instruction_seed stringlengths 17 6.7k | source stringclasses 4
values |
|---|---|
How many moles of H2SO4 are required to react with 6 moles of NH3 to form 3 moles of (NH4)2SO4 Please respond by writing a program in Python. | tiger_lab_math |
Three aluminum cans can be recycled to make a new can. How many new cans can eventually be made from 243 aluminum cans? (Remember that the first new cans that are made can then be recycled into even newer cans!) Do not include the original X cans in your count. The answer is 121. What is the value of unknown variable ... | tiger_math |
Find the slope of the line that is parallel to the line $x - 4y = -8$. | nvidia_math |
After eating half of the sandwiches he made on the first day and 2 sandwiches less on the next day, how many sandwiches does Bert have left if he initially made 12 sandwiches? | tiger_math |
The function $f(x) = -\frac{1}{2} \cos (2x)$ is graphed below.
[asy]
import TrigMacros;
size(400);
real f(real x)
{
return (-1/2)*cos(2*x);
}
draw(graph(f,-3*pi,3*pi,n=700,join=operator..),red);
trig_axes(-3*pi,3*pi,-3/2,3/2,pi/2,1);
layer();
rm_trig_labels(-5, 5, 2);
label("$1$", (0,1), E);
label("$\frac{1}{2}$",... | nvidia_math |
If
\[(1 + \tan 1^\circ)(1 + \tan 2^\circ)(1 + \tan 3^\circ) \dotsm (1 + \tan 45^\circ) = 2^n,\]then find $n.$ | nvidia_math |
For how many integers $n$ is it true that $\sqrt{n} \le \sqrt{4n - 6} < \sqrt{2n + 5}$? | nvidia_math |
Given the linear transformation \( T: P_3 \rightarrow P_3 \) defined by the following equations:
\[
T(-2x^2) = 3x^2 + 3x, \quad T(0.5x + 4) = -2x^2 - 2x - 3, \quad T(2x^2 - 1) = -3x + 2,
\]
determine \( T(1) \) by expressing \( 1 \) in terms of the basis involving the given vectors and applying the transformation ac... | automath |
What is the remainder when the product of the numbers in the set {18, 23, 25, 31, 38, 44} is divided by 11? | nvidia_math |
the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 867 sq m , then what is the breadth of the rectangular plot ? Let's write a Python program. | tiger_lab_math |
Teagan saved 200 pennies in her piggy bank. Rex has a mason jar filled with 100 nickels. Toni has 330 dimes stashed inside a giant mug. How much money did the three kids save altogether? | tiger_lab_math |
What is the sum of the seven smallest distinct positive integer multiples of 9? | tiger_math |
If one canoe weighs a total of 28 pounds, what is the weight of one bowling ball if seven bowling balls weigh the same as three canoes? | tiger_math |
If $x$ and $y$ are positive integers such that $5x+3y=100$, what is the greatest possible value of $xy$? | nvidia_math |
Given two vectors, \(\vec{A}\) and \(\vec{B}\), where \(\vec{A}\) has a magnitude of 12.0 m directed \(20^\circ\) west of north, and \(\vec{B}\) has a magnitude of 20.0 m directed \(40^\circ\) south of west, calculate the resultant displacement and its direction when the walk starts with \(\vec{B}\) followed by \(\vec{... | automath |
Light glows for every 17 seconds . How many times did it between 1:57:58 and 3:20:47 am
Answer Choices: (A) 291 (B) 292 (C) 293 (D) 384 (E) 285 | tiger_lab_math |
Lowry sells bonsai. A small bonsai costs $30 and a big bonsai costs $20. If he sold 3 small bonsai and 5 big bonsai, how much did he earn? | nvidia_math |
Given the linear operator \( T: X \to X \) defined by
\[
T(x_1, x_2, x_3, \ldots) = \left( x_1, \frac{x_2}{2^2}, \frac{x_3}{3^2}, \ldots \right)
\]
on the space \( X \) of all real sequences that are eventually zero with the 'sup' norm, determine whether \( T \) is bounded. If \( T \) is bounded, find a constant \( ... | automath |
What is Mary's average speed, in km/hr, for the round trip if it takes her 30 minutes to walk 1 km uphill from home to school, but only 10 minutes to walk the same route from school to home? | tiger_math |
How many of the integers between 1 and 1000, inclusive, can be expressed as the sum of the cubes of two nonnegative integers? | nvidia_math |
Given the average atmospheric pressure at sea level is approximately 101325 Pa, and considering that 1 Pa is defined as 1 N/m², could you derive the approximate density of air at sea level in kg/m³, assuming standard gravitational acceleration is about 9.81 m/s²? | automath |
Given that 268 * 74 = 19832, find the values of 2.68 * 0.74.
