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John is 24 years younger than his dad. The sum of their ages is 68 years. How many years old is John? | tiger_math |
What is the greatest number of points of intersection that can occur when X different circles and $2$ different straight lines are drawn on the same piece of paper?
If we know the answer to the above question is 11, what is the value of unknown variable X? | tiger_math |
Consider the second order differential equation given by
\[
{u}^{''} + {x}^{-1}{u}^{'} + \sin(u) = 0.
\]
If the initial condition is \( u(x) = r\ln(x) + s + O(x^2) \) as \( x \to 0 \), what is the behavior of the solutions \( u(x) \) as \( x \to 0 \)? Additionally, for large \( x \), what is the leading order asympt... | automath |
Sandy buys an old scooter for $900 and spends $300 on its repairs. If Sandy has a gain of 10%, for how much does she sell the scooter? | tiger_math |
Maya brought 15 dresses and some scarves to the dry cleaner. The total bill was $108, with dresses costing $6 each and scarves costing $3 each. When she arrived to collect her clothes, the staff claimed she had brought only 5 scarves. Maya complained to the supervisor, who instructed the staff to look for the rest of h... | nvidia_math |
Two trains of equal are running on parallel lines in the same direction at 42 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
Answer Choices: (A) 30 m (B) 72 m (C) 80 m (D) 82 m (E) 84 m | tiger_lab_math |
Tim decides to run a campaign for governor. He gets the maximum $1200 donation from 500 people, and three times as many people donated half this sum of money to his campaign. These donations together accounted for 40% of the total money that Tim raised. How much total money did he raise? | nvidia_math |
If $x,y,z$ satisfy the system of equations
\begin{align*}
y + z &= 20-4x \\
x+z &= -10 - 4y \\
x+y &= Y - 4z,
\end{align*}
and $3x + 3y + 3z$ is 3, what is the value of unknown variable Y? | tiger_math |
A deck of 52 cards is shuffled and then one card is removed at random. The remaining cards are then dealt to four players, with each player receiving 13 cards (one card is left over). What is the probability that the player who receives the first set of 13 cards has exactly three Aces? | nvidia_math |
There were x kids in the junior prom. Of those, a fourth of them were dancers. Of the dancers, 25 danced the slow dance. 10 of the dancer students did not slow dance. What is the value of unknown variable x? What is the value of unknown variable x? | tiger_math |
A hairstylist charges $5 for a normal haircut, $6 for a special haircut, and $8 for a trendy haircut. If he cuts 5 normal haircuts, 3 special haircuts, and 2 trendy haircuts per day, how much money does he earn per week? | tiger_lab_math |
Let \(S\) be the set of all positive integers whose digits are alternating 1's and 0's (for example, 1, 10, 101, 1010, 10101,...).
Compute \(\sum_{n\in S}\frac{1}{n^{2}}\). | nvidia_math |
Compute
\[\begin{pmatrix} X & 1 & -2 \\ 0 & 4 & -3 \\ -1 & 4 & 3 \end{pmatrix} \begin{pmatrix} 2 & -2 & 0 \\ 1 & 0 & -3 \\ 4 & 0 & 0 \end{pmatrix}.\]
If we know the answer to the above question is \begin{pmatrix}-5&-2&-3\-8&0&-12\14&2&-12\end{pmatrix}, what is the value of unknown variable X? | tiger_math |
If ‘DELHI’ is coded as ‘15’, ‘RAJASTHAN’ is coded as ’45’, then ‘MUMBAI’ is coded as ?
Answer Choices: (A) 24 (B) 21 (C) 18 (D) 19 (E) None | tiger_lab_math |
Express a speed of 54 kmph in meters per second?
