instruction_seed stringlengths 17 6.7k | source stringclasses 4
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A train 700 m long can cross an electric pole in 40 sec and then find the speed of the train?
Answer Choices: (A) 987 (B) 271 (C) 72 (D) 27 (E) 63 | tiger_lab_math |
Jamie has decided to start harvesting honey from her beehives. She noticed that her two beehives, Hive A and Hive B, produce honey at different rates due to varying bee populations. Hive A produces 5 more pounds of honey than Hive B each month. After six months, Jamie totaled the honey from both hives and found she had... | tiger_math |
Is every Lie group either a matrix Lie group or does it admit a faithful finite-dimensional linear representation, or are there exceptions to this statement? | automath |
In a multi-level parking garage, there are three elevators labeled A, B, and C. Elevator A stops at every 5th floor, Elevator B stops at every 7th floor, and Elevator C stops at every 3rd floor. If the parking garage has 20 floors and all three elevators start at the ground floor, how many floors will be visited by exa... | nvidia_math |
Given that $3^x+ 3^x+ 3^x= 81$, what is the value of $(x + 2)(x - 2)$? | tiger_math |
Determine the smallest positive integer $n$ such that $3^{n+1}$ leaves a remainder of 1 when divided by 41. | nvidia_math |
Lee is saving up for a new pair of sneakers which cost $90. He already has $15 saved. He plans to sell his old action figures to make the rest. If he sells 10 action figures and still has $25 left after buying the sneakers how much did he charge per action figure? | tiger_lab_math |
Carl is taking a class where the whole grade is based on four tests that are graded out of 100. He got an 80, a 75 and a 90 on his first three tests. If he wants an 85 average for the class, what is the minimum grade he needs to get on his last test? | tiger_lab_math |
In which quadrant of the Cartesian plane is the sine function positive, the cosine function negative, and the tangent function also negative? | automath |
Given a dataset with outcomes \(Y\) and predictors \(X_1, X_2\), if we perform quantile regression at three quantiles, \( \tau_1 = 0.25 \), \( \tau_2 = 0.5 \), and \( \tau_3 = 0.75 \), how many different sets of regression coefficients \(\beta_{\tau_1}, \beta_{\tau_2}, \beta_{\tau_3}\) will we estimate from the entire ... | automath |
If there are \( n \) people with masses \( m_1, m_2, \ldots, m_n \) who run up a slope of height \( h \) in times \( t_1, t_2, \ldots, t_n \), and given that the gravitational acceleration \( g \approx 9.81 \, \text{m/s}^2 \), can you calculate the difference in average power calculated using the two methods:
1. \( P_... | automath |
a train running at the speed of 300 km / hr crosses a pole in 15 seconds . what is the length of the train ? | tiger_math |
In the diagram below, $BC$ is 8 cm. In square centimeters, what is the area of triangle $ABC$?
[asy]
defaultpen(linewidth(0.7));
draw((0,0)--(16,0)--(23,20)--cycle);
draw((16,0)--(23,0)--(23,20),dashed);
label("8 cm",(8,0),S);
label("10 cm",(23,10),E);
label("$A$",(23,20),N);
label("$B$",(0,0),SW);
label("$C$",(16,0)... | tiger_math |
Find the sum of all numbers $x$ satisfying $x+25/x = 10.$ | tiger_math |
If $\left\lfloor \frac{n^3}{8} \right\rfloor - \left\lfloor \frac{n}{2} \right\rfloor^3 = 15$, then find all integer values of $n$. | nvidia_math |
The equation $y = -16t^2 + 80t$ describes the height (in feet) of a projectile launched from the ground at 80 feet per second. If the projectile reaches a height of 50 feet for the first time at $t = T$, what is the value of $T$ rounded to the nearest tenth? | tiger_math |
The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
Answer Choices: (A) 58 (B) 59 (C) 62 (D) 70 (E) 74 | tiger_lab_math |
Let
\[\mathbf{B} = \begin{pmatrix} 3 & 2 \\ -5 & -3 \end{pmatrix}.\]
Compute $\mathbf{B}^{50}$. | nvidia_math |
Consider the rational curve C in the projective plane given by the parametrization C: [0,1] → P^2 defined by C(t) = [t^2 − 1 : 2t : t^2 + 1]. Find the degree of the curve C. | tiger_lab_math |
A parabola is defined by the equation y = x^2 + bx + c. The vertex of the parabola is at the point (1, 2), and the parabola passes through the point (0, 1). Find the value of b^2 + c^2. | nvidia_math |
What is the probability of drawing a ticket numbered from 1 to 12 that is a multiple of either 2 or 3? | automath |
