instruction_seed stringlengths 17 6.7k | source stringclasses 4
values |
|---|---|
Maya visited a bookstore and saw three novels on display: "The Quest" for $25, "Tides of Time" for $35, and "Glimpse of Eternity" for $40. If she bought 4 copies of each novel to gift to her classmates, what is the total amount of money Maya spent at the bookstore? | nvidia_math |
Given the system of linear equations in three variables:
\[
\begin{align*}
{{a}_{1}}x + {{b}_{1}}y + {{c}_{1}}z + {{d}_{1}} = 0 \\
{{a}_{2}}x + {{b}_{2}}y + {{c}_{2}}z + {{d}_{2}} = 0 \\
{{a}_{3}}x + {{b}_{3}}y + {{c}_{3}}z + {{d}_{3}} = 0
\end{align*}
\]
If it is known that \(\Delta = \left| \begin{matrix} {{a}_{1}}... | automath |
Find the sum of $221_5 + 432_5 + 243_5$. Express your answer in base $5$. | nvidia_math |
Given that the fundamental vibrational wavenumber for \(^{12}C^{16}O\) is \(2143 \, \text{cm}^{-1}\), calculate the wavelength of the corresponding transition in nanometers. | automath |
In base $b$, there are exactly $b^2$ four-digit numbers whose digits are all distinct and the sum of the digits is a multiple of $b$.
Determine $b$. | nvidia_math |
A set of numbers has the property that for any number x in the set, x+5 is also in the set. If -5 is in the set, which of the following must also be in the set
1. -10
2. 10
3. 0
Answer Choices: (A) 1 only (B) 2 only (C) 1 and 3 only (D) 2 and 3 only (E) 1,2 and 3 | tiger_lab_math |
If \( \theta \) is an acute angle and \( \cos(\theta) = \frac{4}{7} \), what are the possible values of \( \sin(\theta) \)? Enter all possible values, separated by commas. | nvidia_math |
If 6 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed?
Answer Choices: (A) 80 (B) 63 (C) 420 (D) 160 (E) 1260 | tiger_lab_math |
a train passes a train standing in platform in 30 sec and a man standing on the platform in 12 sec . if the speed of the train is 36 km / hr . what is the length of the platform ? Please write a program to solve it | tiger_lab_math |
What is the maximum value of the reconstruction error \( E \) defined as \( E = \max_{x,y} | \exp(-x^2 - y^2) - f_{reconstructed}(x,y) | \) when using a 2D inverse discrete Fourier transform to reconstruct the function \( f(x,y) = \exp(-x^2 - y^2) \) from its Fourier coefficients, assuming an ideal sampling grid of siz... | automath |
The area of an equilateral triangle is numerically equal to half the length of one of its sides. What is the perimeter of the triangle, in units? Express your answer in simplest radical form. | tiger_math |
Given that Anscombe's quartet consists of four sets of bivariate data with the same mean for the x variables (9) and approximately the same mean for the y variables (7.50), if all four data sets have the same correlation coefficient of 0.8, what is the estimated range of values for the y variable when x is equal to 10 ... | automath |
Claire has a total of 90 pets consisting of gerbils and hamsters only. One-quarter of the gerbils are male, and one-third of the hamsters are male. If there are 25 males altogether, how many gerbils does Claire have?
Answer Choices: (A) 39 (B) 50 (C) 66 (D) 57 (E) 60 | tiger_lab_math |
What is the next number in the sequence : 13,17,25,32,37,47,58,71__?
Answer Choices: (A) 78 (B) 79 (C) 71 (D) 76 (E) 73 | tiger_lab_math |
A zoo is designing a rectangular playground to exercise the animals. The length of the playground is twice its width. They've allocated an area of 288 square meters for the playground. Once the playground is constructed, they plan to enclose it with a fence. What is the minimum length of the fence needed for the playgr... | tiger_math |
Given four points \( A, B, C, D \) in the complex plane, let the cross-ratio be defined as
\[
(A, B, C, D) = \frac{A - C}{A - D} \cdot \frac{B - D}{B - C}.
\]
If we place these points such that \( D \) is at infinity, \( C \) is at the origin, and \( B \) is at 1, express the cross-ratio \( (A, B, C, D) \) in terms ... | automath |
Emily has invested $500$ dollars in a savings account with a $6\%$ annual interest compounded annually, while her brother, Ben, has invested $600$ dollars in a certificate of deposit (CD) with a $4\%$ annual interest compounded quarterly. In how many years will Emily's investment surpass Ben's investment, assuming that... | nvidia_math |
If two sides of a triangle are 12 and 4, which of the following could be the area of triangle?
