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Jack bought 3 books a month at $20 each. He sells them back at the end of the year for a certain amount. He lost $220. How much money did he get when he sold the books back? | tiger_math |
rakesh ' s mathematics test had 75 problems , 10 arithmetic , 30 algebra , 35 geometry problems . although he answered 70 % of arithmetic , 40 % of arithmetic and 60 % of geometry problems correctly , still he got less than 60 % problems right . how many more questions he would have to answer more to get passed ? Let's... | tiger_lab_math |
30% of all fishermen in Piscataquis County are also hunters while only 20% of all hunters are fishermen. If there are 1500 hunters in Piscataquis County then how many fishermen are there?
Answer Choices: (A) 800 (B) 1000 (C) 1200 (D) 1500 (E) 1800 | tiger_lab_math |
Given that the circle defined by $x^2 + y^2 = 4$ is tangent to the parabola $y = ax^2 + 1$, calculate the constant $a$. | nvidia_math |
How much time did Mary spend in total downloading Zoom and talking, considering that she initially spent 10 minutes downloading the Mac version but then needed to download the Windows version, which took three times as long? During her first call, the audio glitched twice for 4 minutes each time and the video glitched ... | tiger_math |
Three identical electric dipoles are placed at the vertices of an equilateral triangle. The dipoles are aligned such that each dipole is parallel to the opposite side of the triangle. If the initial configuration stores 20 Joules of energy, how much more energy, in Joules, would be stored if the dipoles are rotated suc... | nvidia_math |
In a triangle with sides $a$, $b$, and $c$, and corresponding angles $A$, $B$, and $C$, find the largest possible value of
\[\frac{a\sin A + b\sin B + c\sin C}{a + b + c}.\] | nvidia_math |
In the context of the differential equation \( y \frac{dy}{dx} = e^x \), if we separate variables and integrate both sides to obtain \( \frac{y^2}{2} = e^x + c \), how can we rigorously justify that this manipulation is valid? Specifically, what foundational principles from calculus support the legitimacy of separating... | automath |
14 different biology books and 8 different chemistry books lie on a shelf. Each book is either published in an even or odd year, and has either a red or blue cover. In how many ways can a student pick 2 books of each type if they must select one book of each subject from an odd year and one with a blue cover? | tiger_math |
What is the smallest positive integer $n$ such that the number $3n$ is congruent to 4 (mod 11)? | nvidia_math |
Simplify $(2r^2 + 5r - 3) + (r^2 - 2r - 1)$.
Note: This problem requires a different approach as it involves adding two polynomials instead of subtracting them, and the terms are not identical, requiring careful combination of like terms. | nvidia_math |
In a city, there are three different types of public transportation: buses, trams, and trains. Each type of transportation has a different fare structure. The number of people who use buses is between 40% and 50% of the total population, the number of people who use trams is between 20% and 30%, and the number of peopl... | nvidia_math |
A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating tha... | tiger_lab_math |
Given a constant vector \(\mathbf{c}\) in three-dimensional space, evaluate the Poisson bracket \(\{\mathbf{c}, \mathbf{l} \cdot \hat{n}\}\), where \(\mathbf{l}\) is the angular momentum given by \(\mathbf{l} = \mathbf{r} \times \mathbf{p}\) and \(\hat{n}\) is a unit vector.
What is the resulting expression for \(\{\... | automath |
The mean of $5,8$ and $17$ is equal to the mean of $12$ and $y$. What is the value of $y$? | nvidia_math |
Given the following statements about Alex and chocolate:
1. \( \forall x (C(x) \implies L(a,x)) \): For all objects \( x \), if \( x \) contains chocolate, then Alex likes \( x \).
2. \( \forall x (C(x) \land L(a,x)) \): For all objects \( x \), \( x \) contains chocolate and Alex likes \( x \).
