instruction_seed stringlengths 17 6.7k | source stringclasses 4
values |
|---|---|
We know the following to be true:
$\bullet$ 1. $Z$ and $K$ are positive integers with $500 < Z < 1000$ and $K > 1;$
$\bullet$ 2. $Z$ = $K \times K^2.$
Find the value of $K$ such that $Z$ is the square of a prime number. | tiger_math |
What is the smallest prime number that is greater than X, if we know that there are 5 prime numbers between X and 40? | tiger_math |
A mathematician is trying to create a new mathematical sequence by combining three different mathematical operations: addition, subtraction, and multiplication. She can create a new sequence by taking three operations and combining them in a specific order. Different orders of the operations give different sequences.
... | nvidia_math |
Tom read three more books than Alex read. Sophia read five times as many books as Alex read. If Sophia read 35 books, how many books did Tom read? | nvidia_math |
Lars owns a bakeshop. She can bake 10 loaves of bread within an hour and x baguettes every 2 hours. If she bakes 6 hours a day, She makes 150 breads. What is the value of unknown variable x? | tiger_math |
If (x + yi) / i = ( 7 + 9i ) , where x and y are real, what is the value of (x + yi)(x - yi)?
Answer Choices: (A) 110 (B) 120 (C) 130 (D) 140 (E) 150 | tiger_lab_math |
In a magic square, the sum of the three entries in any row, column, or diagonal is the same value. The figure below shows four of the entries of a magic square. Find $x$.
[asy]
size(2cm);
for (int i=0; i<=3; ++i) draw((i,0)--(i,3)^^(0,i)--(3,i));
label("$x$",(0.5,2.5));label("$19$",(1.5,2.5));
label("$96$",(2.5,2.5));l... | tiger_lab_math |
When the polynomial $x^4 - 6x^3 + 16x^ 2 - 25x + 10$ is divided by $x^2 - 2x + k,$ the remainder is $x + a.$ Enter the ordered pair $(k,a).$ | nvidia_math |
Evaluate $\left|\frac12 - \frac38i\right|$. | tiger_lab_math |
Given an enclosure divided into two rectangular cages, with one perimeter side against a solid wall and a total length of fencing equal to 275 m, if the smaller cage for 5 male birds has an average area of 250 m² per bird, calculate the average area allocated for each of the 8 female birds in the larger cage, ensuring ... | automath |
A spherical water tank has a radius of 5 meters. A tap is opened and water flows out of the tank at a rate of 100 cubic meters per hour. A second tap is then opened and water flows into the tank at a rate of 50 cubic meters per hour. At what rate is the height of the water in the tank changing after 2 hours? | tiger_math |
Joe's current weekly caloric intake is 20,000 calories. His physician has advised Joe to reduce the number of calories he consumes weekly to 14,000. By what percent does Joe need to reduce his weekly caloric intake?
Answer Choices: (A) 20% (B) 30% (C) 50% (D) 60% (E) 70% Let's write a program. | tiger_lab_math |
The sequence $a_1, a_2, a_3, \ldots$ is defined by the recurrence relation $a_n = a_{n-1} - \frac{1}{2}a_{n-2}$, where $a_1 = 8$ and $a_2 = 4$. How many terms of this sequence are positive integers? | nvidia_math |
Consider the set of functions $f(n)$ that map the positive integers to the positive integers. Find the number of functions that satisfy the functional equation $f(a + b) + f(ab) = f(a) f(b) + 2$ for all positive integers $a$ and $b$. | nvidia_math |
Bill picked 50 apples from the orchard with his wife and two children. He sends each of his kids to school with 3 apples for their two favorite teachers. His wife Jill bakes two apple pies, using 10 apples per pie. How many apples does Bill have left? | tiger_lab_math |
Jeanine bought 18 pencils and Clare bought half as many pencils. If Jeanine gave x third of his pencils to Abby, Jeanine has 3 more pencils than Clare now. What is the value of unknown variable x? | tiger_math |
If there are initially 14 chickens in the coop and twice that number in the run, and the number of free-ranging chickens is 4 less than double the number in the run, what is the total number of chickens that are free-ranging? | tiger_math |
If John is currently \( \frac{3}{4} \) the age of James, and three years ago, John was \( \frac{5}{7} \) the age of James, what is James's current age? | automath |
At the grocery store, I bought $4$ different items. I brought $3$ identical bags, and handed them to the cashier. How many ways are there for the cashier to put the items I bought in the $3$ identical bags, assuming he might leave some of the bags empty? | nvidia_math |
Ashley received a birthday gift card worth $300. She spent one-third of it on a new handbag on Saturday and then one-fifth of the remaining balance on a pair of shoes on Sunday. How much money is left on her gift card? | nvidia_math |
If Hazel received 6 shirts and Razel received twice the number of shirts as Hazel, what is the total number of shirts that they have together? | tiger_math |
James has 18 chocolate bars to sell for the swim team. He sold 5 last week and 7 this week. How many more chocolate bars does he need to sell? | tiger_math |
The functions $f(x) = x^2-2x + m$ and $g(x) = x^2-2x + 4m$ are evaluated when $x = 4$. What is the value of $m$ if $2f(4) = g(4)$? | tiger_math |
Compute $3+4\cdot2-2+6\cdot3\div2$ | nvidia_math |
If \( A = \begin{pmatrix} 0 & -2 \\ 2 & 0 \end{pmatrix} \) is a skew-symmetric matrix, what are the eigenvalues of matrix \( A \)? | automath |
Given the matrix
$A = \begin{bmatrix}
1 & 2 & 3 \\
2 & 4 & 6 \\
3 & 6 & 9 \\
\end{bmatrix}$
Determine the rank of matrix A. | tiger_lab_math |
When three positive integers are divided by $47$, the remainders are $25$, $20$, and X$, respectively.
