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A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 24 seconds. What is the length of the goods train?
Answer Choices: (A) 230 m (B) 240 m (C) 260 m (D) 270 m (E) None of these | tiger_lab_math |
Given a firewood storage cabinet designed to support a total weight of 150 kg with a shelf made from 20 mm thick wooden boards, how many hollow round steel rods with a diameter of 10 mm and a wall thickness of 2 mm are required to effectively prevent bending of the shelf, ensuring that the maximum bending stress remain... | automath |
In a single-elimination tournament with 17 teams, how many games need to be played for a winner to be determined, assuming no ties are possible? | tiger_math |
Let $d$ and $e$ denote the solutions of $3x^2+10x-25=0$. Find $(d-e)^2$. Let's write a program. | tiger_lab_math |
Find the x-coordinate of the vertex of the parabola defined by $y=-x^2- 6x + 12$. | tiger_math |
Suppose two players, A and B, are playing a game with the following payoff matrix:
| Player A/Player B | Left | Right |
| --- | --- | --- |
| **Up** | 2,1 | 5,0 |
| **Down** | 0,4 | 3,3 |
If player A chooses Up, what is the best response for player B and what is the Nash Equilibrium of the game? | tiger_lab_math |
Emily bought a shirt and a coat for $600. What does the shirt cost if it is one-third the price of the coat? | tiger_lab_math |
Joey makes 100 pounds of a coffee mix. Columbian coffee selling for 8.75 dollars per pound is mixed with Brazilian coffee selling for a certain price per pound. The final mix sells for 6.35 dollars per pound. Joey used 52 pounds of Columbian coffee in the mix. What is the price per pound of the Brazilian coffee? | tiger_math |
If a population of bacteria doubles every hour, starting with 100 bacteria, how many bacteria will there be after 5 hours? | automath |
Given a 2π-periodic function \( f : \mathbb{R} \to \mathbb{R} \) that is \( C^2 \) and has only simple zeros, how many zeros does \( f \) have in the interval \([0, 2\pi)\) if the value of the integral
\[
\frac{1}{\pi} \int_0^{2\pi} \frac{f'(x)^2}{f(x)^2 + f(x)^2} \, dx + \lim_{x \to 2\pi} \arctan \left( \frac{f(x)}{... | automath |
What is the total length of the Heighway dragon curve after 10 iterations, where the first iteration has a line segment of length 1? | tiger_lab_math |
Let $f(x) = \log_x 10$. Determine the value of $\sum\limits_{k=1}^{10} f(x_k)$ given that $\prod\limits_{k=1}^{10} x_k = 10^3$ and $\sum\limits_{k=1}^{10} x_k = 100$. | nvidia_math |
two employees x and y are paid a total of rs . 590 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ? Let's program in Python in the response. | tiger_lab_math |
x ÷ 4 × 5 + 10 – 12 = 48 , then x = ? Let's program in Python in the response. | tiger_lab_math |
If a student loses 5 kilograms, he will weigh twice as much as his sister. Together they now weigh a certain amount, and the student's present weight is 71 kilograms. What is the combined weight of the student and his sister now? | tiger_math |
What are the coordinates of the point of intersection of the diagonals of a parallelogram with opposite vertices at (1, -5) and (11, 7)? | tiger_math |
Find all numbers in the range of
\[f(x) = \arctan x + \arctan \frac{x - 1}{x + 1},\]expressed in radians. Enter all the numbers, separated by commas. | tiger_math |
Determine the difference between the $x$-intercept and $y$-intercept of the line described by the equation $y+2=-2(x+4)$. | tiger_math |
The average (arithmetic mean) of 10, 30, and 50 is 8 more than the average of 20, 40, and x. What is x?
Answer Choices: (A) 2 (B) 4 (C) 6 (D) 8 (E) 10 | tiger_lab_math |
Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 16% if no discount was offered?
