Search is not available for this dataset
source stringclasses 4
values | id int64 0 50k | conversations listlengths 2 2 |
|---|---|---|
tiger_math | 16,666 | [
{
"from": "human",
"value": "What is the product of all values of $t$ that satisfy the equation $t^2 = 36$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the product of all values of t that satisfy the equation t squared equals 36. Let me think about how to approach this. Hmm, ... |
tiger_lab_math | 16,667 | [
{
"from": "human",
"value": "A rabbit can run at a speed of 40 kmph in a field and 30 kmph in a cactus field. This means the rabbit gets hotter running through a? \"Option 1\": cactus field, \"Option 2\" :field Please write a program to solve it"
},
{
"from": "gpt",
"value": "<think>\nOkay, let... |
nvidia_math | 16,668 | [
{
"from": "human",
"value": "Twenty-five is 40% of what number?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find out what number 25 is 40% of. Hmm, let's see. I remember that percentages can be converted to decimals by dividing by 100. So 40% would be 0.40. The problem is saying t... |
tiger_math | 16,669 | [
{
"from": "human",
"value": "What three-digit integer is equal to the difference between the sum of the factorials of its even digits and the sum of the factorials of its odd digits?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find a three-digit integer where the difference betwee... |
tiger_math | 16,670 | [
{
"from": "human",
"value": "If I have a $4\\times 4$ chess board, in how many ways can I place four distinct pawns on the board such that each column and row of the board contains no more than one pawn?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out how many ways I can pl... |
tiger_math | 16,671 | [
{
"from": "human",
"value": "Surfers enjoy going to the Rip Curl Myrtle Beach Surf Festival. There were 1500 surfers at the Festival on the first day, 600 more surfers on the second day than the first day, and 2/5 as many surfers on the third day as the first day. What is the average number of surfers at th... |
nvidia_math | 16,672 | [
{
"from": "human",
"value": "A rectangular swimming pool is surrounded by a 3-foot wide walkway. The pool itself measures 15 feet by 20 feet. If a gardener wants to put a 2-foot wide border of flowers around the entire walkway, what is the area of the flowers border?"
},
{
"from": "gpt",
"value"... |
automath | 16,673 | [
{
"from": "human",
"value": "Let \\( X \\) be a locally compact Hausdorff space equipped with a Radon measure \\( \\mu \\). Suppose \\( g: X \\to \\mathbb{C} \\) is a measurable function such that \\( \\int_E g \\, d\\mu = 0 \\) for every Borel set \\( E \\subset X \\) of finite measure. Can we conclude tha... |
tiger_math | 16,674 | [
{
"from": "human",
"value": "If Erica takes 1/5 of an apple pie and 3/4 of a cherry pie at a pie buffet where all the pies are the same size, what is the percentage of a whole pie that Erica took in total?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so Erica went to a pie buffet, right? And sh... |
tiger_math | 16,675 | [
{
"from": "human",
"value": "A can do a work in some days. B can do the same work in 6 days. If both A and B are working together, they will finish the work in 2 days. In how many days can A do the work alone?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. The problem is about A and B ... |
nvidia_math | 16,676 | [
{
"from": "human",
"value": "A large group of people are invited to a party, and each person is given a random task to complete. The tasks are such that each person can either succeed or fail, and the outcomes of the tasks are independent. The person who completes the most tasks successfully wins a prize. I... |
tiger_lab_math | 16,677 | [
{
"from": "human",
"value": "If x ¤ y = (x + y)^2 - (x - y)^2. Then √11 ¤ √11 =\nAnswer Choices: (A) 44 (B) 5 (C) 10 (D) 15 (E) 20"
},
{
"from": "gpt",
"value": "<think>\nAlright, let's see. I need to solve this problem where the operation ¤ is defined as x ¤ y = (x + y)^2 - (x - y)^2. Then, the... |
nvidia_math | 16,678 | [
{
"from": "human",
"value": "Alex buys a 12-piece chicken nugget meal. Her sister eats 3 nuggets, and Alex eats one-third of what remains. How many nuggets does Alex eat?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. The problem is about Alex buying a 12-piece chicken nugget meal. Her... |
tiger_math | 16,679 | [
{
"from": "human",
"value": "How many positive integers, not exceeding 200, are multiples of 5 or 7 but not 10?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out how many positive integers up to 200 are multiples of 5 or 7 but not 10. Hmm, let me break this down step by step.... |
tiger_lab_math | 16,680 | [
{
"from": "human",
"value": "At the end of a circus act, there are 12 dogs on stage. Half of the dogs are standing on their back legs and the other half are standing on all 4 legs. How many dog paws are on the ground? Please respond by writing a program in Python."