Is statement 2 a corr... | automath |
At a store, Emily buys a box of eggs, a basket of figs, a grapefruit, and a bunch of herbs for a total of $30. If a bunch of herbs costs three times as much as a box of eggs and the price of a grapefruit is equal to the price of a box of eggs plus a basket of figs, what is the cost of a basket of figs and a grapefruit? | nvidia_math |
There were 600 people in the stadium when the football game started. Before the game was over, one-fourth of the boys and one-eighth of the girls left early. How many people remained to see the end of the game if there were 240 girls at the beginning of the game? | tiger_lab_math |
Let \( R \) be a ring, and let \( S \) be an \( R \)-algebraic structure. Given a non-empty set \( X \), if \( S^X \) is the set of all mappings from \( X \) to \( S \), and if \( f, g \in S^X \) such that \( \lambda \circ f = g \) for some \( \lambda \in R \), can you determine a necessary condition on \( f \) and \( ... | automath |
Let \( E \subset \mathbb{R}^n \) be the set defined by \( E = (0, 1) \cup \{2\} \). Determine which of the points \( 0, 1, 0.5, \) and \( 2 \) are limit points, isolated points, and interior points of the set \( E \). Provide a justification for your classification of each point. | automath |
Given that the vectors $\mathbf{a} = \begin{pmatrix} 3 \\ -\frac{31}{12} \\ -1 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} 2 \\ X \\ \frac{41}{12} \end{pmatrix}$ are equal in magnitude and orthogonal, find the sum of the components of vector $\mathbf{b}$. | tiger_math |
If the probability that a baby born in a certain hospital will speak in the next day is 1/4, what is the probability that exactly 3 babies out of a cluster of 7 babies will speak tomorrow? | tiger_math |
Given a transfer function \( H(s) = \frac{b(s)}{a(s)} \) with partial fraction expansion defined by residues \( r \) and poles \( p \), if the residues are \( r = [2, -1, 3] \) and the poles are \( p = [1, 2, 2] \) with a tolerance \( tol = 0.001 \), what will the partial fraction expansion of \( H(s) \) look like, spe... | automath |
In a small town, there are 7 streets going from north to south and 8 streets going from east to west. All the streets intersect each other. Sophia begins walking at the northwesternmost intersection and decides to walk towards the southeasternmost intersection, but she can only walk east or south along the streets. Wha... | tiger_math |
Jeremy decides to take Tylenol because of the pain he is experiencing. He decides to take 1000 mg every 6 hours for 2 weeks. How many pills do they take if they are each 500 mg? | tiger_lab_math |
Four workers A, B, C, and D can complete a certain job individually in 10, 15, 20, and 30 days respectively. If they work together on the same job, how long will it take them to complete the job? | tiger_math |
The product of two consecutive integers is 72. What is the smaller of the two integers? | nvidia_math |
How many different arrangements can be made with the letters of the word RADII? | tiger_math |
Does the series \(\sum_{n=1}^{\infty} \left| \frac{\cos(n^{10} - 16n^2)}{n} \right|\) converge or diverge? | automath |
a trader bought a car at 40 % discount on its original price . he sold it at a 80 % increase on the price he bought it . what percent of profit did he make on the original price ? Please write a program to solve it | tiger_lab_math |
Round to the nearest hundredth: 18.4851 | tiger_math |
What is the greatest integer value of $b$ such that $-4$ is not in the range of $y=x^2-bx+12$? | tiger_math |
What are all the solutions of the equation $$\cos 2x - \cos x = 0$$ within the interval $$[0, 2\pi)$$? | automath |
Expand the following expression:
$$(2x-3)(x^2+5x-1)$$ | nvidia_math |
a department store perceived a run on a lower priced garment and raised the price by 20 % to keep stock available until another shipment arrived . customers fumed and the department store manager allowed them to purchase the garments at 80 % of the new price to save face . what was the difference in the new retail pric... | tiger_lab_math |
Consider a function $g(x)$ that satisfies the following equation:
$$g(x) + g\left(\frac{x^2 + 2x - 3}{x^2 - 4x + 3}\right) = x^2$$
for all $x$ such that $x \neq 1,3.$
Find the value of $g(4).$ | nvidia_math |
A student needs to find the missing side length of a right triangle given two sides. If one side is 5 cm long and the other side is 12 cm long, what is the length of the third side? | tiger_lab_math |
Compute the difference between the squares of two consecutive numbers, 27 and 28, without using a calculator. Can you find a pattern or a quick method to calculate this difference mentally? | nvidia_math |
Is there a connected, locally path-connected, locally compact metric space that is not equivalent to any path metric? If so, can you provide an example? | automath |
Find the largest negative integer that is 3 more than a multiple of 8 and 2 less than a multiple of 11. | nvidia_math |
A diagonal of a polygon is an segment between two non-adjacent vertices of the polygon. How many diagonals does a regular 20-sided polygon have?
