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Bill had to finish a project from work that was to take him 4 days, during which he also had to complete two other smaller tasks.
1. The first task required 6 hours of work, which he completed on day 3.
2. The second task needed 3 hours of work, which he finished on day 2.
During these four days, he took naps of var... | tiger_math |
Find the distance from the point $(2,4,1)$ to the line described by
\[\begin{pmatrix} 1 \\ 3 \\ -1 \end{pmatrix} + t \begin{pmatrix} 2 \\ -3 \\ 4 \end{pmatrix}.\] | nvidia_math |
Melanie has 41 books and 31 magazines in her library . She bought several books at a yard sale over the weekend . She now has 87 books in her library. She bought _____ books at the yard sale . Please write a program to solve it | tiger_lab_math |
Suppose f is a function that is twice differentiable for all real numbers. Which of the following statements must be true? I. If f''(x) > 0 for all x, then f is concave up for all x. II. If f'(x) = 0 for some x, then x is a critical point of f. III. If f has a local maximum at x = a, then f'(a) = 0. Answer Choices: (A... | tiger_lab_math |
Emily enjoys reading books and purchases three books every month from her favorite bookstore. Each book costs her $12. At a nearby bookstore, there is a monthly discount, where each book costs only $9. How much would Emily save in four months if she bought her books at the discounted bookstore instead of her favorite o... | nvidia_math |
For what positive value of $n$ does $|3+ni|=3\sqrt{10}$? | tiger_math |
Consider a right pyramid with vertices at $O$ (the origin), $A$ (on the x-axis), $B$ (on the y-axis), $C$ (on the z-axis), and apex $D$. The coordinates of $A$, $B$, and $C$ are $(a,0,0)$, $(0,b,0)$, and $(0,0,c)$, respectively. The center of the base of the pyramid is located at $(p,q,r)$. Find the ratio $\frac{a}{p} ... | nvidia_math |
How many ways can a team of 3 players be chosen from a group of 10 basketball players if any of the 10 players can be part of the team? | nvidia_math |
Find the number of moles of NaNO3 formed on combining 2 moles of NaCl and 2 moles of HNO3 Let's write a program. | tiger_lab_math |
the value of “ a ” varies in inverse proportion as the square of “ b ” . if the value of “ a ” is equal to 40 when “ b ” is equal to 12 . what would be the value of “ a ” when “ b ” is equal to 24 ? Let's write a Python program to solve it. | tiger_lab_math |
Square $ABCD$ has side length $30$. Point $P$ lies inside the square so that $AP = 12$ and $BP = 26$. The centroids of $\triangle{ABP}$, $\triangle{BCP}$, $\triangle{CDP}$, and $\triangle{DAP}$ are the vertices of a quadrilateral. If the quadrilateral is not convex, what is its area? | tiger_math |
Given a projection matrix \( P = A(A^TA)^{-1}A^T \), where \( A \) is a \( m \times n \) matrix with \( m \geq n \), what is the value of \( \det(P) \) if \( P \) is an \( m \times m \) projection matrix, and under what conditions can you conclude that \( \det(P) = 0 \) or \( 1 \)? | automath |
Excluding stoppages, the speed of a train is 54 kmph and including stoppages it is 40 kmph. Of how many minutes does the train stop per hour?
Answer Choices: (A) A) 13.55 (B) B) 14.55 (C) C) 15.55 (D) D) 16.55 (E) E) 17.55 | tiger_lab_math |
Sarah uses 1 ounce of shampoo, and one half as much conditioner as shampoo daily. In two weeks, what is the total volume of shampoo and conditioner, in ounces, that Sarah will use? | nvidia_math |
A rectangular prism $ABCD$ has a triangular hole $DEG$ cut from one face. Points $B$ and $G$ are diagonally opposite vertices. $AB=AE=BC=CG=3$, and $ED=EG=6$. Compute the volume of the solid.
