instruction_seed stringlengths 17 6.7k | source stringclasses 4
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If a quadratic equation is given by y = 2x² + 5x - 3, what are the x-intercepts and the vertex of the corresponding parabola? | tiger_lab_math |
A bag contains 6 red marbles and 4 blue marbles. If you randomly draw two marbles from the bag, one after the other, without replacement, what is the probability that the second marble is a different color than the first one? | nvidia_math |
The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 20 are excluded, the average mark of the remaining will be 95. How many students wrote the exam? | tiger_math |
What is the maximum weight of a k-cut with 50 equal-size pieces in an undirected weighted graph with 5000 vertices, if the weight of the minimum k-cut is denoted as \( x \)? | automath |
In a magical garden, there are 25 exotic trees, of which 7 are bearing blue apples, 10 are bearing red apples, and the rest are bearing golden apples. A mischievous sprite likes to hop from one tree to another. If the sprite randomly picks a tree to rest in, what is the probability that it will land in a tree with gold... | tiger_math |
The pages of a book are numbered $1_{}^{}$ through $n_{}^{}$. When the page numbers of the book were added, one of the page numbers from 10 to 50 was mistakenly added twice, resulting in an incorrect sum of $1990_{}^{}$. What was the number of the page that was added twice? | tiger_math |
Ryan builds model mustang cars with different scales. A full-size mustang is 240 inches long. Ryan creates four different scaled models:
1. The mid-size model is 1/10th the size of the full-size mustang.
2. The small model is 1/4 the size of the mid-size model.
3. The mini model is 1/3 the size of the small model. ... | tiger_math |
A particular store sells two types of sugar: organic cane sugar for $\$1.50$per pound, and regular white sugar for$\$1.20$ per pound. The store owner wishes to mix $x$ pounds of the cane sugar with $y$ pounds of the white sugar to get $10$ pounds of a new blend that can be sold for $\$1.40$per pound. If the amount of w... | nvidia_math |
Walking at 5/6 of her normal speed, a worker is 12 minutes later than usual in reaching her office. The usual time (in minutes) taken by her to cover the distance between her home and her office is
Answer Choices: (A) 36 (B) 42 (C) 48 (D) 54 (E) 60 | tiger_lab_math |
Find the maximum number of real roots for a polynomial $q(x)$ with rational coefficients such that $q(3) = 2$ and $q(x) - x^2$ is divisible by $(x - 1)^3$. | nvidia_math |
Jerry's age is 2 years more than 200% of Mickey's age. If Jerry is Y years old, and Mickey is 8 years old, what is the value of the unknown variable Y? | tiger_math |
Consider the function f(x) = x^3 - 6x^2 + 9x. Find the x-coordinate of the inflection point(s) of the function. | tiger_lab_math |
Find the minimum value of \[\tan \frac{\alpha}{2} \cdot (1 - \sin \alpha)\] for $0 < \alpha < \frac{\pi}{2}$. | nvidia_math |
Let $P$ and $Q$ be real numbers such that $\frac{Px-3}{x+1}+Q(x-2)=\frac{-2x^2+7x-13}{x+1}$. What is $P+Q$? | tiger_math |
$\triangle ABC$ is similar to $\triangle DEF$. If the length of $\overline{AB}$ is 10 cm, the length of $\overline{BC}$ is 16 cm, and the length of $\overline{DE}$ is 5 cm, what is the length of $\overline{EF}$ in centimeters? Express your answer as a decimal to the nearest tenth.
