problem stringlengths 10 3.15k | answer stringlengths 1 1.22k | source stringclasses 11
values | domain listlengths 1 4 | llama8b_solve_rate float64 0 1 ⌀ |
|---|---|---|---|---|
If $(x+i)i = -1 + 2i$ where $x \in \mathbb{R}$, then $x = \boxed{2}$. | 2 | cn_k12 | [
"Mathematics -> Algebra -> Intermediate Algebra -> Complex Numbers"
] | 0.703125 |
In the expansion of $(1+x-2x^2)(1+x)^5$, find the coefficient of the term containing $x^3$. Express your answer as a single integer. | 10 | big_math | [
"Mathematics -> Algebra -> Other"
] | 0.15625 |
The sixteenth and seventeenth terms of an arithmetic sequence are 8 and 10, respectively. What is the second term? | -20 | math | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.96875 |
Find the solution set for the inequality $|x-3|+|x-5|\geq4$. | x\in(-\infty, 2]\cup[6,+\infty) | cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.890625 |
Positive integers \( a, b \), and \( c \) have the property that \( a^b \), \( b^c \), and \( c^a \) end in 4, 2, and 9, respectively. Compute the minimum possible value of \( a + b + c \). | 17 | olympiads | [
"Mathematics -> Number Theory -> Other"
] | 0.078125 |
Amy's hair was eleven inches long at the beginning of the month. During the month, her hair growth varied each week. In the first week, it grew half an inch, in the second week, it grew by three-quarters of an inch, in the third week, it grew one inch, and in the fourth week, it grew by a quarter of an inch. After thes... | 6.5 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.890625 |
Mr. and Mrs. Boyden take their 3 children to a leisure park. They buy tickets for the whole family. The cost of an adult ticket is $6 more than the cost of a child ticket. The total cost of the 5 tickets is $77. What is the cost of an adult ticket? | 19 | gsm8k | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.484375 |
Joan and Karl each bought a telescope and the sum of their purchases was $400. If twice of what Joan paid was $74 more than what Karl paid, what did Joan pay for her telescope? | $158$ | orca_math | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 1 |
Rewrite the general equations of the line in canonical form
$$
\left\{\begin{array}{l}
2 x - 3 y - 3 z - 9 = 0 \\
x - 2 y + z + 3 = 0
\end{array}\right.
$$ | \frac{x}{9} = \frac{y}{5} = \frac{z+3}{1} | olympiads | [
"Mathematics -> Geometry -> Other"
] | 0.21875 |
John sublets his apartment to 3 people who each pay $400 per month. He rents the apartment for $900 a month. How much profit does he make in a year? | 3600 | openmath | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.71875 |
Determine the intersection of the sets M and N, where M = {x | lg x > 0} and N = {x | |x| <= 2}. Express your answer in interval notation. | (1, 2] | big_math | [
"Mathematics -> Algebra -> Other"
] | 0.625 |
Given $\triangle ABC \cong \triangle DEF$, where $AB=3$, find $DE$. | 3 | cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Triangles"
] | 0.984375 |
Given that {a\_n} is an arithmetic sequence, if a\_2 = 2a\_3 + 1 and a\_4 = 2a\_3 + 7, find the value of a\_3. | a_3=-4 | cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.28125 |
1/4 of all the juniors and 2/3 of all the seniors are going on a trip. There are 2/3 as many juniors as seniors. What fraction of the students are not going on the trip? | 5/6 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.03125 |
A cuboid has a volume of 144 m^3 and a certain base area. The height of the cuboid is 8 m. What is the base area of the cuboid? | 18 | orca_math | [
"Mathematics -> Geometry -> Solid Geometry -> Volume"
] | 1 |
Sol sells candy bars to raise money for her softball team. On the first day, she sells ten candy bars and sells four more candy bars than she sold the previous day each day afterward. If she sells six days a week and each candy bar costs 10 cents, how much will she earn in a week in dollars? | 12 | gsm8k | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.734375 |
John decides to go back to school to get his PhD. He first takes 1 year of courses to get acclimated back to school life before starting his PhD. After that, he spends 2 years learning the basics of his field. He then starts research and spends 75% more time on research than he did learning the basics. During his resea... | 7.75 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.140625 |
If \( z \) is a complex number such that \( |z| = 1 \) and \( u = z^{4} - z^{3} - 3z^{2}i - z + 1 \), find the maximum value of \( |u| \) and the complex number \( z \) when this maximum is achieved. | 5 | olympiads | [
