instruction_seed stringlengths 17 6.7k | source stringclasses 4
values |
|---|---|
A person standing on the ground observes a hot air balloon at an angle of elevation of 45°. If the person is standing 100 meters away from the point where the hot air balloon is directly above, find the height of the hot air balloon from the ground. | tiger_lab_math |
Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for his new house. Each TV costs $200 more than the size below it. Alan spends a total of $3,800. How much would he have spent if he had bought only the 28 inch and 30 inch TVs?
Answer Choices: (A) 850 (B) 1,100 (C) 1,900 (D) 2,550 (E) 3,400 Please respon... | tiger_lab_math |
In an interschool athletic meet, there are 24 individual events. A total of 56 points were awarded, with a first place securing 5 points, a second place securing 3 points, and a third place securing 1 point. If the number of athletes who finished in third place is equal to the total number of athletes who finished in f... | automath |
the average height of 35 boys in a class was calculated as 180 cm . it has later found that the height of one of the boys in the class was wrongly written as 156 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . Let's writ... | tiger_lab_math |
Find the value of $\cos 135^\circ$ using the half-angle formula for cosine. | nvidia_math |
If each edge of a cube is increased by 50%, find the percentage increase in its surface area. | tiger_math |
Let \( f(x) = x^3 - 3x + 2 \). If \( a = -2 \) and \( b = 2 \), verify whether the conditions of Rolle's Theorem are satisfied for \( f \) on the interval \([-2, 2]\) and, if applicable, find the value(s) of \( c \) in the interval \((-2, 2)\) such that \( f'(c) = 0 \). What are the values of \( c \)? | automath |
In the polygon shown, each side is perpendicular to its adjacent sides, and all 28 of the sides are congruent. The perimeter of the polygon is 56. Find the area of the polygon.
[asy]
unitsize(0.5 cm);
draw((3,0)--(4,0)--(4,1)--(5,1)--(5,2)--(6,2)--(6,3)--(7,3)--(7,4)--(6,4)--(6,5)--(5,5)--(5,6)--(4,6)--(4,7)--(3,7)... | nvidia_math |
Erika and her 3 siblings are drawing with chalk outside. Another 3 friends join them and ask if they can help with the drawing. Erika loses 2 pieces of chalk as they are counting and the group realizes there isn't enough chalk for everyone. Erika’s mom brings out another 12 pieces of chalk for them to share and there i... | tiger_lab_math |
What is the running time of the best known algorithm for counting the number of perfect matchings in a $k$-regular hypergraph with $n$ vertices and edges of size $k$, and how does this time complexity relate to the parameters $n$ and $k$? | automath |
Aunt Emma baked 375 brownies. She gave 18 brownies to Olivia, 25 brownies to Jackson, saved some in the freezer, and gave the rest to Ethan. How many brownies did she put in the freezer if she gave three times as many brownies as she gave Olivia to Ethan? | nvidia_math |
There have been 15 "Where's Waldo?" books published. Each book has 30 puzzles to find Waldo. The average person takes 3 minutes to find Waldo in a puzzle. How long would it take to find every Waldo? | tiger_lab_math |
If
\[(1 + \tan 1^\circ)(1 + \tan 2^\circ)(1 + \tan 3^\circ) \dotsm (1 + \tan 45^\circ) = 2^n,\]then find $n.$ | tiger_math |
What is the maximum number of completely linked subsets \( A_i \) that can be constructed in a partition of \( \mathbb{R}^2 \) into countably infinite pairwise disjoint connected subsets \( A_i \) such that \( A_i \cup A_j \) is connected for any \( j \notin \{i-1, i, i+1\} \)? | automath |
What is the additional average transmission rate, in bits per sample, required when using uniform quantization prior to entropy coding compared to the theoretically optimum transmission scheme for a continuous-amplitude memoryless source, given that this additional rate is 0.255 bits/sample? | automath |
What is the greatest common divisor of 75 and 360? | tiger_math |
Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 3% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
Answer Choices: (A) 2:9 (B) 2:7 (C) 1:6 (D) 1:4 (E) 1:3 Let's write a program. | tiger_lab_math |
Sofia earns a 20% commission on every electronic device she sells. In one day, she sells 3 laptops for $1,000 each, 8 tablets that cost $200 each, and 4 smartwatches that are $80 each. How much commission does Sofia earn? | nvidia_math |
the length of the bridge , which a train 110 metres long and travelling at 45 km / hr can cross in 30 seconds , is ? Please write a program to solve it | tiger_lab_math |
Find the rank of the following matrix:
A =
1 2 3
4 5 6
7 8 9 | tiger_lab_math |
Every morning, Lucas bikes along a path by the river traveling east. His speed in mph (miles per hour) after t hours is described by the polynomial \( s(t) = 4t^2 + 3t + 15 \). How far does Lucas travel in total if he bikes from morning to noon (a 5-hour period)? | tiger_math |
What is the average distance between two pieces of space debris in low Earth orbit, assuming there are 170 million pieces uniformly distributed within a volume of approximately 1.3 x 10^12 km³? | automath |
In a league with 8 teams where each team plays every other team exactly once, how many total games are played? Please provide the final answer along with your reasoning for the solution. | automath |
A water tank can hold 1000 liters of water. On the first day, 10 liters of water are added to the tank. On each subsequent day, the amount of water added to the tank is twice the amount added on the previous day. On which day will the tank be filled to capacity? | nvidia_math |
Of the teams competing in the world archery championships, Forty percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa.