1. 35
2. 48
3. 56
Answer Choices: (A) a) 1 only (B) b) 1 and 2 only (C) c) 1 and 3 only (D) d) 2 and 3 only (E) e) 1, 2 and 3 only | tiger_lab_math |
What is the value of \(\sin\left(\frac{\pi}{6}\right)\) and how does it relate to the coordinates of a point on the unit circle? | automath |
How many times do the graphs of the line $5x + 8y = 10$ and the circle $x^2 + y^2 = 1$ intersect? | tiger_math |
Given a velocity-time graph for a car, where the slope (acceleration) is constant, and is represented by the equation \( v(t) = at + b \) (where \( a \) is the acceleration and \( b \) is the initial velocity), determine the time \( t \) at which the car's velocity reaches a specific target velocity \( v_t \). What is ... | automath |
Marj has two $20 bills, three $5 bills, and $4.50 in loose coins in her wallet. If she buys a cake that costs $17.50, how much money will be left in her wallet? | tiger_lab_math |
Given a surface charge density \(\sigma\) distributed on a surface \(S\), how would you express the associated volumetric charge density \(\rho(\vec{r})\) in terms of \(\sigma\) using the Dirac delta function? Specifically, what is the form of \(\rho(\vec{r})\) and how does it relate to \(\sigma\) when integrating over... | automath |
Abraham is buying some toiletries and creates a budget of $x for his shopping. He buys 4 shower gels for $4 each, a tube of toothpaste for $3, and a box of laundry detergent. If he has $30 remaining in his budget, how much money, in dollars, Abraham spent 11 on the box of laundry detergent. What is the value of unknown... | tiger_math |
An encrypted message was created using a transposition cipher. The original message was 60 characters long and the encrypted message is also 60 characters long. The encryption was done by arranging the characters in a 6x10 grid and reading them off in columns from left to right. What is the decryption key to recover th... | tiger_lab_math |
A small town has a total of 100 households. The distribution of households by size is as follows:
| Size of household | Number of households |
| --- | --- |
| 1 person | 15 |
| 2 people | 20 |
| 3 people | 25 |
| 4 people | 20 |
| 5 people | 10 |
| 6 people | 10 |
A local non-profit organization wants to provide hous... | nvidia_math |
What is the sum of all two-digit positive integers that are odd and leave a remainder of 1 when divided by 4? | automath |
Jeremy buys 30 watermelons. He eats 3 watermelons per week. Each week he gives 2 to his dad. How many weeks will the watermelons last? Let's program in Python in the response. | tiger_lab_math |
Given a Poisson process where the waiting times between events follow an exponential distribution, suppose that the total time from the first accident to the current time is \( t = X_C + \sum_{i=1}^N X_i \), where \( X_C \) is the time since the last accident and \( X_i \) are the waiting times for the first \( N \) ac... | automath |
Which integer is closest to the square root of 45? | nvidia_math |
Find the range of values for which the function $f(x) = \sqrt{\sin^{-1}(\cos^{-1}x)}$ is defined. | nvidia_math |
A rectangular prism with a length of 6 units, a width of 4 units, and a height of h units has the same volume as a cylinder with a radius of 3 units and a height of 4 units. What is the value of h? | tiger_math |
A box contains 4 red balls and 6 blue balls. Two balls are randomly drawn from the box, one after the other, without replacement. What is the probability that the second ball drawn is red, given that the first ball drawn is blue? | nvidia_math |
Mr. Johnson has a meeting at 3 pm and needs to leave his office by 2:45 pm. He was waiting to use the office printer at 1:45 pm. His coworker used the printer for 20 minutes, and then another colleague used it for 30 minutes. After that, the office manager used it for 15 minutes. How much time will Mr. Johnson have to ... | nvidia_math |
In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected. The number of candidates appeared from each state was 8000. How many more candidates got selected in State B than in State A? | tiger_math |
Tara is saving up to buy a new clarinet. She already has $10 saved. The clarinet costs $90. She plans to sell her old books to make the money. She sells each book of hers for $5. However, when she is halfway towards her goal, she loses all her savings and has to start over. How many books does she sell in total by the ... | tiger_lab_math |