In $\triangle XYZ$, the ratio $XY:YZ$ is $2:5$. The bisector of the interior angle at $Y$ intersects $XZ$ at $Q$. The ratio $XQ:QZ$ is $m:n$. Determine the ratio $m:n$. | nvidia_math |
Let \( f(z) = z^2 \). Determine if \( f(z) \) is holomorphic, and if so, demonstrate that its real part \( u(x,y) \) and imaginary part \( v(x,y) \), where \( z = x + iy \), are harmonic functions. Specifically, find the expressions for \( u(x,y) \) and \( v(x,y) \), and verify that they satisfy the Laplace equation. | automath |
A fair coin is flipped 7 times. What is the probability that at least 5 of the flips come up heads? | tiger_lab_math |
Machiavelli added together $1+3i$ and $2-4i$. What number did he get? | tiger_math |
Ernest bought 50 meters of wire and cut it into 5 equal parts. He then used x parts of the wire. 20 meters of wire is not used. What is the value of unknown variable x? | tiger_math |
The value of $\log_{2}{33}$ is between the consecutive integers $a$ and $b$. Find $a+b$. | tiger_math |
In a park, there are two ponds with both brown ducks and green ducks. In the smaller pond, there are 20 ducks, and in the larger pond, there are 80 ducks. If 20% of the ducks in the smaller pond are green and a certain percentage of the ducks in the larger pond are green, then 16% of the ducks are green. What percentag... | tiger_math |
The sum of the present age of Abe and the age before 7 years is 35. Find the present age of Abe. | tiger_math |
A cylindrical water tank is $\frac{1}{5}$ full. If three liters were added, the tank would be $\frac{1}{4}$ full. How many liters does the tank hold when it is full? | tiger_lab_math |
A ball starts at the origin and moves horizontally with a constant acceleration of 0.2 m/s². What is the position of the ball after 15 seconds? | automath |
6 workers should finish a job in 8 days . after 3 days came 4 workers join them . how many days m do they need to finish the same job ? Please respond by writing a program in Python. | tiger_lab_math |
Can you provide an example of a map of schemes \( f: X \to Y \) such that \( f \) is a homeomorphism onto a closed subset of \( Y \), but the induced map on sheaves is not surjective? Additionally, can you explain the significance of this example in relation to the scheme structures? | automath |
if ( a + b ) = 12 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ? Let's write a Python program to solve it. | tiger_lab_math |
The longest of 4 rivers is 250 miles. The second-longest river is 10 miles less than a third of the length of the longest river. The shortest river is 1/5 the length of the second-longest river. How long is the shortest river? | nvidia_math |
If $A,B$ and $C$ are non-zero distinct digits in base X such that $\overline{ABC}_6 + \overline{BCA}_6+ \overline{CAB}_6 = \overline{AAA0}_6$, find $B+C$ in base $6$. The answer is 5. What is the value of unknown variable X? | tiger_math |
A certain number needs to be added to 1782452 to get a number exactly divisible by some number. The number to be added is 48.00000000010186. What is the divisor? | tiger_math |
Given that $n$ is a positive integer, and given that $\mathop{\text{lcm}}[24,n]=72$ and $\mathop{\text{lcm}}[n,27]=108$, what is $n$? | nvidia_math |
Martinez Supermarket has 3000 loaves of bread in stock at the start of the week. On Monday, 1200 loaves were sold, on Tuesday, 800 loaves were sold, and 75 loaves each day for the rest of the week were sold (from Wednesday until Sunday). On Friday, a shipment of 450 loaves arrives. How many loaves of bread does the sup... | nvidia_math |
Define $a \oplus b$ as $2a - b^2$. If $5 \oplus b = 9$, what is the value of $b$? | tiger_math |
Tom has been keeping track of the number of pages he reads each day for a week. He has recorded the following data:
Monday: 23 pages
Tuesday: 18 pages
Wednesday: 21 pages
Thursday: 15 pages
Friday: 20 pages
Saturday: 12 pages
Sunday: 18 pages
If Tom's goal is to read a total of 150 pages by the end of the week, did h... | nvidia_math |
What is $\frac{0.\overline{81}}{0.\overline{18}}$? Express your answer as a common fraction in lowest terms. | tiger_math |
Given a quadratic objective function \( f(x) = x_1^2 + 10x_2^2 \) with the constraints defined by the equations \( c_1(x) = r_i^2 - x_1^2 - x_2^2 \leq 0 \) and \( c_2(x) = x_1^2 + x_2^2 - r_o^2 \leq 0 \), where \( r_i = 10 \) and \( r_o = 20 \), determine the local minimum values of \( f(x) \) within the feasible regio... | automath |
How many multiples of 2 are there between 1 and 58, exclusive?