Answer Choices: (A) 1.9328 (B) 1.9832 (C) 1.9823 (D) 1.9382 (E) None of them | tiger_lab_math |
Let $f(x) = 5x - 2$ and $g(x) = 2x - 1.$ What is $g(f(g(3)))$? | tiger_math |
A machine, working at a constant rate, manufactures some pens in 30 minutes. It makes 63 pens in 1 hour 45 minutes. How many pens does it make in 30 minutes? | tiger_math |
Consider the limit
\[
\lim_{x \to \infty} \frac{\sqrt{a x^2 + a x}}{x}
\]
for a positive constant \( a \).
1. What is the value of this limit if \( a > 1 \)?
2. What is the value of this limit if \( a = 1 \)?
3. What is the value of this limit if \( 0 < a < 1 \)?
Provide a detailed explanation for each case. | automath |
Determine whether the series \(\sum_{n=1}^\infty \frac{(-3)^{n-1}}{4^n}\) converges or diverges. If it converges, calculate its sum. What is the value of the sum? | automath |
Mike brings 60% as many bottles of juice as sandwiches for the school picnic. Emily brings one-third as many sandwiches as Mike and twice as many bottles of juice as sandwiches. If Emily brings 48 bottles of juice, what is the total number of bottles of juice and sandwiches that Emily and Mike brought to the school pic... | nvidia_math |
A pyramid with a square base is made of modeling clay. The base has side length 12 cm, and each triangular face is an isosceles triangle. The height of the pyramid is 6 cm, and the length of one of the slant edges is 10 cm. How many of the pyramids can be made if there is a total of 3000 cubic centimeters of clay avail... | nvidia_math |
What is the convergence rate of the Conditional Gradient method in convex optimization, particularly when applied to the problem of minimizing a convex function over a convex set? | automath |
Given the function \( f(x) = \frac{\sin x}{1+\cos x} \), find the x-intercept(s) and y-intercept of the function. Confirm whether the points you find fulfill the definition of a function that requires each x-value to correspond to only one y-value. | automath |
ratio between rahul and deepak is 4 : 3 , after 10 years rahul age will be 26 years . what is deepak present age . Let's write a program. | tiger_lab_math |
Let $O$ be the origin. A variable plane has a distance of 1 from the origin, and intersects the $x$-axis, $y$-axis, and $z$-axis at $A,$ $B,$ and $C,$ respectively, such that $O$, $A$, $B$, and $C$ are distinct. Let $G$ be the centroid of triangle $ABC.$ If $OG = \sqrt{3},$ find
\[\frac{1}{OA^2} + \frac{1}{OB^2} + \... | tiger_math |
If a cryptocurrency protocol has a Coin Years Destroyed (CYD) value of 1,000,000 and its total circulating supply is 5,000,000 coins, what is the Supply-Adjusted CYD? | automath |
What is the value of \( x \) that satisfies the equation \( \frac{2}{3}x + \frac{5}{6} = \frac{7}{8}x - \frac{1}{2} \)? | automath |
What is $2.43-1.2$? | tiger_math |
Sharmeeka is putting all of her pens in order by number. One has the number 4 on it, the next has number 8, the next has number 12, and the next has number 16.
What number will the next pen have on it?
Answer Choices: (A) 20 (B) 25 (C) 32 (D) 22 (E) 24 | tiger_lab_math |
If a measured number is reported as 8.0 meters, determine the following:
1. What is the interval of actual values consistent with that measurement?
2. What is the maximum amount that the actual value could differ from the reported value?
3. What is the maximum amount of error as a percentage of the reported number? | automath |
Janet buys a multi-flavor pack of cheese sticks. 15 of the sticks are cheddar, 30 are mozzarella, and 45 are pepperjack. If Janet picks a cheese stick at random, what is the percentage chance it will be pepperjack? | tiger_math |
A cylindrical tank has a height of 10 meters and a radius of 4 meters. How much water can the tank hold when it's completely filled? | tiger_lab_math |
Find a positive integer that is divisible by 14 and has a square root between 25 and 25.3. | tiger_math |
Given a matrix \( Z \in \mathbb{R}^{n \times r} \) and a positive definite matrix \( H \in \mathbb{R}^{r \times r} \), consider the optimization problem
\[
\min_{Y \geq 0} \quad \operatorname{Tr} \left( (Y - Z) H (Y - Z)^T \right).
