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Nadine went to a garage sale and spent $56. She bought a table for $34 and 2 chairs. Each chair cost the same amount. How much did one chair cost? | tiger_math |
Given two integers \( N \) and \( K \), construct a permutation \( P \) of length \( N \) such that exactly \( K \) indices in the permutation are "good." An index \( i \) in the permutation \( P \) is defined as "good" if \( P_i \) is divisible by \( i \). If it's impossible to create such a permutation, return -1. If... | automath |
A computer is programmed to multiply a sequence of numbers until the product is divisible by 1419. The value of n is 86. What is the sequence of numbers the computer is multiplying? | tiger_math |
the least number of 4 digits which is divisible by 15 , 25 , 40 and 75 is : ? Let's write a program. | tiger_lab_math |
The base-10 numbers 217 and 45 are multiplied. The product is then written in base-6. What is the units digit of the base-6 representation? | nvidia_math |
Consider the following statements regarding functions of bounded variation:
1. Any continuous function on the interval \([0, 1]\) is of bounded variation.
2. If \(f : \mathbb{R} \to \mathbb{R}\) is continuously differentiable, then its restriction to the interval \([-n, n]\) is of bounded variation for any positive in... | automath |
Consider a logical argument with the premises \( p \to q \) and \( q \). If we know that the argument concludes with \( p \), under what truth conditions can we determine that the argument is invalid? Specifically, provide an example with truth values for \( p \) and \( q \) that demonstrate the invalidity of this argu... | automath |
Evaluate the following limits:
1. \( \lim_{x \to 1} \frac{\sqrt{x + 3} - 2}{4x - 4} \)
2. \( \lim_{x \to 0} \frac{1 - \sqrt{\cos x}}{x^2} \)
Determine the numerical values of both limits. | automath |
Given a finite set \( X \) with \( n \) elements, how many distinct topological spaces can be defined on \( X \) under the discrete topology? | automath |
in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 2 / 3 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight | tiger_math |
A man can row his boat with the stream at 12 km/h and against the stream at 4 km/h. What is the man's rate? | tiger_math |
Find the number of five-digit numbers that have exactly two different digits. | nvidia_math |
In a group of 10 people, let $e$ be the number of people who have an even number of friends and $o$ be the number of people who have an odd number of friends. If no one has more than 3 friends, determine the number of possible ordered pairs $(e, o)$. | nvidia_math |
Lewis found 4 more items on the scavenger hunt than Samantha. Samantha found x times the amount of items than Tanya who was only able to find 4 items. Lewis found 20 items. What is the value of unknown variable x? What is the value of unknown variable x? | tiger_math |
A train running at the speed of 60 km/hr crosses a pole in a certain amount of time. The length of the train is 350 meters. How long does it take for the train to cross the pole? | tiger_math |
The decimal expansion of $8/11$ is a repeating decimal. What is the least number of digits in a repeating block of 8/11? | tiger_math |
Let $u = 3s - 2$ and $v = 2s + 1$. If $u = 5$, what is the value of $v$? | nvidia_math |
A triangle has an area of 20 square units and its sides are in the ratio of 5:6:7. What is the length of the shortest side, in units? | nvidia_math |
If $x^2 + \frac{1}{x^2} = A,$ and $x - \frac{1}{x} = B,$ where $A$ and $B$ are positive numbers, find the minimum possible numerical value for $\frac{A}{B}.$ | nvidia_math |
Telegraph Road goes through multiple states and is 162 kilometers long. Pardee Road is x meters long. Telegraph Road is 150 kilometers longer than Pardee Road. What is the value of unknown variable x? | tiger_math |
Let \( P = (X, \subseteq) \) be an inclusion ordered set where \( A \) and \( B \) are subsets of \( X \) such that \( A \cup B \in X \). If the number of elements in set \( A \) is 5 and the number of elements in set \( B \) is 7, with the intersection \( |A \cap B| = 3 \), how many unique elements are there in the un... | automath |
Find the coefficient of the $x^3$ term in the expansion of the product $(ax^2 + 2x - 1)^2(bx - 3)$. | nvidia_math |
If a function f satisfies the equation f(3x - 1) = x^2 + x + 1 for all real numbers x, what is the value of f(5)? | tiger_math |
If 25$\%$ of a number is the same as 20$\%$ of X, what is the number?
