prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "An equilateral triangle is inscribed in a square such that one of its sides is parallel to one side of the square. If the side length of the square is \\( s \\) and the area of the equilateral triangle is \\( \\frac{\\sqrt{3}}{4}s^2 \\), find the side length of the square. Express your answer in simplest form. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "s",
"style": "rule"
}
|
numina_math
|
{
"index": 2500,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer has a rectangular field that is divided into two sections. The first section is 3 times as long as it is wide, and the second section is a square with a side length equal to the width of the first section. If the total area of the field is 4000 square meters, what are the dimensions of each section? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10\\sqrt{10}",
"style": "rule"
}
|
numina_math
|
{
"index": 2501,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the sequence defined by \\(a_1 = 1\\) and for \\(n > 1\\), \\(a_n = a_{n-1} + 2n - 1\\). Prove by mathematical induction that \\(a_n = n^2\\) for all positive integers \\(n\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "a_n=n^2",
"style": "rule"
}
|
numina_math
|
{
"index": 2502,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cylindrical water tank with a radius of 0.5 meters and a height of 2 meters is being painted on the outside. If the paint covers 4 square meters per liter, how many liters of paint are needed to cover the entire surface area of the tank, including the top and bottom? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1.9",
"style": "rule"
}
|
numina_math
|
{
"index": 2503,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is organizing a reading marathon where each participant reads for a specific amount of time. She has 5 friends participating. Each friend reads for 3 hours and 15 minutes. After 2 hours, 1/5 of the participants take a break for 30 minutes. How much total reading time is accumulated by the end of the marathon, excluding the break time? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15 \\text{ hours and } 45 \\text{ minutes}",
"style": "rule"
}
|
numina_math
|
{
"index": 2504,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is purchasing a laptop that costs $1200. The store is offering a 10% discount on the laptop. After the discount, she also needs to pay a 7% sales tax on the discounted price. How much does Emily pay in total for the laptop? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1155.60",
"style": "rule"
}
|
numina_math
|
{
"index": 2505,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\) in the equation: \\( 3(2x - 1) + 4(5 - x) = 2x + 10 \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{nosolution}",
"style": "rule"
}
|
numina_math
|
{
"index": 2506,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A jar contains a total of 50 coins, consisting of only nickels and dimes. The total value of the coins is $4.50. How many nickels and how many dimes are in the jar? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2507,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Ella is saving money to buy a bike. She starts with $50 in her savings account and decides to add $20 every week. After how many weeks will she have saved a total of $230? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 2508,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the rational expression: $\\frac{x^3 + 6x^2 + 11x + 6}{x^2 + 3x + 2}$ Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "x+3",
"style": "rule"
}
|
numina_math
|
{
"index": 2509,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider a sequence of integers \\( a_1, a_2, \\ldots, a_{10} \\) such that the product of any two distinct elements in the sequence is a prime number. Determine the number of possible sequences. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2510,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular prism-shaped aquarium has a length of 24 inches, a width of 12 inches, and a height of 18 inches. If the aquarium is filled with water to $\\frac{2}{3}$ of its height, what is the volume of the water in cubic inches? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3456",
"style": "rule"
}
|
numina_math
|
{
"index": 2511,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of friends decided to share a bag of 55 candies equally. Each friend should receive an integer number of candies, and no candies should be left over. Additionally, the number of friends must be a prime number. What is the largest possible number of friends in the group? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11",
"style": "rule"
}
|
numina_math
|
{
"index": 2512,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A charity organization is collecting donations to fund a new community center. They have received donations from three different groups. Group A donated $250 each from 8 members. Group B donated twice as much per person as Group A, and they have 5 members. Group C donated three times the amount per person as Group A, but their donation total was $150 less than the total donation from Group B. How much did Group C donate, and what is the total amount collected by all three groups? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6750",