Answer Choices: (A) 21 (B) 22 (C) 24 (D) 26 (E) 28 | tiger_lab_math |
Aiden's dog drinks a gallon of water every 6 hours. Before leaving for school, Aiden fills his dog's water tank with 4 gallons of water. When he comes home, there are 2 gallons left. How many hours was Aiden away from home? | nvidia_math |
Find the odd man out
445, 221, 109, 46, 25, 11, 4
Answer Choices: (A) 221 (B) 109 (C) 46 (D) 25 (E) 21 | tiger_lab_math |
A 5-person committee is to be formed from a group of 8 people, consisting of 3 men and 5 women. The committee must have at least 2 men and at most 3 women. How many different committees can be formed? | nvidia_math |
a company pays 18.5 % dividend to its investors . if an investor buys rs . 50 shares and gets 25 % on investment , at what price did the investor buy the shares ? | tiger_math |
What is the greatest six-digit perfect square? | automath |
Mark has an egg farm. His farm supplies one store with 5 dozen eggs and another store with 30 eggs each day. How many eggs does he supply these two stores in a week? | tiger_lab_math |
Population of a city in 20004 was 1300000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city at the end of the year 2007
Answer Choices: (A) 354354 (B) 545454 (C) 465785 (D) 456573 (E) 2818075/2 Let's program in Pyth... | tiger_lab_math |
If the age ratio of Halima, Beckham, and Michelle is 4:3:7, and the total age of the three siblings is 126, what is the age difference between Halima and Beckham? | tiger_math |
A student wants to find the average value of the function f(x) = sin(x) on the interval [0, π]. What is the average value of this function on this interval rounded to the nearest hundredth? | tiger_lab_math |
In a particular city, the probability of rain on any given day is 0.3. What is the probability that it will rain at least once during a three-day period in this city? | tiger_lab_math |
Passage: The first run of the magazine was priced at 25 cents for the first fifteen years of its life except for the oversized May/June/July 1924 issue, which was 50 cents. In September 1939 the price was reduced to 15 cents, where it stayed until the September 1947 issue, which was 20 cents. The price went up again ... | tiger_lab_math |
Circle $B$ has its center at $(3, -5)$ and a radius of $7$ units. What is the sum of the $y$-coordinates of the two points on circle $B$ that are also on the $y$-axis? | tiger_math |
Determine the largest value of $n$ such that the sum of the distinct prime factors of $n$ is equal to the number of distinct prime factors of $n!$, where $n!$ denotes the factorial of $n$. | nvidia_math |
When three positive integers are divided by $12$, the remainders are $7,$ $9,$ and $10,$ respectively.
When the sum of the three integers is divided by $12$, what is the remainder? | nvidia_math |
What is the length of the optimal Golomb ruler with 4 ticks? | automath |
Let $\bold{a} = \begin{pmatrix} 7 \\ 4 \end{pmatrix}$ and $\bold{b} = \begin{pmatrix} 2 \\ 9 \end{pmatrix}$. Find the area of the parallelogram with vertices $\bold{0}$, $\bold{a}$, $\bold{b}$, and $\bold{a} + \bold{b}$. | nvidia_math |
A 300 meter long train crosses a platform in some time while it crosses a signal pole in 18 seconds. The length of the platform is 350 meters. How long does it take for the train to cross the platform? | tiger_math |
P and Q started a business investing Rs 75000 and Rs 15000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively? | tiger_math |
Compute
\[\sum_{k = 1}^\infty \frac{6^k}{(3^k - 2^k)(3^{k + 1} - 2^{k + 1})}.\] | nvidia_math |
The function f(x) = |x - 2| + 5 is equal to 7 when x is equal to a and b. What is the sum of a and b? | nvidia_math |
In what ratio must be a grocer mix two varities of tea worth Rs.60 a kg and Rs.65 a Kg so that by selling the mixture at Rs.68.20 a Kg he may gain 10%?