If we know the answer to the above question is 24, what is the value of unknown variable X? | tiger_math |
Suppose that $y$ is a positive multiple of $4$. If $y$ squared is greater than $100$, what is the smallest possible value of $y$? | tiger_math |
What is the minimal period of the decimal representation of \( \frac{1}{n} \) for \( n = 30 \)? | automath |
Let \( G \) be a directed graph represented by an \( n \times n \) adjacency matrix \( A \), where \( A[i, j] = 1 \) if there is an edge from vertex \( i \) to vertex \( j \), and \( A[i, j] = 0 \) otherwise. Define \( P[i, j] \) as the length of the shortest path from vertex \( i \) to vertex \( j \).
1. In the init... | automath |
Hawkeye is driving to his aunt. He has to charge his battery for $3.5 per charge. If he charged his battery four times, and his battery charging budget was $20, how much money was he left with when he reached his aunt's place? | tiger_math |
Consider a graph G that has 12 vertices and 25 edges. What is the chromatic polynomial of G? | tiger_lab_math |
At Academic Academy, to pass an algebra test you must score at least $75\%$. If there are 24 problems on the test, what is the greatest number you can miss and still pass? | tiger_math |
Given a time series that is suspected to follow an AR(1) process and exhibits a quadratic trend with yearly seasonality, how would you formally test whether the series is covariance stationary? Specifically, calculate the minimum degree of differencing required to remove the trend and seasonal components such that the ... | automath |
Let \( S \) be a finite set of propositional formulas. If \( S \) contains \( n \) clauses, what is the maximum number of ground contradictions that can be derived from \( S \) using the projection and ground contradiction rules described? Express your answer in terms of \( n \). | automath |
How many terms do you need to include in the Taylor series expansion of \(\ln(1+x)\) to ensure that the absolute error when estimating \(\ln(0.25)\) is less than or equal to \(0.00005\)? | automath |
Alice and Bob decide to use the Diffie-Hellman key exchange to share a secret key. Alice chooses a prime number p=23 and a primitive root g=5. Alice then chooses a secret number a=6 and computes A = g^a mod p. Bob chooses a secret number b=15 and computes B = g^b mod p. What is the shared secret key that Alice and Bob ... | tiger_lab_math |
"statement 1": The technical investigation commission has determined that some military were reportedly involved in the assassination of the six Jesuits and their two maids , which took place at daybreak on the 16th of November , as reported by president Alfredo Cristiani on the 7th of January ., "statement 2" :The as... | tiger_lab_math |
Arthur baked 115 muffins. James baked a certain multiple of that amount. James baked 1380 muffins. How many times the amount of muffins that Arthur baked did James bake? | tiger_math |
Find the number of moles of KCl formed on combining 1 mole of HCl and 1 mole of KOH | tiger_math |
The right triangular region formed by the points $(0,0)$, $(3,0)$, and $(0,k)$ is partitioned into three congruent triangles by drawing two lines parallel to the hypotenuse. What is the length of the perpendicular segment from the point $(0,k)$ to the line connecting the points $(1,0)$ and $(2,0)$? | nvidia_math |
Compute: $\left(\frac{1}{3} \right)^{2} \cdot \left(\frac{1}{5} \right)$. | nvidia_math |
If $a (a+b) = 55$ and $b (a+b) = 110$, what is the value of $(a-b)^2$? | tiger_math |
What is the value of \( a(4) \), which represents the number of ways to place an equal number of horizontal and vertical dominoes on a \( 4 \times 4 \) chequerboard? | automath |
X percents of the rooms are suits, Y percent of the rooms are painted light blue. Which of the following best represents the least percentage of the light blue painted suits?