Answer Choices: (A) 875 (B) 170 (C) 1425 (D) 2025 (E) 2500 | tiger_lab_math |
Lena has a small business selling handmade candles and soaps at a local market. She sells large candles for $18.00 each, small candles for $8.00 each, and a set of three soaps for $12.00. On Saturday, she sold 8 large candles, 15 small candles, and 10 sets of soap. Additionally, she received 3 orders for a special gift... | nvidia_math |
The equation \[\frac{x}{x+a} + \frac{x}{x+b} = kx\] has exactly two complex roots, where $a$ and $b$ are distinct real numbers. Find all possible complex values for $k.$ | tiger_math |
Consider the nonnegative monotone cone in \(\mathbb{R}^n\), defined as
\[
\mathcal{K} = \{ \mathbf{x} = (x_1, x_2, \ldots, x_n)^\top \in \mathbb{R}^n \mid x_1 \geq x_2 \geq \cdots \geq x_n \geq 0 \}.
\]
Let \(\mathbf{p} = (p_1, p_2, \ldots, p_n)^\top\) be a point in \(\mathbb{R}^n\) such that \(p_1 < p_2 < \cdots < ... | automath |
Suppose a company manufactures a certain product and sells it at $60 per unit. The production cost for each unit is $30. The company wants to increase its profit by optimizing the selling price. If the market demand equation for the product is q = 500 - 5p, where q is the quantity demanded and p is the selling price in... | tiger_lab_math |
The area of a triangle is 600 square feet. If the altitude of the triangle is 40 feet, what is the length of the corresponding base? | tiger_math |
What is the value of the line integral \(\oint_C \mathbf{F} \cdot \mathbf{T} \, ds\) for the vector field \(\mathbf{F}(x,y) = xy \, \mathbf{i} + x^2 \, \mathbf{j}\) around the rectangle with vertices \((0,0), (3,0), (3,1), (0,1)\), traversed in an anticlockwise direction? | automath |
Find the distance between the complex numbers $3+5i$ and $2-3i$ in the complex plane. | nvidia_math |
In a two-dimensional plane, consider a force vector \(\bold{F} = (3, 4)\) acting at a point defined by the position vector \(\bold{r} = (1, 2)\). Calculate the moment of force \(\bold{M} = \bold{r} \times \bold{F}\) and determine its direction according to the right-hand rule. What is the magnitude of \(\bold{M}\)? | automath |
Sue is traveling from New York to San Francisco, 16 hours later after landing in New York from New Orleans. If the journey from New Orleans to New York took 3/4 times as much time as she takes to travel from New York to San Francisco, and she lands in San Francisco 24 hours later after departing from New York, calculat... | tiger_lab_math |
What is the least common multiple of 36 and 84? | tiger_math |
If one of the followings is the product of the two 3-digit integers 8K5 and 6L5 (K and L denote the tens digit of the respective integers), then that product must be
Answer Choices: (A) 478,823 (B) 511,913 (C) 531,875 (D) 538,424 (E) 569,114 | tiger_lab_math |
What is the least four-digit positive integer, with all different digits, that is divisible by each of its digits? Please respond by writing a program in Python. | tiger_lab_math |
Evaluate the limit
\[
\lim_{h\rightarrow0^-}\frac{e^{-1/|h|}}{h^2}.
