instruction_seed stringlengths 17 6.7k | source stringclasses 4
values |
|---|---|
If $f^{-1}(g(x))=x^2+2$ and $g$ has an inverse, find $g^{-1}(f(4))$. | tiger_math |
Let A = {1, 2} and B = {a, b}. Find (A x B) ∪ (A x {c}) and simplify the resulting Cartesian product. | tiger_lab_math |
In Faye's baseball game, their team scored a total of sixty-eight points. The points were scored through singles (1 point), doubles (2 points), triples (3 points), and home runs (4 points). Faye scored a combination of 8 singles, 5 doubles, 2 triples, and 1 home run for a total of twenty-eight points. Each of her teamm... | tiger_math |
Tom has been saving money for a new bike and has $120 in his piggy bank. He wants to buy a bike that costs $180. Tom's parents have agreed to give him an allowance of $5 per week for doing chores, and he also plans to mow lawns in his neighborhood to earn extra money. If it takes Tom 4 hours to mow a lawn and he charge... | nvidia_math |
Triangle $ABC$ is an isosceles right triangle with the measure of angle $A$ equal to 90 degrees. The length of segment $AB$ is 8 cm. What is the area of triangle $ABC$, in square centimeters? | tiger_math |
What is the Lebesgue measure of the set of all Liouville numbers, and how does it compare to the Lebesgue measure of the set of all real transcendental numbers? | automath |
Eddy’s spider plant produces 2 baby plants x times a year. After 4 years, The mother plant will have produced 16 baby plants. What is the value of unknown variable x? | tiger_math |
How many non-abelian groups of order 72 are there, and can you provide an example of one such group? | tiger_lab_math |
Cherry put up a delivery service. She charges $2.50 for a 3-5 kilograms cargo and $4 for a 6-8 kilograms cargo. If she delivers four 5 kilograms cargo and two 8 kilograms cargo per day, how much money will she earn in a week? | tiger_math |
Emily was planting vegetables in her garden. She started with some seeds and planted 29 of them in the big garden, and in each of her 3 small gardens, put 4 seeds each. How many seeds did Emily start with? | tiger_math |
Let \(\mathfrak{A}\) be an algebra with unit and let \(a \in \mathfrak{A}\) be a non-zero element. If the dimension of \(\{ a \}^c\) (the commutant of \(\{ a \}\)) is \(n\), what is the dimension of \(\{ a \}^{cc}\) (the second commutant of \(\{ a \}\)) in terms of \(n\)? | automath |
At a book fair, 25% of the books sold were fiction books, and the average price of these books was $15. The remaining books sold were non-fiction books, with an average price of $20. If the total revenue from book sales was $14,000, what was the total number of books sold? | nvidia_math |
A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 276 metres long in 20 seconds. The length of the train (in metres) is:
Answer Choices: (A) 184 (B) 176 (C) 175 (D) 96 (E) None of these | tiger_lab_math |
Let $a,$ $b,$ $c$ be distinct roots of $x^3 + px + q = 0.$ Compute the determinant
\[\begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix}.\] | tiger_math |
There are 46 rulers in the drawer. Tim put 25 more rulers into the drawer. There are _____ rulers in the drawer now . Please write a program to solve it | tiger_lab_math |
Emily just purchased 2 pairs of curtains for $30.00 each and 9 wall prints at $x each. The store also offers an installation service. For $50.00 they will come to your house and professionally hang your curtains and prints. If Emily agrees to this service, Her entire order will cost 245. What is the value of unknown... | tiger_math |
Given that the angle of elevation to the top of a tower from a point on the horizontal plane through its base is 32°, and after moving towards the tower by 100 meters, the angle of elevation becomes 63°, calculate the height of the tower and the initial distance from the tower to the observer. Use the values of tan 32°... | automath |
Let $m$ be a positive integer and $b$ be an integer such that $b$ is its own inverse modulo $m$. What is the remainder when $b^3$ is divided by $m$? | nvidia_math |
Two days ago, the temperature in the morning went up 1.5 degrees every 2 hours. If the temperature was 50 degrees at 3 A.M., what was the temperature at 11 A.M.? | tiger_lab_math |
Two hunters, A and B, are trying to hunt a stag. Each hunter can either hunt a rabbit alone, in which case they get 1 unit of food or hunt a stag together, in which case they get 3 units of food. If only one hunter decides to hunt a stag alone, they get nothing. If both hunters decide to hunt a rabbit alone, they each ... | tiger_lab_math |