[asy]
draw((0,0)--(10,-2.5)--(7.5,5)-... | tiger_math |
What is the limit of the sum $$\lim_{r \rightarrow \infty} \sum_{(m,n) \in D_r} \frac{(-1)^{m+n}}{m^2 + n^2}$$, where \(D_r\) denotes the closed disk of radius \(r\) centered at the origin? | automath |
Two cyclists, Emily and David, leave from the same intersection at the same time. Emily rides west at 10 mph, and David rides north at 12 mph. How long will it take for them to be 30 miles apart as the crow flies? | tiger_math |
There are 36 students in Jisoo’s class. If you multiply the number of students in Jisoo's class by the number of students in Sunghoon's class, you get 1008. Find the number of students in Sunghoon's class. | tiger_math |
"statement 1": Mike has 87.0 baseball cards and Sam bought 13.0 of Mike 's baseball cards , "statement 2" :Mike has 72.0 baseball cards now, "options: " Entailment or contradiction? Please write a program to solve it | tiger_lab_math |
Out of 8 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
Answer Choices: (A) A) 5/7 (B) B) 5/4 (C) C) 5/14 (D) D) 5/6 (E) E) 9/14 | tiger_lab_math |
A store reduces the price of a shirt by 10%, and then applies an additional 20% discount on the new price. If the original price of the shirt is $50, what is the final price after both discounts? | automath |
A manufacturing company produces two types of products, A and B. The profit per unit for each product is $20 and $30, respectively. The production process requires two machines, and the company has 100 units of machine 1 and 150 units of machine 2 available. Product A requires 2 units of machine 1 and 1 unit of machine... | tiger_lab_math |
One pipe can fill a tank in 20 hours, and another pipe can fill the same tank in some hours. Both the pipes are opened to fill the tank, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. The total time taken to fill the tank is 15.999999999999998 hours. How long does it t... | tiger_math |
Dylan works as a technical support specialist, and his main responsibility is to assist clients with their technical issues via phone calls. Each call is billed at a rate of 8 cents per minute. If he spends an average of 45 minutes per call and handles 40 customers per week, what will be his total phone bill for the mo... | nvidia_math |
jane makes toy bears . when she works with an assistant , she makes 80 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent e ? Please respond by writing a program in Python. | tiger_lab_math |
Topsoil costs $\$6$ per cubic foot. What is the cost, in dollars, of X cubic yards of topsoil?
If we know the answer to the above question is 810, what is the value of unknown variable X? | tiger_math |
How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Answer Choices: (A) 388 (B) 277 (C) 500 (D) 2887 (E) 212 | tiger_lab_math |
A puppy and two cats together weigh 24 pounds. The puppy and the larger cat together weigh exactly twice as much as the smaller cat, and the puppy and the smaller cat together weigh exactly the same as the larger cat. How many pounds does the puppy weigh? | nvidia_math |
Benjamin has a zoo with various animals. He has 15 monkeys, 75% more giraffes. Benjamin also has as many lions as one-quarter of giraffes and monkeys in total. How many animals does Benjamin have in his zoo? | nvidia_math |
Worker W produces n units in 5 hours. Workers V and W, workers independently but at thesame time, produce n units in 2 hours.how long would it take V alone to produce n units?
Answer Choices: (A) 1 hr 26 min (B) 1 hr 53 min (C) 2 hr 30 min (D) 3 hr 30 min (E) 3 hr 20 min | tiger_lab_math |
a box contain the number of balls which is as much greater than 44 is less than 70 . the number of balls is ? Let's write a Python program to solve it. | tiger_lab_math |
The product of 10 and a number is the same as 36 less a certain multiple of that same number. The number is -4.5. What is the multiple? | tiger_math |
At a math academy, 120 students participated in a math olympiad. If there are 36 more students who received certificates than those who did not, find how many students received certificates. | tiger_math |
What is the degree of the splitting field of the polynomial \( f(X) = X^4 - X^3 - 5X + 5 \) over \( \mathbb{Q} \), and what are the elements of this field? Additionally, identify the constructible numbers within this field. | automath |
At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 500-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $200?
Answer Choices: (A) 1,108 (B) 4,100 (C) 2,108 (D) 2,124 (E) 2,256 | tiger_lab_math |
What is the least number which should be added to 2597 so that the sum is exactly divisible by 5, 6, 4, and 3?
Answer Choices: (A) 17 (B) 23 (C) 26 (D) 35 (E) 43 | tiger_lab_math |
lionel left his house and walked towards walt ' s house , 48 miles away . two hours later , walt left his house and ran towards lionel ' s house . if lionel ' s speed was 2 miles per hour and walt ' s 6 miles per hour , how many miles had lionel walked when he met walt ? Let's program in Python in the response. | tiger_lab_math |
Of the 20 members of a kitchen crew in traditional Japanese, 17 can prepare sushi, 18 can prepare noodle, and 15 can prepare both. If one member is chosen at random, what is the probability that the member chosen will be someone who can not prepare either dish?
Answer Choices: (A) a) 1/7 (B) b) 1/5 (C) c) 1/4 (D) d)... | tiger_lab_math |
If \( x \) is a real number such that \( \frac{x}{|x|} < x \), which of the following statements must be true?