},
{
"from": "gpt",
"value":... |
automath | 16,681 | [
{
"from": "human",
"value": "In category theory, consider two functors \\( F: \\mathcal{C} \\to \\mathcal{D} \\) and \\( G: \\mathcal{D} \\to \\mathcal{C} \\) which are adjoint to each other. If \\( F \\) is left adjoint to \\( G \\), under what conditions does the natural isomorphism \\(\\mathrm{Hom}_{\\ma... |
nvidia_math | 16,682 | [
{
"from": "human",
"value": "Find all real numbers $x$ such that \\[2 \\le \\frac{x}{3x-4} < 5.\\](Give your answer in interval notation.)"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to solve the inequality \\(2 \\le \\frac{x}{3x-4} < 5\\). Hmm, this is a compound inequality, right? ... |
nvidia_math | 16,683 | [
{
"from": "human",
"value": "Sophia manages a community library where people can donate and borrow books for free. She initially had 250 books on the shelves. During a charity drive, 12 people donated 8 books each, and a local publisher donated 50 books. However, 120 books were borrowed by readers during th... |
tiger_math | 16,684 | [
{
"from": "human",
"value": "Find the sum of the least common multiple and the greatest common factor of $36$ and $84$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. I need to find the sum of the least common multiple (LCM) and the greatest common factor (GCF) of 36 and 84. Hmm, I rem... |
nvidia_math | 16,685 | [
{
"from": "human",
"value": "Alex and Ava are planning a movie night with three of their friends. They decide to buy individual pizzas and boxes of popcorn for each guest. They also purchase two bottles of juice per person and 2 bags of candy to share among their friends and themselves. Pizzas are $8 each, ... |
automath | 16,686 | [
{
"from": "human",
"value": "Given a dataset with the attributes: credit standing, age, income, and marriage status, suppose the calculated information gains for splitting based on these attributes are as follows:\n\n- Information gain for age vs. credit standing = 0.01\n- Information gain for marriage stat... |
tiger_math | 16,687 | [
{
"from": "human",
"value": "Mr. Fat and Mr. Thin now have a new challenge. They need to eat 5 pounds of cereal together. If Mr. Fat still needs 20 minutes to eat a pound of cereal, but Mr. Thin's eating speed has increased to 25 minutes per pound, how long will it take them to finish the cereal?"
},
{
... |
tiger_math | 16,688 | [
{
"from": "human",
"value": "What is the remainder when $(x - 1)^{2011}$ is divided by $x^2 - x + 1$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the remainder when \\((x - 1)^{2011}\\) is divided by \\(x^2 - x + 1\\). Hmm, let's recall how polynomial division works. When you... |
nvidia_math | 16,689 | [
{
"from": "human",
"value": "Factor the following expression: $45x+30$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to factor the expression 45x plus 30. Hmm, factoring. Alright, let's start by remembering what factoring means. Factoring an expression involves finding the greatest co... |
tiger_math | 16,690 | [
{
"from": "human",
"value": "The distance between two cities on a map is 15 inches. If the scale is 0.25 inches = 3 miles, how many miles apart are the actual cities?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out how many miles apart the two cities are in real life, given... |
tiger_math | 16,691 | [
{
"from": "human",
"value": "The average age of the 10 females in a choir is 30 years. The average age of the 15 males in the same choir is 35 years. What is the average age, in years, of the 25 people in the choir?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the average age ... |
automath | 16,692 | [
{
"from": "human",
"value": "If \\( y = 4x + 10 \\) and \\( y = 7x - 5 \\), what is the value of \\( y \\)?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the value of y when given two equations: y = 4x + 10 and y = 7x - 5. Hmm, let's see. Since both equations are equal to y, ma... |
tiger_lab_math | 16,693 | [
{
"from": "human",
"value": "if p and q are prime numbers , how many divisors does the product p ^ 6 * q ^ 7 have ? Let's write a program."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out how many divisors the product p^6 * q^7 has, where p and q are prime numbers. Hmm, righ... |
nvidia_math | 16,694 | [
{
"from": "human",
"value": "Alex was 7 years old. His brother Ryan was 3 years older than Alex. Their oldest brother Jack was 3 times as old as Ryan. Tom was 5 years older than Jack. How old was Tom?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see here. I need to figure out Tom's age ba... |
nvidia_math | 16,695 | [
{
"from": "human",