In one hour, a boat goes 8 km along the stream and 2 km against the stream. What is the speed of the boat in still water (in km/hr)? | tiger_math |
In an M/M/1 queue where requests arrive following a Poisson process and service times are exponentially distributed, if a request has already waited in the queue for \( x \) minutes, what is the expected time remaining until that request is served? Does this expected time depend on \( x \), and if so, how can we mathem... | automath |
Consider a regular hexagon with side length of 10cm. Divide it into 6 equilateral triangles, as shown below:
Now, divide each of these equilateral triangles into 4 smaller equilateral triangles by connecting the midpoints of adjacent sid... | tiger_lab_math |
How many non-zero integers $m$ satisfy the inequality $\frac{1}{|m|} \geq \frac{1}{8}$? | tiger_math |
Given a binomial random variable \( X \sim B(n, p) \) with \( n = 8 \), and that the cumulative distribution function \( P(X \leq 5) = 0.9 \), calculate the probability \( p \) such that this condition holds. What numerical or approximate value does \( p \) take? | automath |
For every white duck at the lake there are 5 fish. For every black duck there are 10 fish and for every multicolor duck there are 12 fish. Currently there are 3 white ducks, 7 black ducks and 6 multicolored ducks. How many fish are in the lake? | tiger_math |
George and Amelia are picking oranges and apples at an orchard. George picks 45 oranges and x more apples than Amelia. Amelia picks 18 fewer oranges than George and 15 apples. They pick 107 fruits altogether. What is the value of unknown variable x? What is the value of unknown variable x? | tiger_math |
Consider a Thevenin equivalent circuit with a capacitor of capacitance \( C = 0.2 \, \mu F \), a Thevenin voltage \( E_{Th} = 7 \, V \), and a Thevenin resistance \( R_{Th} = 30 \, k\Omega \).
a. What is the voltage across the capacitor \( v_C(t) \) as a function of time immediately after the switch is closed at \( t... | automath |
Given the energy-momentum tensor for a perfect fluid,
$$T^{ab}=(\rho + p) u^a u^b - p g^{ab},$$
where \( p \) is pressure and \( \rho \) is density, what are the conservation laws derived from the equation
$$\nabla_b T^{ab}=0$$
in a curved spacetime? Specifically, if we set \( p = 0 \) (pressureless fluid), wha... | automath |
The ratio of the number of females to males at a party was 1:2 but when 4 females and 4 males left, the ratio became 1:3. How many people were at the party originally?
Answer Choices: (A) 20 (B) 22 (C) 24 (D) 26 (E) 28 | tiger_lab_math |
two tracks are parallel . the first track has 6 checkpoints and the second one has 10 checkpoints . in how many ways can the 6 checkpoints of first track be joined with the 10 checkpoints of the second to form a triangle ? Let's write a Python program to solve it. | tiger_lab_math |
Can you provide an explicit calculation showing that the restriction of the structure sheaf $\mathcal{O}_X$ from $X = \operatorname{Spec}(\mathbf{Z})$ to the closed subscheme $Y = \{(p)\} \cong \operatorname{Spec}(\mathbf{Z}/p\mathbf{Z})$ for a prime $p$ is not a sheaf of $\mathcal{O}_Y$-modules? Specifically, demonstr... | automath |
A construction company is building 2 apartment buildings with 12 floors each. The apartments are almost ready to sell but all of them need doors to be completed. Each floor has 6 apartments, and each apartment needs 7 doors in total. How many doors does the company need to buy? | tiger_math |
At a school event, there are 20 students from the debate team, 15 students from the choir, and some teachers. If they are divided into 4 equally sized groups for a team-building activity, each group has 18 people. How many teachers are attending the event? | nvidia_math |
What is the smallest possible jump length \( K \) that allows a player to reach the field marked \( Z \) from field 1 on a circular game-board of \( N \) fields, given that certain fields have obstacles? The player can only jump clockwise and may not land on an obstacle. Please provide your answer for multiple test cas... | automath |
Simplify the expression $2(x+3) + 3(x+4) + 4(x+5)$.