Answer Choices: (A) 13/20 (B) 15/20 (C) 13/15 (D) 7/20 (E) 13/17 | tiger_lab_math |
Given a fixed integer \( N \) corresponding to an \( N \)-parallelogram defined by the points \( N+1 \), \( N+11 \), \( N+49 \), and \( N+59 \), how many integers in the positions on this \( N \)-parallelogram that are not prime numbers are also divisible by \( 7 \)? Specifically, what would be the exact values of thes... | automath |
Let $P$ be a point inside triangle $ABC$ such that $\overrightarrow{P}=p\overrightarrow{A}+q\overrightarrow{B}+r\overrightarrow{C},$ where $p,$ $q,$ and $r$ are constants such that $p+q+r=1.$ Suppose that $BP$ bisects angle $ABC$ and $CP$ bisects angle $BCA.$ Given that $AB=6,$ $BC=7,$ and $AC=8,$ find the ordered tr... | nvidia_math |
Consider the system of equations given by
$$\frac{d\mathbf{F}_1}{d t}=\left[\mathbf{F}_1 \times \mathbf{G}_1 \right]$$
$$\frac{d\mathbf{F}_2}{d t}=\left[\mathbf{F}_2 \times \mathbf{G}_2\right],$$
where
$$\mathbf{G}_1 = \mathbf{F}_2 -\hat{i}(\hat{i}\cdot\mathbf{F}_1)$$
$$\mathbf{G}_2 = \mathbf{F}_1 -\hat{i}(\hat... | automath |
Samantha, Aira, and Joe received 6 rubber bands each after they divided their bands equally. If Samantha had 5 more bands than Aira and Aira had 1 fewer band than Joe, how many rubber bands did Aira have? | tiger_lab_math |
Given the functions \( f(x, y, z) = z \) and \( g(x, y, z) = x^2 - y^2 + z \), find the values of \( (x, y, z) \) that satisfy \( \nabla f(x, y, z) = \delta \nabla g(x, y, z) \) for some constant \( \delta \), and verify whether these points correspond to extremal points of \( f \) under the constraint \( g(x, y, z) = ... | automath |
Find the remainder when the binary number $101110110_2$ is divided by $1001_2$. Express your answer in base 2. | nvidia_math |
Let \( g_0(z) \) be a true regression function, and consider a model class \( \mathcal{G} \) from which a function \( g \) is selected using the penalized least squares estimator given by
\[
\widehat{g}_n = \arg \min_{g \in \mathcal{G}} \left\{ \|Y - g\|^2 + \text{pen}^2(g) \right\},
\]
where \( Y_i = g_0(z_i) + W_i... | automath |
Evaluate $\lfloor\sqrt{17}\rfloor^2$. | tiger_math |
If we know that the solutions to the equation \[\sqrt{x + 3 - 4 \sqrt{x - 1}} + \sqrt{x + 8 - 6 \sqrt{x - Y}} = 1\] are [5,10], what is the value of unknown variable Y? | tiger_math |
A fair six-sided die is rolled three times. Let $p$ be the probability that the sum of the three rolls is a multiple of $4$. If each of the three rolls is independent of the others, find $p$. Express your answer as a common fraction. | nvidia_math |
The integer $m$ is between $20$ and $70$ and is a multiple of $7$. When $m$ is divided by $9,$ the remainder is $3$. Similarly, when $m$ is divided by $4,$ the remainder is $3$. What is the value of $m$? | tiger_math |
Let $p(x)$ be a monic polynomial of degree 6 such that $p(1) = 1,$ $p(2) = 2,$ $p(3) = 3,$ $p(4) = 4,$ $p(5) = 5,$ and $p(6) = 6.$ Find $p(7).$ | nvidia_math |
If Shelly has ten $10 bills and four fewer $5 bills than the $10 bills, what is the total amount of money that Shelly has? | tiger_math |
I run 12 miles in 90 minutes. What is my average speed in miles per hour? | tiger_math |
If the channel bandwidth of a communication system is doubled while maintaining the same rate of information transmission, what will be the new signal-to-noise ratio in terms of the original signal-to-noise ratio \( \text{SNR}_1 \)?