"style": "rule"
}
|
numina_math
|
{
"index": 2513,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces widgets in batches of 120. In a particular quality check, it was found that 15 out of every 120 widgets are defective. If a defective widget is found, it is discarded. What is the probability of randomly selecting a non-defective widget from a batch? Express your answer as a common fraction and simplify if necessary. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{7}{8}",
"style": "rule"
}
|
numina_math
|
{
"index": 2514,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe calls for 4 cups of flour, but you only have a 1/3 cup measuring cup. How many times do you need to use the 1/3 cup measuring cup to get the required amount of flour? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2515,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning a road trip and wants to calculate the total time it will take. She will be driving a total distance of 360 kilometers. She estimates that she can drive at an average speed of 90 kilometers per hour for the first 200 kilometers and then at 60 kilometers per hour for the remaining distance. Calculate the total time in hours and minutes that Sarah will spend driving. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4 \\text{ hours and } 53 \\text{ minutes}",
"style": "rule"
}
|
numina_math
|
{
"index": 2516,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah works as a software developer and earns $30 per hour for regular hours. Any hours worked beyond 40 hours per week are considered overtime and paid at 1.5 times her regular rate. If Sarah worked 50 hours in a week, how much did she earn in total for that week? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1650",
"style": "rule"
}
|
numina_math
|
{
"index": 2517,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company bought a machine for $50,000. The machine depreciates in value by $5,000 each year. After 4 years, the company invested an additional $8,000 in upgrades to the machine. What is the final value of the machine after these 4 years? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "38000",
"style": "rule"
}
|
numina_math
|
{
"index": 2518,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert the fraction \\(\\frac{7}{8}\\) to a decimal, then divide it by 0.25 and finally subtract 0.5 from the result. What is the answer? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3.0",
"style": "rule"
}
|
numina_math
|
{
"index": 2519,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert the fraction \\(\\frac{27}{50}\\) to its decimal expansion and determine if it is a terminating or repeating decimal. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0.54",
"style": "rule"
}
|
numina_math
|
{
"index": 2520,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Estimate the value of the expression \\( \\frac{\\frac{3}{4} + \\frac{1}{5}}{\\frac{2}{3} - \\frac{1}{6}} \\). Simplify the complex fractions and provide your answer in simplest form. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{19}{10}",
"style": "rule"
}
|
numina_math
|
{
"index": 2521,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In triangle $ABC$, vectors $\\overrightarrow{AB}$ and $\\overrightarrow{AC}$ are given by $\\overrightarrow{AB} = 3 \\mathbf{i} + 4 \\mathbf{j}$ and $\\overrightarrow{AC} = 5 \\mathbf{i} + 2 \\mathbf{j}$. Let $\\overrightarrow{AD}$ be the median from vertex $A$ to side $BC$. If $D$ is the midpoint of $BC$, express $\\overrightarrow{AD}$ as a linear combination of $\\overrightarrow{AB}$ and $\\overrightarrow{AC}$. Verify that $\\overrightarrow{AD}$ can be written as $\\frac{1}{2} \\overrightarrow{AB} + \\frac{1}{2} \\overrightarrow{AC}$. Also, find the magnitude of $\\overrightarrow{AD}$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2522,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma is redecorating her living room and needs to buy new curtains and a rug. The cost of the rug is twice the cost of the curtains. If the curtains cost $75, how much does Emma spend in total on the new curtains and rug? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "225",
"style": "rule"
}
|
numina_math
|
{
"index": 2523,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels at a speed of 60 miles per hour. How far will it travel in 4 hours and 30 minutes? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "270",
"style": "rule"
}
|
numina_math
|
{
"index": 2524,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Amy, Jeremy, and Chris went on a road trip. They traveled a total distance of 600 miles. Amy drove at a speed of 40 mph, Jeremy drove at a speed of 60 mph, and Chris drove at a speed of 50 mph. If the total time they spent driving was 12 hours and Jeremy drove for twice as long as Amy, how long did each person drive and what distance did each person cover? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "600",
"style": "rule"
}
|
numina_math
|
{
