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There are 40 more buyers in the grocery store today than yesterday. There were half the number of buyers yesterday as there were the day before, and the day before had 50 buyers. Nobody visited the store on more than one day. What's the total number of buyers who've visited the store in the three days? Let's write a pr... | tiger_lab_math |
"statement 1": The 44 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees : festival planning , classroom aid , and teacher relations, "statement 2" :The less than 44 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees : festival plannin... | tiger_lab_math |
Calculate the definite integral \( \int_{x_0}^x (t - x_0) \, dt \) and express your answer in terms of \( (x - x_0) \). What is the result? | automath |
What is the minimum length of insulated wire required to construct a solenoid of 50 cm in length and 12 cm in diameter that produces a magnetic field of 2.6 kG when carrying a current of 2.2 A? | automath |
Five food companies sponsored a local food bank. Foster Farms donated 45 dressed chickens; American Summits donated twice the number of bottled water than the number of dressed chicken donated by Foster Farms; Hormel donated three times the number of dressed chickens that Foster Farms donated; Boudin Butchers donated o... | tiger_lab_math |
Each edge length of a rectangular solid is a prime number. If the volume of the rectangular solid is 385 cubic units, what is the total surface area, in square units, of the rectangular solid? | nvidia_math |
If $a$ and $b$ are positive integers less than 10, and they satisfy the equation $a + b + ab = 30$, what is the value of $a + b$? | tiger_math |
The sky currently has 4 times as many cirrus clouds as cumulus clouds, and 12 times as many cumulus clouds as cumulonimbus clouds. If the sky currently has 3 cumulonimbus clouds, how many cirrus clouds are in the sky at this moment? | nvidia_math |
Given that a sound level reading of 132 dB was recorded at a construction site with multiple chippers operating and a sound level of 122 dB was measured when only one chipper was working, how many chippers were in operation when the sound level was recorded at 132 dB? Please provide your answer as a whole number. | automath |
Thrice the sum of a number and 2 equals 24 added with the same number. Write algebraic equation and find the number. | tiger_math |
A cone has a volume of 6 cubic inches. If a cylinder has the same radius and height as the cone, what is the volume of the cylinder? Provide your answer in cubic inches. | automath |
Consider a mass \( m \) attached to a rope of length \( r \), being swung in a circular path with a constant radius \( r \) and an angular velocity \( \omega \). If you begin to pull the rope inwards while keeping the length of the rope constant, such that you apply a radial force \( F_r \) through your hand, how does ... | automath |
. Mr.P and Mr.Q can build a wall in 10 days; Mr.Q & Mr.R can take 14 days to build the same wall; and Mr.P and Mr.R can do it in 8 days. Who among them will take more time when they work alone?
Answer Choices: (A) 8.8 (B) 8.7 (C) 1.3 (D) 8.6 (E) 8.5 | tiger_lab_math |
What prime is 4 greater than a perfect square and 7 less than the next perfect square? Let's write a Python program. | tiger_lab_math |
What is the remainder when the sum of 7145, 7146, 7147, 7148, and 7149 is divided by 8? | tiger_math |
What is the standard error of the mean for a sample of size 16 from a normally distributed population where the population standard deviation is 4.72 years? | automath |
Given an \( N \times M \) matrix initially filled with zeroes, we perform \( Q \) operations where in each operation we select a grid cell \( (x, y) \) and add \( 1 \) to every cell in row \( x \) and every cell in column \( y \). Calculate the number of ways to perform \( Q \) operations such that there are exactly \(... | automath |
The $\$4.25$ in Carol's piggy bank consists of quarters and nickels. There are five more nickels than quarters. How many nickels does Carol have in her bank? | tiger_math |
The value of $y$ varies inversely as $\sqrt x$ and when $x=2$, $y=4$. What is $x$ when $y=1$? | tiger_math |
12 balls numbered 1 through 12 are placed in a bin. In how many ways can 3 balls be drawn, in order, from the bin, if each ball remains outside the bin after it is drawn? | nvidia_math |
Given a matrix $\mathbf{B}$ such that
\[\mathbf{B} \begin{pmatrix} 2 & 1 \\ -1 & 0 \end{pmatrix} = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix},\]determine $\mathbf{B}^{-1} \begin{pmatrix} 3 & 2 \\ 1 & 1 \end{pmatrix}.$ | nvidia_math |