Can you simplify this expression and find the solution? | nvidia_math |
A right triangle has an area of 36 square units, and a leg length of 6 units. What is the perimeter of the triangle, in units? | nvidia_math |
If there were initially 1800 cats on the island and 600 cats were relocated to a neighboring island on the first mission, and then half of the remaining cats were relocated to a rescue center on the second mission, how many cats remained on the island after the rescue mission? | tiger_math |
If a rectangle has a width of 42 inches and an area of 1638, how many rectangles of the same size would reach a length of 390 inches? | tiger_math |
On Friday, a snowboard originally priced at $\$100$ was discounted $50\%$. On Monday, that sale price was reduced by $30\%$. In dollars, what is the price of the snowboard after the Monday reduction? | nvidia_math |
Add $1_3 + 12_3 + 212_3 + 2121_3.$ Express your answer in base X. The answer is 3. What is the value of unknown variable X? | tiger_math |
Biff is getting ready for a long bus trip. He spends $11 on the ticket, $3 on drinks and snacks, and $16 on a new pair of headphones to listen to music. Biff plans to do online tasks using the bus's WiFi during his trip. If Biff makes $12/hour working online and has to pay $2/hour to access the bus's WiFi, how many hou... | tiger_lab_math |
Determine a positive integer that is a multiple of 27 and whose fourth root is a number between 1.4 and 1.41. | tiger_math |
In a survey of 75 students in the school orchestra, 40 take French, 32 take Spanish, and 18 students take both French and Spanish. How many orchestra students take neither French nor Spanish? | nvidia_math |
Let $\mathbf{a},$ $\mathbf{b},$ and $\mathbf{c}$ be three nonzero vectors in $\mathbb{R}^3,$ such that $\mathbf{b}$ and $\mathbf{c}$ are not parallel. Find all possible values of
\[\frac{\mathbf{a} \cdot \mathbf{b}}{\|\mathbf{a}\| \|\mathbf{b}\|} + \frac{\mathbf{a} \cdot \mathbf{c}}{\|\mathbf{a}\| \|\mathbf{c}\|} + \f... | nvidia_math |
The distance between Robin's house and the city center is 500 meters. He leaves the house to go to the city center. After he walks some meters he realizes that he forgot his bag. So he returns to his house, then goes back to the city center. He walks a total of 900 meters. How far did he walk before realizing he forgot... | tiger_math |
Evaluate the definite integral \(\int_{0}^{8} \sqrt{8x - x^2} \, dx\) using trigonometric substitution. What is the final numerical result of this integral? | automath |
If there are 50 people at a party and 30% of them are boys, how many girls are present at the party? | tiger_math |
In the town of Hamlet, there are 3 people for each horse, 4 sheep for each cow, and 3 ducks for each person. Given this information, which of the following totals cannot possibly represent the sum of the number of people, horses, sheep, cows, and ducks in Hamlet?
A. 41
B. 47
C. 59
D. 61
E. 66 | automath |
Suppose that $x^2$ varies directly with $\sqrt{w}$. If $x=3$ when $w=16$, find the value of $w$ when $x=5$. Express your answer in simplest fractional form. | nvidia_math |
What is the present value of receiving $50 at the end of each year for 15 years if the interest rate is 4%? | automath |
Consider the one-dimensional heat equation given by:
∂u/∂t = k ∂²u/∂x²
where k = 0.1 is the thermal diffusivity constant.
A metal rod of length L=1m is initially at a temperature of u(x,0) = sin(πx/L). The ends of the rod are kept at constant temperatures such that u(0,t) = u(L,t) = 0 for all t.
Find the solution ... | tiger_lab_math |
One fourth of a solution that was 10% sugar by weight was replaced by a second solution resulting in a solution that was 17 percent sugar by weight. The second solution was what percent sugar by weight?
Answer Choices: (A) 34% (B) 24% (C) 22% (D) 38% (E) 8.5% | tiger_lab_math |
What is the 39th number in the row of Pascal's triangle that has 41 numbers? | nvidia_math |
What are two examples of topological spaces that have the same homology groups and cohomology groups, but different cohomology rings? | automath |
If $\frac{1}{2}$ of $2^{20}$ is $4^x$, then what is the value of $x$ ? | tiger_math |
The function $g(t)$ satisfies
\[g(tz) = \frac{g(t)}{z^2}\]for all positive real numbers $t$ and $z.$ If $g(48) = 16,$ find $g(60)$. | nvidia_math |
Carla is taking attendance for her sixth-grade class. She knows that 2 students are in the restroom, and one less than three times that number of students are absent. If there are four rows with six desks each that are all 2/3 full, how many students does Carla teach, including the ones in and out of the classroom? | tiger_math |
What conditions must be satisfied for a set of continuous functions from a compact metric space \( M \) to itself to be compact in the sense of the Heine-Borel theorem, and can you provide an example to illustrate these conditions? | automath |