Answer Choices: (A) X-Y (B) Y-X +100 (C) 100X-Y (D) X+Y-100 (E) 100-XY | tiger_lab_math |
A parallelogram has a base of 9 cm and a height of 5 cm. Find its area. | tiger_lab_math |
What are the values of \(x\) and \(y\) that satisfy the system of equations \(5x - y = -14 + 2x + y\) and \(7x + 9y + 4 = 3x + 8y\)? | automath |
Given two real numbers $a>2$ and $b>2$ so that $\frac{1}{a} + \frac{1}{b} = \frac{1}{2}$ and $ab = 9$, what is $b$? | nvidia_math |
Determine the number of positive integers less than 3500 that are not square tails, where a positive integer n is defined as a square tail if there exists a positive integer m such that the decimal representation of m^2 ends with exactly n zeroes. | nvidia_math |
What is the sum of the cubes of the integers from -10 to 10, inclusive? | nvidia_math |
The function $f(x)$ satisfies $f(x + 1) - f(x) = 12x^2 - 3x - 4.$ Find $f(10) - f(0).$ | nvidia_math |
What is the SHA-256 hash value of the message "math is awesome!"? | tiger_lab_math |
Find the sum of seven consecutive odd integers if the first integer is 2n+1. | tiger_math |
When three standard dice are tossed, the numbers $a,b,c$ are obtained. Find the probability that $abc = 1$. | tiger_math |
How can we derive the expression for the divergence of a vector field in Smoothed Particle Hydrodynamics (SPH) given by the formula $$\nabla \cdot \mathbf{v} = \frac{\nabla \cdot (\rho \mathbf{v}) - \nabla \rho \cdot \mathbf{v}}{\rho}$$, and what does the presence of the density $\rho$ signify in this context? | automath |
A room is 7 meters 68 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.
Answer Choices: (A) 107 (B) 144 (C) 175 (D) 165 (E) 130 | tiger_lab_math |
Consider the rational numbers \( a = \frac{4}{5} \), \( b = \frac{16}{30} \), and \( c = -\frac{8}{15} \). Verify if the inequality \( a > b > c \) holds true by determining the values of \( a \), \( b \), and \( c \) in decimal form and comparing them. What is the relationship among \( a \), \( b \), and \( c \)? | automath |
Find the Taylor polynomial of degree 3 for the function \( f(x) = \arcsin(x) \) centered at \( c = \frac{1}{2} \), and then calculate the accuracy of this polynomial at \( x = \frac{\sqrt{2}}{2} \). What is the absolute error? | automath |
What is the series expansion of the Gauss Hypergeometric function \( \,_2F_1(a, b; c; z) \) around \( z = 1 \) when \( c - a - b \) is a positive integer? Please express your answer in terms of Gamma functions and other standard mathematical functions. | automath |
In a class of $40$ students, $18$ said they liked apple pie, $15$ said they liked chocolate cake, and $7$ said they did not like either. How many students in the class liked both? | tiger_math |
In an amusement park, Sally and her four friends decided to ride the Ferris wheel, which can seat exactly 20 people per round. Each ticket costs $5. After each of them bought a ticket, they noticed that the total revenue collected from the Ferris wheel rides for the day was $380. Assuming they were the last group to ri... | tiger_math |
If Arthur walks 3 miles north and then twice that distance east, and each block is one-quarter of a mile, how many blocks did he walk? | tiger_math |
Mac has £ 3 more than Ken, but then Ken wins on the horses and trebles his money, so that he now has £ 2 more than the original amount of money that the two boys had between them. How much money did Mac and Ken have between them before Ken's win ?