[asy]
unitsize(0.8 cm);
pair A, B, C, D, E, F, G;
A = (0,0);
B = (3,0);
C = (3,3);
D = (0,3);
E = (-3,3);
F = (3,6);
G = (0,... | nvidia_math |
A rectangular garden is enlarged so that the new length and width are both twice the old length and width. What is the ratio of the original area to the enlarged area? Express your answer as a common fraction. | tiger_math |
Consider the surface defined by the equation:
z=2(x^2+y^2)
Find the sectional curvature of the surface at the point (1,1,4). | tiger_lab_math |
A group of 6 friends goes to a restaurant for dinner. They decide to split into two groups of 3, where one group orders pizza and the other group orders pasta. How many different ways can they split into groups? | tiger_math |
Emily visited the veterinarian with her cat for a vaccination, two check-ups, and a flea treatment. The veterinarian charges $40 for a vaccination and $60 for a check-up. Emily's total bill was six times the cost of a check-up. What did Emily pay for the flea treatment? | nvidia_math |
If a convex polyhedron \( P \) has a shadow graph \( G_S \) with 14 nodes, where each node is labeled by the integer \( k \) corresponding to the number of edges of the shadows projected in different directions, what is the possible number of vertices \( V \), edges \( E \), and faces \( F \) of \( P \)? Specifically, ... | automath |
A rancher owns a mixture of 8 sheep and 5 cattle that graze on his land. In a typical year, the rancher will allow his animals to feed off his pastures for as long as possible before they run out of grass. After the pastures run out of grass, he must buy feed corn for $10 per bag. Each cow eats 2 acres of grass per ... | tiger_math |
A painting at an art gallery is framed such that the area of the square frame is 2/3 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 10, what is the area of the painting inside the frame?
Answer Choices: (A) 10 (B) 20 (C) 30 (D) 40 (E) 50 | tiger_lab_math |
Given the complete bipartite graph \( K_{m,n} \), with \( m \) red vertices and \( n \) blue vertices, what is the total number of edges in this graph? Additionally, if \( m = 3 \) and \( n = 5 \), how many edges does \( K_{3,5} \) have? | automath |
Given the conditions \( \frac{x}{y} < 0 \) and \( y > x \), compare the two quantities:
Quantity A: \( y - x \)
Quantity B: \( xy \)
Which of the following statements is true?
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from... | automath |
Convert 500 miles into meters?
Answer Choices: (A) 784596 (B) 845796 (C) 804670 (D) 784596 (E) 864520 | tiger_lab_math |
A container with a capacity of 24 liters can hold Y bottles of water. Another container with a capacity of 72 liters can hold 225 bottles of water. What is the value of Y? | tiger_math |
Denny, an Instagram influencer, has 100000 followers and gets 1000 new followers every day. How many followers will he have if 20000 people unfollowed him in a year? Let's write a Python program to solve it. | tiger_lab_math |
What is the total volume in cubic feet of three boxes if each box is a cube with edge length 4 feet? | nvidia_math |
What is the LaTeX code for aligning a system of equations in the align environment, and how can you ensure a consistent horizontal alignment of the domains in these equations? | automath |
A circular sector with a radius of 10 units and an angle of 60 degrees is inscribed in a square. If a point is selected at random from the region determined by the square, what is the probability that the point is within the circular sector? Express your answer as a common fraction. | nvidia_math |
What is the value of the sum $$\sum_{k=0}^p (-1)^k {n \choose k}$$ for natural numbers $$p$$ and $$n$$? | automath |
Akira is three times as old as Kaito. In 2 years, Kaito's current age will be 12. What is Akira's current age? | nvidia_math |
Calculate the value of $64^2 - 36^2$. | tiger_math |
In a competition to spin plates, Alex has 6 plates that each spin 75 times and her rival, Ben, has 5 plates that each spin 90 times. How many total spins are made by the winner? | nvidia_math |
A librarian had $150 to purchase three different types of books. A fiction novel costs $10. A biography costs 1.5 times the price as the fiction novel, while a reference book costs twice the price as the biography. How much change did she receive after buying those three different types of books? | nvidia_math |
"statement 1": Kiran is younger than Bineesh by 7 years and their ages are in the respective ratio of 7 : 9, "statement 2" :Kiran is younger than Bineesh by less than 7 years and their ages are in the respective ratio of 7 : 9, "options: " Entailment or contradiction or neutral? Let's write a Python program to solve i... | tiger_lab_math |
Evaluate the integral \( \int_{-\infty}^\infty \frac{x^2}{x^4 + 1} \, dx \). What is the numerical value of this integral? | automath |
Let \( F(x) = x^2 \cos\left(\frac{1}{x}\right) \) for \( x \neq 0 \) and \( F(0) = 0 \). Define the function \( V_F(x) = \int_0^x |F'(t)| dt \). Calculate the value of \( V_F'(0) \). | automath |
In a car dealership, Fiona worked for 40 hours a week, John for 30 hours, and Jeremy for 25 hours. If the employees are paid $20 per hour, how much money does their boss spend paying all of them every month? | tiger_lab_math |
Given an array \( a = [1, 0, 0, 0] \) and a number \( k \), calculate the \( i \)-th element \( b_i \) of the array \( b \) after performing the prefix sum operation \( k \) times, as described in the snippet. Derive a general formula for \( b_i \) in terms of \( a \) and \( k \), and determine \( b_2 \) when \( k = 10... | automath |
What is the area of the circle defined by $x^2-6x +y^2-14y +33=0$ that lies beneath the line $y=7$? | nvidia_math |
Micah picks 2 dozen strawberries from the field. He eats 6 and saves the rest for his mom. How many strawberries are there for his mom? | tiger_lab_math |
Emily has 50 songs in her music library. She deletes 5 songs she no longer likes, downloads 8 new songs from her favorite artist, and then records some songs at a music festival. After editing the festival recordings, she decides to delete 2 of them. Her music library has 67 songs in the end. How many songs did Emily r... | nvidia_math |
Solve for $z$ in the following equation: $3-2iz = -2 + 6iz$.