Let \( f : \mathcal{P}(\omega) \to \omega \cup \{ \omega \} \) be defined by \( f(x) = \bigcup \{ n \in \omega : n \subset x \} \). Determine whether \( f \) is surjective, and if so, provide a specific example of a set \( A \in \mathcal{P}(\omega) \) such that \( f(A) = \omega \). | automath |
What is the equation of the line that is perpendicular to the line connecting the origin to the point (–2, 9) and passes through that point? | automath |
Let $a,$ $b,$ $c$ be non-zero real numbers such that $a + b + c = 1.$ Find all possible values of
\[\frac{a^3 + b^3 + c^3 - 3abc}{abc}.\]Enter all the possible values, separated by commas. | tiger_math |
Why does the equation $\sqrt{x} = -3$ have no solutions in the complex plane, considering the properties of the square root function? | automath |
What is the smallest positive integer that can be expressed as the sum of three different perfect squares, each of which is a multiple of 3? | nvidia_math |
Ina is organizing her large collection of books into new shelves. She decides to sort her books into three shelves. She places twice as many books on the second shelf as on the first shelf and triple the number of books on the first shelf onto the third shelf. If she uses 54 books in total to fill the shelves, how many... | tiger_math |
Arthur decided to treat himself to dinner at a nice restaurant. He ordered an appetizer, a delicious ribeye steak for his entrée at $20, had two glasses of nice red wine with dinner for $3 each, and a slice of caramel cheesecake for dessert for $6. He used a voucher for half off the price of his entrée, but he very tho... | tiger_math |
Twenty percent more than three times the total number of students who attended the history class last week are present in class today. If there were 40 students in the class last week and 20 students are absent today, calculate the number of students enrolled in the course. | nvidia_math |
During a certain two-week period, 70 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 5 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms o... | tiger_lab_math |
Ashley is planning a road trip and wants to visit a series of cities. She has a map with 15 cities marked on it, and she wants to find the most efficient route that visits each city exactly once and returns to the starting city. However, she has a constraint: she can only drive on roads that are marked as "scenic route... | nvidia_math |
Myrtle’s 3 hens lay 3 eggs a day. She would be gone for x days and told her neighbor to take as many as they would like. The neighbor took 12 eggs. Once home, Myrtle collected the remaining eggs, dropping 5 on the way into her house. Myrtle has 46 eggs. What is the value of unknown variable x? | tiger_math |
A necklace consists of 5 different colored beads, with 2 beads of each color. How many distinct reflectional symmetries can be created by arranging the beads around the necklace, if two arrangements are considered the same if one can be transformed into the other by a rotation or a reflection? | nvidia_math |
From the 450 students that Sarah interviewed at her school, 70 students said they liked oranges, 120 students said they liked pears, and 147 students said they liked apples. How many students chose strawberries as their favorite fruit from the given options? | tiger_math |
A cylinder with a height of 10 feet and a diameter of 6 feet is to be covered with a layer of carpet that is 2 inches thick. If the carpet comes in rolls that are 2 feet wide and 12 feet long, how many rolls are needed to cover the entire cylinder? | nvidia_math |
In the fifth grade at Parkway elementary school there are 420 students. 320 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?
Answer Choices: (A) 69. (B) 73. (C) 81 (D) 65 (E) 108 | tiger_lab_math |
Let's consider a pyramid with a square base, where each layer is formed by smaller squares. The top layer consists of a single square, the second layer consists of 9 squares (3x3), the third layer consists of 25 squares (5x5), and so on. Each layer is connected to the one below it by a set of identical, shorter rods (w... | nvidia_math |
Given a set \( S \) and a group \( G \) acting on \( S \), consider the action groupoid generated by \( G \) on \( S \). How many distinct arrows (morphisms) can be identified in this action groupoid if the group \( G \) has \( n \) elements and acts freely and transitively on \( S \) consisting of \( m \) elements? | automath |
Josh buys 3 packs of string cheese. Each piece of string cheese cost 10 cents. Each pack has 20 string cheeses in them. How many dollars did he pay? | nvidia_math |
Let $A,B,C$ be three points on the Cartesian plane. A line passing through point $A$ with slope 2 intersects the segment $\overline{BC}$ at point $D$. If $BD:DC=3:7$ and $A=(-1,0)$, then determine the coordinates of point $D$.
