25 | <think>
To determine where the Second Player should place their next piece, we need to follow the rules of Ultra TicTacToe as described:
1. **Initial Move**: The first player (X) places a piece in any cell in the middle Nine-grid, which is Nine-grid (2, 2).
2. **Subsequent Moves**: After the initial move, the coordin... |
mmfr_761 | "/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAYsAj4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRI... | <image>If the gray shape is a combination of a rectangle and an equilateral triangle and the area of the gray shape is 96, compute the length of the side of the gray shape marked with question mark. Round computations to 2 decimal places. | 13.42 | WaltonColdStart | math | close | numeric | qwen3.5-27b | 0.25 | <think>
We are told that the gray shape is a combination of a rectangle and an equilateral triangle, and its total area is 96. The top side of the rectangle is labeled as 6. Since it’s a rectangle, the bottom side (which becomes the base of the equilateral triangle) must also be 6.
The equilateral triangle attached at... |
mmfr_795 | "/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEFAxYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRI... | <image>
What does the trend in the fitted polynomial curves in both plots of Figure 1 suggest about the relationship between expectancy models and human ratings of music? | quadratic relationship | FineVision-visualwebinstruct(filtered) | chart/table/doc | close | short_phrase | qwen3.5-27b | 0.75 | <think>
The image displays two scatter plots: “IDyOM Expectancy vs. Human Rating” and “Diffusion Expectancy vs. Human Rating.” Each plot shows a large number of cyan data points (representing individual song ratings plotted against an expectancy metric) and a yellow curve labeled “Fitted polynomial,” which represents t... |
mmfr_809 | "iVBORw0KGgoAAAANSUhEUgAAAJ0AAABiCAIAAADFgEZNAAAdUUlEQVR4nO19f3QURbb/re75HZKYxOgCK0hIsjEYkVl+LW8lLDyRCAjfg4LLWYH3zOpDVmSNEWUP+NBddv0BIq4LwjkCK7jwdNnDV0CT4ImBjaI+BBFBgQRIskAiCSFDkpmerrrvj5qp6en5HZLJoH7+SLqra7pv1a2699atW1UEEUEDxpgkSYgUiEzADwyoBDIkGBCREKK9+B6Cc02bImmficeEyAjIGDtZ8VrZSQbAAEACmTEWZ4ojQvDye8tUANAxFQAkBoiUc8v... | <image>In the figure, in rectangle ABCD, a semicircle with diameter AD is tangent to side BC at point E, and given that AD = 8 and AB = 4, the area of the shaded part is ______. | 4π | MMR1 | math | close | numeric | qwen3.5-27b | 0.25 | <think>
We are given rectangle $ABCD$ with:
- $AD = 8$, so since it’s a rectangle, $BC = AD = 8$
- $AB = 4$, so height of rectangle is 4
A **semicircle** with diameter $AD$ is drawn. Since $AD = 8$, the radius of the semicircle is $r = 4$. The center of the semicircle is the midpoint of $AD$, let's call it $O$. So $A... |
mmfr_823 | "iVBORw0KGgoAAAANSUhEUgAAATsAAAEHCAIAAABeBnZGAAB23klEQVR4nO19V3fbWLbmAQMYwJwzlSVbThW76vbcCXfdx/mP8xdmzdOseei5d810V1dXcDkpZ5EUMwkwIJAE5uEr7oGpZMuyrbLxPWhJFAiA4Nln529zhmEwC9dhMpnYbDaO4/Cnrus2m23mGMMwDMM4/7oFC7cIzpLYqzEejzmOM4srYwwPDT8tEbXwIWFJ7DXA85kRV9Kl+J3jOByA3z/WrVr4HOD42Ddw1wEJHI/H+H0ymWiapmnaeDzmeZ7nebvd7nQ6LYm18GF... | <image>In a surface heat exchanger, hot water is used to heat air. The inlet and outlet parameters of the air are: $p_1 = 0.13\ MPa$, $t_1 = 20^{\circ}C$, $p_2 = 0.12\ MPa$, $t_2 = 60^{\circ}C$, with an air mass flow rate of $q_m = 1\ kg/s$. The hot water inlet temperature is $t_{w1} = 80^{\circ}C$, with a flow rate of... | 10.12 \, \text{kW} | BMMR | science | close | numeric | qwen3.5-27b | 0.5 | <think>
To determine the exergy loss in the heat exchanger, we use the exergy balance equation for a steady-flow system:
Exergy loss = Exergy in – Exergy out
Since there is no work output and heat loss is neglected, the exergy loss arises from irreversibilities due to finite temperature difference heat transfer betwe... |
mmfr_835 | "iVBORw0KGgoAAAANSUhEUgAAAKsAAAC2CAIAAAApwuoLAAAktklEQVR4nO2df1SUVf7433fGb+MWNm7NWWhjI51po6CElYIO2KD88gfglLbqcUo4q0IH3MacgfGIggslCiUdMQbRsl066QkPCGzGDCWkFCa7YIth60zRUTdY6bMgeoCAud8/7szDM8/8YH48AwPO6w9lnh/3uc+97+d93/fX+w2YPRTJAACK8gaMsR5fTQZQa7Fer2fxEV5YhwPsceA0Vh+R/1vbDQAIRJlH5ACAECJnT5069dlnn7H4OC+sMIfFtDDGCx4Vnq7Xkp8... | <image> (2009, Xicheng District Mock Exam) Given: In the Cartesian coordinate system xOy, the line $y=\frac{3}{4}x+6$ intersects the x-axis and y-axis at points A and B, respectively. The angle ∠OBA is bisected, causing point O's corresponding point H to fall on line AB, and the crease intersects the x-axis at point C.... | [0, 4] | MMR1 | math | close | numeric | qwen3.5-27b | 0.25 | <think>
We are given a geometry and algebra problem involving lines, parabolas, reflections (angle bisector), parallelograms, and absolute difference of distances. We’ll solve step by step.