Answer Choices: (A) 3 : 4 (B) 3 : 2 (C) 3 : 5 (D) 4 : 5 (E) None | tiger_lab_math |
Grant scored 10 points higher on his math test than John. John received twice as many points as Hunter who scored a 45 on his math test. What was Grant's test score? Please respond by writing a program in Python. | tiger_lab_math |
Consider the function defined by \( f(x) = -2x^2 + 12x - 3 \).
(i) Express \( -2x^2 + 12x - 3 \) in the form \( 2(x + a)^2 + b \) where \( a \) and \( b \) are constants.
(ii) State the greatest value of \( f(x) \).
(iii) For the function \( g(x) = 2x + 5 \), find the values of \( x \) for which \( g(f(x)) + 1 > 0 \... | automath |
Billy made 49 sandwiches; Katelyn made 47 more than that. Chloe made a quarter of the amount that Katelyn made. How many sandwiches did they make in all? | tiger_lab_math |
In how many ways can a President and a Vice-President be chosen from a group of 5 people (assuming that the President and the Vice-President cannot be the same person)? | tiger_math |
Let \( V \) be a finite-dimensional vector space over the field \( \mathbb{R} \) with dimension \( n \). If \( f : V \to \mathbb{R} \) is a linear functional, what is the maximum possible number of linearly independent linear functionals that can be defined on \( V \)? | automath |
A charge of -12 nC is located at the origin. Calculate the strength of the electric field at the following points:
1. At the position (0 cm, 5.0 cm).
2. At the position (-5.0 cm, -5.0 cm).
3. At the position (-5.0 cm, 5.0 cm).
Provide the numerical values for the electric field strengths at these positions in uni... | automath |
Construct a sequence of functions \( f_n \) such that each function \( f_n \) is of Baire class \( n \) and the sequence converges pointwise to a function \( g \), which is not of any finite Baire class. Additionally, determine if \( g \) can be of Baire class \( n \) for any finite \( n \) and explain your reasoning. | automath |
Tom decides to lease a car. He drives 50 miles on Monday, Wednesday, and Friday, and Sunday for the rest of the days he drives 100 miles. He has to pay $.1 per mile he drives. He also has to pay a weekly fee of $100. How much does he have to pay in a year. | tiger_lab_math |
A long straight wire has a radius of 0.1 cm and carries a current of 2 A. Determine the magnitude of the magnetic field at a distance of 5 cm from the center of the wire, using Maxwell's equations for electromagnetic fields. | tiger_lab_math |
The graph of the equation \[ x^2 + 4y^2 - 10x + 56y = k\]is a non-degenerate ellipse if and only if $k > a.$ What is $a?$ | nvidia_math |
Let \( P \) be the dihedral group \( D_8 \) of order 8. Determine the number of distinct abelian subgroups \( A \) of \( P \) such that the minimum number of generators \( d(A) \) equals the maximum number of generators \( m(P) \). What is this value? | automath |
Given two independent random variables \( X \) and \( Y \), where \( X \) follows a Lognormal distribution with parameters that yield a mean of 10 and a standard deviation of 2, and \( Y \) follows a Normal distribution with mean 5 and standard deviation 2, what is the probability that \( Y \) is greater than \( X \)? | automath |
Let $p$ and $q$ be two prime numbers such that $p^2 + q^2 = 113$. If $\frac{p}{q}$ is equal to $2$ plus the remainder when $p$ is divided by $q$, what is the value of $p$? | nvidia_math |
What is the value of $y$ if $\frac{x}{y}=\frac{12}{5}$ and $x-y=12$? | nvidia_math |
A man is facing northwest. He turns 90 degrees in the clockwise direction and then 135degrees in the anti-clockwise direction. Which direction is he facing now?