"value": "Expand $(3x^2 - 2x - 1)(2x^3 + 4x^2 - 5)$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to expand this polynomial expression: (3x² - 2x - 1)(2x³ + 4x² - 5). Hmm, let me think. I remember that expanding two polynomials means I have to use the distributive p... |
automath | 16,696 | [
{
"from": "human",
"value": "What is the simplified form of the expression $$\\displaystyle \\frac{x^2-4x+3+(x+1)\\sqrt{x^2-9}}{x^2+4x+3+(x-1)\\sqrt{x^2-9}}$$ for $$x > 3$$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to simplify the expression \\(\\frac{x^2 - 4x + 3 + (x + 1)\\sqrt{... |
nvidia_math | 16,697 | [
{
"from": "human",
"value": "A parking garage has a height of 6 meters and the average height of a car is 2 meters. If the garage is full and the cars are parked in a way that the distance between the front bumper of one car and the rear bumper of the next car is 0.5 meters, what is the maximum number of ca... |
tiger_math | 16,698 | [
{
"from": "human",
"value": "If $a$ is inversely proportional to $b^2$ and $a = 9$ when $b = 2$, what is the value of $a$ when $b = 3$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to solve this problem where a is inversely proportional to b squared. Hmm, inverse proportionality... Le... |
tiger_math | 16,699 | [
{
"from": "human",
"value": "What is the distance between the vertex and the focus of the parabola defined by the equation $y = -2x^2$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the distance between the vertex and the focus of the parabola defined by the equation y = -2x². ... |
nvidia_math | 16,700 | [
{
"from": "human",
"value": "Find the quotient of the division $(2x^5 + 5x^4 - 3x^3 - 7x^2 + x - 1)/(x - 2)$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to divide the polynomial \\(2x^5 + 5x^4 - 3x^3 - 7x^2 + x - 1\\) by \\(x - 2\\) and find the quotient. Hmm, I remember there are a... |
tiger_lab_math | 16,701 | [
{
"from": "human",
"value": "In the infinite sequence 2, 4, 6, 8, 10, . . . , where each term is 2 greater than the previous term, the 72th term is\nAnswer Choices: (A) 144 (B) 263 (C) 176 (D) 344 (E) 287"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out the 72nd term in the ... |
automath | 16,702 | [
{
"from": "human",
"value": "Find the value of the constant \\( k \\) such that the function \n\n\\[\nF(x) = 2\\sqrt{1+e^x} + \\ln(\\sqrt{1+e^x}-1) - \\ln(\\sqrt{1+e^x}+1) + k\n\\]\n\nis equal to the indefinite integral \\( \\int \\sqrt{e^x+1} \\, dx \\). Specifically, what is the value of \\( k \\) when \\... |
nvidia_math | 16,703 | [
{
"from": "human",
"value": "It takes 1.75 hours to clean a car and 0.25 hours to clean a motorcycle. What is the number of minutes it takes to clean 4 cars and 6 motorcycles?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out how long it takes to clean 4 cars and 6 motorcycle... |
tiger_math | 16,704 | [
{
"from": "human",
"value": "6 is a number added 3 to the number. What number is it that is 5 greater than the number?"
},
{
"from": "gpt",
"value": "<think>\nAlright, let's try to figure out this problem. So the question is: \"6 is a number added 3 to the number. What number is it that is 5 gre... |
nvidia_math | 16,705 | [
{
"from": "human",
"value": "A librarian has 5 shelves, each with 3 slots, to display 15 books of different genres (history, fiction, science, art, and music). Each genre has 3 books, and no two books of the same genre can be placed on the same shelf. In how many ways can the librarian arrange the books on ... |
tiger_math | 16,706 | [
{
"from": "human",
"value": "Find the sum of the squares of the solutions to\n\\[\\left| x^2 - x + \\frac{1}{2023} \\right| = \\frac{1}{2023}.\\]"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to solve the equation \\(\\left| x^2 - x + \\frac{1}{2023} \\right| = \\frac{1}{2023}\\) and t... |
tiger_lab_math | 16,707 | [
{
"from": "human",
"value": "In a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?\nAnswer Choices: (A) 1/3 (B) 2/3 (C) 2/5 (D) 2/7 (E) 3/7"
},
{
"from": "gpt",
"value": ... |
tiger_math | 16,708 | [
{
"from": "human",
"value": "At Luna's Bakery, Luna sold 3 types of pastries during the week: croissants, muffins, and scones. On Monday, she sold 10 more croissants than muffins but 15 fewer scones than croissants. Throughout the day, she found that the total number of these pastries sold was 150. How many... |
nvidia_math | 16,709 | [
{
"from": "human",
"value": "In a cylindrical tank with a height of 5 units and a radius of 4 units, water is poured to a height of 3 units. Find the volume of the region between the surface of the water and the top of the tank. Express your answer in terms of π."