Provide the expression for the new signal-to-noise ratio \( \text{SNR}_2 \) based on ... | automath |
The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 13. What is the last numbers?
Answer Choices: (A) 7 (B) 6 (C) 5 (D) 4 (E) 3 | tiger_lab_math |
Find: S.l. on Rs 6250 at 14% per annum for 146 days.
Answer Choices: (A) Rs.350 (B) Rs.450 (C) Rs.550 (D) Rs.650 (E) Rs.600 | tiger_lab_math |
Determine the value of $\cot 45^\circ$. | tiger_math |
there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 68 % | tiger_math |
A family had 10 eggs, but the mother used 5 of them to make an omelet. Then, 2 chickens laid 3 eggs each. How many eggs does the family have now? | tiger_math |
there are 1200 jelly beans divided between two jars , jar x and jar y . if there are 400 fewer jelly beans in jar x than 3 times the number of beans in jar y , how many beans are in jar x ? Let's write a Python program to solve it. | tiger_lab_math |
What is the greatest three-digit multiple of 19? | nvidia_math |
Consider the differential equation \(y'' + \omega^2 y = 0\). Find the general solution to this equation, and then solve the initial value problem given by \(y(0) = 1\) and \(y'(0) = 0\). What is the specific solution for this initial value problem? | automath |
What is the total area, in square yards, of carpet needed to cover the floor of a rectangular room measuring 12 feet by 6 feet? | tiger_math |
Passage: Social Securitys benefit formula provides 90% of average indexed monthly earnings (AIME) below the first "bend point" of $791/month, 32% of AIME between the first and second bend points $791 to $4781/month, and 15% of AIME in excess of the second bend point up to the Ceiling cap of $113,700 in 2013. The low in... | tiger_lab_math |
If a coin has a success probability \( p = 0.3 \) of landing heads, what is the expected number of flips required to get the first heads, and what is the variance of the number of flips needed? | automath |
Given a linear relationship represented by a set of points in a scatter diagram that declines from left to right, let the slope of the line be \( m \). If the line passes through the points \( (1, 3) \) and \( (5, -1) \), what is the value of the slope \( m \)? | automath |
What is the remainder when $(x - 1)^{2011}$ is divided by $x^2 - x + 1$? | tiger_math |
What is the correct formula to calculate the overall average time to process a page in a category, given the average processing time for each document and the total number of pages in each document? | automath |
A man spends 2/5 of his salary on house rent,3/10 of his salary on food and 1/8 of his salary on conveyence.if he has Rs.1400 left with him,find his expenditure on food and conveyence.
Answer Choices: (A) 800 (B) 900 (C) 100 (D) 700 (E) 500 | tiger_lab_math |
Caprice is taking piano lessons. Her mother pays the teacher $10 for every half-hour of teaching her daughter. If Caprice is taking one lesson per week, and the lesson lasts 1 hour, how much money would the teacher earn in 5 weeks? | tiger_math |
A snail is slowly making its way up a garden path that is divided into sections, each labeled with a number in base 5. The snail starts at the section labeled $23_5$ and slides down to the section labeled $17_5$, then back up to the section labeled $34_5$, and finally back down to the section labeled $25_5$. How many s... | nvidia_math |
What is the minimum number of production rules needed to define a context-free grammar for the language
$$L = \{x \in L(a^∗b^∗c^∗) : |x|_a > |x|_c; |x|_b > 0; |x|_c ≥ 0\}$$
such that for any string generated, the number of 'a's is greater than the number of 'c's, and there is at least one 'b'? | automath |
A searchlight on top of the watch-tower makes 3 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least some seconds, given that the probability is 0.25? | tiger_math |
A certain compound has a molecular weight of 56 and consists of an element with an atomic weight of 40 combined with another element. The other element has an atomic weight of 16. What is the other element in the compound? | tiger_math |
Determine the value of $\cos 315^\circ$. | tiger_math |
Given a bandpass signal centered at 2 MHz with a bandwidth of 50 kHz, sampled at 10 MHz, how many samples do I need to obtain a frequency resolution of 100 Hz using the FFT, and what should be the size of the FFT points required to achieve this resolution? | automath |
Let $C$ be the circle with equation $x^2+10y+45=-y^2-8x$. If $(a,b)$ is the center of $C$ and $r$ is its radius, what is the value of $a+b+r$? | tiger_math |
Consider the sequence defined by the terms 7, 2, -3, -8, -13.