When the sum of the three integers is divided by $47$, what is the remainder?
If we know the answer to the above question is 1, what is the value of unknown variable X? | tiger_math |
Gopi gives some amount plus one turban as salary to his servant for one year. The servant leaves after 9 months and receives Rs. 55 and the turban. The price of the turban is Rs. 50. What is the total annual cash salary that Gopi gives to his servant? | tiger_math |
the speed of the boat in still water in 12 kmph . it can travel downstream through 54 kms in 3 hrs . in what time would it cover the same distance upstream ? | tiger_math |
Let \( M \) be a smooth manifold and \( f: M \rightarrow \mathbb{R} \) a smooth function. Consider a point \( p \in M \). If \( p \) is a local extremum of \( f \), what can be said about the differential \( df_p \)? Specifically, what condition must hold true for \( df_p \) at that point? | automath |
If $2^{10} \cdot 2^{15}$ is expressed as some integer to the fifth power, what is that integer? | tiger_math |
Let $a_1, a_2, \ldots, a_n$ be the roots of the equation
$x^n + p_{n - 1} x^{n - 1} + \ldots + p_1 x + p_0 = 0$,
where all coefficients are positive real numbers.
Find the minimum value of the expression
$\sum_{i = 1}^n \frac{1}{\sqrt[n]{1 + a_i}}$. | nvidia_math |
Miriam takes care of the flowers in the botanical garden. She works 5 hours a day and can take care of 60 different flowers in one day. How many flowers can Miriam take care of in 6 days of work? | tiger_lab_math |
Find the 200th digit after the decimal point in the decimal expansion of $\frac{13}{31}$. | tiger_math |
Find the coefficient of $x^2$ in the expansion of $\left(x^2+2x\sin\theta+\dfrac1{x^2}\right)^5$, where $\theta$ is a constant angle such that $\cos\theta=\dfrac34$. | nvidia_math |
Is the particular solution \( u_1 \) obtained from the variation of parameters method uniquely defined, or can it differ based on the limits of integration used in the integral \( u_1 = -\int_{x_0}^x \frac{y_2 f(s)}{W} ds \) compared to an indefinite integral \( u_1 = -\int \frac{y_2 f(x)}{W} dx \)? What is the signifi... | automath |
How much does 8 moles of Carbon tetrachloride weigh Let's write a Python program. | tiger_lab_math |
What is the total number of formula units of NaOH present in 100 µL of a 0.1 M NaOH solution? | automath |
Given a non-empty set \( M \) and a non-trivial group \( G \) acting on \( M \) via a right action \( \mu: M \times G \to M \), define the stabilizer of an element \( x \in M \) as \( \text{Stab}(x) = \{g \in G \mid \mu(x,g) = x\} \). Which of the following statements is true regarding the relationships between the con... | automath |
John's car needs a new engine. The labor costs $75 an hour for 16 hours. The part itself cost $1200. How much did the repairs cost in total? | tiger_math |
Consider the continuous function \( f(x) = x^2 \) defined on the interval \([1, 4]\). Using the Extreme Value Theorem, determine the values of \( c_* \) and \( c^* \) such that \( f(c_*) \) is the minimum and \( f(c^*) \) is the maximum of \( f(x) \) on the interval \([1, 4]\). What are the values of \( f(c_*) \) and \... | automath |
At what positive time does the position function \( x(t) = 4.0 - 6.0t^2 \) pass through the origin? Calculate the solution. | automath |
The sum of first eight prime numbers is?