\]
What is the result of this limit? | automath |
What is the simplified form of the expression \( 1 - \frac{x}{y} \) in terms of a single fraction? | automath |
Express $\frac{165_7}{11_2}+\frac{121_6}{21_3}$ in base X. The answer is 39. What is the value of unknown variable X? | tiger_math |
Let $a,$ $b,$ $c$ be the roots of $x^3 - 4x^2 + 7x - 3 = 0.$ Find $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}.$ | nvidia_math |
In a univariate linear regression setting, if the slope estimate \(\hat{\beta}_1\) is equal to zero, does this imply that the variables involved exhibit no non-linear relationship? Provide an example to support your answer. Additionally, in the context of multiple regression, if \(\hat{\beta}_i = 0\) for some regressor... | automath |
bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 49 more . what was his original selling price ? Let's write a program. | tiger_lab_math |
An old pirate wants to leave his treasure on an island. He has 3500 gold coins. He wants to spread this equally across 5 chests. Additionally, he will put a total of 500 silver coins and twice as many bronze coins as silver, all distributed equally across the chests. How many coins in total will be in each chest? Let's... | tiger_lab_math |
A park had 200 visitors last Saturday and 40 more visitors on Sunday than on Saturday. Calculate the total number of people in the park over the two days. | tiger_math |
Suppose that on a family trip, the probability of a car breaking down is 0.15 and the probability of encountering heavy traffic is 0.35. What is the probability that the family has encountered heavy traffic or their car has broken down? | tiger_lab_math |
In a yard, 51 trees are planted at equal distances, one tree being at each end of the yard. The distance between 2 consecutive trees is 5 meters. How long is the yard? | tiger_math |
Victoria runs at a constant speed of 95 m/s. How many kms can he cover in 2 minutes Please respond by writing a program in Python. | tiger_lab_math |
A washing machine uses 20 gallons of water for a heavy wash, 10 gallons of water for a regular wash, and 2 gallons of water for a light wash per load of laundry. If bleach is used, there is an extra light wash cycle added to rinse the laundry thoroughly. There are two heavy washes, three regular washes, and one light w... | tiger_math |
Rollo has 3 guinea pigs, the first guinea pig eats 2 cups of food, the second guinea pig eats twice as much as the first one, and the third guinea pig eats 3 cups more than the second one. How many cups of food does Rollo need to feed all his Guinea pigs? | tiger_lab_math |
Given the function defined by $\phi(x) = |x|$ for $x \in [-1, 1]$ and $\phi(x + 2) = \phi(x)$ for all $x \in \mathbb{R}$, determine the values of $\phi(5)$ and $\phi(-1)$. Are these values equal? If they are equal, explain why the behavior of the function $\phi$ is consistent across its definition. | automath |
Find all real numbers $x$ so that the product $(x + i)((x + 1) + i)((x + 2) + i)$ is pure imaginary. Enter all the solutions, separated by commas. | tiger_lab_math |
ACME’s manufacturing costs for sets of horseshoes include a $11,450 initial outlay, and $19.75 per set. They can sell the sets $51.50. If profit is revenue from sales minus manufacturing costs, and the company producessells 987 sets of horseshoes, what was their profit?
Answer Choices: (A) $19,887.25 (B) $30,943.25 (C)... | tiger_lab_math |
What is the minimum rank of a matrix that can be expressed as the sum of two rank 1 matrices, and how does this relate to the results obtained from penalty decomposition methods for rank minimization problems? | automath |
If 1 > 1 - ab > 0, which of the following must be true?
I. a/b > 0
II. ab < 1
III.a/b > 1
Answer Choices: (A) I only (B) II only (C) III only (D) I and II only (E) I and III only | tiger_lab_math |
A garden has 50,000 trees. 12% of the trees are guava trees, 15% are orange trees, 10% are coconut trees and the rest are mango trees. Find the number of mango trees.
Answer Choices: (A) 30000 (B) 30200 (C) 30800 (D) 31200 (E) 31500 | tiger_lab_math |
What is the remainder when $1 + 2 + 3 + 4 + \dots + 14 + 15$ is divided by 12? | nvidia_math |
A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 4.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beg... | tiger_lab_math |
What is the minimum number of perfect square numbers that sum to 30? | automath |
A biased coin has a probability of $\frac{2}{5}$ of landing on heads when flipped. A player wins $\$1$for each head and loses$\$0.25$ for each tail. If the player flips the coin 10 times, what is the expected value of the player's winnings? Express your answer as a decimal. | nvidia_math |
What is the minimum number of iterations \( N \) required by the bisection method to guarantee an absolute error of less than \( 0.0001 \) when approximating the root of the function \( f(x) = x^2 - x - 1 \) over the interval \([1, 2]\)? | automath |
Let \( I = \int_0^\infty \sin x \, dx \) and \( J = \int_{-1}^1 \frac{1}{x} \, dx \). Calculate \( I + J \) using the appropriate regularization techniques, and provide the final result. | automath |
At what point does the line containing the points $(1, 7)$ and $(3, 11)$ intersect the $y$-axis? Express your answer as an ordered pair. | tiger_math |
If the 1st of the month occurs on a Thursday, on which day of the week does the 20th occur?
Answer Choices: (A) Wednesday (B) Saturday (C) Tuesday (D) Thursday (E) Sunday | tiger_lab_math |
In the diagram, what is the perimeter of pentagon $PQRST$? [asy]
import olympiad;
size(6cm); // ADJUST
pair p = (0, 6);
pair q = (3, 6);
pair r = (3, 3);
pair t = (0, 0);
pair s = (7, 0);
draw(p--q--r--s--t--cycle);
label("$P$", p, NW);
label("$Q$", q, NE);
label("$R$", r, E + NE);
label("$S$", s, SE);
label("$T$"... | tiger_math |
A canteen requires 112 kgs of wheat for one week. How many kgs of wheat will it require for 69 days?