Express your answer in standard form. | tiger_math |
A soccer team has 24 players. They have scored 150 goals on the season. There have been x games played. 1/3 of the players have averaged 1 goal each per game. The other players have scored 30 total goals. What is the value of unknown variable x? What is the value of unknown variable x? | tiger_math |
Given a finite population of size \( N = 200 \) and a sample size of \( n = 33 \) with sample mean \( \bar{x} = 147.7 \) pounds and sample standard deviation \( s = 26.7 \) pounds, calculate the 95% confidence interval for the population mean \( \mu \) using the finite population correction factor. What is the resultin... | automath |
What is the complete domain of the function \( F(x, y) = \arcsin\left(\frac{y}{x}\right) \) in the \( xy \)-plane, and how can it be expressed in terms of inequalities for the values of \( x \) and \( y \)? | automath |
Here's a question for a math student to solve related to Morse homology:
Consider the function $f(x,y,z)=x^2+y^2+z^2$ on the unit 3-sphere $S^3=\{(x,y,z,w) \in \mathbb{R}^4 : x^2+y^2+z^2+w^2=1\}$. Define $h_t(x,y,z,w)=f(x,y,z,w)+t$, where $t \in \mathbb{R}$ is a real number. Determine the Morse function for $h_t$ and ... | tiger_lab_math |
Susan is making jewelry with a repeating pattern that has 3 green beads, 5 purple beads, and twice as many red beads as green beads. If the pattern repeats three times per bracelet and 5 times per necklace, how many beads does she need to make 1 bracelets and 10 necklaces? | tiger_math |
A rectangular prism measures 10-inches by 20-inches by 10-inches. What is the length, in inches, of the diagonal connecting point A and point B? Express your answer in simplest radical form. [asy]
unitsize(0.75cm);
defaultpen(linewidth(0.7pt)+fontsize(10pt));
dotfactor=4;
draw((0,1)--(1,1)--(1,0)--(0,0)--(0,1)--(1,2)-... | nvidia_math |
If Roberto has four pairs of trousers, seven shirts, and three jackets, how many unique combinations of outfits can he create, with each outfit consisting of one pair of trousers, one shirt, and one jacket? | tiger_math |
Stella and Twinkle are filling up a truck with a capacity of x stone blocks at the rate of 250 blocks per hour per person. They work for four hours and are then joined by 6 other people who also work at the same rate. Filling the truck took 6 hours. What is the value of unknown variable x? | tiger_math |
If James is responsible for cleaning 3 bedrooms, 1 living room, and 2 bathrooms in the class, with each bedroom taking 20 minutes to clean, the living room taking the same amount of time as the 3 bedrooms combined, and the bathroom taking twice as long as the living room, how many hours does James work in total? | tiger_math |
Calculate the area of the region bounded by the curves \(y = 8 - 6x + x^2\), \(y = -4 + 2x\), and \(y = 2 + x\). Provide the definite integrals used to find this area and specify which regions are included in the area calculation. | automath |
If Allen ordered five boxes of pizza at $7 per box and gave a tip equivalent to 1/7 of the total cost of his order, and he paid the delivery man $100, how much change did he receive? | tiger_math |
Using the trapezium rule, estimate the value of the integral $$\displaystyle \int_0^1 {1\over 1+e^x} \:dx$$ with 4 trapeziums. Please provide your answer to four decimal places. | automath |
If $f(x) = X$ for all real numbers $x$ and $f(x - 3) = 5$, what is the value of $x$? | tiger_math |
Lily and Leo prepared 145 care packages to be donated to a local shelter. Later, Pet Palace donated 30 more care packages. If Lily and Leo have already distributed 90 care packages, how many more care packages are left to be given away? | nvidia_math |
A student stands at point A and spots a building at point B. The angle of elevation from the student to the top of the building is 30 degrees. The distance from the student to the building is 50 meters. Using trigonometry, what is the height of the building? | tiger_lab_math |
What is the 95% confidence interval for the mean income of a population if a sample of 25 students yields a sample mean of $400 and a sample standard deviation of $100? | automath |
A racecar travels around a circular track with a constant speed of 60 miles per hour. The car starts at a fixed point $P_0$ on the track. At the end of each hour, the car turns $45^{\circ}$ clockwise and continues moving with the same speed. How far will the car be from $P_0$ after 2016 hours? | nvidia_math |
If Mark made a chalkboard that is 3 feet wide and 2 times as long as it is wide, what is the area of the chalkboard? | tiger_math |
after decreasing 20 % in the price of an article costs rs . 620 . find the actual cost of an article ? Let's program in Python in the response. | tiger_lab_math |
Let \( f(z) = z^3 - z^2 - z - 1 \), where \( z = x + iy \). What are the approximate coordinates of the roots of the function \( f(z) = 0 \) in the complex plane, accurate to three decimal places? | automath |
Given that $x_1,$ $x_2,$ $\dots,$ $x_n$ are nonnegative real numbers such that $x_1 + x_2 + \dots + x_n = 1$ and $x_1^2 + x_2^2 + \dots + x_n^2 \le \frac{1}{100}$, find the smallest possible value of $n$.