Answer Choices: (A) 10 mps (B) 18 mps (C) 15 mps (D) 17 mps (E) 12 mps Let's write a program. | tiger_lab_math |
A group of 8 children are taken to an amusement park. They all try a variety of rides with the following costs:
Ferris wheel: $5 per child (5 children)
Roller coaster: $7 per child (3 children)
Merry-go-round: $3 per child (everyone)
Bumper cars: $4 per child (6 children)
During their visit, they also bought some sna... | tiger_math |
A farmer has a rectangular field with an area of 50 square meters. If the length of the field is 3 meters more than its width, what is the perimeter of the field? | nvidia_math |
What is the remainder when the largest three-digit multiple of 13 is divided by 11? | tiger_math |
Given two sets of real numbers \( S_1 = [0, N_1] \) and \( S_2 = [0, N_2] \), where \( N_1 \) and \( N_2 \) are positive integers, what is the probability that a value \( x_1 \) chosen uniformly at random from \( S_1 \) and a value \( x_2 \) chosen uniformly at random from \( S_2 \) satisfy the condition \( x_1 + x_2 <... | automath |
Chandra is going on a monster hunt. After a big storm, there have been lost monsters all around the castle grounds for the last 5 days. Chandra wants to rope them all up and return them to the swamps where they will be the most comfortable. On the first day she saw 2 monsters near the castle walls. Every day after that... | tiger_math |
Cassidy collects movie posters from newly released sci-fi movies. After this summer, she will have six more posters in her collection, making it double the size it was four years ago when she had 22 posters. Unfortunately, Cassidy lost 3 posters and sold 4 posters from her initial collection in these years. Surprisingl... | tiger_math |
A block is given an initial velocity of 2 m/s up a frictionless plane inclined at an angle of 60 degrees to the horizontal. What is the maximum vertical height that the block reaches above its starting position? | automath |
Find all real $x$ such that \[\left\lfloor x \lfloor x \rfloor\right \rfloor = 35.\] | tiger_math |
If a company initially had 500 employees, each earning $12 per hour, working 10 hours a day, five days a week, for four weeks in a month, and then hired 200 more employees due to increased workload in August, what is the total amount of money the company pays per month after the new hires? | tiger_math |
How many triangles with positive area are there whose vertices are points in the $xy$-plane whose coordinates are integers $(x,y)$ satisfying $1\le x\le 4$ and $1\le y\le 4$?
$\text{(A) } 496\quad \text{(B) } 500\quad \text{(C) } 512\quad \text{(D) } 516\quad \text{(E) } 560$
| nvidia_math |
I have 5 books, two of which are identical copies of the same math book (and all of the rest of the books are different). In how many ways can I arrange them on a shelf? | nvidia_math |
Distance between two stations A and B is 1108 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of train during the whole journey.
Answer Choices: (A) 60 km/hr (B) 30.5 km/hr (C) 57 km/hr (D) 67.2 km/hr (E) None of these | tiger_lab_math |
Ava has 45 pencils. Her friend Emily has 32 pencils, and Emily's brother, Max, has 5 more pencils than Emily. How many pencils do they have in total? | nvidia_math |
Determine whether the following functions are one-to-one. Provide justification for each answer.
1. \( f(x) = \sqrt[3]{x + 2} - 1 \)
2. \( g(x) = x^2 - 8 \)
3. \( h(x) = |x - 1| \)
4. \( k(x) = \frac{1}{x - 8} \)
5. \( m(x) = -\sqrt{25 - x^2} \)
For each function, state if it is one-to-one and explain why or why not. | automath |
Suppose that $a^2$ varies inversely with $b^3$. If $a=7$ when $b=3$, find the value of $a^2$ when $b=6$. | nvidia_math |
Rationalize the denominator of the expression $$\frac{7}{\sqrt{2} + \sqrt{5}}$$ and express the result in the form $$\frac{a + b\sqrt{c}}{d}$$, where \( a, b, c, d \) are integers and \( \sqrt{c} \) is in its simplest form. What is the value of \( a + b + c + d \)? | automath |
Can the group of real numbers \(\mathbb{R}\) be expressed as a countable ascending union of proper additive subgroups, and if so, what is the cardinality of the smallest collection of proper additive subgroups that achieve this union? | automath |
A box measuring 35 inches long by 20 inches wide by some inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. The smallest number of cubes that can accomplish this objective is 56. What is the depth of the box? | tiger_math |
in a class total 34 students , 16 are have a brother , 15 are have sisters , 9 students do n ' t have either brothers or sisters . find the number of students having both brother and sisters . Please respond by writing a program in Python. | tiger_lab_math |
The sequence $a_1, a_2, \ldots$ is geometric with $a_1=a$ and common ratio $r,$ where $a$ and $r$ are positive integers. Given that $\log_8 a_1+\log_8 a_2+\cdots+\log_8 a_{12} = 2006,$ find the number of possible ordered pairs $(a,r).$
| nvidia_math |
A box contains 24 marbles, each labeled with a different integer from 1 to 24. John randomly selects one marble from the box. What is the probability that the number on the selected marble is a multiple of 3 or 7? Express your answer as a common fraction. | nvidia_math |
In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 4 and that the product of the given number and the sum of its digits is equal to 90, then the number is:
Answer Choices: (A) 15 (B) 27 (C) 38 (D) 46 (E) 48 | tiger_lab_math |
A salad bar offers eight ingredients. What is the greatest number of five-ingredient salads that can be made such that no two salads have the same ingredient combination? | nvidia_math |
Suppose a principal wants to hire an agent for a certain project. The agent can exert high or low effort, and the payoff to the principal will depend on the effort exerted by the agent. If the agent exerts high effort, the principal gets a payoff of 5, and if the agent exerts low effort, the principal gets a payoff of ... | tiger_lab_math |
A sun is divided among X, Y and Z in such a way that for each 2 rupees X gets, Y gets 1 rupee 50 paisa and Z gets 1 rupee 20 paisa. If the share of X is RS. 125, what is the total amount?