},
{
"from": "gpt",
"value": "<... |
tiger_lab_math | 16,710 | [
{
"from": "human",
"value": "a certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts , by weight . what is the number of pounds of almonds in 150 pounds of the mixture ? Let's write a Python program."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out how many ... |
tiger_math | 16,711 | [
{
"from": "human",
"value": "Each turtle lays a clutch of 20 eggs. If x% of the eggs successfully hatch, 6 turtles produce 48 hatchlings. What is the value of unknown variable x?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out the percentage of eggs that successfully hatch,... |
tiger_lab_math | 16,712 | [
{
"from": "human",
"value": "A group of 10 people consists of 3 married couples and 4 single men. A committee of 4 is to be formed from the 10 people. How many different committees can be formed if the committee can consist of at most 1 married couple?\nAnswer Choices: (A) 105 (B) 207 (C) 210 (D) 540 (E) 5,... |
tiger_lab_math | 16,713 | [
{
"from": "human",
"value": "Given a graph G with 10 vertices and 20 edges, determine its edge connectivity."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem where I need to determine the edge connectivity of a graph G that has 10 vertices and 20 edges. Hmm, edge connectivity... |
tiger_lab_math | 16,714 | [
{
"from": "human",
"value": "Consider the one-dimensional heat equation given by:\n\n∂u/∂t = k ∂²u/∂x²\n\nwhere k = 0.1 is the thermal diffusivity constant. \n\nA 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... |
tiger_lab_math | 16,715 | [
{
"from": "human",
"value": "In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?\nAnswer Choices: (A) 160 (B) 170 (C) 1... |
nvidia_math | 16,716 | [
{
"from": "human",
"value": "A regular hexagon with side length 4 is divided into six equilateral triangles. A circle is inscribed in each triangle, touching the sides of the triangle and the other two circles. Find the area of the shaded region, which is the area of the hexagon minus the areas of the six c... |
automath | 16,717 | [
{
"from": "human",
"value": "Negate the statement \"For all \\( x \\), if \\( p(x) \\) is true, then \\( q(x) \\) is false,\" and simplify the expression to find an equivalent statement. What is the simplified form?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to negate the statement ... |
nvidia_math | 16,718 | [
{
"from": "human",
"value": "A triangle has an area of 10 square centimeters. Its height is equal to the length of one of its sides. Determine the length of the base."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem here: A triangle has an area of 10 square centimeters. Its h... |
automath | 16,719 | [
{
"from": "human",
"value": "Evaluate the definite integral using the Fundamental Theorem of Calculus: $$\\int_0^5 (5 + 2t) \\, dt.$$ What is the total area under the curve over the interval [0, 5]?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to evaluate the definite integral of 5 + ... |
nvidia_math | 16,720 | [
{
"from": "human",
"value": "Ryan wants to buy a pair of sneakers that costs $\\$51.25$. He empties his wallet and finds he only has two $\\$20$ bills, four $\\$1$ bills, and a handful of nickels. What is the minimum number of nickels that must be in his handful so he can pay for the sneakers?"