(A) \( x > 1 \)
(B) \( x > -1 \)
(C) \( |x| < 1 \)
(D) \( |x| = 1 \)
(E) \( |x|^2 > 1 \)
Provide a justification for your answer. | automath |
The base six number $53_{6}$ is equal to the base $b$ number $113_{b}$. What is the positive value of $b$? | tiger_math |
If John releases 3 videos on his channel per day, with two of them being short 2-minute videos and one of them being 6 times as long, how many minutes of video does he release in total per week, assuming a 7-day week? | tiger_math |
Find the minimum value of
\[(\sin x + \csc x)^2 + (\cos x + \sec x)^2\]for $0 < x < \frac{\pi}{2}.$ | nvidia_math |
Given two identical wedges of mass \( M \) and height \( h \) on a frictionless floor, a mass \( m \) slides down the first wedge and then moves onto the second wedge. Using the principles of conservation of momentum and energy, derive an expression for the maximum height \( h' \) that the mass \( m \) reaches on the s... | automath |
Rookie police officers have to buy duty shoes at the full price of $85, but officers who have served at least a year get a 20% discount. Officers who have served at least three years get an additional 25% off the discounted price. How much does an officer who has served at least three years have to pay for shoes? | nvidia_math |
How many non-empty subsets of $\{ 1, 2, 3, 4, 5, 6, 7, 8 \}$ have exactly two even numbers? | nvidia_math |
Taylor and his friends decide to bring their pets together for a walk. 3 of his friends come first, each having twice as many pets as Taylor has. Another two of his friends have 2 pets each. If Taylor has 4 pets, what's the total number of pets they have together? | tiger_math |
What will be the compound interest on a sum of Rs. 21,000 after 3 years at the rate of 12% p.a.?
Answer Choices: (A) Rs. 8503.49 (B) Rs. 9720 (C) Rs. 10123.20 (D) Rs. 10483.20 (E) None | tiger_lab_math |
On a clock, how many times a day do the minute and hour hand overlap?
Answer Choices: (A) 10 (B) 11 (C) 20 (D) 22 (E) 24 | tiger_lab_math |
The points A(0,0), B(2,0), C(4,0), D(6,0), and E(8,0) form the vertices of a triangle. The point F is chosen inside the triangle so that |AF| + |BF| + |CF| + |DF| + |EF| = 20. Find the shortest possible distance between F and line segment CD. | nvidia_math |
A library has 8 books on a shelf, and Michael wants to arrange 3 of them in a specific order on his desk. However, there is a constraint: one of the books is a reference book and must be placed in the middle of the arrangement. How many different arrangements of the 3 books can Michael make? | nvidia_math |
517 + 5.017 + 0.517 + 5.0017 = ?
Answer Choices: (A) 558.3657 (B) 527.5357 (C) 229.6357 (D) 629.5637 (E) 629.6753 | tiger_lab_math |
Each year Dani gets 4 pairs of two pants each as pay winning the best Amazon buyer of the season. If he initially had 50 pants, calculate the number of pants he'll have in x years. The answer is 90. What is the value of unknown variable x? | tiger_math |
In a rhombus $EFGH$, the sum of the squares of the lengths of the diagonals is equal to $392$. Find the length of the segment $EF$. | nvidia_math |
A conical pile of sand is formed such that the height of the pile is always double the radius of its base. If sand is being poured into the pile at a rate of 10 cubic feet per minute, at what rate is the height of the pile increasing when the height is 6 feet? | automath |
Evaluate the integral \( I = \int_0^{\pi} \cos^2 x \, dx \). What is the value of \( I \)? | automath |
What is the coefficient of the $x^2y^4$ term in the expansion of $(x+y)^6$? | tiger_math |
in a 100 m race , a covers the distance in 36 seconds and b in 45 second . in this race a beats b by : ? Please respond by writing a program in Python. | tiger_lab_math |
The sides of a triangle have lengths of $15$, $20$, and X$. Find the length of the shortest altitude. The answer is 12. What is the value of unknown variable X? | tiger_math |
Simplify the expression: $\frac{x^2+3x-4}{x^2-4} - \frac{x^2+2x-3}{x^2-4}$ and express the result as a single fraction. | nvidia_math |
The circle with equation $x^2 + y^2 - 2x - 4y + 1 = 0$ is inscribed in a square. What is the area of the square? | nvidia_math |
Michelle is bringing sandwiches to work to give to her co-workers. She gives 4 sandwiches to one of her co-workers and keeps twice this amount for herself. If she had originally made 20 sandwiches, how many sandwiches does she have left to give to her other co-workers? Let's write a Python program. | tiger_lab_math |
Jordan's dog, Max, was born on the same day that Luka turned 4 years old. Luka is exactly 2 years older than is Aubrey. On Aubrey's 8th birthday, how many years old was Jordan's dog, Max? Let's write a Python program. | tiger_lab_math |
If $h(x) = 2 + \!\sqrt{2x}$ and $j(x) = x^2 - 3x + 1$, what is $h(j(2))$? | nvidia_math |
Is there a specific example of a relationship between two variables \( x \) and \( y \) for which the equality \( \frac{\partial x}{\partial y} = \frac{1}{\partial y/\partial x} \) does not hold true when both \( x \) and \( y \) are related by an explicit function? Provide the example along with the relevant calculati... | automath |
In a City, 35% of the population is composed of migrants, 20% of whom are from rural areas. Of the local population, 48% is female while this figure for rural and urban migrants is 30% and 40% respectively. If the total population of the city is 728400, what is its female population ?