"index": 2525,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two pipes, A and B, can fill a tank in 6 hours and 8 hours, respectively. If both pipes are opened together, how long will it take to fill the tank? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2526,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\( h(x) = 2x - 1 \\) and \\( k(x) = x^2 + 3 \\), what is \\( h(k(2)) \\)? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 2527,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires 3/4 cup of sugar. If you only have 1 1/2 cups of sugar and you use 1/3 of it for a different recipe, how much sugar will you have left after making the first recipe? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{4}",
"style": "rule"
}
|
numina_math
|
{
"index": 2528,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jessica is baking cookies and needs to keep the oven temperature between 325°F and 350°F. If the oven is currently at 280°F, how many more minutes does she need to wait for the oven to reach at least the minimum temperature if the oven heats up at a rate of 5°F per minute? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 2529,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mr. Li deposited 5,000 yuan in a bank account that offers an annual interest rate of 4% compounded annually. He plans to leave the money in the account for 5 years. How much will Mr. Li have in his account at the end of the 5 years, including both the principal and interest? Round your answer to the nearest hundredth. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6083.26",
"style": "rule"
}
|
numina_math
|
{
"index": 2530,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels from City A to City B at a speed of 60 miles per hour. On the return trip, due to traffic, the car travels at a speed of 40 miles per hour. If the total travel time for the round trip is 5 hours, what is the distance between City A and City B? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 2531,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a certain city, two delivery drivers, Dave and Tom, are assigned to deliver packages. Dave starts from point A and drives towards point B, while Tom starts from point B and drives towards point A. The distance between point A and point B is 120 kilometers. Dave drives at a constant speed of 40 kilometers per hour, and Tom drives at a constant speed of 60 kilometers per hour. There is a checkpoint exactly halfway between points A and B where both drivers must stop and wait for 15 minutes before continuing their journey. If both drivers start at the same time, how long will it take for them to meet after they start their journey? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.35",
"style": "rule"
}
|
numina_math
|
{
"index": 2532,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a deck of 52 standard playing cards, how many different 5-card hands can be drawn if the hand must contain exactly 3 hearts and 2 spades? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "22308",
"style": "rule"
}
|
numina_math
|
{
"index": 2533,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that $2^x + 2^{x+1} = 48$, find the value of $x$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2534,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The sum of the first three terms of a geometric sequence is 21, and the common ratio is 3. If the first term is a fraction, express the first term in simplest form. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{21}{13}",
"style": "rule"
}
|
numina_math
|
{
"index": 2535,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many 5-digit numbers have at least one zero? Find the remainder when this number is divided by 1000. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "951",
"style": "rule"
}
|
numina_math
|
{
"index": 2536,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma works two part-time jobs. In her first job, she earns $15 per hour and works 12 hours a week. In her second job, she earns $20 per hour and works 8 hours a week. How much does Emma earn in total per week from both jobs? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "340",
"style": "rule"
}
|
numina_math
|
{
"index": 2537,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider a geometric sequence where the first term \\(a = 2\\) and the common ratio \\(r = 3\\). If you select any 4 terms from this sequence, what is the probability that their product is a perfect square? Express your answer as a common fraction. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 2538,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company is planning to paint the exterior of a cylindrical storage tank. The tank has a height of 10 meters and a diameter of 4 meters. The cost to paint is $5 per square meter. Calculate the total cost to paint the entire exterior surface area of the tank, excluding the top and bottom surfaces. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "628",
"style": "rule"
}
|
numina_math
|
{
"index": 2539,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma is training for a marathon. She runs a certain distance every day. On Monday, she ran for 2 hours at a speed of 6 miles per hour. On Tuesday, she ran for 1.5 hours at a speed of 8 miles per hour. How many hours would she need to run on Wednesday at a speed of 7 miles per hour to have run a total of 40 miles over the three days? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.29",
"style": "rule"
}
|
numina_math