},
{
... |
tiger_lab_math | 16,721 | [
{
"from": "human",
"value": "a beats b by 50 m in a race of 500 m , then b beats by c by 25 m in a race of 500 m . find the distance by which a beats c in a race of 400 ? Let's program in Python in the response."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out by how much di... |
automath | 16,722 | [
{
"from": "human",
"value": "What is the derivative of the arcsecant function \\( y = \\arcsec(x) \\) with respect to \\( x \\), and what is its domain?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the derivative of the arcsecant function, y = arcsec(x), with respect to x, and... |
automath | 16,723 | [
{
"from": "human",
"value": "Consider the demand function given by \\( p = \\frac{8}{5} - \\frac{12,500}{x} \\), where \\( p \\) is the price and \\( x \\) is the quantity demanded. If the price increases from \\( p_1 = 50 \\) to \\( p_2 = 70 \\) and the quantity demanded decreases from \\( x_1 = 10,000 \\)... |
tiger_lab_math | 16,724 | [
{
"from": "human",
"value": "What is the greatest three-digit multiple of 19? Please respond by writing a program in Python."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the greatest three-digit multiple of 19. Hmm, let's think. The problem is to find the largest number that's... |
nvidia_math | 16,725 | [
{
"from": "human",
"value": "Determine the value of $|x^2-1|$ given $x$ satisfies the equation $\\left| \\frac{1}{|x+1|} - \\frac{1}{|x-1|} \\right| = 2$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out the value of |x² - 1| given that x satisfies the equation |1/|x + 1| - ... |
tiger_math | 16,726 | [
{
"from": "human",
"value": "If a pound of strawberries costs $2.20 and a pound of cherries costs 6 times the price of strawberries, how much will Briget spend if she buys 5 pounds of strawberries and 5 pounds of cherries?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. So the problem s... |
automath | 16,727 | [
{
"from": "human",
"value": "Suppose \\( x \\) and \\( y \\) are two distinct real numbers. What is the value of \\( \\phi(x \\vee y) + \\phi(x \\wedge y) \\), where \\( \\phi \\) is defined as \\( \\phi(x) = -x \\)?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out the value... |
tiger_lab_math | 16,728 | [
{
"from": "human",
"value": "Max was doing homework in three different subjects. It took him 20 minutes to finish tasks from biology and two times more time to finish history. Geography took him the most time, three times more than history. How much time did Max spend on doing his homework? Let's program in... |
automath | 16,729 | [
{
"from": "human",
"value": "What is the maximum number of distinct game configurations that need to be evaluated to compute the equity of a PreFlop hand for a player with 9 opponents at the table, using the given combinatorial formula?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to ... |
tiger_lab_math | 16,730 | [
{
"from": "human",
"value": "A clock loses a minute every three hours for 4 days and gains 2% in the subsequent 6 days. If it was set right on Friday at 11 AM, what will be the time at the end of 10 days?\nAnswer Choices: (A) 11:54:40 AM (B) 01:20:13 PM (C) 12:16:40 PM (D) 11:54:24 AM (E) 12:06:36 PM"
},
... |
automath | 16,731 | [
{
"from": "human",
"value": "What is the moment of inertia of a uniform circular disk with a mass of \\( M \\) and a radius of \\( R \\) about an axis perpendicular to its plane and passing through its center?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the moment of inertia ... |
automath | 16,732 | [
{
"from": "human",
"value": "How many distinct ways can we color the faces of a regular tetrahedron using two colors, considering that colorings are equivalent if they can be transformed into one another by rotation?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out how many ... |
tiger_math | 16,733 | [
{
"from": "human",
"value": "If $a @ b$ is defined as $a @ b$ = $3a - 3b$, what is the value of $2 @ (X + 1)$ if $X = 5$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let me try to figure out this problem. So, the question is about this operation @ defined as a @ b = 3a - 3b. And we need to fin... |
nvidia_math | 16,734 | [
{
"from": "human",
"value": "A jogger runs at a constant pace of 6 miles per hour. If she starts at 7:00 AM and runs for 45 minutes, what is the distance between her starting point and the point where she stops to drink water, assuming she stops at the halfway point of her route? Express your answer in mile... |
automath | 16,735 | [
{
"from": "human",
"value": "In the context of Generative Adversarial Networks (GANs), if the prior distribution on the input noise variable \\( z \\) is a standard normal distribution, how does the behavior of the optimal discriminator \\( D^*_G(x) \\) change as the generator distribution \\( p_g(x) \\) ap... |
nvidia_math | 16,736 | [
{
"from": "human",