Answer Choices: (A) 17608 (B) 17606 (C) 17604 (D) 17600 (E) 1... | tiger_lab_math |
Functions that aren't invertible can be made invertible by restricting their domains. For example, the function $x^2$ is invertible if we restrict $x$ to the interval $[0,\infty)$, or to any subset of that interval. In that case, the inverse function is $\sqrt x$. (We could also restrict $x^2$ to the domain $(-\infty,0... | nvidia_math |
What is the value of the integral \(\int_{\mathbb{R}^N} \exp\left(-\frac{1}{2} \mathbf{x}^T \mathbf{A} \mathbf{x}\right) d\mathbf{x}\) where \(\mathbf{A}\) is a real symmetric positive definite matrix? | automath |
A florist offers for sale 75 narcissus flowers and 90 chrysanthemums. Using all the flowers, how many bouquets containing 5 flowers each can he make? | tiger_math |
What is the decimal equivalent of the number $10101_3$? | tiger_math |
What is the greatest common divisor of $39$ and $91$? | nvidia_math |
Given a piecewise-defined function f(n) = {
n/2 if n is even,
2n + 1 if n is odd,
Suppose f(f(f(f(9)))) = n and n > 100, what is the greatest integer value of n? | nvidia_math |
Given a group of \( n \) prisoners, each wearing a hat of one of \( n \) different colors, and each prisoner can see the hats of all the others except his own, what is a strategy that allows at most one prisoner to guess incorrectly about the color of his own hat? In this context, if the first prisoner announces a colo... | automath |
on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 20 miles on saturday and sunday , how many miles did bill run on sunday ? | tiger_math |
Will initially had twenty-eight bottles of water. He drank seven bottles each day, shared three bottles with his friends every two days, and bought an extra five bottles every three days. How many days would the bottles last him? | tiger_math |
A game consists of drawing a card from a standard deck of 52 cards. If the card drawn is a king, the player wins $\$10$. If the card drawn is a queen, the player loses $\$5$. If the card drawn is any other card, the player wins $\$1$. What is the expected value of the player's winnings after one draw, in dollars? Expre... | nvidia_math |
What is the largest possible median for the five number set $\{x, 2x, 3, 2, 5\}$ if $x$ can be any integer? | nvidia_math |
Find how many positive integers less than 10,000 are there suchthat the sum of the digits of the no. is divisible by 3?
Answer Choices: (A) 1256 (B) 2354 (C) 2678 (D) 3334 (E) 3568 | tiger_lab_math |
Given a sequence of positive integers \( A_1, A_2, \ldots, A_N \), let \( d = \gcd(A_1, A_2, \ldots, A_N) \). Determine the maximum number of elements that can be removed from the sequence such that the GCD of the remaining elements is equal to \( d \). If it is possible to remove all but one element while maintaining ... | automath |
What is the probability that in two independent quizzes, each with 5 multiple-choice questions, a student gets exactly 7 correct answers if the first quiz has 4 choices per question and the second quiz has 5 choices per question, assuming the student answers purely by guessing? | automath |
Let \( X \) and \( Y \) be independent random variables uniformly distributed on the interval \([0, 1]\). Define \( Z = X + Y \).
1. Calculate the probability density function \( f_Z(z) \) for \( Z \) over the range \( z \in [0, 2] \).
2. Specifically, find \( f_Z(z) \) for the following intervals:
- \( 0 < z < 1 ... | automath |
at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 10 pencils and 8 charts have been brought to the meeting , how many... | tiger_math |
Jamie and Oliver are planning to go on a vacation. A plane ticket costs $24 for each person and a hotel stay costs $12 for each person per day. They also need to consider meals expenses which cost $15 per person per day and transportation costs which are $20 per person for the entire trip. Additionally, they plan to pa... | tiger_math |
What is the least value of x, So that 2x5475 is divisible by 9
Answer Choices: (A) 7 (B) 8 (C) 4 (D) 3 (E) 2 | tiger_lab_math |
The graphs of $y = 2x^2 + ax - 2$ and $y = x^2 - 1$ intersect in two points. Find the value of $a$ for which the line passing through these two points has a slope of $3$. | nvidia_math |
If a certain number of labours can dig earth 100m deep, 25m long, and 30m broad in 12 days, then find the number of days the same number of labours will require to dig earth 75m deep, 20m long and 50m broad.
Answer Choices: (A) 12 (B) 18 (C) 6 (D) 1 (E) 2 | tiger_lab_math |
A hardware store sold 10 graphics cards, 14 hard drives, 8 CPUs, and 4 pairs of RAM in one week. The graphics cards cost $600 each, hard drives cost $x each, CPUs cost $200 each, and RAM cost $60 for each pair. How much money did the store earn this week?