Let $x_1,$ $x_2,$ $\dots,$ $x_n$ be nonnegative real numbers satisfying $x_1 + x_2 + \dots + x_n = 1$ and $x_1^2 ... | nvidia_math |
A jar of peanut butter which is 3 inches in diameter and 4 inches high sells for $\$$0.60. At the same rate, what would be the price for a jar that is 6 inches in diameter and 6 inches high? | nvidia_math |
how many consecutive zeros are there at the end of 100 ! ( 100 factorial ) ? | tiger_math |
If Roxanne purchased 2 cups of lemonade for $2 each and 2 sandwiches for $2.50 each, how much change should she receive from a $20 bill? | tiger_math |
Lindsey bought 2 exercise bands to intensify her workout. Each band adds an extra 5 pounds of resistance to her workout. If she doubles up both sets of bands and places them around her legs and picks up a 10-pound dumbbell, how much weight will she squat? | tiger_lab_math |
In a certain school, each student is required to take either one or two of three available courses: physics, chemistry, and biology. The number of students who take only physics is 10, only chemistry is 8, and only biology is 6. Additionally, 15 students take both physics and chemistry, 12 take both physics and biology... | nvidia_math |
When 30 can divided by some numbers, how many divisible numbers are there? | tiger_math |
Given a tetrahedron with isoperimetric faces, if the lengths of the opposite edges are represented as \(a\), \(a'\), \(b\), \(b'\), \(c\), and \(c'\) such that the perimeters of the four faces are equal, what can be concluded about the relationships between the edges \(a\), \(b\), and \(c\)? Specifically, what are the ... | automath |
Compute $\tan 3825^\circ$. | nvidia_math |
If $f(x)=\frac{ax+b}{cx+d}, abcd\not=0$ and $f(f(x))=x$ for all $x$ in the domain of $f$, what is the value of $a+d$? | tiger_math |
Hans reserved a table at a fine dining restaurant for twelve people. He has to pay a deposit for the reservation, which is a flat amount plus an extra $3 per adult but only $1 per child. Two of the people in Hans's party are his kid cousins, and the rest are adults. Hans has to pay $52 as a deposit for the restaurant r... | tiger_math |
Find
\[\sum_{n = 1}^\infty \frac{n^2 + n - 1}{(n + 2)!}.\] | tiger_math |
What is the politeness of the number 30, defined as the number of ways it can be expressed as a sum of two or more consecutive positive integers? | automath |
Alex made 6 batches of cookies for the holiday party. The cookies took 15 minutes to mix and 25 minutes to bake per batch. How long did it take Alex to make the cookies? | nvidia_math |
"statement 1": At the faculty of Aerospace Engineering , 302 students study Random - processing methods , 232 students study Scramjet rocket engines and 112 students study them both, "statement 2" :At the faculty of Aerospace Engineering , 102 students study Random - processing methods , 232 students study Scramjet ro... | tiger_lab_math |
Passage: This overall downturn affected Holdens profits; the company recorded a combined gain of A$842.9 million from 2002 to 2004, and a combined loss of A$290 million from 2005 to 2006. Factors contributing to the loss included the development of an all-new model, the strong Australian dollar and the cost of reducing... | tiger_lab_math |
A company has two models of computers, model M and model N. Operating at a constant rate, a model M computer can complete a certain task in 36 minutes and a model N computer can complete the same task in 18 minutes. If the company used the same number of each model of computer to complete the task in 1 minute, how many... | tiger_lab_math |
A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits o... | tiger_lab_math |
Find all two-digit numbers such that the sum of the number and the number obtained by reversing its digits is 99, and the digits of the number differ by 3. | automath |
Billy ate x apples this week. On Monday, he ate 2 apples. On Tuesday, he ate twice as many as he ate the day before. He’s not sure what he ate on Wednesday. On Thursday, he ate four times as many as he ate on Friday. On Friday, he ate half of the amount he ate on Monday. He ate 9 apples on Wednesday. What is the value ... | tiger_math |
Given the function \( f(\mathbf{x}) = \frac{1}{2} \|\mathbf{A}(\mathbf{y} - \mathbf{x})\|_2^2 \), where \( \mathbf{A} \) is an \( m \times n \) matrix, find the expression for the Legendre transform \( f^{\star}(\mathbf{s}) \) and identify the conditions under which the transform is maximized. Specifically, if \( \math... | automath |
If adjacent stripes must be different colors, how many different flags can be designed by the students of Crestview using three solid-colored horizontal stripes, using one or both of the school colors, purple and gold? | tiger_math |
A glass vase is filled with water and has the shape of an inverted truncated cone. The vase has a height of 12 inches and a large base radius of 8 inches. The small base radius is half of the large base radius. Determine the volume of water in the vase when the water level is 4 inches from the top of the vase.