"value": "Suppose that $a$ is a multiple of $3$ and $b$ is a multiple of $6$. Which of the following statements must be true?\n\nA. $b$ is a multiple of $3$.\nB. $a-b$ is a multiple of $3$.\nC. $a-b$ is a multiple of $6$.\nD. $a-b$ is a multiple of $2$.\n\nList the choices in your answe... |
automath | 16,737 | [
{
"from": "human",
"value": "If the price of sugar increases by 7%, by what percentage should a housewife reduce her sugar consumption to maintain the same total expenditure?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so the problem is: If the price of sugar increases by 7%, by what percentag... |
automath | 16,738 | [
{
"from": "human",
"value": "Consider the system of linear equations:\n\n\\[\n\\begin{align*}\n2x + 4z &= -2 \\\\\n-x + 2y - 3z &= 4 \\\\\nx + 2y + z &= k\n\\end{align*}\n\\]\n\nWhat are the values of \\( k \\) for which the system has:\n\na) a unique solution?\n\nb) no solution?\n\nc) infinitely many solut... |
nvidia_math | 16,739 | [
{
"from": "human",
"value": "Find the product of all the solutions to $3^{|x|} + 2|x| = 25.$"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the product of all the solutions to the equation \\(3^{|x|} + 2|x| = 25\\). Hmm, let's start by understanding what this equation is asking.... |
tiger_math | 16,740 | [
{
"from": "human",
"value": "The complement of an angle is $5^{\\circ}$ more than four times the angle. What is the number of degrees in the measure of the angle?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the measure of an angle where its complement is 5 degrees more than f... |
nvidia_math | 16,741 | [
{
"from": "human",
"value": "Two spheres with centers at $(3, 4, 5)$ and $(8, 11, 1)$ are both tangent to the $xy$-plane. What is the distance between the closest points of the two spheres?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the distance between the closest points of... |
tiger_lab_math | 16,742 | [
{
"from": "human",
"value": "Let set A = {1, 2, 3, 4, 5} and set B = {2, 4, 6, 8, 10}. Find the intersection of set A and set B."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the intersection of set A and set B. Let me remember what intersection means. I think it's the set of e... |
nvidia_math | 16,743 | [
{
"from": "human",
"value": "Violet is planning a hike through the desert with her dog. Violet needs 800 ml of water per hour hiked and her dog needs 400 ml of water per hour. If Violet can carry 4.8 L of water, how many hours can she and her dog spend hiking?"
},
{
"from": "gpt",
"value": "<thi... |
tiger_lab_math | 16,744 | [
{
"from": "human",
"value": "Find the greatest common divisor (GCD) of 252 and 105 using Euclidean algorithm."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the greatest common divisor (GCD) of 252 and 105 using the Euclidean algorithm. Hmm, let me remember how that works. The E... |
nvidia_math | 16,745 | [
{
"from": "human",
"value": "Emily is working out with dumbbells. She does bicep curls with 8 pounds for 12 reps and completes 4 sets. How much total weight does she lift?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so Emily is doing bicep curls with 8-pound dumbbells. She does 12 reps in each... |
nvidia_math | 16,746 | [
{
"from": "human",
"value": "Emily wants to purchase a total of 15 flowers for her bouquet. She has already picked out 5 roses and a bunch of carnations containing 6 flowers. How many lilies does she need to select to have 15 flowers in total?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's ... |
tiger_math | 16,747 | [
{
"from": "human",
"value": "Out of the 450 students that Sarah interviewed at her school and asked about their favorite fruit - oranges, apples, pears, or strawberries - 70 students chose oranges, 120 students chose pears, and 147 students chose apples. How many students chose strawberries as their favorit... |
tiger_math | 16,748 | [
{
"from": "human",
"value": "A biologist is studying a particular breed of bacteria that doubles in quantity every hour. At the start of her observations at 9 AM, there was only one bacterium. The biologist took a lunch break and recorded the quantity of bacteria again at 1 PM that day. Calculate the total ... |
nvidia_math | 16,749 | [
{
"from": "human",
"value": "Find the only positive real number $x$ for which $\\displaystyle \\frac{x-4}{9} = \\frac{4}{x-9}$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the positive real number x that satisfies the equation (x - 4)/9 = 4/(x - 9). Let me see. Hmm, this look... |
automath | 16,750 | [
{
"from": "human",
"value": "Given a sine wave represented by the function \\( f(x) = \\sin(x) \\), we differentiate it using two methods: the central difference method and convolution with the kernel \\([0.5, 0, -0.5]\\). If we denote the sample points as \\( x_k \\) where \\( k = 0, 1, \\ldots, n-1 \\), a... |
tiger_math | 16,751 | [
{
"from": "human",
"value": "Henry has 30 more lollipops than Alison does. With 60 lollipops, Alisson has half the number of lollipops Diane has. If they combine the lollipops and eat 45 lollipops each day, calculate the total number of days it will take for them to finish the lollipops."