"Mathematics -> Algebra -> Complex Numbers"
] | 0.015625 |
a cylinder and a cone have the same height and same radius of base . the ratio between the volumes of the cylinder and the cone is : | 3:1 | orca_math | [
"Mathematics -> Geometry -> Solid Geometry -> Volume"
] | 0.09375 |
There are two types of camels: the dromedary with one hump and the Bactrian camel with two humps. The dromedary is taller with longer legs and can walk or run in the desert, while the Bactrian camel has shorter, thicker legs and is suitable for walking in both desert and snowy terrain. In a group of camels, there are 2... | 15 | olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.390625 |
Given angle \( AOB \) and line \( l \). Draw a line \( l_1 \) such that the angle between the lines \( l \) and \( l_1 \) is equal to the angle \( AOB \). | l_1 = X O \text{ or } l_1 = Y O | olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Angles"
] | 0.03125 |
James is trying to create a new breed of kittens with extra-long tails. Each generation of kittens he breeds has a tail 25% longer than the last generation. If the first generation has tails 16 cm long, how long are the third generation's tails? | 25 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.953125 |
The axis of symmetry for the function $y=|x-a|$ is $x=3$. Find the value of $a$. | a=3 | cn_k12 | [
"Mathematics -> Algebra -> Intermediate Algebra -> Other"
] | 0.921875 |
In the convex quadrilateral \(ABCD\), the length of the segment connecting the midpoints of sides \(AB\) and \(CD\) is 1. The lines \(BC\) and \(AD\) are perpendicular. Find the length of the segment connecting the midpoints of the diagonals \(AC\) and \(BD\). | 1 | olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.1875 |
In trapezoid \(ABCD\) with the shorter base \(BC\), a line is drawn through point \(B\) parallel to \(CD\) and intersects diagonal \(AC\) at point \(E\). Compare the areas of triangles \(ABC\) and \(DEC\). | The areas of the triangles are equal. | olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Triangles"
] | 0.171875 |
Given the function $f(x)=\begin{cases}
& (a-2)x, & x\geqslant 2 \\
& \left( \frac{1}{2} \right)^{x}-1, & x < 2 \\
\end{cases}$, find the range of the real number $a$ such that $f(x)$ is a monotonically decreasing function on $\mathbb{R}$. Express your answer as an interval. | \left( -\infty,\frac{13}{8} \right] | big_math | [
"Mathematics -> Calculus -> Other"
] | 0 |
Sixty apples and sixty pears are to be packed into boxes so that each box contains the same number of apples, and no two boxes contain the same number of pears. What is the largest possible number of boxes that can be packed in this way? Express your answer as a whole number. | 10 | big_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 |
A salesman sold some pears in the morning and in the afternoon. He sold 480 kilograms of pears that day, with 320 kilograms sold in the afternoon. What is the ratio of the number of pears sold in the afternoon to the number of pears sold in the morning? | 2:1 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.484375 |
The price of a coat in a certain store is $500. If the price of the coat is to be reduced by some amount, the price is reduced by 30%. What is the amount by which the price is reduced? | $150 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.859375 |
Micah has 7 fish in his aquarium. Kenneth has three times as many fish in his aquarium as Micah, and Matthias has 15 less fish than Kenneth. Gabrielle has twice as many fish as the combined total of the other three boys' aquariums. How many fish do the four friends have in total? | 102 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.90625 |
The ages of three contestants in the Cayley Contest are 15 years, 9 months; 16 years, 1 month; and 15 years, 8 months. Calculate the average (mean) age of these contestants. Express your answer in years and months. | 15 years, 10 months | big_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.109375 |
A sample with a capacity of $n$ is divided into several groups. It is known that the frequency and frequency rate of a certain number are 36 and 0.25, respectively. Find the value of $n$. | 144 | cn_k12 | [
"Mathematics -> Applied Mathematics -> Statistics -> Mathematical Statistics"
] | 1 |