If we know the answer to the above question is 8960, what is the... | tiger_math |
A function $g$ is defined for all positive integers $n$ and satisfies the following conditions:
* $g(1) = 2$
* For any positive integer $n$, $g(n+1) = 2g(n) - 1$
* For any two distinct positive integers $m$ and $n$, the ratio $\frac{g(m)}{g(n)}$ is not an integer.
What is the value of $g(5)$? | nvidia_math |
The length of the longest rod that can fit in a cubical room of 4 m side is?
Answer Choices: (A) 6.978 m (B) 6.928 m (C) 6.829 m (D) 6.248 m (E) 6.982 m | tiger_lab_math |
Calculate the number of ways to choose 3 students from a class of 15. | tiger_math |
Given a concave function \( f : \mathbb{R}^n_{\ge 0} \to \mathbb{R}^n \) such that \( f(0) = 0 \) and \( f(a) \ge 0 \) for some \( a \in \mathbb{R}^n_{\ge 0} \), under what conditions is the set \( P = \{ x \in \mathbb{R}^n_{\ge 0} \mid 0 \le f(x) \le f(a) \} \) path-connected? Specifically, can you determine a criteri... | automath |
If n and k are integers whose product is 2500, which of the following statements must be true?
Answer Choices: (A) n+k>0 (B) n does not equal k (C) Either n or k is a multiple of 10 (D) If n is even, then k is odd (E) If n is odd, then k is even | tiger_lab_math |
A triangle has one angle measuring 52 degrees and two sides measuring 8 meters and 10 meters. Find the perimeter of the triangle using trigonometry. | tiger_lab_math |
A circular garden has a diameter of 10 meters. What is the perimeter of the garden? | tiger_lab_math |
Nancy replaced all of the old vinyl tiles in her bathroom with new hardwood flooring. She replaced flooring in two areas of the bathroom: a 10 foot by 10 foot central area, and a 6 foot by x foot hallway. How many square feet of hardwood flooring did Nancy install in her bathroom?
If we know the answer to the above q... | tiger_math |
Consider the following nonlinear differential equation:
$$ \frac{dy}{dx} = \sin(y) $$
Starting from the initial condition $y(0)=\pi/2$, what is the value of $y$ when $x=\pi$ with an accuracy of $0.01$ using the fourth-order Runge-Kutta method? | tiger_lab_math |
Find the greatest common divisor of three positive integers, x, y, and z, if their product is 9000 and x, y, and z are pairwise relatively prime. | nvidia_math |
What must be the value of the coefficient $c$ in $P(x)=x^3+2x^2+cx+10$, in order for $x-5$ to be a factor of $P$? | nvidia_math |
What is the total number of distinct ways to paint the faces of a regular icosahedron with 20 distinct colors, given that no two adjacent faces can have the same color? | automath |
Susie babysits every day for 3 hours a day at the rate of $10 per hour. She spent 3/10 of the money she earned from last week to buy a make-up set. She then spent 2/5 of her money on her skincare products. How much is left from her earnings last week, in dollars? | tiger_lab_math |
Given a ball in free fall from a height \( h \) under the influence of gravity \( g \), derive a formula for the time \( t \) it takes for the ball to reach the ground using dimensional analysis. Provide the final expression for \( t \) in terms of \( h \) and \( g \). What is the expression you derive? | automath |
A bus stops for taking passengers. The speed of the bus with stoppages is 36 km/hr and without stoppages is 45 km/hr.For how many minutes bus stopped per hour?