\]
If \( H \) has a Cholesky decomposition \( H = R^T R \), how can we efficiently so... | automath |
the perimeter of a triangle is 40 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ? Let's write a Python program to solve it. | tiger_lab_math |
The sum of the digits in Emily's student ID number and the digits in her locker number are equal. Her student ID number is 985-6271, and the digits in her locker number are distinct. What is the largest possible value of Emily's locker number? | nvidia_math |
Find the maximum value of
\[f(x) = 3x - x^3\]for $0 \le x \le \sqrt{3}.$ Please respond by writing a program in Python. | tiger_lab_math |
Use Stoke's Theorem to evaluate $\iint_S curl \vec{F} \cdot d \vec{r}$ where $\vec{F} = z^2 \vec{i} - 3xy \vec{j} + x^3y^3 \vec{k}$ and $S$ is the part of $z = 5 - x^2 - y^2$ above the plane $z$=1. Assume that S is oriented upwards. Let's program in Python in the response. | tiger_lab_math |
What is the smallest five digit number that is divisible by 16, 36, 40, and 54?
Answer Choices: (A) 10200 (B) 10500 (C) 10800 (D) 11000 (E) 11400 | tiger_lab_math |
There are 45 children in a classroom. One-third of them are girls. How many boys are in the classroom? Let's program in Python in the response. | tiger_lab_math |
An ice cube tray has 15 identical square compartments arranged in a 3x5 grid. A rectangular solid ice cube is placed in each compartment, and the compartments are then filled with water, forming a solid rectangular block of ice when frozen. If the block of ice is cut along the edges of the compartments, what is the few... | nvidia_math |
A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
Answer Choices: (A) 6 cm (B) 5 cm (C) 2 cm (D) 7 cm (E) 9 cm | tiger_lab_math |
An electronic shop offers smartphones for $300 each, personal computers for $500 more than smartphones, and advanced tablets for the sum of the prices of a smartphone and personal computer. How much do you have to pay to buy x of each of the three mentioned products?
If we know the answer to the above question is 2200,... | tiger_math |
The region shown consists of two semicircles with diameters AB and BC, where point C is the midpoint of AB, and point D is the midpoint of BC. Point E is the midpoint of segment CD. Arc CD of the larger semicircle is divided into two equal parts by radius CE. What is the degree measure of angle ACE? Express your answer... | nvidia_math |
Vijay sells a cupboard at a certain percentage below cost price. Had he got Rs. 1500 more, he would have made a profit of 12%. The cost price of the cupboard is Rs. 6250. What is the percentage below cost price at which he sold the cupboard? | tiger_math |
Determine the value of $b$ for which the number $56b8$ is divisible by $45$. | nvidia_math |
Anish borrowed 15000 at the rate of 12% and an other amount at the rate of 15% for two years. The total interest paid by him was 9000. How much did he borrow?
Answer Choices: (A) 32,000 (B) 33,000 (C) 30,000 (D) 35,000 (E) None of these | tiger_lab_math |
Determine the smallest positive integer $N$ such that exactly one of $N$, $N+1$, and $N+2$ is divisible by 2, one is divisible by $3^2$, one is divisible by $5^2$, and one is divisible by $7^2$. | tiger_math |
In a right pyramid with a square base, the altitude intersects the base at a point 5 cm from the center of the base. If the area of the lateral face is 240 square centimeters and the slant height is 15 cm, what is the length of the side of the base? | nvidia_math |
Given two points \( P_1(x_1, y_1) \) and \( P_2(x_2, y_2) \) on the circumference of an ellipse with semi-major axis \( a \) and semi-minor axis \( b \), where the major axis is rotated by an angle \( \alpha \) relative to the x-axis, determine the coordinates of the center of the ellipse. Provide the final results in ... | automath |
Consider the region enclosed by two concentric spheres with radii \( r = 2 \) and \( r = 4 \), and bounded by the angles \( \theta = 30^\circ \) to \( 50^\circ \) and \( \phi = 20^\circ \) to \( 60^\circ \) in spherical coordinates. Calculate the total surface area of this enclosed region. | automath |
Maria's art teacher assigns her a project that requires 48 seashells and 36 pebbles, to be completed in 12 days. How many items does Maria need to collect each day if she wants to maintain a consistent daily collection amount? | nvidia_math |
Nate went out to do his daily exercises. In 8 seconds, he ran a distance equal to four times the length of a football field. He rested for a while, then ran 500 more meters. If the field's length is 168 meters, how far did Nate ran? | tiger_lab_math |
Calculate the value of the integral \( I = \int_0^{1} \int_0^{3y^2} e^{y^3} \, dx \, dy \). Provide the exact answer. | automath |
Compute the number of ways to choose two non-overlapping pairs of letters from a set of eight distinct letters, such that the two pairs are disjoint. | nvidia_math |
Given the utility function \( u(x_1, x_2) = ax_1 + bx_2 \) where \( a > 0 \) and \( b > 0 \), if we normalize this utility function such that the coefficients of \( x_1 \) and \( x_2 \) sum to 1, find the expression for the Marginal Rate of Substitution (MRS) in terms of the normalized weight \( \alpha \). | automath |
A multi-national corporation has 2041 part-time employees and 63093 full-time employees. _____ employees work for the corporation . | tiger_math |
Five students are sitting in a row, and each student has a different favorite color (red, blue, green, yellow, and purple). If each student writes their name and favorite color on a piece of paper, and then the papers are collected and distributed randomly back to the students, what is the probability that exactly thre... | nvidia_math |
In a urban village of india named "owlna" , 90% people have refrigerator , 86% people have television , 80% people got computers and 80% got Air-conditionor. how many people(minimum) got all these luxury.