Jude is trading his bottle cap collection to Arthur for some of Arthur's matchbox vehicles. Arthur charges Jude 5 bottle caps for a car and 6 bottle caps for a truck. Jude has 100 bottle caps. If he buys 10 trucks and spends 75% of his remaining bottle caps on cars, how many total matchbox vehicles does he buy? | tiger_lab_math |
A spaceship is traveling from Earth to the Planet X which is 1.5 light-years away. The spaceship travels at a speed of \(\frac{1}{3}\) light-year per Earth year. How long in Earth years will it take for the spaceship to reach Planet X? | tiger_math |
Tracy has been collecting novels from her friends to donate to the Children For The Future charity organization. In the first week she collects a certain number of books. In the next five weeks, she collects ten times as many books as she did in the first week. How many books did she collect in the first week if she ha... | tiger_lab_math |
Yanni has $0.85. His mother gave him $0.40 in addition. While going to the mall, Yanni found $0.50. He bought a toy that cost $1.6. How much money in cents did Yanni have left? Let's program in Python in the response. | tiger_lab_math |
Kylie has 5 daisies. Her sister gave her another 9 daisies. Kylie then gave half her daisies to her mother. How many daisies does Kylie have left? | tiger_math |
Find the angle, in degrees, between the vectors $\begin{pmatrix} 3 \\ 2 \end{pmatrix}$ and $\begin{pmatrix} 4 \\ -6 \end{pmatrix}$. | nvidia_math |
Evaluate $(x-a+3)$ if the value of $x$ is $(a+7)$. | tiger_lab_math |
Let $\mathcal{X}$ be a gerbe that is represented as an algebraic stack. If $X$ is an algebraic space such that $\mathcal{X}$ is a gerbe over $X$, what are the necessary conditions that the sheafification of the presheaf \( \mathcal{F} \) defined as \( (\mathit{Sch}/S)_{fppf}^{opp} \to \textit{Sets}, \quad U \mapsto \ma... | automath |
John buys 2 shirts. The first shirt costs $6 more than the second shirt. If the first shirt costs $15, how much, in dollars, did the shirts cost in total? | nvidia_math |
Juanita goes through 1 bottle of sunscreen a month. She likes to stock up for the entire year when a certain website offers 30% off her entire purchase. If each bottle is $30.00 how much will all of the sunscreen cost after the discount? Let's write a program. | tiger_lab_math |
What is the largest integer $y$ for which $y > \frac{3y}{2} + 5$? | nvidia_math |
What is the difference in spacing between using \( x^{\sim} \), \( \overset{\sim}{x} \), \( \tilde{x} \), and \( \widetilde{x} \) in LaTeX, and how does each notatio affect the visual representation of the variable \( x \) in a mathematical context? | automath |
What is the sum of all the positive divisors of 143, which is the product of two distinct prime numbers? | tiger_math |
Find the greatest common divisor of 91 and 72. Let's write a program. | tiger_lab_math |
What is the volume of the solid generated when the region enclosed by the curves \( y^2 = x \), \( y = 1 \), and \( x = 0 \) is revolved about the x-axis? Use cylindrical shells to compute this volume. | automath |
Given that $x^2 + x^2 + x^2 = 27$, what is the value of $x$? | nvidia_math |
A circle's area is $x$ square units, and its circumference is $y$ units. The value of $x - y$ is $20\pi$. What is the radius of the circle, in units? | tiger_math |
What is the maximum number of mistakes that the perceptron algorithm can make when classifying a dataset of linearly separable points in two-dimensional space, given a perfect hypothesis exists? | automath |
A bag contains 10 balls, 8 of which are blue. If we randomly select 2 balls from the bag without replacement, what is the probability that both balls are blue? | tiger_math |
Zachary paid for a $\$1$ burger with 32 coins and received no change. Each coin was either a penny or a nickel. What was the number of nickels Zachary used? | tiger_math |
Compute the matrix $\mathbf{B}^3$ where
\[\mathbf{B} = \begin{pmatrix} 0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}.\] | nvidia_math |
Is the number \( \sqrt[3]{7 + \sqrt{50}} + \sqrt[3]{7 - 5\sqrt{2}} \) a rational number, and if so, what is its value? | automath |
Given the polynomial $p(x) = x^5 + ax^3 + bx^2$, find the sum of the cubes of the coefficients when $p(x)$ is multiplied by $(x^2 + 2)$.
Answer: (1 + a)^3 + (2b)^3 + 2^3.
Reasoning Skill: Identifying Pros And Cons
In this problem, we need to identify the pros and cons of different approaches to finding the sum of th... | nvidia_math |
What is the minimum number of iterations required by the bisection method to ensure that the error is less than \(10^{-3}\) for a root of the equation \(e^{x} - 3x^{2} = 0\) located in the interval \((3,4)\)? Provide a detailed calculation to support your answer, and choose one of the following options:
(a) 10
(b) ... | automath |
The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Answer Choices: (A) 17 kmph (B) 40 kmph (C) 16 kmph (D) 18 kmph (E) 20 kmph | tiger_lab_math |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.