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Noah has just got a new smartphone and wants to download some games. Each game costs $3 on average, and Noah wants to buy 12 of them. He has $50 for this purpose. How much money will he be left with if he buys all the games he wants? | nvidia_math |
Some friends wanted to make a road trip from New York to Los Angeles. They drove at a constant speed of 62 miles/hour, taking breaks of 30 minutes every 5 hours. Once in the city, they looked for the hotel for 30 minutes. If the trip took around 2,790 miles, how many hours will they have to spend to complete the trip t... | tiger_math |
Given the function \( f : \mathbb{R}^3 \to \mathbb{R}^2 \) defined by \( f(x, y, z) = (x^2 + y^2 + z^2, xyz) \), what is the differential \( df \) evaluated at the point \( (1, 0, -1) \)? Please provide the resulting vector in \( \mathbb{R}^2 \). | automath |
Find the largest prime divisor of 15! - 14! | tiger_math |
Find the focus of the parabola $y = 4x^2 - 3.$ | nvidia_math |
In a poker game consisting of 32 cards, where each of the four suits includes the numbers 1, 7, 8, 9, 10, 11, 12, and 13, Jesse and three friends each draw five cards.
1) What is the probability that Jesse receives exactly two cards with the number "1" when drawing his five cards?
2) Calculate the probability that J... | automath |
A population of bacteria grows exponentially, doubling in size every 3 hours. If there are initially 100 bacteria, at what time will the population exceed 10,000? | nvidia_math |
Consider two statements, P and Q, where the logical operators "and" and "or" are used. If P is true and Q is false, evaluate the truth values of the expressions "P and Q" and "P or Q". What are the truth values of these expressions? | automath |
Evaluate $\lceil (13.9)^2 \rceil - \lceil 13.9 \rceil \cdot \lceil 13.9 \rceil$. | tiger_math |
Let \( f(x) = x^3 + 2x^2 + 3x + 4 \). How many incongruent solutions does the equation \( f(x) \equiv 0 \mod 5 \) have? | automath |
What are the Akaike Information Criterion (AIC) and Schwarz Information Criterion (SIC) values for the autoregressive models AR(1), AR(2), and AR(3) when applied to the time series generated by the equation \( y_{t} = 1.2y_{t-1}-0.3y_{t-2}+e_{t} \) with \( e_{t} \sim N(0,1) \) over \( t=1,\ldots,180 \)? | automath |
What is the maximum number of vertices in a directed graph that can be part of an infinite antichain under the butterfly minor relation? | automath |
A 2000 kg car is experiencing a net force of 4000 N acting on it. What is the acceleration of the car? | automath |
Given the symmetric matrix
\[
M = \begin{bmatrix} x & x & y \\ x & z & 0 \\ y & 0 & x \end{bmatrix},
\]
compute the determinant of \( M \) and find the discriminant locus of the associated net of conics. What type of singularities do you find in this locus, and how does this relate to the classification of nodal pla... | automath |
Given two non-decreasing sequences \( A \) and \( B \), both of length \( N \), can you determine if it is possible to reorder the elements of \( B \) such that for all indices \( i \) (where \( 1 \leq i \leq N \)), the condition \( A_i \neq B_i \) holds? If such a reordering exists, output "Yes" followed by one viable... | automath |
Determine the complex number $z$ satisfying the equation $2z-3\bar{z}=-2-30i$. Note that $\bar{z}$ denotes the conjugate of $z$. | nvidia_math |
A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 150 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?