Answer Choices: (A) 1,204kgs (B) 1,401kgs (C) 1,104kgs (D) 1,014kgs (E) None Please respond by writing a program in Python. | tiger_lab_math |
Before she spent 8 dollars, Emma had 3 more than triple the amount of money her brother Max had. If Max has 12 dollars, how much money does Emma have now? | nvidia_math |
A man cheats while buying as well as while selling. While buying he takes 10% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 12% below the cost price of the claimed weight.
Answer Choices: (A) 19.81% (B) 21% (C) 37.5% (D) 25% (E) 37.5% | tiger_lab_math |
Given two sets of feature vectors \( X \) and \( Y \) where \( X \) contains \( n \) vectors, each of dimension \( p \), and \( Y \) contains \( m \) vectors, can you compute the total number of distinct linear kernel values \( K(x_i, y_j) \) that can be obtained from all pairs \( (x_i, y_j) \) where \( x_i \in X \) an... | automath |
If 0.75: x :: 5:9, then x is equal to:
Answer Choices: (A) 1.12 (B) 1.16 (C) 1.2 (D) 1.35 (E) None of these | tiger_lab_math |
Given the parameters in the uncertainty traps model where \( \rho = 0.99 \), \( \gamma_x = 0.5 \), and \( \sigma_\theta = 0.5 \), calculate the steady-state precision \( \gamma \) for \( M = 6 \) active firms in the long run. What is the value of \( \gamma \) at this steady state? | automath |
If Mark's old phone plan costs $150 per month and his new plan is 30% more expensive, what is the cost of his new plan? | tiger_math |
Let $g$ be a function satisfying $g(x+y) = g(x)g(y)$ for all real numbers $x$ and $y$. If $g(2) = 4$ and $g(5) = 3$, what is the value of $g(7)$? | nvidia_math |
A triangle has three different integer side lengths and a perimeter of 20 units. What is the maximum length of any one side? | nvidia_math |
Calculate the perimeter of the triangle formed by the points A(1,2), B(1,8), and C(5,5) on a Cartesian coordinate plane. | tiger_math |
What is the minimum number of perfect out shuffles required to restore a standard deck of 52 cards to its original order? | automath |
Suppose two players are trying to split a cake that is worth $10. If player 1 gets a piece that is worth $x, then player 2 gets the remaining piece that is worth $10 - x. Each player's utility (or satisfaction) is equal to the value of the piece they receive. How much should player 1 claim their piece is worth in order... | tiger_lab_math |
Ava and Liam went blueberry picking to make jam. They need 2 pounds of blueberries per jar of jam. Ava picked 12 pounds of blueberries and Liam picked 3 times as much as Ava. Together, how many jars of jam can they make? | nvidia_math |
Our school's girls volleyball team has 14 players, including a set of 3 triplets: Alicia, Amanda, and Anna. In how many ways can we choose 6 starters if all three triplets are in the starting lineup? | tiger_lab_math |
A graduating class has a number of students that satisfies the following conditions:
* It is more than 50 and fewer than 100.
* It is 5 less than a multiple of 3.
* It is 1 less than a multiple of 4.
* It is 4 less than a multiple of 5.
If the number of students in the class is Y, what is the value of Y? | tiger_math |
Suppose two children, one weighing 20 kg and the other weighing 30 kg, are sitting on a seesaw that is balanced at its center. If the distance between the children is 3.00 m, how far from the pivot point must the lighter child sit to maintain balance? | automath |
Let \( A \) be a \( 3 \times 3 \) matrix with a determinant \( \det(A) = 5 \). If matrix \( B \) is obtained from \( A \) by swapping two rows, what is \( \det(B) \)? | automath |
Lindsey saved $x in September, she saved $37 in October, and $11 in November. Lindsey's mom said that since Lindsey had saved more than $75, she would give Lindsey $25. Then Lindsey spent $87 on a video game. How much money did Lindsey have left?
If we know the answer to the above question is 36, what is the value of... | tiger_math |
Find the coordinates of the center of the hyperbola \[\frac{(2y-2)^2}{5^2} - \frac{(3x-4)^2}{4^2} = 1.\] | tiger_lab_math |
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