Answer Choices: (A) 283.75 (B) 193.75 (C) 293.75 (D) 290.75 (E) 313.75 Let's write a Python program. | tiger_lab_math |
Lily wants to buy a new bike and needs to save up $120. She makes a deal with her neighbor to walk their dog for extra pay. Normally, she walks the dog 3 times a week. Her neighbor agrees to pay her $3 for every additional dog walk she does during the week. If she walks the dog 2 times a day for three weeks, how much d... | nvidia_math |
What is the homotopy type of the subcomplex formed by all clutter hypergraphs on $n$ vertices, and does this subcomplex have any interesting topological properties or simplicial representations that are significantly better than representing hypergraphs as a simplex on $2^n$ vertices? | automath |
Of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 5 grades are D's. What is the number of students in the course?
Answer Choices: (A) 80 (B) 110 (C) 160 (D) 100 (E) 400 | tiger_lab_math |
Given that $-1 - 4\sqrt{2}$ is a root of the equation \[x^3 + ax^2 + bx + 31 = 0\]and that $a$ and $b$ are rational numbers, compute $a.$ | tiger_lab_math |
A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
Answer Choices: (A) 1.5 (B) 2.8 (C) 5.8 (D) 3.4 (E) 2.3 | tiger_lab_math |
What is the smallest value of \( r \) for which the logistic map exhibits chaotic behavior, expressed as a decimal rounded to two decimal places? | automath |
Bobby has 16 toy cars, and the number of cars he has increases by 50% every year. How many toy cars will Bobby have in three years? | tiger_math |
36 people { a 1 , a 2 , . . . , a 36 } meet and shake hands in a circular fashion . in other words , there are totally 36 handshakes involving the pairs , { a 1 , a 2 } , { a 2 , a 3 } , . . . , { a 35 , a 36 } , { a 36 , a 1 } . then size of the smallest set of people such that the rest have shaken hands with at least... | tiger_lab_math |
Find the largest possible value of $k$ such that the polynomial $x^4 - kx^3 + kx^2 - kx + k$ has four distinct real roots. | nvidia_math |
Assuming we are underground, and the only thing we can observe is whether a person brings an umbrella or not. The weather could be either rainy or sunny. Assuming the P(rain)=0.6 and P(sunny)=0.4. Assuming the weather on day $k$ is dependent on the weather on day $k-1$. We can write the transition probability as P(sunn... | tiger_lab_math |
Consider a circular domain of radius \( R \) where the temperature \( u(r, \theta) \) satisfies the 2D heat equation under zero Neumann boundary conditions on its boundary. If an elevated heat flux is applied at the center of the circle, model the temperature distribution \( u(r, \theta) \) given that the center has an... | automath |
The average age of the 10 females in a choir is 30 years. The average age of the 15 males in the same choir is 35 years. What is the average age, in years, of the 25 people in the choir? | nvidia_math |
Two identical circles intersect such that their centers and the points at which they intersect form a square of side 1 cm. What is the area of the region where the two circles intersect?