Answer Choices: (A) 50 (B) 100 (C) 150 ... | tiger_lab_math |
Suppose that the number $b$ satisfies the equation $6 = b + b^{ - 1}.$ What is the value of $b^{6} + b^{ - 6}?$ | nvidia_math |
In Henry's collection of music CDs, he has 3 more country CDs than rock CDs but twice as many rock CDs as classical CDs. If he has 23 country CDs, how many classical CDs make up his collection? | tiger_math |
A basement with a rectangular floor measuring 24 feet by 32 feet is flooded to a depth of 18 inches. If each of the three pumps used to remove the water can pump 8 gallons of water per minute, and a cubic foot of water contains 7.5 gallons, how long will it take to pump all the water out of the basement? | tiger_math |
Let A = {1, 2} and B = {2, 3}. Find A × B ∩ B × A. | tiger_lab_math |
Please find the closest option to 112.0. The options are (A) 16 (B) 72 (C) 112 (D) 128 (E) 142 | tiger_lab_math |
Given that $\mathbf{a}$, $\mathbf{b}$, and $\mathbf{c}$ are mutually orthogonal unit vectors, find the minimum value of $\|\mathbf{v} - p\mathbf{a} - q\mathbf{b} - r\mathbf{c}\|$ where $\mathbf{v} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}$ and $p,$ $q,$ and $r$ are scalars. | nvidia_math |
If Murtha continues collecting pebbles in the same pattern, how many days will it take her to collect a total of 5050 pebbles? | tiger_math |
It takes 15 minutes for Dante to go to Hidden Lake. From Hidden Lake, he has to walk back to the Park Office and it takes him 7 minutes. When he arrives there, he will have been gone from the Park Office 32 minutes altogether. If he had walked to the Lake Park restaurant from the Park office before taking the 15 minute... | tiger_math |
A rectangular prism has a rectangular base with length 15 cm and width 8 cm. Its height is 10 cm. What is the total surface area of the prism, in square centimeters, if a cylindrical hole with radius 2 cm is drilled through the center of the prism, from the top face to the bottom face? | nvidia_math |
What is the circumference of a circle if the length of an arc corresponding to a 90-degree central angle is 5π? | automath |
If a DC milliammeter with a full-scale deflection of 10 mA and a resistance of 50 Ω is adapted to serve as a voltmeter for measuring a maximum voltage of 150 V, what resistance must be placed in series with the milliammeter? Additionally, if this voltmeter is used to measure the potential difference across a 100 kΩ res... | automath |
If $5,000 is deposited into a savings account at an annual interest rate of 5%, compounded monthly, how much money will be in the account after 10 years? | automath |
Nancy replaced all of the old vinyl tiles in her bathroom with new hardwood flooring. She replaced flooring in two areas of the bathroom: a 10 foot by 10 foot central area, and a certain hallway. Nancy installed 124 square feet of hardwood flooring in her bathroom. What is the width of the hallway if its length is 6 fe... | tiger_math |
Find a non-zero vector in \(\mathbb{R}^4\) that spans the intersection of the subspaces \(V = \text{span}\{(1,1,0,-1)^T, (0,1,3,1)^T\}\) and \(W = \text{span}\{(0,1,2,-1)^T, (1,2,2,-2)^T\}\). What is that vector? | automath |
Find the sum of the solutions of the equation $-32x^2 + 84x + 135=0$. | tiger_math |
What is the modulo $13$ residue of $247+5 \cdot 39 + 7 \cdot 143 +4 \cdot 15?$ | nvidia_math |
Let $n$ represent the smallest integer that satisfies the following conditions:
$\frac n2$ is a perfect square.
$\frac n3$ is a perfect cube.
$\frac n5$ is a perfect fifth.
How many divisors does $n$ have that are not multiples of 10?
| nvidia_math |
Mark plants some strawberries in his backyard. Every month, the number of strawberry plants doubles. After 3 months, Mark digs up 4 strawberry plants and gives them to his friend. If he still has 20 strawberry plants, how many did he initially plant? | tiger_lab_math |
"statement 1": In Josephs convent school , 80 % are boys at the same time 75 % are girls students, "statement 2" :In Josephs convent school , more than 10 % are boys at the same time 75 % are girls students, "options: " Entailment or contradiction or neutral? Let's write a Python program to solve it. | tiger_lab_math |
the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 6 ? Please respond by writing a program in Python. | tiger_lab_math |
Given the differential equation \((xy + y^2 + x^2) \, dx - x^2 \, dy = 0\), determine the general solution. What is the form of the solution, and specifically, find the value of \(C\) where the solution takes the form \(y = Cx\) for some constant \(C\). | automath |
What is the 15th smallest number in lexicographical order among the integers from 1 to 1000? | automath |