[asy]
import markers;
size(9cm);
pair A, B, C, D;
A = (-1,0);
B = (0,-3);
C = (5,7);
D =... | nvidia_math |
Assume a temperature of 300 K and find the wavelength of the photon necessary to cause an electron to jump from the valence to the conduction band in germanium in nm. | tiger_lab_math |
Given the parametric representation \( r(s,t) = 2t \cos(s) \mathbf{i} + 2t \sin(s) \mathbf{j} + t \mathbf{k} \) for \( s \in \mathbb{R} \) and \( t \in \mathbb{R} \), which surface does this represent? Additionally, express the relationship between \( x, y, \) and \( z \) in a non-parametric form. What is the identifyi... | automath |
Let positive integers k, m, and n be such that when k is divided by m, the remainder is r1, and when k is divided by n, the remainder is r2. Given that the quotients are q1 and q2 when k is divided by m and n respectively, it is also known that q1 / q2 = p/q, where p and q are coprime positive integers. Determine the v... | tiger_math |
Calculate: $11 - 10 + 9 \times 8 + 7 - 6 \times 5 + 4 - 3$ | nvidia_math |
Given an observation vector \( x_i \) in \( \mathbb{R}^n \) and a unit vector \( w \) in the same space, what is the geometric interpretation of \( a_i = w^T x_i \), and how can it be understood as a projection of \( x_i \) onto the direction defined by \( w \)? Additionally, compute the value of \( a_i \) if \( w = \b... | automath |
In the arithmetic sequence $2 - \sqrt{3}, 5, 8 + \sqrt{3}, \dots$, find the smallest index $n$ such that the $n$th term is an integer. | nvidia_math |
Claire has a total of 90 pets consisting of gerbils and hamsters only. Some fraction of the gerbils are male, and one-third of the hamsters are male. There are 25 males altogether. Claire has 66 gerbils. What fraction of the gerbils are male? | tiger_math |
Problem:
Compute $\cos \left(\frac{\pi}{2} \right) + \cos \left(\frac{3\pi}{2} \right) + \cos \left(\frac{5\pi}{2} \right) + \cdots + \cos \left(\frac{1199\pi}{2} \right) + 1$, where $i^2=-1$. | nvidia_math |
Given two vectors \( \mathbf{v_1} \) and \( \mathbf{v_2} \) in three-dimensional space, if we consider them as directions with antipodal symmetry, what is the relationship between the angle \( \theta \) formed by the axes corresponding to these vectors and the directions represented by \( \mathbf{v_1} \) and \( \mathbf... | automath |
[( 3.242 x 14 ) / 100] = ?
Answer Choices: (A) 0.045388 (B) 4.5388 (C) 453.88 (D) 473.88 (E) None of these | tiger_lab_math |
Find the equation of the directrix of the parabola $y = \frac{1}{8} x^2.$ | tiger_math |
Let \( S = \{ p_1(x), p_2(x), p_3(x) \} \) be the set of polynomials defined by
\[
p_1(x) = 1 + x, \quad p_2(x) = x^2, \quad p_3(x) = 2x - 1.
\]
Determine if the set \( S \) is a basis for the vector space \( P_2 \) of all polynomials of degree 2 or less. If it is not a basis, find a basis of \( \text{Span}(S) \). W... | automath |
Solve for $n$: $0.03n + 0.08(20 + n) = 12.6$. | tiger_math |
The volume of a sphere is 36π cubic units. What is the radius of the sphere, in units? | nvidia_math |
What is the joint distribution of the magnitude \( r \) and phase \( \phi \) for a circular bivariate normal distribution where the means are \( \mu_x \) and \( \mu_y \) and the standard deviation is \( \sigma \)? Specifically, express the joint distribution \( P(r, \phi | r_0, \phi_0, \sigma) \) in terms of the centra... | automath |
A car accelerates from an initial speed of 60 kmph at a rate of 4 m/s². What distance will it cover in 15 seconds? | tiger_math |
Machine A produces 100 parts twice as fast as Machine B does. Machine B produces 100 parts in 40 minutes. If each machine produces parts at a constant rate, how many parts does Machine A produce in 10 minutes?
Answer Choices: (A) 20 (B) 50 (C) 60 (D) 40 (E) 30 Let's write a program. | tiger_lab_math |
Given the regression model for returns based on ad exposures:
\[
\text{Returns} = \beta_1 nExp + \beta_2 nExp^2
\]
where \(\beta_1\) is positive and statistically significant, and \(\beta_2\) is negative, determine and describe the behavior of the returns as the number of ad exposures (\(nExp\)) increases. Specifical... | automath |
Jared counted 15% fewer cars than his sister Ann while they were watching the road from the school, and Ann counted 7 more cars than their friend Alfred. If Jared counted 300 cars, how many cars did all of them count? | tiger_math |
Let \( z = x + iy \) be a complex number in the set \( \mathbb{H} \) (the upper half-plane), and let \( U(t, \theta) = A_\theta(it) \) where
\[
A_\theta(z) = \frac{z \cos \theta - \sin \theta}{z \sin \theta + \cos \theta}.