Find the sum of all positive integers $k$ such that $2.5k-8<11.2$. | nvidia_math |
A Lamplighter monkey has long arms and can swing from branch to branch at a speed of 10 feet per second. But when the monkey is frightened, it will run along the branches at a speed of 15 feet per second. If a Lamplighter monkey runs for x seconds to evade a predator, then swings for another 10 seconds to add distanc... | tiger_math |
A bookseller has 12 books of different titles on a shelf. How many ways can 3 books be selected from the shelf if the order of selection doesn't matter, but the books must be chosen such that the title of the first book starts with a letter that comes before the title of the second book, and the title of the second boo... | nvidia_math |
What is the equation of the perpendicular bisector of the line segment connecting the points \(-1 + 2i\) and \(1 - 2i\)? | automath |
Given the function $f(x) = \frac{x}{1+x^2}$ with period $2\pi$, find its Fourier series up to the third harmonic, that is, find the coefficients $a_0, a_1, a_2, a_3, b_1, b_2, b_3$. | tiger_lab_math |
The spinner for a game is circular with a radius of 10 cm. The probability of winning on one spin is 2/5. What is the area, in square cm, of the WIN sector? Express your answer in terms of π. | tiger_math |
A right pyramid with a square base has total surface area 432 square units. The area of each triangular face is half the area of the square face. What is the volume of the pyramid in cubic units?
New Problem:
A sphere is inscribed in a right circular cone. The volume of the sphere is 1/3 of the volume of the cone. T... | nvidia_math |
Point $C$ is the midpoint of $\overline{AB}$, and point $D$ is the midpoint of $\overline{AC}$. If $AD=5$, what is the length of $\overline{AB}$? | tiger_math |
How many additional home runs did the Chicago Cubs score compared to the Cardinals in the game, considering the Cubs scored 2 home runs in the third inning, 1 home run in the fifth inning, and 2 more home runs in the eighth inning, while the Cardinals scored 1 home run in the second inning and 1 home run in the fifth i... | tiger_math |
Evaluate the integral
\[
\int \sin^{-1}(4x) \, dx
\]
and explain why the final answer includes a factor of \(\frac{1}{8}\). | automath |
Adam has just bought some new books so he has decided to clean up his bookcase. After he adds his new books to his bookshelf he realizes that he has bought enough books to finish completely filling his bookcase with 2 books left over. Before his shopping trip, Adam had 56 books in his bookcase. If his bookcase has 4 sh... | tiger_lab_math |
What is the total number of vertices and triangles in a unit square mesh created with \( m = 5 \) rows and \( n = 4 \) columns, where each grid cell is divided into two triangles? | automath |
A group of hikers is planning a trip that will take them up a mountain using one route and back down using another route. On the ascent, they will encounter three different terrains: forest, rocky, and snowy terrain. On the descent, they will traverse through grasslands and sandy terrain. Their travel speed is affected... | tiger_math |
Tom has a machine that can cut a 20-foot long wooden plank into three equal pieces. How many planks can he cut into equal pieces if he has a 48-foot long wooden plank? | nvidia_math |
A cylindrical container with a radius of Y inches and a height of 6 inches is filled with water. If the volume of water in the container is equal to the volume of a sphere with a radius of 2 inches, what is the value of Y? | tiger_math |
Find a fraction with a denominator of 1000 that is equivalent to the terminating decimal 0.6258. | tiger_math |
According to a survey conducted in two countries, China and India, 20% of the population are vegetarians. If the ratio of the population is 14:13, respectively, and the percentage of Chinese who are vegetarian is 5%, what percentage of Indians are vegetarians?
Answer Choices: (A) 51% (B) 54% (C) 25% (D) 36% (E) 47% | tiger_lab_math |
In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 14 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
Answ... | tiger_lab_math |
Worldwide production of motor vehicles was 3.9 million vehicles in 1946 and 61.3 million in 1987. Of the following, which is closest to the average (arithmetic mean) annual increase, in millions, in worldwide production of motor vehicles during this period?