Eddy’s spider plant produces 2 baby plants 2 times a year. After 4 years, how many baby plants will the mother plant have produced? Let's write a Python program to solve it. | tiger_lab_math |
In the given example with 15 stadium areas and 8 camera locations, where each camera location covers a specific subset of stadium areas, what is the minimum number of cameras needed to ensure that all 15 stadium areas are covered, and which specific camera locations should be selected to achieve this minimum coverage? | automath |
If the sum of the third and fifth terms of an arithmetic sequence is $10$, what is the fourth term? | tiger_math |
Is it possible to partition \(\mathbb{R}^3\) into a countable collection of disjoint unit circles, and if so, what is the cardinality of such a partition? | automath |
What is the concentration of the HCl solution, in moles per liter, used to achieve a pH of 6.54 when 1.265 g of ACES-K+ is dissolved in 88.42 mL of water and 27.59 mL of HCl is added? The molar mass of ACES-K+ is 220.29 g/mol, and the pKa of ACES is 6.85. Please provide your calculations. | automath |
In a certain state, gasoline stations compute the price per gallon p, in dollars, charged at the pump by adding a 3 percent sales tax to the dealer's price per gallon d, in dollars, and then adding a gasoline tax of $0.18 per gallon. Which of the following gives the dealer's price per gallon d in terms of the price per... | tiger_lab_math |
Find the square root of $640000$, simplifying your answer as much as possible. | tiger_math |
Given the Josephus problem with \( n = 41 \) people and executing every \( k = 3 \)-rd person, what is the position of the last remaining survivor? | automath |
A rectangle with a length of 6 cm and a width of 8 cm is inscribed in a circle. What is the area of the circle in terms of $\pi$? | tiger_math |
Given two independent continuous random variables \( X \) and \( Y \) with mean \( \mu_X \) and \( \mu_Y \), and variances \( \sigma_X^2 \) and \( \sigma_Y^2 \) respectively, if we apply two different Monte Carlo integration techniques to estimate the expected value \( E[\varphi_1(X) \varphi_2(Y)] \) with \( \varphi_1(... | automath |
What is the proper time or proper length corresponding to the spacetime interval between two events, and how does the choice of metric signature affect the sign of the interval? Specifically, if \( ds^2 \) is positive, can you determine whether the interval is timelike or spacelike based on conventions of spacetime met... | automath |
In 2010, the population of Greenfield was approximately 525,000 residents. By 2015, the population had grown to around 575,000 residents. What is the average annual increase in population? | nvidia_math |
A baker is preparing a batch of sugar cookies. The recipe requires a mixture of sugar and flour in a ratio of 3:5. If the baker needs 2.5 cups of the mixture to make a single batch, and she has a 4-quart container filled to the top with the mixture, how many batches can she make? Express your answer as a whole number. | nvidia_math |
In a regular polygon with 15 sides, one vertex is connected to every third vertex, forming a pattern of triangles and quadrilaterals. What is the ratio of the area of one of the triangles to the area of one of the quadrilaterals? | nvidia_math |
A group of 10 friends wants to form 4 different teams. Each team can have any number of friends from 0 to the total number of friends. In how many ways can the teams be formed if the order of the teams does not matter? | tiger_math |
Simplify $$(2x^4+3x^3-x^2+5x-2)+(-3x^4-2x^3+4x^2-5x+1).$$ Express your answer as a polynomial with the terms in order by decreasing degree. | nvidia_math |
Mark loves to see shows in theaters. He decided to visit the theater at least once a week. One performance lasts 3 hours. The price of the ticket depends on the time spent in the theater and stands at $5 for each hour. Mark will spend 90 on visits to the theater in x weeks. What is the value of unknown variable x? What... | tiger_math |
A standard cube has a volume of $V = s^3$, where $s$ is the length of its edge. If the sum of the lengths of the edges of the cube is 240 cm, find the sum of the areas of all its faces. | nvidia_math |
A box contains 5 red balls, 3 blue balls, and 2 green balls. If 3 balls are randomly selected from the box, what is the probability that at least 2 of the selected balls are of the same color? Express your answer as a common fraction. | nvidia_math |
The positive number z is divisible by a certain number. The remainder of dividing z (2 + 4 + z) + 3 by 2 is 1. What is the number that z is divisible by? | tiger_math |