Write the first $n$ natural numbers in decimal form on a (very long) strip of paper, then cut the strip so that each piece contains exactly one digit. Place these pieces in a box, mix them up, and draw one at random. Let $p_{n}$ denote the probability that the drawn piece of paper has the digit 0 on it. Determine the l... | \frac{1}{10} | olympiads | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability"
] | 0.21875 |
Find the equation of the trajectory of a point whose sum of distances to the two coordinate axes is 6. Express your answer as a mathematical equation. | |x|+|y|=6 | big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0 |
At Academic Academy, to pass an algebra test you must score at least $80\%$. If there are 35 problems on the test, what is the greatest number you can miss and still pass? | 7 | math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.984375 |
Given that the augmented matrix of a system of linear equations is \\( \begin{pmatrix} 2 & 3 & t\_{1} \\\\ 0 & 1 & t\_{2}\\end{pmatrix}\\) and its solution is \\( \\begin{cases} x=3 \\\\ y=5\\end{cases}\\), find the value of the third-order determinant \\( \\begin{bmatrix} 1 & -1 & t\_{1} \\\\ 0 & 1 & -1 \\\\ -1 & t\_{... | 14 | cn_k12 | [
"Mathematics -> Algebra -> Linear Algebra -> Determinants"
] | 0.015625 |
Mike needs a certain percentage to pass. He scored 212 marks and falls short by 25 marks. The maximum marks he could have got is 790. What percentage does he need to pass? | 30\% | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.5625 |
Excluding stoppages, the speed of a bus is 60 kmph, and including stoppages, it is 50 kmph. For how many minutes does the bus stop per hour? | 10 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.53125 |
Find the domain of the function $f(x)=\frac{1}{\lg x}+\sqrt{2-x}$. Express your answer as an interval or set. | (0,1)\cup(1,2] | big_math | [
"Mathematics -> Algebra -> Other"
] | 0.25 |
A can finish a piece of work in 4 days. B can do it in some days. They work together for two days and then A goes away. B finishes the work in 3.0000000000000004 days. In how many days can B finish the work alone? | 10 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.1875 |
Given that $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$ are two non-collinear vectors, and $\overrightarrow{AB} = 2\overrightarrow{e_{1}} + m\overrightarrow{e_{2}}$, $\overrightarrow{BC} = \overrightarrow{e_{1}} + 3\overrightarrow{e_{2}}$, if points $A$, $B$, and $C$ are collinear, then the real number $m =$ \... | m = 6 | cn_k12 | [
"Mathematics -> Geometry -> Other"
] | 0.625 |
The distance formula from a point $(x_0, y_0)$ to a line $Ax + By + C = 0$ is given by $$d = \frac{|Ax_0 + By_0 + C|}{\sqrt{A^2 + B^2}}$$. By analogy, find the distance from the point $(0, 1, 3)$ to the plane $x + 2y + 3z + 3 = 0$ in space. | \sqrt{14} | cn_k12 | [
"Mathematics -> Geometry -> Solid Geometry -> Other"
] | 0.921875 |
if the average ( arithmetic mean ) of 102 consecutive odd integers is 414 , then the least of these integers is | 313 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.203125 |
Rita the painter rolls a fair $6\text{-sided die}$ that has $3$ red sides, $2$ yellow sides, and $1$ blue side. Rita rolls the die twice and mixes the colors that the die rolled. What is the probability that she has mixed the color purple? | \frac{1}{6} | aops_forum | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability"
] | 0.5625 |
Calculate: $(\frac{1}{2})^{-1}+4\cos 45^{\circ}-\sqrt{8}+\left(2023-\pi \right)^{0}$. | 3 | cn_k12 | [
"Mathematics -> Algebra -> Other",
"Mathematics -> Precalculus -> Trigonometric Functions",
"Mathematics -> Precalculus -> Other"
] | 0.953125 |
A large high school has 2,500 students. Of these students, 200 are taking music, 150 are taking art, 100 are taking dance, 75 are taking music and art, 50 are taking art and dance, 40 are taking music and dance, and 25 are taking all three subjects - music, art, and dance. How many students are taking neither music, no... | 2,190 | orca_math | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability -> Counting Methods -> Other"
] | 0.03125 |
a pupil ' s marks were wrongly entered as 73 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is : | 56 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.796875 |
Mrs. Hilt saw 3 bugs eat two flowers each. How many flowers total did the bugs eat? | 6 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 1 |
A number, when divided by 2, leaves a remainder of 1; when divided by 3, leaves a remainder of 2; and when divided by 4, leaves a remainder of 3. What is the smallest such number? | 11 | cn_k12 | [