Answer Choices: (A) 0.08 (B) 1.0 (C) 1.1 (D) 10.5 (E) 1.4 | tiger_lab_math |
How many integers (positive and negative) are divisors of 20? | nvidia_math |
In a geometric sequence, the sum of the first three terms is 28, and the sum of the last three terms is 448. Find the common ratio of the sequence. | nvidia_math |
Given that there are several homology theories such as simplicial, singular, and cubical homology, can you provide a comparison of their strengths in terms of the types of topological properties or invariants that can be computed using each theory? Specifically, are there any topological spaces for which one homology t... | automath |
If Annie has 6 barrettes, twice as many scrunchies as barrettes, and three fewer bobby pins than barrettes, what is the percentage of her hair decorations that are bobby pins, rounded to the nearest percent? | tiger_math |
A rabbit can run at a speed of 40 kmph in a field and 30 kmph in a cactus field. This means the rabbit gets hotter running through a? "Option 1": cactus field, "Option 2" :field Please write a program to solve it | tiger_lab_math |
What is the mean absolute deviation of the 'mpg' variable from the 'mtcars' dataset? | automath |
The numbers $\sqrt{2u-1}$, $\sqrt{2u+1}$ and $2\sqrt{u}$ are the side lengths of a triangle. How many degrees are in the measure of the largest angle? | nvidia_math |
Consider the rational function \( \frac{2x^2 - 3x + 1}{(x-1)(x+2)} \).
Perform partial fraction decomposition on this expression and find the coefficients \( A \) and \( B \) such that
\[
\frac{2x^2 - 3x + 1}{(x-1)(x+2)} = \frac{A}{x-1} + \frac{B}{x+2}.
\]
What are the values of \( A \) and \( B \)? | automath |
Is it possible for two distinct probability distributions to have the same mean and variance, and can you provide an example that demonstrates this? | automath |
Given the transformation matrix \( A = \begin{bmatrix} 3 & 1 \\ 0 & 2 \end{bmatrix} \), calculate its eigenvalues and corresponding eigenvectors. What are the eigenvalues, and in what directions do the eigenvectors lie? Additionally, determine the scaling factor associated with each eigenvector. | automath |
If a terrorist prevention system has a 99% accuracy rate in identifying future terrorists and a 99.9% accuracy rate in identifying non-terrorists, what is the probability that an individual randomly chosen from a population of 300 million people, in which there are 1000 actual future terrorists, is indeed a future terr... | automath |
Chewbacca has 20 pieces of cherry gum and 30 pieces of grape gum. Some of the pieces are in complete packs, while others are loose. Each complete pack of cherry gum has exactly $x$ pieces, and each complete pack of grape gum has exactly $y$ pieces. If Chewbacca loses one pack of cherry gum, then the ratio of the numb... | tiger_math |
A deck of 52 playing cards is shuffled and one card is drawn at random. What is the probability that the drawn card is a face card (King, Queen, or Jack) or an Ace, given that the card is not a heart? | nvidia_math |
In 6 months Bella and Bob will be celebrating their 4th anniversary. How many months ago did they celebrate their 2nd anniversary? | nvidia_math |
An assembly line produces 15 cogs per hour until an initial order of some cogs is completed. The speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced. The overall average output, in cogs per hour, for the assembly line during this whole time... | tiger_math |
The remainder is 19, the quotient is 61, the dividend is some number, and the divisor is 8. What is the dividend? | tiger_math |
What is the maximum number of hidden layers in a neural network configuration that minimizes validation loss without causing overfitting, based on your findings from testing configurations with (5, 8), (8, 12), and (100, 100) hidden layers? | automath |
Oliver is two years younger than Ava. If Ava is 9 years old, how old was Oliver two years ago? | nvidia_math |
If there are 50 students in Kylie's class and in a specific test, ten students scored 90 marks, 15 scored ten marks less than the first ten students, and the remaining students scored 60 marks each, what is the average mark for the entire class? | tiger_math |
Solve for x: |2x + 3| = 7 | tiger_lab_math |
by selling an article at rs . 120 , a profit of 25 % is made . find its cost price ? | tiger_math |
Given the vector \( \mathbf{X} = (x + 3) \frac{\partial}{\partial x} - (y + x + 1) \frac{\partial}{\partial y} \) and the set of vectors \( S_4 = \left\{ \frac{\partial}{\partial x}, \frac{\partial}{\partial y}, x \frac{\partial}{\partial x}, y \frac{\partial}{\partial x}, x \frac{\partial}{\partial y}, y \frac{\partia... | automath |
In an examination, 35% candidates failed in one subject and 40% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared at the end of the examination how many passed in either subject but not in both?