Answer Choices: (A) pi/2 - 1 (B) pi/4 - 1 (C) 1 - pi/4 (D) pi/8 + 1 (E) 4 - pi | tiger_lab_math |
Carla needs to dry-clean 80 pieces of laundry by noon. If she starts work at 8 AM, how many pieces of laundry does she need to clean per hour? | tiger_math |
The average of 15, Y, and $y$ is 20. It is known that $y$ equals 25. Determine the value of the unknown variable Y. | tiger_math |
Define the operation $\clubsuit$ as $a\,\clubsuit\,b = |a + 2b|$. What is the value of $3\,\clubsuit\,(2\,\clubsuit\,5)$? | nvidia_math |
In a treasure hunt game on a magical island, the treasure is hidden at coordinates that can only be found by solving for X in a mathematic equation. The coordinates on the map are determined by the functions \(h(p) = 4p + 2\) and \(j(p) = p^2 - 2p\). To find the treasure, one must calculate \(h(j(X)) - j(h(X))\). If th... | tiger_math |
Statement 1| If a group has a trivial center, then the group must be cyclic. Statement 2 | Every cyclic group is abelian. Answer Choices: (A) True, True (B) False, False (C) True, False (D) False, True | tiger_lab_math |
Find the number of real roots of the equation
$$2^x + 3^x + 5^x = x^2$$
such that $x$ is an integer. | nvidia_math |
Emily loves collecting books. In her library, there are fiction books, non-fiction books, and poetry books. There are 8 fiction books. There are 3 times as many non-fiction books as fiction books, and there are 5 more poetry books than non-fiction books. How many books are there in Emily's library? | nvidia_math |
In a max-heap, when the last level is exactly half filled, what is the maximum number of nodes that can be present in the left subtree in terms of the total number of nodes \( n \) in the heap? Provide a detailed reasoning or calculation to justify your answer. | automath |
Joe buys 2.13 dollars worth of paper for each ream he purchases. If he has a budget of 10.65 dollars, how many full reams of paper can he buy? | automath |
Find the derivative of the function \( y = \sqrt{3} + x^{\frac{1}{3}} + \frac{1}{x} \) with respect to \( x \). | automath |
5 geckos on the kitchen window eat 6 insects each. 3 lizards eat twice as much as the geckos. How many total insects were eaten? | tiger_math |
Given a rectangular beam with a length of 10 meters and a cross-sectional width of 0.2 meters, we want to find the optimal height of the beam that maximizes its bending stiffness. The bending stiffness is given by the formula EI, where E is the modulus of elasticity of the beam material (assume E = 2e11 N/m^2) and I is... | tiger_lab_math |
Ezekiel hikes as a hobby. This past summer, he did a challenging three-day hike across 50 kilometers of wilderness. The first day, he covered 10 kilometers of steep mountainside. The second day was flatter and he was able to cover half the full hike distance. How many kilometers did he have to hike on the third day to ... | tiger_lab_math |
In a square piece of paper, two congruent right triangles are removed from adjacent corners to create a trapezoid. If the side length of the square is 24 units and one of the acute angles of each triangle is $30^\circ$, what is the area of the remaining trapezoid, in square units? | nvidia_math |
Given a Gaussian mixture model with three components, where the weights are 0.35, 0.4, and 0.25, and the means are 0, 2, and 5 with standard deviations of 0.5, 0.5, and 1 respectively, what is the expected value of a sample drawn from this mixture model? Round your answer to two decimal places. | automath |
The decimal representation of a rational number is $2.343434...$ and it is known that its denominator is a two-digit number. Find this rational number. | nvidia_math |
Simplify the product \[\frac{8}{4}\cdot\frac{12}{8}\cdot\frac{16}{12} \dotsm \frac{4n+4}{4n} \dotsm \frac{2008}{2004}.\] | nvidia_math |
In a 1000 m race, A beats B by 100 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
Answer Choices: (A) A) 190m (B) B) 829m (C) C) 822m (D) D) 929m (E) E) 132mj | tiger_lab_math |
What is the smallest decimal interval \([a, b]\) such that it contains the true value of 0.1 stored as a Float64 in Julia, and what are the values of \(a\) and \(b\)? | automath |
Solve for $x$:
$$\sqrt{x^2 + 4x + 3} = \sqrt{-(x + 3)(x + 5)}.$$ | nvidia_math |
Alexia designed a logo 2 inches wide and X inches tall to be used on her school's notebooks. The school wants the logo on the notebook to be 8 inches wide. How tall, in inches, It will be 6 if it is enlarged proportionately. What is the value of unknown variable X? | tiger_math |
Emily is designing a 25-story skyscraper. The first 15 floors are each 10 feet high, while the remaining floors are each 5 feet taller. What is the total height of the skyscraper? | nvidia_math |
15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 5 hrs . each would it take for 21 women if 3 women do as much work as 2 men ? | tiger_math |
Mary is baking a cake . She already put in 8 cups of flour . She added 2 cups more of flour. The recipe wants _____ cups of flour. Let's program in Python in the response. | tiger_lab_math |
Roger rode his bike for 2 miles this morning, and then x times that amount in the evening. How many miles did Roger ride his bike for?