Answer Choices: (A) 12 (B) 23 (C) 24 (D) 77 (E) 30 | tiger_lab_math |
In triangle \( PQR \), the angle \( P \) measures \( 29^\circ \), side \( p \) measures \( 16 \, \text{m} \), and side \( q \) measures \( 25 \, \text{m} \). What are the possible lengths of side \( r \) to the nearest tenth of a meter? | automath |
Mary is paying her monthly garbage bill for a month with exactly four weeks. The garbage company charges Mary $10 per trash bin and $5 per recycling bin every week, and Mary has 2 trash bins and 1 recycling bin. They're giving her an 18% discount on the whole bill before fines for being elderly, but also charging her a... | tiger_lab_math |
Let $F(0) = 0,$ $F(1) = \frac{3}{2},$ and
\[F(n) = \frac{5}{2} F(n - 1) - F(n - 2)\]for $n \ge 2.$ Find
\[\sum_{n = 0}^\infty \frac{1}{F(2^n)}.\] | tiger_lab_math |
Cheryl bought 5 identical hollow pine doors and 6 identical solid oak doors for her house. If each hollow pine door costs $40, and each solid oak door's regular price is twice that of the pine doors but comes with a 25% discount, what is the total amount she spent on all the doors?
A. $320
B. $540
C. $560
D. $6... | automath |
Mihye worked out for 1 and 5/12 hours and Seongjae did it for 1 and 3/12 hours. Who has been exercising longer? | tiger_math |
Let $S$ be the set of all real numbers that can be represented as $x + \sqrt{y}$, where $x$ and $y$ are non-negative integers and $y \leq 1000$. Determine the number of elements in $S$. | nvidia_math |
A cylindrical container with a height of 30 cm and a diameter of 20 cm is filled with water. A spherical stone is submerged in the water, causing the water level to rise by 4 cm. What is the radius of the stone? | nvidia_math |
Let \( p(x) \) be a probability distribution over some dataset \( x \) and \( q(x) \) be an approximating distribution. If the Kullback-Leibler divergence \( D(q || p) \) is minimized when \( q = p \), what is the maximum value of the evidence lower bound (ELBO) \( L(w, q) = E_q \log \frac{w}{q} \) in terms of the norm... | automath |
A shopkeeper sold an article for Rs 2552.36. Approximately what was his profit percent if the cost price of the article was Rs 2400
Answer Choices: (A) 4% (B) 5% (C) 6% (D) 7% (E) 8% Let's write a program. | tiger_lab_math |
Given a functional
$$J(y) = \int_{x_1}^{x_2} f(x, y, y') \, dx$$
with a corresponding differential constraint
$$\phi(x, y, y') = 0$$
for \(y: [x_1, x_2] \rightarrow \mathbb{R}^n\) and a boundary condition
$$\psi(x_1, y(x_1), x_2, y(x_2)) = 0,$$
which bounds the problem. If the rank of the matrix \(\left\| \f... | automath |
Tom has eaten a total of 75 cookies in five days. Each day after the first day, he eats 3 more cookies than he did on the previous day. How many cookies did Tom eat on the fourth day? | nvidia_math |
A bag contains 8 red, 12 orange, 11 green, and 16 blue gumballs. What are the odds of randomly selecting a gumball that is neither red nor blue? | automath |
There are magnets with numbers 8, 7 and 0 written respectively. What is the largest number you can make by arranging them? | tiger_math |
In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
Answer Choices: (A) 65 (B) 44 (C) 86 (D) 29 (E) 26 | tiger_lab_math |
If $a$ and $b$ are positive integers for which $ab - 3a + 4b = 137$, what is the minimal possible value of $|a - b|$? | tiger_lab_math |
What profit/loss percent did Ravi earn if he purchased an item of Rs.5,600 and sold it at three-fourth of its cost price?
Answer Choices: (A) Loss of 20 percent (B) Gain of 25 percent (C) Neither gain or loss (D) Loss of 15 percent (E) None of these | tiger_lab_math |
during a certain season , a team won 65 percent of its first 100 games and 50 percent of its remaining games . if the team won 70 percent of its games for the entire season , what was the total number of games that the team played ? Please respond by writing a program in Python. | tiger_lab_math |
A certain list of 300 test scores has an arithmetic mean of 75 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 301 test scores with a standard deviation less than d?