Answer Choices: (A) East (B) West (C) North (D) South (E) none | tiger_lab_math |
Given \( n \) points in the plane, you want to determine the optimal placement of two centers that minimizes the sum of the squares of the distances from these points to the centers. Assume an optimal configuration exists. What is the computational complexity of finding this optimal configuration using a brute-force ap... | automath |
A cylindrical can is made of a material whose thickness is negligible. When the radius of the can is increased by 25%, by what percent is the volume of the can increased? | nvidia_math |
Jade had $38 and her sister Julia had half as much money she had. On New Year's eve, their aunt gave each of them an equal amount of money so that they had a total of $97. How much did their aunt give each of them? | nvidia_math |
How many of the numbers from the set $\{1,\ 2,\ 3,\ldots,\ 60\}$ have a perfect cube factor other than one? | nvidia_math |
Audrey's key lime pie calls for 1/4 cup of key lime juice but she likes to double this amount to make it extra tart. Each key lime yields 1 tablespoon of juice. There are 16 tablespoons in 1 cup. How many key limes does Audrey need? | tiger_lab_math |
The volume of a right pyramid with a square base is 256 cubic meters. If the height of the pyramid is 16 meters, what is the perimeter of its base, in meters? | nvidia_math |
In a workshop, the average salary per head of all the workers is Rs. 750. There are 5 technicians with a certain average salary per head and the average salary per head of the rest is Rs. 700. The total number of workers in the workshop is 20. What is the average salary per head of the technicians? | tiger_math |
Rachel is writing an essay. She writes 1 page every 30 minutes. She spends x minutes researching the topic. She writes a total of 6 pages. Then she spends 75 minutes editing her essay. Altogether, how many hours did she spend completing the essay?
If we know the answer to the above question is 5, what is the value... | tiger_math |
Oliver had 135 stickers. He used 1/3 of his stickers, gave 2/5 of the remaining to his friend, and kept the remaining stickers. How many stickers did he keep? Let's write a program. | tiger_lab_math |
What is the limit of the sum of the sequence defined by the reciprocal products of consecutive integers, specifically $\lim_{n \to \infty} \sum_{j=1}^n \frac{1}{j(j+1)}$? | automath |
Four prime numbers are randomly selected without replacement from the first ten prime numbers. What is the probability that the sum of the four selected numbers is odd? Express your answer as a common fraction. Let's write a program. | tiger_lab_math |
x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 36 days . how long will y take to complete the work ? Please respond by writing a program in Python. | tiger_lab_math |
There are 39 dogwood trees currently in the park. Park workers will plant some dogwood trees today and 20 more dogwood trees tomorrow. The park will have 100 dogwood trees when the workers are finished. How many dogwood trees will the workers plant today? | tiger_math |
Given the lotteries defined as follows:
- $L_1 = [a: 0.5, c: 0.5]$
- $L_3 = [c: 1]$
Find a lottery $L_2$ such that:
1. $L_1 \succ L_2 \succ L_3$
2. There exists no probability $p \in (0, 1)$ such that $L_2 \sim [L_1:p, L_3:(1-p)]$.
Additionally, specify your choice of $L_2$, illustrating how it satisfies the condi... | automath |
in a mixture 60 litres , the ra ɵ o of milk and water 2 : 1 . if the this ra ɵ o is to be 1 : 2 , then the quanity of water to be further added is ? Let's write a Python program. | tiger_lab_math |
In a certain diving competition, 5 judges score each dive on a scale from 1 to 10. The point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty. If a dive with a degree of difficulty of 3.2 received scores of 7.5, ... | tiger_lab_math |
What are the homotopy groups \(\pi_n\) of an uncountable infinite wedge of 2-spheres, and how do they compare to the homotopy groups of finite wedges of 2-spheres? | automath |
Given a graph \( G = (V, E) \) where each vertex \( v \in V \) has an associated terraforming cost \( C(v) \in \{0, 1, 2, 3\} \) and a total of \( s \) spades available to spend, what is the maximum size of a connected subgraph \( V^* \subseteq V \) such that the total terraforming cost does not exceed \( s \)? What is... | automath |
15 - nineteenths of 9 - twenty-thirds of a number is 92. What is the square root of 420 per cent of that number? | tiger_math |
Joe went on a diet 4 months ago when he weighed 212 pounds. If he now weighs 188 pounds and continues to lose at the same average monthly rate, in approximately how many months will he weigh 160 pounds?
Answer Choices: (A) 3 (B) 3.5 (C) 4 (D) 4.5 (E) 5 | tiger_lab_math |
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