},
{
"from... |
nvidia_math | 16,752 | [
{
"from": "human",
"value": "Factor the expression $x^2+4x+4$ using two different methods: by grouping and by completing the square. Which method do you find more efficient, and why?"
},
{
"from": "gpt",
"value": "<think>\nAlright, so I need to factor the quadratic expression \\( x^2 + 4x + 4 \\... |
tiger_lab_math | 16,753 | [
{
"from": "human",
"value": "In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:\nAnswer Choices: (A) 21 m (B) 26 m (C) 28m (D) 29m (E) 30m"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's try to figure out how much A can beat C by in a 100 m race... |
tiger_math | 16,754 | [
{
"from": "human",
"value": "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?\nIf we know... |
tiger_lab_math | 16,755 | [
{
"from": "human",
"value": "Triangle $ABC$ with vertices of $A(6,2)$, $B(2,5)$, and $C(2,2)$ is reflected over the x-axis to triangle $A'B'C'$. This triangle is reflected over the y-axis to triangle $A''B''C''$. What are the coordinates of point $C''$?"
},
{
"from": "gpt",
"value": "<think>\nOk... |
tiger_lab_math | 16,756 | [
{
"from": "human",
"value": "39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?\nAnswer Choices: (A) 10 (B) 16 (C) 13 (D) 18 (E) 19"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out how m... |
nvidia_math | 16,757 | [
{
"from": "human",
"value": "Ben operates a lemonade stand. He buys lemons for 25 cents each and sells lemonade for 50 cents per cup. Each lemon can make 2 cups of lemonade. If Ben buys 36 lemons and sells 60 cups of lemonade, how much profit does he make in cents?"
},
{
"from": "gpt",
"value": ... |
automath | 16,758 | [
{
"from": "human",
"value": "Given the second-order linear homogeneous differential equation \n\n\\[\ny'' + 5y' + 6y = 0,\n\\]\n\ndetermine the general solution of the equation."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the general solution to the differential equation y'' ... |
nvidia_math | 16,759 | [
{
"from": "human",
"value": "A boat travels the 90 miles from $C$ to $D$ at 30 miles per hour, and then returns to $C$ on the same route. If the average rate of the round trip is 36 miles per hour, what is the rate, in miles per hour, of the boat traveling back from $D$ to $C$?"
},
{
"from": "gpt",
... |
tiger_lab_math | 16,760 | [
{
"from": "human",
"value": "In shop there are 10 bulbs, a total of 4 are defective. If a customer buys 4 bulbs selected at random from the box, what is the probability that neither bulbs will be defective?\nAnswer Choices: (A) 2/19 (B) 3/29 (C) 4/15 (D) 1/15 (E) 1/2"
},
{
"from": "gpt",
"value"... |
nvidia_math | 16,761 | [
{
"from": "human",
"value": "A bakery sells a rectangular cake with dimensions $20$ inches by $30$ inches for $\\$50$. If you wanted to buy a cake with the same area, but with dimensions $10$ inches by $X$ inches, how much would it cost?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so the probl... |
tiger_lab_math | 16,762 | [
{
"from": "human",
"value": "If 48 men can do a piece of work in 25 hours, in how many hours will 15 men\ndo it ?\nAnswer Choices: (A) 80 hours (B) 75 hours (C) 70 hours (D) 65 hours (E) 60 hours Let's program in Python in the response."
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. Th... |
tiger_lab_math | 16,763 | [
{
"from": "human",
"value": "How many distinct, natural-number factors does $4^3 \\cdot 5^4 \\cdot 6^2$ have? Let's write a Python program to solve it."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find out how many distinct natural-number factors the expression 4³ × 5⁴ × 6² has. Hm... |
tiger_math | 16,764 | [
{
"from": "human",
"value": "Farmer Joe is constructing a fence around his rectangular carrot farm, which contains exactly 300 square meters of land for his beloved carrots. To keep the rabbits out, he wants to minimize the fence’s perimeter to reduce costs. Which dimensions should Joe use for his carrot fa... |
nvidia_math | 16,765 | [
{
"from": "human",
"value": "Solve the inequality $x^2 - 25 \\leq 0$."
},
{
"from": "gpt",
"value": "<think>\nOkay, let me try to figure out how to solve the inequality \\( x^2 - 25 \\leq 0 \\). Hmm, so I remember that inequalities can sometimes be tricky, but maybe I can start by solving the eq... |
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