Answer Choices: (A) 23% (B) 36% (C) 30% (D) 34% (E) 42% | tiger_lab_math |
a hall is 15 meters long and 10 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ? | tiger_math |
Consider the equation $\left(\frac{2x}{3}\right)^{2} \cdot \left(\frac{x+1}{2}\right)^{-5} = \frac{1}{32}$. Find the value of $x$. | nvidia_math |
The manager of a bookstore wants to determine the most popular type of book among its customers. A survey of 100 customers showed the following distribution of book preferences:
| Type of Book | Number of Customers |
| --- | --- |
| Romance | 28 |
| Mystery | 25 |
| Science Fiction | 22 |
| Non-Fiction | 15 |
| Childr... | nvidia_math |
Christina and her friend are driving across the state. When Christina is driving the speed limit is 30 miles per hour. When her friend is driving, the speed limit is 40 miles per hour. The drive is 210 miles total. If her friend drives for 3 hours and both drive at the speed limit, how many minutes will Christina drive... | tiger_math |
What is the greatest common factor (GCF) of the numbers 84, 126, and 210? | automath |
Given the regular surface \( M \subset \mathbb{R}^3 \) with the induced metric
\[
ds^2 = \frac{du^2 + dv^2}{(u^2 + v^2 + c)^2}
\]
where \( c > 0 \) is a constant, calculate the Gaussian curvature \( K \) of the surface and verify that it is constant. What is the exact value of \( K \)? | automath |
Evaluate the expression \( 4^{\frac{3}{2}} \) and provide the answer. | automath |
A circle with center $(-1 + 4i)$ and radius 7 is drawn on the complex plane. What is the distance between the circle's center and the point representing the city of Albuquerque, which corresponds to the complex number $x + yi$, if the line connecting the circle's center and Albuquerque is perpendicular to the line conn... | nvidia_math |
Leonard and his brother Michael bought presents for their father. Leonard bought a wallet at $50 and two pairs of sneakers at $100 each pair, while Michael bought a backpack at $100 and two pairs of jeans at $50 each pair. How much did they spend in all? | tiger_lab_math |
A man’s speed with the current is 19 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is :
Answer Choices: (A) 8.5 km/hr (B) 9.5 km/hr (C) 10 km/hr (D) 14 km/hr (E) None of these | tiger_lab_math |
Archie received his medical receipt from his doctor, and he needs to take antibiotics three times a day. If antibiotic costs $3 each and he needs to take it for a week, how much money does he need to buy the antibiotics? | tiger_lab_math |
A train 150 m long passes a man, running at a certain speed in the direction opposite to that of the train, in 6 seconds. The speed of the train is 83.99280057595394 kmph. What is the speed of the man in kmph? | tiger_math |
What is the value of \( \frac{1}{0} \) in the context of real numbers, and explain why it is considered undefined? | automath |
Hannah sold 40 pieces of cookies for $0.8 each and 30 cupcakes for $2 each. She used the money to buy 2 sets of measuring spoons for $6.5 each. How much money does she have left? | tiger_lab_math |
There are three prizes to be distributed among ten students. If no students gets more than one prize, then this can be done in?