Answer Choices: (A) £ 9 (B) £ 11 (C) £ 13 (D) £ 15 (E) None of the these | tiger_lab_math |
An army’s recruitment process included N rounds of selection tasks. For the first A rounds, the rejection percentage was 60 percent per round. For the next B rounds, the rejection percentage was 50 percent per round and for the remaining rounds, the selection percentage was 70 percent per round. If there were 100000 pe... | tiger_lab_math |
To buy a book, you pay $20 for each of the first 5 books at the supermarket, and for each additional book you buy over $20, you receive a discount of $2. If Beatrice bought 20 books, how much did she pay at the supermarket? Let's write a Python program to solve it. | tiger_lab_math |
Michael has a chicken farm. His chickens increase in number by 150 chickens annually. If the number of chickens on his farm now is 550, how many will he have after 9 years? | tiger_math |
There is three less than four times the number of students in Elementary School as there are in Middle School. If the number of students in Middle school is x, calculate the total number of students in both levels.
If we know the answer to the above question is 247, what is the value of unknown variable x? | tiger_math |
Let $a$ and $b$ be the roots of the quadratic equation
$$x^2+5x+2=0.$$
Compute the remainder of the number
$$a^{-1}+b^{-1}+a^{-2}+b^{-2}+a^{-3}+b^{-3}$$
when divided by 11. | nvidia_math |
The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?
Answer Choices: (A) 4.7 (B) 4.6 (C) 4.2 (D) 4.1 (E) 4.9 Let's write a Python program to solve it. | tiger_lab_math |
Find the equation of the line that passes through the points (6, 8) and (-10, 4), and determine the y-coordinate of the point on the line with an x-coordinate of -2. | tiger_math |
When a=3+(2/3) and b=3-(2/3), (2^a^2)/(2^b^2)=?
Answer Choices: (A) 256 (B) 156 (C) 250 (D) 150 (E) 125 | tiger_lab_math |
Can you provide an example of a closed set in the real numbers that contains at least one isolated point, thus making it non-perfect? | automath |
Lark has forgotten her locker combination. It is a sequence of three numbers, each in the range from 1 to 30, inclusive. She knows that the first number is odd, the second number is even, and the third number is a multiple of X. There could possibly be 2250 combinations that are Lark's. What is the value of unknown var... | tiger_math |
two heavily loaded sixteen - wheeler transport trucks are 1025 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a ,... | tiger_lab_math |
Find the area, in square units, of a triangle with vertices at $(0,0)$, $(6,8)$, and $(9,15)$. Express your answer as a decimal to the nearest tenth. | nvidia_math |
If Casey is considering hiring two employees, one earning $20 per hour and the other earning $22 per hour with a $6 per hour government subsidy for hiring a disabled worker, and both employees will work 40 hours per week, how much money would Casey save per week by hiring the cheaper employee? | tiger_math |
Find the length of the altitude from vertex $Q$ to side $AC$ in triangle $QCA$, in terms of $p$. | tiger_math |
If a box contains \( p \) white balls and \( q \) black balls, and the probability of drawing two white balls without replacement is \( \frac{1}{2} \), where \( q \) is even, what is the minimum total number of balls in the box? | automath |
Find the integer $n,$ $-180 \le n \le 180,$ such that $\sin n^\circ = \sin 700^\circ.$ | tiger_math |
Given a geometric series where the first term is 5 and the common ratio is 3, determine the sum of the first \( n \) terms of this series if the \( n \)-th term equals 10935. | automath |
In a restaurant, one cup of coffee is $6 and a piece of cheesecake x. When buying them together, the client gets a 25% discount. What is the final price of such a set?