Let \( n \) be a positive integer. If \( E \) is a trivial bundle over \( S^n \), what is the relationship between \( \text{dim}(TS^n) \) and \( \text{dim}(TS^n \oplus E) \)? Specifically, compute \( \text{dim}(TS^n \oplus E) \) in terms of \( n \). | automath |
Consider a temperature field defined in one-dimensional space given by the function \( T(x) = 298 + x \), where \( T \) is the temperature in Kelvin and \( x \) is the position in meters. Calculate the temperature gradient at \( x = 2 \) meters, and describe its physical meaning in terms of temperature change per unit ... | automath |
What is the smallest four-digit number which is a multiple of 17? | tiger_math |
There were 100 jelly beans in a bag to be given away on Halloween. Out of the 40 children taking part in the Halloween celebration, 80% were allowed to draw jelly beans from the bag. Each child drew two jelly beans out of the bag. How many jelly beans remained in the bag after the children took their share? Please writ... | tiger_lab_math |
If a radioactive substance has a half-life of 3000 years and remains at 27.3% of its initial amount, how many years have passed since the original amount was measured? Round your answer to the nearest year. | automath |
What is the sum of all of the positive even factors of $504$? | tiger_lab_math |
Given a geodesic segment defined by points \( p_0 = (x_0, y_0, z_0) \) and \( p_1 = (x_1, y_1, z_1) \) on the surface of a unit sphere, where \( p_0 \) and \( p_1 \) are not opposite each other, determine the necessary and sufficient conditions under which a point \( p = (x, y, z) \) lies on the shorter geodesic path b... | automath |
What is the largest value of $n$ less than 100,000 for which the expression $8(n-2)^5-n^2+14n-24$ is a multiple of 5? | nvidia_math |
Find $x$ such that $\log_{12}3x=2$. | nvidia_math |
Let $f(x)$ be a rational function of the form $\frac{ax+b}{cx+d}$ such that $f(n) = \frac{1}{n^2}$ for $n = 1,$ 2, 3, $\dots,$ 8. Find $f(0)$. | nvidia_math |
Let \( X, Y, Z \) be three different prime numbers. What is the total number of distinct positive divisors of the product \( XYZ \)? | automath |
A person walks from one end to the other of a 90-meter long moving walkway at a constant rate in 30 seconds, assisted by the walkway. When this person reaches the end, they reverse direction and continue walking with the same speed, but this time it takes 120 seconds because the person is traveling against the directio... | tiger_lab_math |
The ages of two person differ by 20 years. If 8 years ago, the elder one be 5 times as old as the younger one, their present ages(in years) are respectively
Answer Choices: (A) 33, 13 (B) 25, 5 (C) 29, 9 (D) 50, 30 (E) 20,10 | tiger_lab_math |
Maximoff's monthly bill is $60 per month. After he started working from home, his monthly bill increased by forty-five percent, and he also had to pay an additional $25 for a faster internet connection and $15 for a cloud storage subscription. How much is his total monthly bill working from home? | tiger_math |
In the diagram, $BP$ and $BQ$ trisect $\angle ABC$. $BM$ bisects $\angle PBQ$. Find the ratio of the measure of $\angle MBQ$ to the measure of $\angle ABQ$. | nvidia_math |
Dante needs half as many cups of flour to bake his chocolate cake as he needs eggs. If he uses x eggs in his recipe, calculate the total number of cups of flour and eggs that he uses altogether.
If we know the answer to the above question is 90, what is the value of unknown variable x? | tiger_math |
Let $p$ be the product of the digits of a number in base 6. What is the largest prime factor of $p$ such that $p$ is divisible by 10? | nvidia_math |
If 3 cards from a standard deck are selected randomly, what is the probability that either three kings or at least 1 ace occurs? (There are 4 Aces, 4 kings and 52 total cards in a standard deck.) | tiger_math |
Let \(\vec{V}(x, y, z) = (-y, x, 0)\) represent a two-dimensional velocity field embedded in three-dimensional space. Compute the curl of \(\vec{V}\), and interpret the result in terms of the angular velocity of a particle situated at the origin as it moves through this velocity field. What is the angular velocity of t... | automath |
What is the measure of each interior angle of a hexagon with 6 congruent sides? | tiger_math |
On the first day of the journey, the Skipper sailed his ship halfway to the destination by traveling due east for 20 hours at a speed of 30 kilometers per hour, and then turned the ship's engines off to let them cool down. But while the engines were off, a wind storm blew his vessel backward in a westward direction. A... | tiger_lab_math |
Problem:
If $x+\frac1x=-5$, what is $x^3+\frac1{x^3}$?