Answer Choices: (A) 10 (B) 45 (C) 95 (D) 120 (E) None of these | tiger_lab_math |
A message was encrypted using the rail fence cipher with a key of 4. The encrypted message is `TMTTEEHPREOOWSRAAFNYSIIGSNA`. Determine the original message. | tiger_lab_math |
Helen cuts her lawn starting in March and finishes in October. Her lawn mower uses 2 gallons of gas every 4th time she cuts her lawn. For March, April, September and October, she only cuts her law 2 times per month. In May, June, July and August, she has to cut her lawn 4 times per month. How many gallons of gas wi... | tiger_math |
The bar graph shows the number of students enrolled in five different sports at a high school. The following clues provide information about the sports:
1. Track has more students enrolled than soccer.
2. Basketball has more students enrolled than volleyball, but fewer students than football.
3. Soccer has more than 5... | tiger_math |
Emily has a collection of 72 colored pencils in blue, purple, pink, and orange. One-third of them are blue, and 15 are purple. The number of pink pencils is 25% less than the number of purple pencils. How many pencils are orange? | nvidia_math |
Christopher uses 1 packet of a sugar substitute in his coffee. He has 2 coffees a day. The packets come 30 to a box and cost $4.00 a box. How much will it cost him to have enough sugar substitutes to last him 90 days? | tiger_lab_math |
What is the 100th digit after the decimal point of the decimal representation of 1/7? Let's write a Python program to solve it. | tiger_lab_math |
Let $f(x,y)=ax^2+2bxy+cy^2+2dx+2ey+k$. Given the matrix of the quadratic form
$$A=\begin{pmatrix}
a&b\\
b&c\\
\end{pmatrix},$$
the constant matrix
$$D=\begin{pmatrix}
d\\
e\\
\end{pmatrix},$$and its representation $\ds f(x,y)=(x,y)A(x,y)^T+2(x,y)D+k$, determine all the values of $D$ and $k$ such that $\ds \min_{(x,y)\i... | nvidia_math |
The news announced a $0.4 oil price rollback this Friday. Mr. Deane decided to only fill his gas tank with 10 liters of gas today and then another 25 liters on Friday. If the cost per liter of gas is $1.4 today, how much will Mr. Deane spend for his 35 liters of gas? | tiger_lab_math |
The isosceles triangle and the rectangle shown here have the same area in square units. What is the height of the triangle, $h$, in terms of the length and width of the rectangle, $l$ and $w$?
[asy]
draw((0,0)--(0,10)--(10,10)--(10,0)--cycle);
fill((0,0)--(17,5)--(0,10)--cycle,white);
draw((0,0)--(17,5)--(0,10)--cycle... | tiger_math |
Calculate the total number of people that will get infected during the outbreak, given that the infection rate is modeled by the function \( y = 200xe^{-0.5x} \). Evaluate the improper integral
\[
\int_0^\infty 200xe^{-0.5x} \, dx.
\] | automath |
In a more difficult version of this problem, each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If 6 of the slips are drawn without replacement, what is the probability that exactly 4 slips have an odd number written on them and exactly 2 ... | tiger_math |
Which number is the odd one out?
Answer Choices: (A) 47632 (B) 36119 (C) 84129 (D) 67626 (E) 72927 | tiger_lab_math |
Lucas and Sophia are making stuffed animals for a charity event. Sophia makes 12 teddy bears and 8 rabbits, and Lucas makes 10 rabbits. If a teddy bear requires 2 bags of stuffing and a rabbit requires 3 bags of stuffing, how many bags of stuffing did Lucas and Sophia use in total? | nvidia_math |
A circle is inscribed inside a triangle with side lengths 10, 12, and 15. What is the radius of the circle, expressed as a decimal to the nearest hundredth? | nvidia_math |
Find the range of the function $f(x) = \arctan(x^2) + \arcsin(x^3)$. All functions are in radians. | nvidia_math |
Consider the function defined by tetration, \( ^n x = x^{x^{x^{\cdots}}} \) (with \( n \) occurrences of \( x \)). For a positive integer \( n \geq 1 \), evaluate the derivative \( \frac{d}{dx} (^{n} x) \) at the point \( x = e \). What is the value of \( \frac{d}{dx} (^{n} x) \) when \( x = e \)? | automath |
Increasing the radius of a cylinder by $6$ units increased the volume by $y$ cubic units. Increasing the height of the cylinder by $6$ units also increases the volume by $y$ cubic units. If the original height is $2$, then the original radius is:
$\text{(A) } 2 \qquad \text{(B) } 4 \qquad \text{(C) } 6 \qquad \text{(D)... | nvidia_math |
A biased coin has been tossed 100 times and resulted in 79 heads. What is the relative frequency of heads in simplest fractional form? | automath |
for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 37 , the mean is how much greater than the median ? Let's write a program. | tiger_lab_math |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.