Answer Choices: (A) 324138 (B) 248... | tiger_lab_math |
Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 7200 interest only for the period. The principal amount borrowed by her was
Answer Choices: (A) Rs. 2000 (B) Rs. 10000 (C) Rs. 15000 (D) Rs. 20000 (E) None of these | tiger_lab_math |
We have a triangle $\triangle ABC$ such that $AB = AC = 8$ and $BC = 10.$ What is the length of the median $AM$? Let's write a program. | tiger_lab_math |
Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled ?
Answer Choices: (A) 2.5 hours (B) 2 hours (C) 3.5 hours (D) 3 hours (E) None of these | tiger_lab_math |
Solve the rational equation:
(2/x) + (1/(x-5)) = 1
where x can't be equal to 0 or 5. | tiger_lab_math |
A trader sells 80 meters of cloth for Rs. 10000 at the profit of Rs. 7 per metre of cloth. What is the cost price of one metre of cloth?
Answer Choices: (A) 118 (B) 88 (C) 90 (D) 42 (E) 22 | tiger_lab_math |
Given a point in polar coordinates $\left(r, \theta\right)$, find its mirror image across the line $y = x$. Express your answer in polar coordinates. | nvidia_math |
What is the area, in square units, of triangle $ABC$? [asy]
unitsize(1.5mm);
defaultpen(linewidth(.7pt)+fontsize(8pt));
dotfactor=4;
pair A=(-3,1), B=(7,1), C=(5,-3);
pair[] dots={A,B,C};
real[] xticks={-4,-3,-2,-1,1,2,3,4,5,6,7,8};
real[] yticks={3,2,1,-1,-2,-3,-4,-5,-6,-7};
draw(A--B--C--cycle);
dot(dots);
label("... | tiger_math |
Here's a numerical problem for a math student related to the Feigenbaum constant and universality in chaotic systems:
Given that the Feigenbaum constant is approximately equal to 4.6692016, and considering a family of logistic maps with the equation:
xₙ₊₁ = rxₙ(1 - xₙ)
where x₀ = 0.5 and r is a parameter between 3.5... | tiger_lab_math |
Let $f(x)$ and $g(x)$ be two polynomials such that $f(x)=x^4-x^2+1$ and $g(x)=x^4+x^2+1$. Determine the product of all possible values of $x$ satisfying $\ds\dfrac{f(x)}{g(x)}=-\ds\dfrac{1}{2}$. | nvidia_math |
Let $P$ be a point on the circle $x^2 + y^2 - 10x + 25 = 0$, and let $Q$ be a point on the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$. Find the smallest possible distance $PQ$. | nvidia_math |
The total age of the people in Kaydence's family is 200. If Kaydence's father is 60 years old, Kaydence's mother 2 years younger than Kaydence's father, Kaydence's brother 1/2 the age of Kaydence's father, and Kaydence's sister 40 years old, how old is Kaydence? | tiger_math |
For which integers \( N \) in the range \( 1 \leq N \leq 28 \) does the second player have a winning strategy in the triangle-rod game, and what is the winning strategy for those \( N \)? | automath |
John decides to learn how to play the piano. He buys a piano for a certain amount. He then hires a teacher for 20 lessons at $40 per lesson but ends up getting a 25% discount. Everything cost him $1100. How much did the piano cost? | tiger_math |
What is the maximum number of edges \( E \) that a simple graph with \( N \) vertices can have without containing a complete subgraph \( K_5 \) or a complete bipartite graph \( K_{3,3} \), according to Kuratowski's theorem, and how can this bound be expressed quantitatively? | automath |
Given the system of equations \(5x - 8y = 18\) and \(4x + y = 7\), determine the point of intersection \((x, y)\). What is the value of \(x + y\) at this intersection? | automath |
John buys 100 shares of par value Rs. 5 each, of a company, which pays an annual dividend of 12% at such a price that he gets 10% on his investment. Find the market value of a share.
Answer Choices: (A) 2 (B) 4 (C) 5 (D) 6 (E) 8 | tiger_lab_math |
Let \( G \) be a finite group and \( H \) a subgroup of \( G \). Given a \( k[H] \)-bimodule \( W \) and a \( k[G] \)-bimodule \( V \), consider the left \( k[H] \)-module \( \Ind^G_H W \).