Write another problem inspired by this one:
Problem:
Given that $x^2+\frac1{x^2}=3$, find the value of $x^4+\frac1{x^4}$. | nvidia_math |
If Carl needs to drive a car for 2 hours every day to make a living, and after getting promoted he needs to drive for an additional 6 hours every week, how many hours will Carl drive in a span of two weeks? | tiger_math |
10% loss on the selling price is what percent loss on the cost price?
Answer Choices: (A) 9/55% (B) 100/11% (C) 99/110% (D) 90/11% (E) 9/11% | tiger_lab_math |
a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction q of the selected films are in color ? | tiger_math |
Consider the complex projective plane curve given by the equation $x^3+y^3+z^3=0$. Calculate the Hodge numbers $h^{1,0}$ and $h^{2,0}$ for this curve. | tiger_lab_math |
two pipes a and b can separately fill a cistern in 60 minutes and 120 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 60 minutes . in how much time , the third pipe alone can empty the cistern ? Let's ... | tiger_lab_math |
If you roll three standard 6-sided dice, how many different combinations of outcomes are possible if the order of the dice does not matter?
(A) 24
(B) 30
(C) 56
(D) 120
(E) 216 | automath |
How many non-negative integer solutions exist for the equation
\[
x_1 + x_2 + x_3 + x_4 = 20
\]
given the restrictions \(x_1 < 7\) and \(x_2 < 6\)? | automath |
"statement 1": John has more than 5 friends who want to ride in his new car that can accommodate only 5 people at a time ( John plus 4 passengers ), "statement 2" :John has 6 friends who want to ride in his new car that can accommodate only 5 people at a time ( John plus 4 passengers ), "options: " Entailment or contr... | tiger_lab_math |
A solid is generated by rotating the region bounded by the curves y = 2x^2 and y = x^3 about the x-axis. Find the volume of this solid. | tiger_lab_math |
If we multiply 18 by 30 and add the product of 27 and 15, what is the final result? | tiger_math |
Let i equal the sum of the prime even integers from 2 to √500, inclusive, k equal the sum of the even integers from 8 to √200, inclusive, and j equal the sum of the prime odd integers from 5 to √133, inclusive. What is the combined value of 2i - k + 3j, where only prime numbers between the square roots are considered? | tiger_math |
Mary purchased a new laptop for $1200 for her online business. She earns $50 for each product she sells, but she incurs a cost of Y for materials and shipping for each product. If Mary needs to sell a minimum of 32 products to recoup the cost of the laptop, what is the value of Y? | tiger_math |
Gerald is a furniture maker. He has 672 pieces of wood and he wants to make some tables and chairs. It takes 12 pieces of wood to make a table and 8 pieces of wood to make a chair. How many chairs can he make if he makes 24 tables? | tiger_lab_math |
"statement 1": If Yolanda ' s walking rate was 3 miles per hour and Bob т ' s was 4 miles per hour , how many miles had Bob walked when they met ?, "statement 2" :If Yolanda ' s walking rate was more than 2 miles per hour and Bob т ' s was 4 miles per hour , how many miles had Bob walked when they met ?, "options: " E... | tiger_lab_math |
Bob and Jim decide to skip rocks. Bob can skip a rock x times. Jim can skip a rock 15 times. If they each skipped 10 rocks how many total skips did they get?
If we know the answer to the above question is 270, what is the value of unknown variable x? | tiger_math |
In the expression $c \cdot a^b - d$, the values of $a$, $b$, $c$, and $d$ are 1, 2, 3, and 4, although not necessarily in that order. What is the maximum possible value of the result? | tiger_math |
A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold? | tiger_math |
Suppose $f(x)$ is a function such that $f(x) + (x^4-2x^2+1) = (3x^2+2x+1)$. Express $f(x)$ as a polynomial with the degrees of the terms in decreasing order. | nvidia_math |
Find the number of degrees in the measure of angle $y$ in the following figure:
[asy]
import markers;
size (5cm,5cm);
pair A,B,C,D,F,H;
A=(0,0);
B=(5,0);
C=(9,0);
D=(3.8,7);
F=(2.3,7.2);
H=(5.3,7.2);
draw((4.2,6.1){up}..{right}(5.3,7.2));
draw((3.6,6.1){up}..{left}(2.3,7.2));
draw (A--B--C--D--A);
draw (B--D);
ma... | tiger_math |
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