|
{
"index": 2540,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A class of students took four math tests. Their scores were 78, 85, 92, and 88. What is the average score of the students on these four tests? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "85.75",
"style": "rule"
}
|
numina_math
|
{
"index": 2541,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the sum of the infinite geometric series \\( S \\) where the first term \\( a = 5 \\) and the common ratio \\( r = \\frac{1}{3} \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{15}{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 2542,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is shopping for a new laptop that originally costs $800. The store is offering a 25% discount on all laptops. After the discount, she needs to pay an additional 8% sales tax on the discounted price. How much will Sarah pay in total for the laptop? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "648",
"style": "rule"
}
|
numina_math
|
{
"index": 2543,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company produces gadgets and sells them in packs of 6. Each gadget costs $15 to produce and they sell each pack for $120. If the company produces 240 gadgets in a month, how much profit do they make after subtracting the production costs? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1200",
"style": "rule"
}
|
numina_math
|
{
"index": 2544,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the arithmetic sequence defined by \\( a_n = 2 + 3(n-1) \\) for \\( n \\geq 1 \\). Find the sum of the first 20 terms of this sequence, and then determine the value of the product of the sequence sum and \\( 3^5 \\sqrt{4} \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "296460",
"style": "rule"
}
|
numina_math
|
{
"index": 2545,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels a certain distance with an average speed of 60 km/h. On its return trip, the car travels the same distance but with an average speed of 40 km/h. If the total travel time for the round trip is 5 hours, what is the distance of the one-way trip? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 2546,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In trapezoid \\(ABCD\\), the parallel sides \\(AB\\) and \\(CD\\) have lengths of 8 and 20 units, respectively, and the altitude is 12 units. Points \\(E\\) and \\(F\\) are the midpoints of sides \\(AD\\) and \\(BC\\), respectively. What is the area of quadrilateral \\(EFCD\\) in square units? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "204",
"style": "rule"
}
|
numina_math
|
{
"index": 2547,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the vectors \\(\\mathbf{a} = \\begin{pmatrix} 3 \\\\ -4 \\\\ 1 \\end{pmatrix}\\) and \\(\\mathbf{b} = \\begin{pmatrix} 1 \\\\ 2 \\\\ -1 \\end{pmatrix}\\), find the projection of \\(\\mathbf{a}\\) onto \\(\\mathbf{b}\\). Also, verify that the projection vector is orthogonal to the vector obtained by subtracting the projection vector from \\(\\mathbf{a}\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\begin{pmatrix}-1\\-2\\1\\end{pmatrix}",
"style": "rule"
}
|
numina_math
|
{
"index": 2548,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression $\\frac{\\sqrt{6!}}{\\sqrt{2! \\cdot 3!}}$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2\\sqrt{15}",
"style": "rule"
}
|
numina_math
|
{
"index": 2549,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels at a constant speed. He covers 45 kilometers in 3 hours. If he maintains the same speed, how long will it take him to travel 75 kilometers? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2550,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\(f(x)\\) be a polynomial function such that \\(f(x)\\) has roots \\(r, s,\\) and \\(t\\). If \\(f(x)\\) is symmetric with respect to its roots, \\(f(r) + f(s) + f(t) = 0\\), and \\(f(x)\\) can be expressed as \\(f(x) = x^3 - 3x + 2\\), find the value of \\(r^2 + s^2 + t^2\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2551,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A research team recorded the daily number of steps taken by five participants over a week. The participants recorded the following average daily steps: 8000, 7500, 9200, 8800, and 7800. If a sixth participant's average daily steps need to be included so that the overall average daily steps for all six participants is 8500, how many average daily steps did the sixth participant take? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9700",
"style": "rule"
}
|
numina_math
|
{
"index": 2552,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Susan is picking strawberries. She's trying to fill her basket, but out of every handful of 5 strawberries, she can't help but eat one of them herself. If her basket holds 60 strawberries, how many berries will she actually pick before she fills it? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "75",
"style": "rule"
}
|
numina_math
|
{
"index": 2553,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression: \\(\\frac{\\sqrt{18} + 2i}{3 - \\sqrt{2}i}\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{7\\sqrt{2}}{11}+\\frac{12i}{11}",
"style": "rule"
}
|
numina_math
|
{