Answer Choices: (A) 10 min (B) 11 min (C) 12 min (D) 13 min (E) None of these | tiger_lab_math |
What is the sample standard deviation of the following five test scores: 42, 31, 67, 50, and 45? | automath |
Cara has 60 marbles in a bag. 20 of them are yellow, half as many are green, and the remaining marbles are equally divided between red and blue. If Cara picks a marble at random, what are the odds it's blue (expressed as a percentage)? Please write a program to solve it | tiger_lab_math |
A manufacturer claims that the mean weight of their cereal boxes is 15 ounces with a standard deviation of 0.5 ounces. A consumer advocacy group believes that the actual weight is less than this and randomly samples 36 boxes, finding an average weight of 14.8 ounces. Is there sufficient evidence at the 5% significance ... | tiger_lab_math |
Find the sum of all positive integers less than 1000 that are not divisible by 2, 3, or 5. | nvidia_math |
The graph of the function $f(x)$ is shown below. How many values of $x$ satisfy $f(f(x)) = 3$? [asy]
import graph; size(7.4cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-4.4,xmax=5.66,ymin=-1.05,ymax=6.16;
for(int i = -4; i <= 5; ++i) {
draw((i,-1)--(i,6), dashed+med... | tiger_math |
Solve the system of linear equations for x, y, and z:
- 3x + 2y - z = 4
- 6x + 4y - 2z = 8
- 9x + 6y - 3z = 12
What is the solution for the equation set above? | tiger_lab_math |
How many edges are present in a disconnected simple graph consisting of three components, where the first component has 3 vertices fully connected to each other, the second component has 2 vertices connected by one edge, and the third component consists of a single isolated vertex? | automath |
If $(x,y)$ is a solution to the system
\begin{align*}
x+y &= a, \\
xy &= b,
\end{align*}find $x^2 + y^2.$ | nvidia_math |
James invested $5000 in scheme A for 1 year at a simple annual interest rate of 5% and invested another $10000 in scheme B for 1 year at an annual interest rate of 10% compounded semi-annually. What is the positive difference between the interest earned by James from scheme A and scheme B? | automath |
The equation $x^2 - (1A)x + A0 = 0$ has positive integer solutions where $A$ is a positive single digit. How many such $A$s exist? (Since $A$ is representing a digit, if $A = 2$ then $A0$ represents the integer 20.) | tiger_math |
If $2010a + 2014b = 2018$ and $2012a + 2016b = 2020$, what is the value of $a - b$ ? | nvidia_math |
The greatest number by which the product of three consecutive multiples of 2 is always divisible is
Answer Choices: (A) 48 (B) 76 (C) 152 (D) 162 (E) None of these | tiger_lab_math |
Let $\mathcal{E}$ be the ellipse in the plane determined by the equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. Suppose a circle $\mathcal{C}$ intersects $\mathcal{E}$ at four distinct points. If three of these points are $(-a,0),$ $(0,b),$ and $(a,0),$ find the area of the quadrilateral formed by all four of the int... | nvidia_math |
Peter and Kristin are to read 20 fantasy novels each in a week. Peter can read three times as fast as Kristin. If Peter reads one book in 18 hours, how long will Kristin read half of her books? Please respond by writing a program in Python. | tiger_lab_math |
If the positive numbers $x$, $y$, $z$ and $w$ satisfy
$x+y+z+w=4$,
then compute the maximum value of
$\ds\f{x}{y} \cdot \ds\f{y}{z} \cdot \ds\f{z}{w} \cdot \ds\f{w}{x}$. | nvidia_math |
What is the probability of rolling a sum of 7 with two standard six-sided dice? | tiger_lab_math |
What is $\dbinom{n}{2}$ for any positive integer $n$? | nvidia_math |
Haleigh needs to buy leggings for her pet animals. She has 4 dogs and 3 cats. How many pairs of leggings does she need? | tiger_math |
A certain number of loggers can cut down 6 trees per day. The forest is a rectangle measuring 4 miles by 6 miles, and each square mile has 600 trees. If there are 30 days in each month, it takes these loggers 10 months to cut down all the trees. How many loggers are working to cut down the trees? | tiger_math |
On a Cartesian plane, a set of $n$ points is randomly chosen such that there are no three collinear points. For each point $P$ in the set, we denote $f(P)$ as the number of triangles whose vertices are among the $n$ points and contain $P$ as one of the vertices. It is observed that the average value of $f(P)$ over all ... | nvidia_math |
Expand the product ${(x^2+3x-1)(x^2-2x+4)}$ using the distributive property and combine like terms. | nvidia_math |
Let $f(x)$ and $g(x)$ be two polynomials with integer coefficients such that the greatest common divisor of $f(x)$ and $g(x)$ is $x^2+2x+1$, and the least common multiple of $f(x)$ and $g(x)$ is $(x^2+2x+1)(x^2-7x+12)$. If $f(1)=g(1)=2$, find $f(-1)+g(-1)$. | nvidia_math |
What is the new function obtained by shifting the graph of \( y = \sqrt{3x - x^2} \) two units to the right, and what are the x-intercepts of the transformed graph? | automath |
James can buy a new computer for $600 and have it last 6 years, or buy 2 used computers for $200 each that each last 3 years. How much money will he save by picking the cheaper option? | tiger_math |
Let $S$ be the sum of all positive integers less than $5!$ that are not divisible by $3$. Find the remainder when $S$ is divided by $5!$. | nvidia_math |
A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives?