Answer Choices: (A) 975 (B) 1020 (C) 1175 (D) 1243 (E) 1125 | tiger_lab_math |
A ship travels from Port A to Port B and back. The journey from Port A to Port B takes 4 hours, and the return journey takes 6 hours due to a strong current. The total distance of the round trip is 200 miles. What is the speed of the ship in still water and what is the speed of the current? | tiger_math |
John writes 20 pages a day. How long will it take him to write 3 books that are 400 pages each? | nvidia_math |
Consider the following system of linear equations:
3x + 2y + 4z = 10
6x - 3y + 2z = -5
5x + 7y - 3z = 15
Use sparse matrix representation to solve for x, y, and z. | tiger_lab_math |
James needs to get a new pair of glasses. His frames cost $200 and the lenses cost $500. Insurance will cover 80% of the cost of lenses and he has a $50 off coupon for frames. How much does everything cost? | nvidia_math |
Benny is baking pies for a bake sale. He plans to make ten pumpkin pies, which cost $3 each to make, and twelve cherry pies, which cost $5 each to make. If he wants to make a profit of $20 selling all the pies, how much does he have to charge for each pie if both kinds sell at the same price? | tiger_lab_math |
A cyclist wants to train regularly. She plans to ride 300 kilometers, 5 days a week. Her bike tires have a lifespan of 1500 kilometers, and a new set of tires costs $120. She can get a 15% discount on the tires from her sponsor. If she also has to pay a weekly bike maintenance fee of $20, how much does she spend on her... | nvidia_math |
Three different 6th grade classes are combining for a square dancing unit. If possible, the teachers would like each male student to partner with a female student for the unit. The first class has 17 males and 13 females, while the second class has 14 males and 18 females, and the third class has 15 males and 17 fema... | nvidia_math |
3 Pairs of jeans and 6 shirts costs 104.25 dollars. The cost of 4 jeans and 5 shirts is 112.15 dollars. Find the cost of each shirt. Please respond by writing a program in Python. | tiger_lab_math |
Given a dataset of $n$ patients with $p$ symptoms, where each symptom's severity is measured on a scale from $1$ to $5$, and a class variable indicating whether the patient has a disease (0 or 1), suppose the prior distribution for the probability of having the disease, $\pi$, is modeled as $\text{Beta}(1,1)$ (uniform ... | automath |
Round to the nearest tenth: 36.89753 | nvidia_math |
Given the string "hello world" in cell A2, what would be the output of the formula =LEFT(A2, FIND(" ", A2) - 1)? Provide the final string returned by the formula. | automath |
Expand the product ${(x^2-3x+2)(x+5)}$. | nvidia_math |
Given the function \( y = \sqrt{x+5} + \sqrt[3]{\frac{x}{4}} \), determine the value of \( x \) for which \( y = 0 \). Additionally, identify the intervals where the function \( y \) is positive and where it is negative. | automath |
Find the last three digits of the following sum: $$7! + 14! + 21! + \cdots + 70!$$ | nvidia_math |
"statement 1": After they have worked together for less than 82 days Matt stops and Peter completes the remaining work in 8 days, "statement 2" :After they have worked together for 12 days Matt stops and Peter completes the remaining work in 8 days, "options: " Entailment or contradiction or neutral? Let's write a Pyt... | tiger_lab_math |
In the context of simply typed $λ$-calculus, if we define a type $A$ as containing all elements satisfying the formula $P(x)$, how many distinct elements can exist in the set defined by the comprehension axiom $λx.P(x)$ if $P(x)$ is the property "x is an even integer less than 10"? Provide the complete list of elements... | automath |
Let A = {1,2} and B = {a,b} be two sets. Calculate the following:
(A x B) ∪ (A x C) , where C = {c,d}
(A x B) ∪ (C x B) , where C = {1,2}
Verify that the above results satisfy the distributive law of Cartesian product over union. | tiger_lab_math |
Alexandra is preparing a cake. It takes her 25 minutes to whip the cream and half of that time to mix the batter. It takes her 40 minutes to bake the cake, three times as long to let it cool, and 1/8th the combined baking and cooling time to decorate the cake. How many minutes does Alexandra spend on the cake total? | nvidia_math |
In the chicken coop at the Boisjoli farm, there are 270 hens and 3 roosters. Every morning, Ms. Mosel collects the eggs, with each hen laying one egg. After 1 hour of collection, she puts the eggs into boxes of 6, which takes an additional 40 minutes. Ms. Mosel repeats this process from Monday to Sunday. How many boxes... | tiger_math |
If a set of numbers consists of \( \frac{1}{4} \) and \( \frac{1}{6} \), what number \( x \) can be added to the set so that the average of the three numbers equals \( \frac{1}{4} \)?