\]
Define \( A_\theta(it) \) explicitly. What is the expression for \( U(t, \theta) \) in term... | automath |
If $12m - 7n = 72$ and $n$ is three more than $m$, what is the value of $m + n$? | tiger_math |
For which values of \( n \) does there exist an order-\( n \) L-polyomino that can tile the plane such that no rectangular region is completely covered by L-polyominoes, and no infinite periodic staircase structure exists within the tiling? | automath |
A train 125 m long passes a man, running at 6 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Answer Choices: (A) 35 km/hr (B) 50 km/hr (C) 45 km/hr (D) 65 km/hr (E) 51 km/hr | tiger_lab_math |
There are 30 major league baseball stadiums. Zach has a goal to take his son to see at least one game at each one. He has calculated the average cost for them to travel and see a game will be $900 per stadium. Zach can save $x per year for his baseball stadium trips. It will take Zach 18 years to accomplish his goal. W... | tiger_math |
Given a finite set of nonzero rational numbers \( r_1, r_2, \ldots, r_n \), express each \( r_i \) in simplest form as \( \frac{a_i}{b_i} \) where \( a_i \) and \( b_i \) are integers and \( b_i \neq 0 \). If \( p \) is a prime that does not divide the product \( b_1 b_2 \cdots b_n \), can a rational number of the form... | automath |
Compute
\[\sum_{k = 3}^\infty \frac{2k - 3}{(k - 2)(k - 1)k}.\] | tiger_math |
Given the series \( \sum_{n=1}^{\infty} \frac{1}{n^p} \), for what values of \( p \) does this series converge? | automath |
Find the number of non-similar quadrilaterals with distinct positive integer side lengths in geometric progression. | nvidia_math |
Calculate the limit:
\[
\lim_{n\rightarrow \infty} n \int_X \log \left(1 + \frac{f(x)}{n}\right) d\mu,
\]
where \(\mu\) is a strictly positive measure and \(f : X \rightarrow [0, \infty]\) is a measurable function such that \(\int_X f d\mu = 1\). What is the value of this limit? | automath |
Solve the equation $\ds \frac{1}{x + i} + \frac{1}{x - i} = 1$ for real $x$. Express your answer in the form $a + bi$, where $a$ and $b$ are integers. | nvidia_math |
Given a line \( l \) and a segment \( AB \) where the length of \( AB \) is \( x \) inches (with \( x > 1 \)), can you construct a point \( C \) on the line \( l \) where the circle centered at \( A \) with radius \( AB \) intersects the line \( l \), using only a ruler and a compass whose radius is fixed at 1 inch? If... | automath |
Alex plans to fill his large aquarium with a special type of mineral water. The aquarium has a capacity of 75 gallons. Each bottle of mineral water contains 1/2 gallon. If each bottle costs $30, but Alex gets a 15% discount for purchasing in bulk, how much will he spend on mineral water? | nvidia_math |
Given a dataset with a categorical variable (treatment) that has two levels (control and "mice added") and two continuous variables (plant density and elephant density), how can one statistically test if the treatment significantly affects the relationship between plant density and elephant density? Specifically, would... | automath |
What is the smallest positive integer $n$ such that $n$ and $2n$ have the same number of digits, and $3n$ has one more digit than $n$ and $2n$? | nvidia_math |
Simplify the expression $(a^2-b^2)(a^2+b^2)$. | nvidia_math |
"statement 1": more than 4000 which he and Dave earned at the end of 1 years, "statement 2" :9000 which he and Dave earned at the end of 1 years, "options: " Entailment or contradiction or neutral? Let's write a Python program. | tiger_lab_math |
Given the following set of data representing the test scores of 7 students on a mathematics exam with a maximum possible score of 20: 15, 13, 16, 4, 14, 12, and x, where x is an unknown score. If the mean of the scores is 12.5, what is the value of x? | automath |
A function machine accepts a single-digit input and performs the following operations in sequence:
1. If the input is even, it is multiplied by 4; otherwise, it is increased by 7.
2. The result is then compared to 25.
3. If the result is less than or equal to 25, it is increased by 3; otherwise, it is decreased by ... | nvidia_math |
Find the point on the circle
\[x^2 + y^2 = 9\]that is closest to the line \[2x + 5y + 3 = 0.\] | nvidia_math |
Passage: Hoping to rebound from their home loss to the Eagles, the Redskins flew to the Louisiana Superdome for a Week 15 intraconference fight with the New Orleans Saints. In the first quarter, Washington started off strong as kicker Shaun Suisham nailed a 37-yard field goal, while QB Jason Campbell completed a 31-y... | tiger_lab_math |
Andy has 4 times as many white socks as he has black socks. If he loses half his white socks, how many more white socks does he still have than black socks if he has 6 black socks? Let's write a program. | tiger_lab_math |
The product of two inches and the circumference of a circle, in inches, is equal to the circle's area. What is the length of the radius of the circle, in inches? | nvidia_math |
Let the sum of the first \( m \) terms of an arithmetic series be \( n \) and the sum of the first \( n \) terms be \( m \). If \( m \) and \( n \) are distinct positive integers, what is the sum of the first \( m+n \) terms of the series? Provide a specific example of an arithmetic series that satisfies these conditio... | automath |
Tom initially plans to take 10 dance lessons at different studios. Studio A charges $15 per lesson, Studio B charges $12 per lesson, and Studio C charges $18 per lesson. He takes 4 lessons from Studio A, 3 lessons from Studio B, and remains 3 lessons are from Studio C. However, he gets a 20% discount on the lessons fro... | tiger_math |
A row of 225 tiles (red, blue, and green) are arranged in a repeating pattern. The first seven tiles are red, followed by five blue, followed by three green, followed by seven red, followed by five blue, followed by three green,.... What is the color of the 199th tile? | tiger_math |
Two triangles are similar. The ratio of their areas is 1:4. If the height of the smaller triangle is 3 cm, how long is the corresponding height of the larger triangle, in centimeters? Let's program in Python in the response. | tiger_lab_math |
If New York recorded 5000 new coronavirus cases in the first week, half as many cases in the second week, and an additional 2000 cases in the third week, what is the total number of recorded new coronavirus cases in the state after the three weeks? | tiger_math |
A triangle has three sides of the following side lengths: $8$, $12$, and $y^3$. What are all of the positive integer values of $y$ such that the triangle exists? Separate your answers using commas and express them in increasing order. | nvidia_math |
there are 20 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ? Let's write a Python program. | tiger_lab_math |
Find the value of $c$ such that the polynomial $x^3 + cx^2 + (3c + 5)x + 2010$ can be factored into a product of three linear polynomials with integer coefficients, where one of the linear factors is $(x + 2)$. | nvidia_math |
What is the surface area of the solid of revolution generated by rotating the curve \( y = x^3 \) about the x-axis from \( x = 0 \) to \( x = 1 \)? | automath |
If 3 boys each make 12 muffins for a bake sale, and x other girls are making 20 muffins each, how many total muffins will be for sale?
If we know the answer to the above question is 76, what is the value of unknown variable x? | tiger_math |
What is the geometric mean of the solutions to the equation $x^2 + 5x + 6 = 0$? | nvidia_math |
Given a set of seven concentric circles, such that the radius of the smallest circle is 1, and the radius of each subsequent circle is 2 more than the previous one. Three parallel lines are drawn, such that the length of their segments within the seven circles are 3, 4, and 5 units long, respectively. Find the perimete... | nvidia_math |
What is the sum of all the prime numbers between 11 and 20? | nvidia_math |
Travis wants to fly to Australia. The regular tickets cost about $2000. As Travis is a student, he will get a 30% discount on this price. How much does he need to pay for his ticket? | tiger_lab_math |
Consider a data set with ten variables. Using factor analysis, we want to extract three factors. How many unique factor loadings can be obtained in this scenario? | tiger_lab_math |
Regular hexagon $ABCDEF$ is divided into six smaller equilateral triangles, such as $\triangle ABG$, shown in boldface in the diagram. By connecting every other vertex, we obtain a larger equilateral triangle $\triangle ACE$, also shown in boldface. Compute the ratio $[\triangle ABG]/[\triangle ACE]$. [asy]
size(150)... | tiger_lab_math |
Quadrilateral $ABCD$ has angles $A$ and $C$ congruent. The measure of angle $D$ is three times the measure of angle $B$. What is the number of degrees in the measure of angle $C$? | nvidia_math |
Find the least common multiple of 120, 180, and 240. | nvidia_math |
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