1. Write an explicit formula for this sequence.
2. Using your explicit formula, calculate the 14th term of the sequence, \( a_{14} \). | automath |
In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
Answer Choices: (A) 20 (B) 99 (C) 88 (D) 27 (E) 21 | tiger_lab_math |
The number of diagonals of a regular polygon is subtracted from the number of sides of the polygon and the result is zero. What is the number of sides of this polygon?
New problem:
In a certain polygon, the number of diagonals is three times the number of sides. Determine the number of sides of this polygon. | nvidia_math |
what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular decagon ( 10 - sided polygon ) ? Let's write a Python program to solve it. | tiger_lab_math |
A rectangle has sides of length 8 and 12, and a circle centered at one of its corners has radius 6. What is the area of the union of the regions enclosed by the rectangle and the circle? Express your answer in terms of $\pi$. | nvidia_math |
Consider the reaction-diffusion equation:
$\frac{\partial u}{\partial t} = D\frac{\partial^2 u}{\partial x^2} + \alpha u - \beta u^2$
where $u(x,t)$ is the concentration of a chemical substance in a medium, $D$ is the diffusivity, $\alpha$ and $\beta$ are reaction rate constants.
Find the steady-state solution for $... | tiger_lab_math |
A rectangular prism has a square base with a side length of 14 centimeters. If the volume of the prism is $686\pi$ cubic centimeters, what is the height of the prism? | tiger_math |
Lily's Bookstore sold 60 books on its first day. On their second day, they sold 25 more books than they did on their first day. On the third day, they sold 15 less than twice the books that were sold on the second day. If the bookstore sold a total of 420 books for 4 days, how many books were sold on the 4th day? | nvidia_math |
In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Answer Choices: (A) 3 km/hr (B) 4 km/hr (C) 5 km/hr (D) 6 km/hr (E) 8 km/hr Let's program in Python in the response. | tiger_lab_math |
In how many ways can a president and a 2-person committee be chosen from a group of 8 people (where the order in which we choose the 2 people doesn't matter)? (The president cannot be on the committee.) | nvidia_math |
Compute $\arcsin X Express your answer in radians.
If we know the answer to the above question is 0, what is the value of unknown variable X? | tiger_math |
If Sarah purchased 12 caramel-filled lollipops for a total of 3 dollars and offered to share one-quarter of them with her friend Julie, but Julie insisted on reimbursing Sarah for the shared lollipops, how much money did Julie give Sarah, in cents, to pay for the shared lollipops? | tiger_math |
Tom is planning a road trip from City A to City B. The distance between the two cities is 240 miles. Tom's car gets an average fuel economy of 30 miles per gallon. If gas costs $\$2.50$per gallon, and Tom has a budget of$\$100$ for gas, will he have enough money to complete the trip? | nvidia_math |
Find the smallest prime divisor of 13! - 14! | nvidia_math |
A town has ten neighborhoods, each having x roads passing through them. Each of the roads has 250 street lights on each opposite side. Calculate the total number of street lights on all the roads of the neighborhoods in the town.
If we know the answer to the above question is 20000, what is the value of unknown variabl... | tiger_math |
A plane flies 880 km with the wind and 720 km against the wind in the same length of time. If the speed of the wind is 20 km/h, what is the speed of the plane in still air?