"Mathematics -> Number Theory -> Congruences"
] | 0.375 |
The average score of 35 students in a class is 37. If every student is given 3 grace marks, what is the new average of the class? | 40 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 1 |
In a cube with side length 6, what is the volume of the tetrahedron formed by any vertex and the three vertices connected to that vertex by edges of the cube? | 36 | olympiads | [
"Mathematics -> Geometry -> Solid Geometry -> Volume"
] | 0.15625 |
Given that point $P$ is in the fourth quadrant, with a distance of $2$ to the $x$-axis and a distance of $3$ to the $y$-axis, the coordinates of point $P$ are ______. | (3, -2) | cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.484375 |
Adrian and Colton are standing some distance apart. Adrian started running towards Colton at a constant speed of 17 meters per sec. After 13 seconds, the distance between them is 68 meters. What was the initial distance between Adrian and Colton? | 289 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.921875 |
Given the standard deviation of sample data $x_{1}$, $x_{2}$, $\ldots $, $x_{10}$ is $8$, find the standard deviation of the data after applying the transformation $3x_{i}-1$ to each data point. Express your answer as a numerical value. | 24 | big_math | [
"Mathematics -> Applied Mathematics -> Statistics -> Mathematical Statistics"
] | 0.875 |
Find the functions \( f: \mathbb{R} \rightarrow \mathbb{R} \) such that for all \( x, y \),
\[ f(x+y)^{2}=f(x)^{2}+f(y)^{2} \] | f(x) = 0 | olympiads | [
"Mathematics -> Algebra -> Other"
] | 0.328125 |
Find the remainder when \( 7^{2008} + 9^{2008} \) is divided by 64. Express your answer as a single number. | 2 | big_math | [
"Mathematics -> Number Theory -> Other"
] | 0.421875 |
Mrs. Dunbar was creating floral arrangements for her niece's wedding. She needed to make 5 bouquets and 7 table decorations. She uses a certain number of white roses in each table decoration and 5 white roses in each bouquet. She needs a total of 109 white roses to complete all bouquets and table decorations. How many ... | 12 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 1 |
If $x$ and $y$ are real, and $x^2 + y^2 = 1,$ compute the maximum value of $(x + y)^2.$ | 2 | math | [
"Mathematics -> Calculus -> Other"
] | 0.703125 |
In one hour, a boat goes 6 km along the stream and 2 km against the stream. What is the speed of the boat in still water (in km/hr)? | 4 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.984375 |
On Monday, Sydney sends 5 texts each to Allison and Brittney. On Tuesday, she sends 15 texts to each of them. In total, how many texts did Sydney send to Allison and Brittney on both days? | 40 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.984375 |
Find the mass percentage of O in Dinitrogen pentoxide. The mass percentage of O is what percent? | 74.07\% | orca_math | [
"Mathematics -> Applied Mathematics -> Other"
] | 0.46875 |
If set $A=\{x|(k+1)x^2+x-k=0\}$ has exactly two subsets, find the value of the real number $k$. | -1 \text{ or } -\frac{1}{2} | cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.5 |
On a map with a scale of 1:500,000, if the distance between points A and B is 4 cm, then the actual distance between A and B is ___ km. | 20 \text{ km} | cn_k12 | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.484375 |
Petya wants to create an unusual die, which should have the shape of a cube, with dots drawn on the faces (different numbers of dots on different faces). Additionally, on each pair of adjacent faces, the number of dots must differ by at least two (it is allowed to have more than six dots on some faces). How many dots i... | 27 | olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.015625 |
Eleven members of the Middle School Math Club each paid the same amount for a guest speaker to talk about problem solving at their math club meeting. The total amount paid to the guest speaker is $1A2. What is the missing digit A of this 3-digit number? Express your answer as a single digit. | 3 | big_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.28125 |
If the function \( f\left(x-\frac{1}{x}\right)=\frac{x}{x^{2}-1}-x^{2}-\frac{1}{x^{2}} \) (where \( x \neq 0 \) and \( x \neq \pm 1 \)), then \( f(x)= \) $\qquad$ . | -x^2 + \frac{1}{x} - 2 | olympiads | [
"Mathematics -> Algebra -> Algebraic Expressions"
] | 0 |