"index": 2554,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Anna's house is 2 miles away from the library. On her way back from the library, she takes a different route that is 3 miles long. If Anna visits the library and returns home 3 times in a week, how many miles does she travel in total? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 2555,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the point on the line \\( y = 2x + 3 \\) that is closest to the point \\( (4, 0) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "(-\\frac{2}{5}\\frac{11}{5})",
"style": "rule"
}
|
numina_math
|
{
"index": 2556,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Linda is planning a trip where she will be covering a total distance of 300 miles. She will be driving at an average speed of 60 miles per hour. After reaching her destination, she will be staying at a hotel that charges $120 per night. If Linda plans to stay for 3 nights, how much will she spend in total, including both the cost of the hotel and the travel time calculated in hours? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "360",
"style": "rule"
}
|
numina_math
|
{
"index": 2557,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice has a total of 15 candies that she wants to distribute among her 4 friends such that each friend gets at least one candy. How many different ways can she do this? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "364",
"style": "rule"
}
|
numina_math
|
{
"index": 2558,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A population of bacteria doubles every 3 hours. If the initial population of bacteria is 500, how many hours will it take for the population to reach 16,000? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 2559,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Compare the following two expressions and determine which one is larger:\n\\[\n\\frac{3}{5} \\quad \\text{or} \\quad \\sqrt{\\frac{1}{2}}.\n\\] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\sqrt{\\frac{1}{2}}",
"style": "rule"
}
|
numina_math
|
{
"index": 2560,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a circle with radius 10 units, a chord is 12 units away from the center of the circle. Find the length of the chord. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 2561,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In the diagram, $\\triangle ABC$ is an isosceles triangle with $\\angle BAC = 120^\\circ$. The circle with center $O$ and radius 6 cm passes through points $B$ and $C$ such that $O$ lies on the perpendicular bisector of $\\overline{BC}$. Find the perimeter of $\\triangle ABC$ in centimeters.\n[asy]\ndraw(Circle((0,0),6));\npair O, B, C, A;\nO = (0,0);\nB = 6 * dir(120);\nC = 6 * dir(240);\nA = (0, sqrt(108));\ndraw(B--A--C--cycle);\ndraw(O--B--C--O);\nlabel(\"$O$\", O, S);\nlabel(\"$B$\", B, W);\nlabel(\"$C$\", C, E);\nlabel(\"$A$\", A, N);\nlabel(\"$6$ cm\", (-3,0), SW);\n[/asy] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12+6\\sqrt{3}",
"style": "rule"
}
|
numina_math
|
{
"index": 2562,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, the ratio of the number of students in Class A to Class B is 3:2. If there are 45 students in Class A, how many students are there in total in both classes? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "75",
"style": "rule"
}
|
numina_math
|
{
"index": 2563,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the polynomial function \\( P(x) = 2x^4 - 3x^3 + x - 6 \\) and the rational expression \\(\\frac{P(x)}{x^2 - 4}\\), find the values of \\(x\\) that make the rational expression undefined. Additionally, evaluate \\(P(x)\\) at these points. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2564,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, there are four classes with the following number of students: Class A has 25 students, Class B has 30 students, Class C has 28 students, and Class D has 32 students. If each student is required to submit a project that takes up 2 square feet of display space, how much total display space is needed for all the projects? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "230",
"style": "rule"
}
|
numina_math
|
{
"index": 2565,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given a recursively defined sequence \\( a_n \\) where \\( a_1 = 2 \\) and \\( a_{n+1} = 3a_n + 1 \\), find the value of \\( a_4 \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "67",
"style": "rule"
}
|
numina_math
|
{
"index": 2566,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is trying to decide between two different brands of detergent. Brand A offers 2 liters for $5, while Brand B offers 3 liters for $7. She wants to know which brand is more cost-effective per liter and how much she would save per liter by choosing the more cost-effective brand. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "17",
"style": "rule"
}
|
numina_math
|
{
"index": 2567,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is a marathon runner and she has to complete a 26-mile marathon. She runs the first 10 miles at an average speed of 5 miles per hour, the next 10 miles at an average speed of 6 miles per hour, and the final 6 miles at an average speed of 4 miles per hour. Calculate her total time to complete the marathon. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5.17",