---
**Step 1: Find coordinates of points A and B**
The line is $ y = \frac{3}{4}x + 6 $.
- **Point A**: x-intercept → set $ y ... |
mmfr_846 | "iVBORw0KGgoAAAANSUhEUgAAAbcAAACZCAIAAAAjJONOAAB3QklEQVR4nO1dd0ATyfef3TRKAgoiSJAm9lN/X695d5ZrevZy9oa9nF1REVSwd/HOLnZF7+wd21lA7L1XqoqFmmST7TO/PzYJSxIQbKCXzx8adqe82fLZN2/evIchhIAddthhhx0FAC9pAeywww47SjWkJS2AHXbY8UGBaFIPcYWjQmZ5AnKEnrQ4iGGYwtFJJsGFAnoD56R0EJQpyLEGDiodFObCNEngcmNhEyBJGOROSkl+BYxjaYoH4roAQFKn5woVHcOkTkrHElf... | <image>
A certain high school conducted a survey on the uniform sizes that ninth-grade students will wear, in order to ensure that the new first-year students can wear well-fitting uniforms promptly after entering school. Based on the survey results, two incomplete statistical charts were drawn (the uniform sizes are c... | (1) The class has 50 students in total, of which 10 students wear size 175 uniforms. (2) In the bar chart, the missing parts should be filled as follows: * For size 170, draw a bar up to 15 (representing 15 students). * For size 175, draw a bar up to 10 (representing 10 students). * For size 185, draw a bar up to 2 (re... | MMR1 | math | close | numeric | qwen3.5-27b | 0.75 | <think>
We are given two incomplete charts: a bar chart (showing number of students per uniform size) and a pie chart (showing percentages for some sizes). We need to find:
(1) Total number of students, and how many wear size 175.
(2) Fill in the missing part of the bar chart (which is size 175 — we’ll compute its va... |
mmfr_848 | "iVBORw0KGgoAAAANSUhEUgAAALwAAAB1CAIAAAB7zByAAAAGRUlEQVR4nO3dv2sTbxwH8E+/uPTaBFotCJVoCYVkkAoieFlKFhclgwmlhSJ0KdVZh+Ls32Do5GYo6qB3Sx3OW7QQDwIKVwkdWlpwqQ6Nj2O/w4NHekabBy/Pj8v7td053JOHt88999xzn46cnJwQgIj/VDcAzIPQgDCEBoQhNCDu5Jd79+6pbgto6uS0kejpaWRkRG3LQFuxR+xzf/9no/H/Bmn6RfL1HEowpwFhCA0IQ2hAGEIDwhAaEIbQgDCEBoQhNCAMoQFhCA0... | <image>
In the figure, a rectangular sports field is divided into 5 areas: A, B, A, B, and C. Area A is a square with a side length of \(a\), and area C is a square with a side length of \(b\). (1) Write an expression for the perimeter of each rectangular area B and simplify it; (2) Write an expression for the perimete... | 1500 | MMR1 | math | close | numeric | qwen3.5-27b | 0.25 | <think>
We are given a diagram (described in text) of a rectangular sports field divided into 5 regions: two squares labeled A (side length $a$), two rectangles labeled B, and one square labeled C (side length $b$). The layout is as follows (based on typical such problems and the description):
- On the left side: top ... |