In order to obtain an income of Rs. 900 from a certain percentage of stock at Rs. 102, one must make an investment of Rs. 4590. What is the percentage of the stock? | 19.61\% | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 |
In the arithmetic sequence $\{a_n\}$, if $2(a_1+a_4+a_7)+3(a_9+a_{11})=24$, then the sum of the first 13 terms of this sequence equals \_\_\_\_\_\_. | 26 | cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.5625 |
All people named Barry are nice, while only half of the people named Kevin are nice. Three-fourths of people named Julie are nice, while 10% of people named Joe are nice. Additionally, 85% of people named Alex are nice, and two-thirds of people named Lauren are nice. 25% of people named Chris are nice, and 95% of peopl... | 534 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 |
In the polar coordinate system, the minimum distance between point $P(1, \frac{\pi}{2})$ and the moving point $Q$ on the curve $\rho = 2\cos\theta$ is $\_\_\_\_\_\_$. | \sqrt{2} - 1 | cn_k12 | [
"Mathematics -> Calculus -> Other"
] | 0.046875 |
Randomly select two numbers x and y in the interval [0,1]. Calculate the probability that y > 3x. Express your answer as a simplified fraction. | \dfrac{1}{6} | big_math | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability"
] | 0.484375 |
There are 7 people standing in a row. If persons A, B, and C must not stand next to each other, how many different arrangements are there? | 1440 | cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Other"
] | 0.015625 |
Calculate the limit: $\lim_{n\to \infty} \frac{1+2+3+\ldots+n}{n^2}$. | \frac{1}{2} | cn_k12 | [
"Mathematics -> Precalculus -> Limits"
] | 0.96875 |
How many integers fall between $\sqrt5$ and $\sqrt{50}$ on a number line? | 5 | math | [
"Mathematics -> Number Theory -> Other"
] | 0.921875 |
In a right-angled triangle ($\angle C = 90^{\circ}$), the point $P$ where the incircle touches the hypotenuse divides it into segments $A P = 12$ and $B P = 5$. Find the lengths of the legs. | The legs are 8 and 15. | olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0 |
In ancient China, it was believed that the basic elements constituting all things in the universe were gold, wood, water, fire, and earth, known as the "Five Elements." The ancient Chinese developed the theory of mutual generation, where gold generates water, water generates wood, wood generates fire, fire generates ea... | \frac{1}{2} | cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Other"
] | 0.703125 |
For two positive numbers $m$ and $n$, both not equal to $1$, define: $m*n=\left\{{\begin{array}{l}{{{log}_m}n,m≥n}\\{{{log}_n}m,m＜n}\end{array}}\right.$. Let $a$, $b$, and $c$ be positive numbers less than $1$, and $ab=c$. Then the value of $\left(a*c\right)^{-1}+\left(b*c\right)^{-1}$ is ______. | 1 | cn_k12 | [
"Mathematics -> Algebra -> Other"
] | 0.25 |
Dale just learned how to make homemade macaroni and cheese. He decided to make a big batch for his family reunion. The original recipe calls for 2 pounds of pasta and serves 7 people. Dale needs to buy 10 pounds of pasta. How many people will be at Dale's family reunion? | 35 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.953125 |
Point $E$ is on side $AB$ of square $ABCD$. If $EB$ has length one and $EC$ has length two, then the area of the square is | $3$ | harp | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0 |
For every 3 sit-ups Peter does, Greg does 4. Peter did some sit-ups and Greg did 32 sit-ups. How many sit-ups did Peter do? | 24 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 1 |
A line passing through the focus of the parabola $y^{2}=2x$ intersects the parabola at points $A$ and $B$. If the distance from the midpoint $M$ of $AB$ to the parabola's axis is $5$, find the length of the line segment $AB$. | 10 | cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.03125 |
Lois has 150 books. She gives a quarter of her books to her nephew. In her remaining collection, 60% of the books are non-fiction, and she decides to keep only half of those non-fiction books. From the remaining fiction books, she lends a third of them to her neighbor. Afterward, she purchases 12 new books from the boo... | 76 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.34375 |
26 children were riding on the bus. At the bus stop, some more children got on the bus. There are now 64 children on the bus. How many children got on the bus at the bus stop? | 38 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 1 |