If we know the answer to the above question is 12, what is the value of unknown variable x? | tiger_math |
If a boat capsized while carrying 20 sheep, 10 cows, and 14 dogs, and 3 sheep drowned while twice as many cows drowned as sheep, how many animals in total made it to the shore? | tiger_math |
Given two independent Poisson random variables \(X_1\) and \(X_2\) with parameters \(\lambda_1\) and \(\lambda_2\), what is the parameter of the resulting Poisson distribution when you sum \(X_1\) and \(X_2\)? | automath |
The length of a rectangle is three times its width. The perimeter is 160 cm. What is the number of square centimeters in the area of the rectangle? | tiger_math |
Find the coordinates of the critical points of the function \( f(x,y) = -x^4 - 32x + y^3 - 12y + 7 \) and determine whether each critical point is a local minimum, local maximum, or saddle point. | automath |
An airplane travels a distance of 400 km at an average speed of \( x \) km/hr. On the return journey, the speed is increased by 40 km/hr. If the return journey takes 30 minutes less than the onward journey, what is the value of \( x \)? | automath |
Find all real values of $x$ that satisfy $\frac{1}{x+2} + \frac{3}{x+8} \ge \frac25.$ (Give your answer in interval notation.) | tiger_math |
The h.c.f. of two numbers is 15 and the other two factors of their l.c.m. are a certain value and 15. The larger of the two numbers is 225. What is the other factor of their l.c.m.? | tiger_math |
Jerry’s two daughters play softball on different teams. They each have 8 games this season. Each team practices 4 hours for every game they play. If each game lasts for 2 hours, how many hours will Jerry spend at the field watching his daughters play and practice altogether? | tiger_math |
If two letters are chosen at random (without replacement) from the word HORSEBACK, what is the probability that none of the letters are vowels?
Answer Choices: (A) 4/9 (B) 5/9 (C) 5/12 (D) 7/24 (E) 11/36 Let's write a Python program. | tiger_lab_math |
Emily baked 72 cupcakes; Ethan made 34 more than that. Jackson made a third of the amount that Ethan made. How many cupcakes did they bake in all? | nvidia_math |
If $x\circ y=xy+x-y$, evaluate $5\circ 4$. | tiger_math |
Given a constant vector \(\mathbf{A}\) representing the radius of a circular motion and an angular displacement \(\Delta \theta\), if the magnitude of the change in vector \(\mathbf{A}\) is given by \(| \Delta \mathbf{A} | = 2A \sin (\Delta \theta / 2)\), determine the limit of the average velocity of the change in \(\... | automath |
A piece of string fits exactly once around the perimeter of a square whose area is 144 cm². If the string is placed on a scale with a ratio of 1 cm:10 m, how long is the string in meters? | nvidia_math |
Evaluate the integral \( I = \int_0^{\infty} \frac{1}{4x + 7\sqrt{x}} \, dx \) and express the answer in terms of natural logarithms. | automath |
Find the product of the distinct prime factors of 504 that are also factors of 315. | nvidia_math |
A box contains 4 white balls and 4 black balls. I draw them out of the box, one at a time. What is the probability that all of my draws alternate colors? | nvidia_math |
A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
Answer Choices: (A) 10% (B) 12% (C) 14% (D) 20% (E) 22% | tiger_lab_math |
Two trains, each 100 m long, moving in opposite directions, cross other in 6 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Answer Choices: (A) 26 km/hr (B) 17 km/hr (C) 90 km/hr (D) 77 km/hr (E) 46 km/hr | tiger_lab_math |
A line segment begins at $(2, 5)$. It is 10 units long and ends at the point $(x, -3)$ where $x < 0$. What is the value of $x$? | tiger_math |
Given a function $g(t) = \frac{2t}{t-1}$ defined for all real numbers except $t = 1$, find the range of $g$ in interval notation. | nvidia_math |
What is the general solution to the fifth order non-homogeneous differential equation \( y^{(5)} - y(1) = x \)? | automath |
"statement 1": Beltrame said two rival gangs joined forces to launch the attacks ., "statement 2" :Two rival drug gangs collaborated to launch the attacks , he says, "options: " Entailment or neutral? Let's write a Python program. | tiger_lab_math |
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