"style": "rule"
}
|
numina_math
|
{
"index": 2568,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A certain gas is contained in a cylinder with a movable piston. According to Boyle's Law, the pressure \\(P\\) of the gas varies inversely with its volume \\(V\\). If the volume of the gas is 3 liters when the pressure is 10 atmospheres, what will the pressure be when the volume is increased to 6 liters? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2569,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The function \\( f : \\mathbb{R} \\to \\mathbb{R} \\) satisfies\n\\[ f(x) + f(2 - x) = x + 1 \\]\nfor all \\( x \\). Find \\( f(4) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2570,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A pie shop sold a total of 75 slices of pie in one day. Each whole pie is cut into 5 slices. If there were 15 whole pies delivered to the shop that day, how many whole pies are left unsold? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2571,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let $r$, $s$, and $t$ be the roots of the polynomial \\(P(x) = x^3 - 4x^2 + 3x + 1 = 0\\). Compute the value of \\(r^2 + s^2 + t^2\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 2572,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer wants to buy enough fencing to enclose a rectangular field that is twice as long as it is wide. If the total length of fencing needed is 600 meters, what are the dimensions of the field? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{width:100meterslength:200meters}",
"style": "rule"
}
|
numina_math
|
{
"index": 2573,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If 5 workers can paint a house in 12 days working 8 hours each day, how many hours would it take for 8 workers to paint the same house, assuming they work the same number of hours each day? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 2574,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice has a collection of 5 different types of flowers. She has twice as many roses as tulips, three times as many lilies as roses, half as many daisies as lilies, and the same number of sunflowers as roses and tulips combined. If she has 8 tulips, how many flowers does Alice have in total? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 2575,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A baker makes 120 cookies and plans to package them in boxes. He initially plans to put 12 cookies in each box but realizes that he needs to set aside 24 cookies for a special order. After setting aside the special order, he decides to divide the remaining cookies equally among 8 boxes. How many cookies will be in each box? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2576,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Henry has 50 apples. He gives 15 apples to his friend and then buys 10 more apples. How many apples does Henry have now? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45",
"style": "rule"
}
|
numina_math
|
{
"index": 2577,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find all integer solutions to the equation $2x^2 - 3xy + y^2 = 17$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "(1633)(1615)",
"style": "rule"
}
|
numina_math
|
{
"index": 2578,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression: $(3x^2 + 2x - 5) - (2x^2 - 4x + 1)$ Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "x^2+6x-6",
"style": "rule"
}
|
numina_math
|
{
"index": 2579,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, there are 5 classes with the same number of students in each. The total number of students in the school is 180. If 30 students from one class go on a field trip, how many students are left in the school? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "150",
"style": "rule"
}
|
numina_math
|
{
"index": 2580,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sam's car travels at a constant speed of 60 miles per hour. His friend's car travels at a constant speed of 45 miles per hour. If Sam starts from the same point 30 minutes after his friend, how long will it take Sam to catch up with his friend? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 2581,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe for a fruit punch requires a ratio of 2 parts orange juice to 3 parts pineapple juice. If you want to make 15 liters of fruit punch, how many liters of orange juice and pineapple juice will you need? Additionally, what percentage of the total fruit punch is orange juice? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2582,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the equation: $\\frac{5}{x} + \\frac{2}{x+2} = \\frac{7}{2}$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\pm\\frac{2\\sqrt{35}}{7}",
"style": "rule"
}
|
numina_math
|
{
"index": 2583,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces 15 gadgets every hour. If the factory operates for 8 hours each day and runs 5 days a week, how many gadgets will the factory produce in 4 weeks? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2400",
"style": "rule"
}
|
numina_math
|
{