1. Suppose \( f: k[G] \times W \to P \) is a balanced map where \( P \) is a left \( k[G] \)-module. Using the properties of the... | automath |
A standard deck of 52 cards contains four suits: hearts, diamonds, clubs, and spades. If two cards are drawn at random without replacement, what is the probability that they are from different suits? | nvidia_math |
Given the list of positive integers \( \text{data} = \{1, 1, 2, 3, 3, 3, 5, 5, 5, 7, 7, 8, 8, 9, 10, 10, 12, 16, 23\} \), how many subsets can be formed such that the sum of the elements in each subset is less than or equal to 20? | automath |
Beth is looking at her book collection and is wondering how many comic books she owns. She has 120 books and 65% are novels. 18 are graphic novels. The rest are comic books. What percentage of comic books does she own? Please respond by writing a program in Python. | tiger_lab_math |
Given a piecewise continuous function \( f(x) \) with a period of \( 2\pi \), assume that the Fourier coefficients \( a_n \) and \( b_n \) are defined for \( n \geq 0 \). If \( f(x) \) is continuous everywhere except at two points within the interval \( [-\pi, \pi] \), determine the conditions under which the Fourier s... | automath |
What are the coordinates of the other endpoint of a segment if one endpoint is $(2, 5)$ and the midpoint is $(4, 9)$? | tiger_math |
Given that \( g(x) \) is a differentiable function and \( f \) is its inverse, can you derive \( f(s) \) explicitly if you know \( g(x) \) and the relationship \( f'(g(x))g'(x) = 1 \)? If so, provide a step-by-step solution for a specific case, such as \( g(x) = x^3 - 2 \). | automath |
Calculate the value of \(\text{atan}(-2i + 3)\) using the given formula for the complex inverse tangent function, and express your answer in rectangular form \(a + bi\), where \(a\) and \(b\) are real numbers. What are the values of \(a\) and \(b\)? | automath |
Circle $A$ has its center at $A(4, 4)$ and has a radius of 4 units. Circle $B$ has its center at $B(12, 4)$ and has a radius of 4 units. What is the area of the gray region bound by the circles and the $x$-axis? Express your answer in terms of $\pi$. [asy]
import olympiad; size(150); defaultpen(linewidth(0.8));
xaxis(0... | nvidia_math |
Evaluate the definite integral \( \int_{-1}^2 \sin(x) \, dx \) and provide the numerical value. | automath |
Given the polynomial equation
\[x^3 - 2x^2 - 5x + 1 = 0,\]
find the sum of the squares of its real roots. | nvidia_math |
A small water pump would take some hours to fill an empty tank. A larger pump would take 1/4 hour to fill the same tank. It would take both pumps 0.23076923076923078 hours, working at their respective constant rates, to fill the empty tank if they began pumping at the same time. How many hours would it take the small w... | tiger_math |
What is the value of the function f(x) = x² + 3x - 4 at x = 5 in Higher-order logic? | tiger_lab_math |
A hotel has 10 rooms and is currently full. Each room holds a family of 3. If each person receives 2 towels, how many towels does the hotel hand out? Let's write a Python program to solve it. | tiger_lab_math |
Find the arithmetic mean of 18, 25, and 31. | nvidia_math |
The graph of $y = f(x)$ is shown below.
[asy]
unitsize(0.5 cm);
real func(real x) {
real y;
if (x >= -3 && x <= 0) {y = -2 - x;}
if (x >= 0 && x <= 2) {y = sqrt(4 - (x - 2)^2) - 2;}
if (x >= 2 && x <= 3) {y = 2*(x - 2);}
return(y);
}
int i, n;
for (i = -5; i <= 5; ++i) {
draw((i,-5)--(i,5),gray(0.7));
... | tiger_math |
Toby is counting goldfish in the local pond. He knows that only 25% of goldfish are at the surface and the rest are too deep below the surface to be able to see. If he counts 15 goldfish, how many are below the surface? | nvidia_math |
Aaron wants to purchase a guitar under a payment plan of $100.00 per month for 12 months. His father has agreed to lend him the entire amount for the guitar, plus a one-time x% interest fee for the entire loan. With interest, Aaron will owe his dad 1320 money. What is the value of unknown variable x? | tiger_math |
Consider a triangle with sides of lengths \( 2x \), \( 3x \), and \( 4x \) where \( x > 0 \). Given these side lengths, determine whether this triangle can exist according to the triangle inequality. If it can, calculate the area of the triangle in terms of \( x \). If it cannot exist, explain why. | automath |
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