Answer Choices: (A) 140 km/h (B) 160 km/h (C) 180 km/h (D) 200 km/h (E) 220 km/h | tiger_lab_math |
Consider the set \( S = \{2, 3, 5, 7, 11\} \). If you construct an array \( q \) such that \( q \) contains only prime numbers satisfying the properties mentioned (each element \( q_i \) must have \( \gcd(q_i, q_j) = 1 \) for \( i < j \)), what would be the maximum size of \( q \) if you were to add elements from \( S ... | automath |
Ginger owns a flower shop, where she sells roses, lilacs, and gardenias. On Tuesday, she sold three times more roses than lilacs, and half as many gardenias as lilacs. If she sold 10 lilacs, what is the total number of flowers sold on Tuesday? | tiger_math |
how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 112 m length ? Let's program in Python in the response. | tiger_lab_math |
The difference of two numbers is a certain value. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. The larger number is 1656. What is the difference between the two numbers? | tiger_math |
Three workers have different hourly rates for their regular pay. Worker A has a regular pay of $5 per hour up to 40 hours, worker B has a regular pay of $6 per hour up to 40 hours, and worker C has a regular pay of $7 per hour up to 40 hours. Overtime pay for each worker is twice their regular hourly rate. If the total... | tiger_math |
On the complex plane consider five points $A$, $B$, $C$, $D$, and $E$ with $AB= BC= CD= DE= EA= 3$ and $\angle ABC = \angle CDE = \angle
DEA = 90^\circ$. The real axis is parallel to $\overline{DE}$. What is the imaginary part of the complex number corresponding to point $B$? | nvidia_math |
The average of the numbers $1, 2, 3,\dots, 98, 99,$ and $x$ is $100x$. What is $x$? | nvidia_math |
Compute $\tan 225^\circ$. Let's program in Python in the response. | tiger_lab_math |
The distance from City A to City B is 200 miles. While driving from City A to City B, Glen drives at a constant speed of 40 miles per hour. Hannah leaves City A 108 minutes after Glen. What is the minimum constant speed in miles per hour that Hannah must exceed in order to arrive in City B before Glen?
Answer Choices: ... | tiger_lab_math |
Jackson buys a computer game for $66 and three movie tickets for $12 each. How much did he spend on entertainment total? | tiger_math |
One digit of the decimal representation of $\frac{3}{11}$ is randomly selected. What is the probability that the digit is a 7? Express your answer as a common fraction. | nvidia_math |
Given an integer \( n > 15 \) such that \( n = \sum_{i=1}^{n} i c_i \) for non-negative integers \( c_i \) with \( c_1 < 4 \), does the inequality
\[
\frac{n!}{\prod_{i=1}^{n} i^{c_i} \prod_{i=1}^{n} c_i!} > n(n-1)(n-2)(n-3)
\]
hold true? If so, for which integers \( n \) and under what conditions on the \( c_i \)? | automath |
a tailor trims 6 feet from opposite edges of a square piece of cloth , and 5 feet from the other two edges . if 120 square feet of cloth remain , what was the length of a side of the original piece of cloth ? Let's program in Python in the response. | tiger_lab_math |
Papi Calot prepared his garden to plant potatoes. He planned to plant 7 rows of 18 plants each. But he still has a bit of room left, so he’s thinking about adding 15 additional potato plants. How many plants does Papi Calot have to buy? | tiger_math |
Emma rents a bike for $\$$15 a day and $\$$0.10 a mile. If she rents it for 3 days and rides it 120 miles, how many dollars does she pay? | nvidia_math |
It's Ava's birthday party. Her parents bought a unicorn piñata for $x and filled it with all of her favorite treats. They bought 4 bags of Reese's for $9 per bag, 3 bags of Snickers for $5 per bag, and 5 bags of Skittles for $7 per bag. How much did the unicorn piñata and the treats cost altogether?
If we know the answ... | tiger_math |
Sam has forgotten his friend’s seven-digit telephone number. He remembers the following: the first three digits are either 635 or 674, the number is odd, and the number nine appears once. If Sam were to use a trial and error process to reach his friend, what is the minimum number of trials he has to make before he can ... | tiger_lab_math |
What is the simplified form of the expression \(\frac{2}{\sqrt[4]{4a}}\)? | automath |
A rocket takes off vertically from the ground, following the height equation \( s(t) = 50t^2 \) feet, while a camera is positioned 2000 feet away from the launch site. At what rate is the angle \( \theta \) of the camera changing with respect to time 10 seconds after liftoff? | automath |
In a competition between two athletes to determine the best jumping ability, they performed the long jump, triple jump, and high jump to calculate their average jump. The first athlete achieved distances of 26 feet in the long jump, 30 feet in the triple jump, and 7 feet in the high jump. The second athlete achieved di... | tiger_math |
Alex chooses two different numbers at random from the set {1, 2, 3, 4} and takes their difference. Jake chooses two different numbers at random from the set {2, 3, 5, 7} and takes their sum. What is the probability that Alex's result is greater than Jake's result? Express your answer as a common fraction. | nvidia_math |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.