Answer Choices: (A) 75 and 80 (B) 80 and 85 (C) 70 and 75 ... | tiger_lab_math |
Given that a clock on a GPS satellite appears to tick 38 microseconds faster per day compared to a clock on Earth due to gravitational time dilation, what would be the difference in the rate of ticking of the Earth clock as observed from the satellite if we disregard gravitational effects, specifically, what is the net... | automath |
John buys a chair. He then buys a table that is 3 times the price of the chair. Then, he buys a couch that is 5 times the price of the table. If John paid $380 for all these items, what is the price of the couch? | tiger_math |
"statement 1": Store Z : $ 90 , a 20 % sales tax , and $ 10 rebate after tax
Isaac can purchase a certain item in four different ways , as shown in the table, "statement 2" :Store Z : $ 20 , a 20 % sales tax , and $ 10 rebate after tax Isaac can purchase a certain item in four different ways , as shown in the table, "... | tiger_lab_math |
Given the NSDF formula $$nsdf(\tau)=\frac{2\sum s(i)s(i+\tau)}{\sum s^2(i)+\sum s^2(i+\tau)}$$ and the range of NSDF being \([-1, 1]\), how does the clarity of a frame defined as \(acf(\tau_0)\) relate to the periodicity of the associated waveform, and what implications does this have for the selection of the pitch poi... | automath |
In a certain country, there are 5 political parties. A survey indicates that the probability of a citizen voting for the first party is 0.25, for the second party is 0.2, for the third party is 0.15, for the fourth party is 0.1 and for the last party is 0.3. What is the probability that a citizen will vote for either t... | tiger_lab_math |
There are 20 students in the orchestra and twice that number in the band. There are 12 boys and 16 girls in the choir. If each student only participates in one group, how many students, in total, are there in the orchestra, the band, and the choir? | tiger_lab_math |
On a standard chessboard with 64 squares, a person labels each square with a number from 1 to 64. On each square $n$, they place $3^n$ pennies. What is the difference in the number of pennies on the $12^{th}$ square and the total number of pennies on the first 7 squares? | nvidia_math |
John buys x balloons. Each balloon holds 10 liters of air. If he buys 500-liter tanks of gas, how many tanks does he need to buy to fill all the balloons?
If we know the answer to the above question is 20, what is the value of unknown variable x? | tiger_math |
How many multiples of 4 are there between 12 and 108, inclusive?
Answer Choices: (A) 21 (B) 22 (C) 23 (D) 24 (E) 25 | tiger_lab_math |
Suppose A and B are two sets such that A = {1, 3, 5, 7} and B = {2, 4, 6, 8}. Find the intersection of A and B. | tiger_lab_math |
Emily's classroom is on the second floor, and she has to walk up 2 flights of stairs to get to her classroom. In a single day, she goes up the two flights of stairs 4 times, down the two flights of stairs 2 times, and takes the elevator the rest of the time. How many flights of stairs does Emily walk (up and down) in a... | nvidia_math |
Three natural numbers $a$, $b$, and $c$ are randomly chosen from the set $\{1,2,3,4,5,6,7,8,9\}$. What is the probability that the sum $a+b+c$ is divisible by $3$? | nvidia_math |
An aluminum plate of length 10 cm and width 5 cm is subjected to a temperature variation of sin(2000t) degrees Celsius, where t is the time in seconds. Determine the heat flux through the plate using Fourier transform analysis, assuming the thermal diffusivity of aluminum is 9.7 x 10^-5 m^2/s. | tiger_lab_math |
A class of 15 students has an average grade of 80% on a test. If 3 of the students scored exactly 100%, what is the average grade of the remaining 12 students? | nvidia_math |
Given the manufacturing data for Alberta Inc.'s product lines "B", "L", and "T" as follows:
- **Selling Price**:
- B: $100
- L: $120
- T: $140
- **Direct Materials**:
- B: $12
- L: $12
- T: $12
- **Direct Labor** (at $12 per hour):
- B: $24 (2 hours)
- L: $24 (2 hours)
- T: $4... | automath |
If f(x) = Log(x), then f -1(x) =
Answer Choices: (A) 10 x (B) -10 -x (C) 1 / 10 x (D) x 10 (E) NONE | tiger_lab_math |
The ratio of fuel used in gallons to the distance covered in miles by Haley's car is 4:7. If Haley's car used 44 gallons of gas, calculate the distance it covered in miles. Please write a program to solve it | tiger_lab_math |
Bob is building a garden on his land, and he wants it to be fenced in to keep out varmints. The garden is a rectangular plot 225 feet long by 125 feet wide. He also wants to have a small 3-foot wide gate to walk through and a larger 10-foot wide gate to move his gardening equipment through. How much fencing is Bob goin... | tiger_lab_math |
In a contest, six boys and four girls participate in a series of competitions. In each competition, one participant is randomly selected to compete against another randomly selected participant. What is the probability that, in a single competition, either two boys or two girls are selected, but not a boy and a girl? | nvidia_math |
Buoys are placed in the ocean at even intervals away from the beach to help swimmers monitor how far away from the beach they have swum. If a swimmer reaches the third buoy, they have swum out 72 meters. How many meters from the beach is the fourth buoy? | tiger_lab_math |
A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 170, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
Answer Choices: (A) 3... | tiger_lab_math |
In a factory, there are 300 workers. The probability of a worker having an accident in a week is 0.05. What is the probability of at least 15 workers having an accident in a week? | tiger_lab_math |
What is the total number of ways to choose a male and a female leader from a group of \( n \) men and \( n \) women, where each group must have at least one member? | automath |
In an examination, a pupil’s average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination?