Draw a ... | nvidia_math |
In a magical forest, there are two types of trees: Whispering Willows and Talking Tamarinds. Each Whispering Willow speaks 3 enchanting words per minute, while each Talking Tamarind utters 5 mystic words per minute. Today, the trees held a grand discussion that lasted for 120 minutes, and a total of 1236 enchanting and... | tiger_math |
A problem in hyperbolic geometry:
A hyperbolic triangle on the hyperbolic plane has angles of 60 degrees, 70 degrees, and 50 degrees. Find the area of the hyperbolic triangle. | tiger_lab_math |
Ava scored six points in the final basketball game of the season. Her sister has scored three times as many points as Ava scored in the last game in each match she's played in each of the four seasons she's been on the team. Each season has 20 matches. What is the total number of points the sisters have scored between ... | nvidia_math |
A restaurant meal cost $35.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then the total amount paid must have been between
Answer Choices: (A) $40 and $42 (B) $39 and $41 (C) $38 and $40 (D) $37 and $39 (E) $36 and $37 | tiger_lab_math |
Sarah is checking out books from the library to read on vacation. She can read 40 words per minute. The books she is checking out have 100 words per page and are 80 pages long. She will be reading for 20 hours. How many books should she check out? | tiger_math |
In triangle $ABC,$ $AB = 20$ and $BC = 15.$ Find the largest possible value of $\tan A.$ | nvidia_math |
Karla is planning a garden party for her grandmother's birthday and wants to ensure she has enough seating for all her guests. If she arranges the tables into a circle and puts 4 chairs at each table, the number of chairs exceeds the number of guests by 8. However, if she increases each table by 1 chair, she finds she ... | tiger_math |
Given a sequence of points \( x_n \) in \( \mathbb{R}^2 \) defined by \( x_n = \frac{1}{n} e_1 \) if \( n \) is odd and \( x_n = \frac{1}{n} e_2 \) if \( n \) is even, is it possible to construct a differentiable path \( \gamma(t) \) such that \( \gamma(0) = 0 \) and \( \gamma(t_n) = x_n \) for a sequence \( t_n \) tha... | automath |
An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time D will it take to fill the bucket to full capacity?
Answer Choices: (A) 7/18 (B) 9/18 (C) 2 (D) 18/7 (E) 18/5 | tiger_lab_math |
The vertices of the square are (-a, -a), (a, -a), (-a, a), (a, a).
In this square, two lines y=x and y=-x are drawn which intersect at the origin (0, 0).
Find the ratio of the area of the square to the sum of the areas of the four smaller triangles created by the intersection of the two lines.
Express the answer in ... | nvidia_math |
Suppose we have a financial time series data that has 120 monthly data points, and the monthly return of a stock fund is given by $r_n$ at the end of month $n$. Apply the Fourier transform to the data, and calculate the amplitude and phase of the frequency component corresponding to a 6-month cycle. | tiger_lab_math |
Find the smallest composite number that has no prime factors less than 10. | tiger_lab_math |
Difference between two numbers is 5, six times of the smaller lacks by 4 from the four times of the greater. Find the numbers?
Answer Choices: (A) 5,3 (B) 7,5 (C) 9,7 (D) 11,9 (E) 13,8 | tiger_lab_math |
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