A football match started at 15:30 and lasted for 145 minutes. Determine the time when the match ended. | 17:55 | cn_k12 | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.71875 |
Let $M = \{(x, y) \,|\, |\tan(\pi y)| + \sin^2(\pi x) = 0\}$, and $N = \{(x, y) \,|\, x^2 + y^2 < 1\}$. Calculate the number of elements in $M \cap N$. Express your answer as a single integer. | 1 | big_math | [
"Mathematics -> Calculus -> Other"
] | 0.546875 |
How many pairs of positive integers $(a,b)$ are there such that $\gcd(a,b)=1$ and \[ \frac{a}{b}+\frac{14b}{9a}
\]is an integer? | 4 | math | [
"Mathematics -> Number Theory -> Greatest Common Divisors (GCD)"
] | 0 |
The Pinedale bus line travels at an average speed of 60 km/h, and has stops every 5 minutes along its route. Yahya wants to go from his house to the Pinedale mall, which is a certain number of stops away and 40 kilometers away from his house. How many stops away is the Pinedale mall from Yahya's house? | 8 | orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.875 |
Let the function $f(x) = x^3\cos{x} + 1$. If $f(a) = 11$, then $f(-a) = \underline{\quad}$. | -9 | cn_k12 | [
"Mathematics -> Algebra -> Other"
] | 0.75 |
If $j$ and $k$ are inversely proportional and $j = 42$ when $k = 56$, what is the value of $j$ when $k = 32$? Express your answer as a decimal rounded to the nearest tenth. | 73.5 | math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 1 |
Find the range of the function $y=3^{-x}$ over the interval $-2\leq x \leq 1$. Express your answer in interval notation, including the endpoints. | \left[ \frac {1}{3},9\right] | big_math | [
"Mathematics -> Precalculus -> Functions"
] | 0.59375 |
For the fraction $\frac{x-3}{x+5}$ to be meaningful, what condition must the value of $x$ satisfy? Express your answer as an inequality or equation that indicates the specific value that $x$ cannot be equal to. | x \neq -5 | big_math | [
"Mathematics -> Algebra -> Rational Expressions -> Other"
] | 0.546875 |
Find: $\frac{12}{30}-\frac{1}{7}$ | \frac{9}{35} | math | [
"Mathematics -> Algebra -> Prealgebra -> Fractions"
] | 0.953125 |
Given the original parabola equation y = (x-2)^2 + 1, find the analytical expression of the graph obtained by first shifting this parabola 3 units to the left and then 2 units down. Express your answer as an equation in the form y = f(x). | y = (x+1)^2 - 1 | big_math | [
"Mathematics -> Algebra -> Functions -> Other"
] | 0.890625 |
Find all positive integers $n$ for which $(x^n+y^n+z^n)/2$ is a perfect square whenever $x$ , $y$ , and $z$ are integers such that $x+y+z=0$ . | n = 1, 4 | aops_forum | [
"Mathematics -> Algebra -> Other"
] | 0.015625 |
Given $U = \mathbb{R}$, $A = [0, 2]$, $B = \{y | y = 2^x, x > 0\}$, calculate the intersection of $A$ and the complement of $B$ with respect to the universal set $U$, denoted as $A \cap C_U B$. Express your answer using standard interval notation. | [0, 1] | big_math | [
"Mathematics -> Set Theory -> Other"
] | 0.078125 |
If the plane vectors $ \overrightarrow{a}=(\cos \theta,\sin \theta)$ and $ \overrightarrow{b}=(1,-1)$, and $ \overrightarrow{a} \perp \overrightarrow{b}$, then the value of $\sin 2\theta$ is ______. | 1 | cn_k12 | [
"Mathematics -> Algebra -> Other",
"Mathematics -> Geometry -> Other",
"Mathematics -> Trigonometry -> Functions"
] | 0.6875 |
Heather helps her neighbour pick weeds out of her garden. She gets paid 5 cents for every weed she picks. On average, how many seconds can she take to pick a weed if she wants to earn $10 an hour? | 18 | openmath | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.796875 |
If $3\in\{a+3,2a+1,a^{2}+a+1\}$, find the value(s) of the real number $a$. | a=-2 | cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.03125 |
We divided a right triangle with the perpendicular bisector of its hypotenuse into a triangle and a quadrilateral. The ratio of the diagonals of the quadrilateral is
$$
(1+\sqrt{3}): 2 \sqrt{2}
$$
What are the acute angles of the right triangle? | 15^
\circ \text{ and } 75^
\circ | olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.015625 |
Let the real numbers \( a_{1}, a_{2}, \ldots, a_{2016} \) satisfy \( 9a_{i} > 11a_{i+1}^2 \) for \( i = 1, 2, \ldots, 2015 \). Find the maximum value of \[ \left(a_{1}-a_{2}^{2}\right) \cdot \left(a_{2}-a_{3}^{2}\right) \cdots \cdot \left(a_{2015}-a_{2016}^{2}\right) \cdot \left(a_{2016}-a_{1}^{2}\right) \]. | \left(\frac{1}{4}\right)^{2016} | olympiads | [
"Mathematics -> Algebra -> Other"
] | 0.140625 |
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