If we know the answer to the above question is 12, what is the value of unknown variable x? | tiger_math |
What is the terminal speed \( v \) of a metal bar of length \( L \), mass \( m \), and resistance \( R \) sliding down frictionless rails inclined at an angle \( \phi \) in a uniform magnetic field of magnitude \( B \) directed downward? | automath |
The average of a non-zero number and its square is a certain multiple of the number. The number is 9. What is the multiple that the average is equal to? | tiger_math |
Determine the greatest common factor of 32 and 48. | tiger_math |
Brianna got $75 for her birthday. She wants to purchase three art books that cost $12 each and a painting set that costs $30. How much money will she have left? | nvidia_math |
Evaluate the expression 3x² - 2x + 5 when x = 4. | tiger_lab_math |
John wants to buy a $100 trouser at the store, but he thinks it's too expensive. Finally, it goes on sale for $30. What is the percent decrease in the price of the trouser? | tiger_math |
Evaluate the limit \( \lim_{x \to 0} x \ln(2x) \) and determine whether the application of L'Hôpital's Rule and the variable substitution \( u = \frac{1}{x} \) were performed correctly. What is the final value of the limit? | automath |
Suppose we have two different sampling methods from a uniform distribution. The first method samples uniformly from the interval \( [0, 1] \) and rejects values outside the interval \( (0.50, 0.51) \). The second method samples uniformly from the interval \( (0.50, 0.51) \).
1. What is the probability density functio... | automath |
The ratio of two quantities is 1 to 2. If each of the quantities is increased by 15, what is the ratio of these 2 new quantities?
Answer Choices: (A) 5:6 (B) 25:27 (C) 15:16 (D) 20:21 (E) It cannot be determined from the information given | tiger_lab_math |
If $x + y = 16$ and $x-y = X$, what is the value of $x^2 - y^2$?
If we know the answer to the above question is 32, what is the value of unknown variable X? | tiger_math |
Find the coordinates of the other endpoint of a line segment if one endpoint is (1, 5) and the midpoint is (6, -2). | tiger_math |
A circular buffer contains 15 integers, each between 0 and 4. The buffer is rotated one position to the right every second. If the sum of the integers in the buffer is 30, find the number of integers that have been rotated to the right after 10 seconds. | nvidia_math |
In Mr. Sanchez's class, the students were given a task to add two positive integers. However, Juan subtracted instead and obtained a result of 2. On the other hand, Maria made a mistake and multiplied the numbers, resulting in 120. What is the correct answer to the original task? | tiger_math |
A certain company has two types of machines: old machines that produce 100 units per hour and new machines that produce 200 units per hour. The company has a total of 30 machines. If the total production of all machines is 5200 units per hour, and the average age of the old machines is 10 years, while the average age o... | nvidia_math |
Given a discrete-time system described by the equation
\[
y[n] = \sum_{i} b_i x[n-i] + \sum_{i} a_i y[n-i],
\]
where we have five coefficients \( b_i \) and four coefficients \( a_i \), if we use a step input of amplitude \( A = 16 \) and assume the initial condition \( y[0] = 1 \), how many iterations will be requi... | automath |
Cedric has deposited $\$12,\!000$ into an account that pays $5\%$ interest compounded annually.
Daniel has deposited $\$12,\!000$ into an account that pays $7\%$ simple annual interest.
In $15$ years Cedric and Daniel compare their respective balances. To the nearest dollar, what is the positive difference between th... | tiger_lab_math |
Dan has a membership at a local gym that also gives classes three nights a week. On any given class night, Dan has the option of taking yoga, weight training, or kickboxing classes. If Dan decides to go to either one or two classes per week, how many different combinations T of classes are available?
Answer Choices: (A... | tiger_lab_math |
In the trapezoid $ABCD$, the length of $AB$ is congruent to the length of $BC$, $\angle A$ measures $60^{\circ}$, and $\overline{BE}$ bisects $\angle A$ with $E$ on $\overline{CD}$. If $F$ is on $\overline{AD}$ such that $\overline{EF}$ is parallel to $\overline{AB}$, how many isosceles triangles are in the figure?
[a... | nvidia_math |
A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is :
Answer Choices: (A) Rs. 700 (B) Rs. 690 (C) Rs. 650 (D) Rs. 698 (E) Rs. 765 | tiger_lab_math |
Last year Sandy saved 6% of her annual salary. This year, she made 10% more money than last year, and she saved 9% of her salary. The amount saved this year was what percent of the amount she saved last year?
Answer Choices: (A) 140% (B) 152% (C) 165% (D) 176% (E) 190% | tiger_lab_math |
A standard deck of 52 cards is shuffled, and 5 cards are randomly drawn without replacement. What is the probability that exactly 2 of the drawn cards are black? | nvidia_math |
Ava opens a lemonade stand and spends $0.50 on a cup and $1 on lemons and sugar for each serving. She sells each cup of lemonade for $2. If she sells 30 cups, how much profit will she make? | nvidia_math |
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