Answer Choices: (A) 14700 (B) 15700 (C) 16700 (D) 18700 (E) 24700 | tiger_lab_math |
A company produces two products, X and Y. The profit for product X is $5 per unit and for product Y is $7 per unit. The production constraints demand that production of product X can't exceed 500 units while production of product Y can't exceed 400 units. The production process also requires that for every unit of X pr... | tiger_lab_math |
There is a playground that is surrounded by a square fence that has a side length of 27 yards. There is a 12 yard by 9 yard garden that has fencing around it. How many yards of fencing do the playground and garden have together? | tiger_lab_math |
What is the sum of the matrices $\begin{pmatrix} 3 & 0 \\ 1 & 2 \end{pmatrix}$ and $\begin{pmatrix} -5 & -7 \\ 4 & -9 \end{pmatrix}$? | tiger_math |
Jean has 60 stuffies. She keeps 1/3 of them and then gives away the rest. She gives 1/4 of what she gave away to her sister Janet. How many stuffies did Janet get? | tiger_math |
Given the net income of Jonick Company is $248,000 and the average total stockholders' equity for 2019 is calculated as $\frac{2,675,000 + 2,447,000}{2}$, what is the exact value of the average total stockholders' equity, and what is the calculated Return on Equity (ROE) expressed as a percentage? | automath |
The sum of the three sides of a triangle is 50. The right side of the triangle is 2 cm longer than the left side. Find the value of the triangle base if the left side has a value of 12 cm. | tiger_math |
Which of the following is the equation of the line in the xy-plane that has slope 0
(I) x = 2
(II) y = 6
(III) x + y = 0
Answer Choices: (A) II &III (B) III (C) I and II only (D) I (E) II | tiger_lab_math |
For the functions \( f(x) = e^x \), \( g(y) = \sin(y) \), \( h(\alpha) = \tan(\alpha) \) (defined on the interval \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)), \( i(u) = \cos(u) \), and \( j(x) = 42 \), classify each function as even, odd, or non-symmetric. What are the classifications for all five functions? Prov... | automath |
there are , in a certain league , 20 teams , and each team face another team for a total of 10 times . how many games are played in the season ? Please respond by writing a program in Python. | tiger_lab_math |
If a Bayesian posterior predictive p-value is calculated to be exactly 0.5, what can we conclude about the relationship between the observed data and the model being used? In particular, how does this value indicate the model's predictive performance compared to a situation where the p-value is much larger (e.g., 0.8) ... | automath |
Find the point on the sphere defined by the equation $x^2 + y^2 + z^2 = 9$ that is closest to the point $(3,4,5)$. | nvidia_math |
Let \( A \) be a ring and \( K \) a finitely generated \( A \)-module. Given the exact sequence \( 0 \to K \to A^{\oplus m} \to M \to 0 \), can you determine the structure of the module \( J/J^2 \) in terms of \( K \) and \( C = \text{Sym}^*_A(M) \)? Specifically, what is the relationship between \( (J/J^2)_d \) and \(... | automath |
The side of a square has the length $(x-2)$, while a rectangle has a length of $(x-3)$ and a width of $(x+4)$. If the area of the rectangle is twice the area of the square, what is the sum of the possible values of $x$? | tiger_lab_math |
What are the eigenvalues of the matrix \( A=\begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix} \) and what are their geometric multiplicities? | automath |
Given a quantum state where the probability of measuring spin up along the z-axis is 50%, what can be concluded about the amplitudes of the components \(\alpha_u\) and \(\alpha_d\) without additional information? Specifically, can we determine their individual values, or are there multiple valid combinations of these a... | automath |
There were 18 stamps in Parker’s scrapbook. If Addie put one fourth of her 72 stamps in Parker’s scrapbook, how many stamps does he have now? | tiger_math |
Bethany loved riding horses. She rode 1 hour after school every Monday, Wednesday, and Friday. On Tuesday and Thursday, she rode for 30 min and on Saturdays, she could ride for 2 hours. How many hours in total did she ride over a 2 week period? | tiger_math |
Emma is trying to organize her collection of stickers into albums. When she tries to divide her stickers equally among 4, 5, or 9 albums, she finds that she always has exactly 3 stickers left over. Assuming Emma has more than three stickers, what is the smallest possible number of stickers that Emma could have in her c... | tiger_math |
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