A. \( \frac{1}{6} \)
B. \( \frac{1}{5} \)
C. \( \frac{1}{4} \)
D. \( \frac{1}{3} \)
E. \( \frac{1}{2} \) | automath |
In Johnstown, the population is 80 and every single person drives by themselves to work. Each car on a road pollutes 10 pounds of carbon a year. A single bus pollutes 100 pounds of carbon a year. A bus can hold 40 people. The town decides to start running a bus and 25% of the people who used to drive now take the bus. ... | tiger_lab_math |
A positive number $k$ has the property that there are exactly $12$ integers between $1$ and $k$ (inclusive) that are divisible by $2$ or $3.$ Find the remainder when $k$ is divided by $100$. | nvidia_math |
Determine the sum of all the numbers on a collection of numbered indexed cards that includes one card with a 1 written on it, two cards with a 2, and so forth up to $n$ cards showing an $n$, if the average value of a card in this collection is 500. | tiger_math |
Find the sum of the digits in the base 12 representation of $9876_{10}$. | nvidia_math |
Bill has played 200 games of poker and won 63% of them. If he plays 100 more games and loses 43 of them, what is his new win percentage? | tiger_lab_math |
Given a fixed perimeter \( p \), what shape among the triangle, rectangle, and semicircle maximizes the area-to-perimeter ratio \( R = \frac{A}{p} \)? Specifically, calculate the maximum area for each shape when \( p = 12 \) and determine which shape yields the highest area-to-perimeter ratio. | automath |
Consider a stock that currently sells for $27. A 145-day put option with a strike price of $30 uses the Black-Scholes-Merton model parameters as follows: the risk-free rate is 4% per annum, and the annualized volatility is 30%. Calculate the value of this put option and choose the closest option from the following valu... | automath |
The Lion King cost 10 million to make and earned 200 million at the box office. If it earned a profit that was half of what Star Wars made and Star Wars cost 25 million to make, how many millions did Star Wars earn? | tiger_lab_math |
Math City has eight streets, all of which are straight. No street is parallel to another street. One police officer is stationed at each intersection. What is the greatest number of police officers needed? | nvidia_math |
if the cost price of 20 articles is equal to the selling price of 16 articles , what is the percentage of profit or loss that the merchant makes ? | tiger_math |
Martin has to secure 80% marks to clear his exam of class 9th.
He got 200 marks and failed by 200 marks.
What is the maximum marks ?
Answer Choices: (A) 500 (B) 505 (C) 510 (D) 515 (E) 525 | tiger_lab_math |
Let the matrix A be
$$\begin{pmatrix} 5 & 2 \\ 1 & 2 \end{pmatrix}.$$
Using the standard inner product, find the orthogonal projection of the vector $\begin{pmatrix} 4 & -4 \end{pmatrix}$ onto the column space of A. | nvidia_math |
What value of \( x \) makes the following matrix singular, meaning it does not have an inverse?
\[
A = \begin{bmatrix} 2 & 3 \\ x & -2 \end{bmatrix}
\]
Provide the calculated value of \( x \). | automath |
If a standard six-sided die is rolled once, what is the probability of rolling a number that is at least a 4? | automath |
Passage: Gender Development Index (GDI) was .942 in 2015 with an HDI of .600 for females and .637 for males. Life expectancy at birth for males is 70.9 and 75.9 for females. Expected years of schooling in Honduras is 10.9 years for males (mean of 6.1) and 11.6 for females (mean of 6.2). These measures do not reveal a l... | tiger_lab_math |
It takes Emmalyn and her research team, the Polar Bears, 30 minutes to fully navigate around a volcanic island. On Saturday, they decided to start off by rounding the island once. They then re-grouped and planned out the rest of their weekend research schedule. They completed 10 more round that day and then went home. ... | tiger_math |
When designing a flag for Crestview using their school colors of purple and gold, the students plan to have three solid-colored horizontal stripes. Adjacent stripes are allowed to be the same color. How many different flag designs are possible? | tiger_math |
A School Bus is used to transport students from home to college. There are total of 20 students who want to take the bus. There are 10 seats in the bus. 2 in the front row, 4 in the middle row and 4 in the last row. Bus driver has to make sure that front 2 seats are for nausea students. 4 students have nausea and can o... | tiger_lab_math |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 8