Answer Choices: (A) 8 (B) 9 (C) 10 (D) 11 (E) 12 | tiger_lab_math |
Given the system of equations:
\[
\begin{cases}
x + 3y = 0 \\
x + y + z = 1 \\
3x - y - z = 11
\end{cases}
\]
use Gaussian elimination or Gauss-Jordan elimination to find the values of \(x\), \(y\), and \(z\). What is the value of \(x + y + z\)? | automath |
How many internal diagonals does a dodecagon (12-sided polygon) have? | tiger_math |
There are 5 green candies, 3 blue candies, and 4 red candies in a bag. If Violet randomly picks a candy from the bag, how likely is it that it's blue? | tiger_math |
When $\frac{3^6}{6^4\cdot625}$ is written as a decimal, how many digits are there to the right of the decimal point? | tiger_math |
The sum of two consecutive integers is 51. Find the numbers.
Answer Choices: (A) 17, 18 (B) 7, 8 (C) 5, 6 (D) 1, 2 (E) 25,26 | tiger_lab_math |
a couple who own an appliance store discover that if they advertise a sales discount of 10 % on every item in the store , at the end of one month the number of total items sold increases 30 % . their gross income from sales for one month increases by what percent ? Let's write a Python program to solve it. | tiger_lab_math |
The region between the graph of $y = f (x)$ and the $x$-axis, shaded in this figure, has an area of 10 square units. What will be the area between the graph of $y = -2f (x +1)$ and the $x$-axis?
[asy]
defaultpen(linewidth(0.75));
fill((10,0)..(30,20)..(40,15)--(50,40)..(58,39)--(70,0)--cycle,gray(.7));
draw((10,0)..(3... | tiger_math |
The ski lift carries skiers all the way from the bottom of the mountain to the very top of the mountain, and then drops them off so they can ski back down the mountain. If it takes a skier 15 minutes to ride the lift from the bottom to the top of the mountain, and then it takes 5 minutes to ski back down the mountain, ... | tiger_lab_math |
What is the largest natural number \( m \) such that the inequality
\[
\sum_{i=m}^{\infty} \frac{1}{i^2} \leq \frac{2}{2m-1}
\]
holds true? | automath |
Carmen is selling girl scout cookies. She sells three boxes of samoas to the green house for $4 each; two boxes of thin mints for $3.50 each and one box of fudge delights for $5 to the yellow house; and nine boxes of sugar cookies for $2 each to the brown house. How much money did Carmen make? | tiger_lab_math |
A pipe is divided into four sections in the ratio of 5:4:3:2. If the longest section is 25 cm, what was the total length of the pipe before it was divided? | nvidia_math |
287 x 287 + 269 x 269 - 2 x 287 x 269 = ?
Answer Choices: (A) 534 (B) 446 (C) 354 (D) 324 (E) None of them | tiger_lab_math |
Is the function \( d(\Gamma_1, \Gamma_2) \) defined as the revenue of the first player, where both players employ optimal strategies in a game involving simple graphs with countably many vertices, a metric on the set of isomorphism classes of these graphs, specifically fulfilling the triangle inequality \( d(\Gamma_1, ... | automath |
Frank bakes two trays of cookies per day, for 6 days. Frank eats x cookie each day to make sure they taste good. Ted comes over on the sixth day and eats 4 cookies. If each tray makes 12 cookies, how many cookies are left when Ted leaves?
If we know the answer to the above question is 134, what is the value of unknown ... | tiger_math |
Given two positive charges, \( Q_1 \) and \( Q_2 \), placed a distance \( s \) apart, we know that the electric field \( E \) at a point on the line connecting these two charges can be expressed as follows:
\[
E_1 = \frac{k Q_1}{x^2} \quad \text{(due to \( Q_1 \))} \quad \text{and} \quad E_2 = -\frac{k Q_2}{(s - x)^2}... | automath |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.