"index": 2584,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels a distance of 150 miles at a constant speed. If it takes the car 3 hours to cover this distance, how long will it take the same car to travel 250 miles at the same speed? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2585,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression \\(\\frac{2 + \\sqrt{3}}{1 - \\sqrt{3}}\\) and express your answer in the form \\(a + b\\sqrt{3}\\), where \\(a\\) and \\(b\\) are rational numbers. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-\\frac{5}{2}-\\frac{3\\sqrt{3}}{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 2586,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Liam swims at a rate of 50 meters per minute. If he swims for 2 hours each day, how many meters will he have swum after a week? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "42000",
"style": "rule"
}
|
numina_math
|
{
"index": 2587,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe for a fruit punch requires 3 parts of orange juice to 5 parts of pineapple juice. If you want to make 16 liters of fruit punch, how many liters of orange juice and pineapple juice are needed? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 2588,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A train travels at a constant speed of 60 kilometers per hour. If the train travels for 3.5 hours, how many kilometers does it cover? Additionally, if the train had to make 4 stops, each lasting 15 minutes, what is the total time taken for the journey including stops? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{distancecovered:210kilometerstotaljourneytime:4.5hours}",
"style": "rule"
}
|
numina_math
|
{
"index": 2589,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\) in the equation: \\[ 2\\left|3x - 5\\right| + 4 = 18. \\] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-\\frac{2}{3}",
"style": "rule"
}
|
numina_math
|
{
"index": 2590,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist is riding around a circular track with a radius of 100 meters at a constant speed of 20 meters per minute. Another cyclist is riding around the same track at a constant speed of 30 meters per minute. If both cyclists start at the same point and time, what percentage of the track will the slower cyclist have covered when they next meet at the starting point? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2591,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Determine all integer solutions for \\( a \\) such that the inequality \\( |x^2 - 4ax + 4| \\leq 9 \\) holds for all \\( x \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "a\\in\\{\\ldots-3-223\\ldots\\}",
"style": "rule"
}
|
numina_math
|
{
"index": 2592,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A school is planning a field trip and needs to budget for transportation costs. The school can rent a bus for $500 or vans for $120 each. If they choose to rent 3 buses and 4 vans, the total cost is $2,180. However, if they opt for 2 buses and 6 vans, the total cost is $1,720. How many buses and vans can they rent with a budget of $1,300? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2593,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Marta works on her grandparent's farm to raise money for a new phone. So far, she has collected $340. For every hour she works, she receives $15. Her grandmother often gives her tips, and she has collected $50 in tips in total. How many hours has Marta worked on the farm so far? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "19",
"style": "rule"
}
|
numina_math
|
{
"index": 2594,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that $\\cos 30^\\circ = \\frac{\\sqrt{3}}{2}$ and $\\sin 30^\\circ = \\frac{1}{2}$, find the value of $\\sin 120^\\circ$ using reference angles and trigonometric identities. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{\\sqrt{3}}{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 2595,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the smallest positive integer \\( n \\) such that \\( 2^n - 1 \\) is divisible by 3. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2596,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has the opportunity to work an additional 5 hours at her job, where she earns $20 per hour. However, if she chooses to work, she will miss a local event where she could win a $100 gift card and enjoy $40 worth of free meals. Calculate Sarah's opportunity cost if she decides to work instead of attending the event. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2597,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden is 30 meters long and 20 meters wide. The owner wants to increase the length by 25% and the width by 10%. After the increase, by what percentage has the area of the garden increased? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "37.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2598,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces 200 gadgets per hour. During a 7-hour shift, the factory had a 1-hour break, and the production rate was doubled for the last 2 hours. How many gadgets did the factory produce by the end of the shift? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1600",
"style": "rule"
}
|
numina_math
|
{
"index": 2599,
"name": "numina_math",
"split": "train"
}
|
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