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初始化项目，由ModelHub XC社区提供模型 Model: hector-gr/RLCR-5x-priority-overconf-math Source: Original Platform
2026-04-22 02:36:00 +08:00
{
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"prompt_preview": "What is the molecular weight of Acetic acid?",
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"prompt_preview": "Two trains, each 150 m long, moving in opposite directions, cross each other in 18 sec. If one is moving three times as fast as the other, then the speed of the faster train is?",
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"prompt_preview": "Three builders build a single floor of a house in some days. Each builder is paid $100 for a single day\u2019s work. It would cost $270000 to hire 6 builders to build 5 houses with 6 floors each. How many days does it take for three builders to ",
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"prompt_preview": "Abby is building 2 raised beds to grow vegetables. The beds are both 8 feet long, 4 feet wide and have a certain height. Each bag of soil has 4 cubic feet. She will need 16 bags of soil. How high are the beds?",
"answer_preview": "1",
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"prompt_preview": "Given the function $y= \\frac {x-b}{x+2}$, if its range on the interval $(a,a+6)$ $(b < -2)$ is $(2,+\u221e)$, then $a+b=$ _____ .",
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"prompt_preview": "a small company reduced its faculty by approximately 13 percent to 195 employees . what was the original number of employees ?",
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"prompt_preview": "Given $a=(-1,3)$, $b=(1,t)$, if $(a-2b) \\perp a$, then the real number $t=$ ?",
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"prompt_preview": "In a class of 50 students, it is required to select 10 students using systematic sampling. The 50 students are randomly assigned numbers from 1 to 50 and grouped, with group one containing numbers 1 to 5, group two containing numbers 6 to 1",
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"prompt_preview": "Given a geometric sequence \\(\\{a_n\\}\\) where each term is a positive number, the sum of the first two terms is 6, and the sum of the first six terms is 126, calculate the sum of the first four terms. Express your answer as a single integer.",
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"prompt_preview": "Rahul can complete a work in 5 days, and Meena can complete the same work in some days. When they work together, they can complete the work in 3.333333333333333 days. In how many days can Meena complete the work alone?",
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"prompt_preview": "Let $(a_1, b_1),$ $(a_2, b_2),$ $\\dots,$ $(a_n, b_n)$ be the real solutions to \\begin{align*} a + \\frac{17a + 6b}{a^2 + b^2} &= 6, \\\\ b + \\frac{6a - 17b}{a^2 + b^2} &= 0. \\end{align*}Find $a_1 + b_1 + a_2 + b_2 + \\dots + a_n + b_n.$ Hint: ",
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"prompt_preview": "Given the function $f(x) = \\ln(x + \\sqrt{x^2 + 1}) + ax^7 + bx^3 - 4$, where $a$ and $b$ are constants. If $f(-3) = 4$, then $f(3) = \\_\\_\\_\\_\\_\\_$.",
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"prompt_preview": "63 men working some hours per day dig 30 m deep. To dig to a depth of 50 m working 6 hours per day, 77 extra men should be put to work. How many hours per day were the initial men working?",
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"prompt_preview": "A fan can create an airflow of 10 liters per second. If the fan works for a certain amount of time each day, the amount of airflow it will create in one week is 42000 liters. How long does the fan work each day?",
"answer_preview": "10",
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"prompt_preview": "A pet store had 1700 puppies. In one week they sold 621 of them and put the rest into cages with 26 in each cage. How many cages did they use?",
"answer_preview": "42",
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"prompt_preview": "A seven-digit number, where the sum of every two adjacent digits from left to right is 9, 7, 9, 2, 8, 11. What is this seven-digit number?",
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"prompt_preview": "There are 80 cable cars traveling in a circular route between ski resorts A and B, all moving in the same direction. The distance between two adjacent cable cars is the same. Xiaoming, who is sitting in one of the cable cars, encounters an ",
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"prompt_preview": "Given the function \\(f(x)=\\sin ^{4} \\frac{k x}{10}+\\cos ^{4} \\frac{k x}{10}\\), where \\(k\\) is a positive integer, if for any real number \\(a\\), it holds that \\(\\{f(x) \\mid a<x<a+1\\}=\\{f(x) \\mid x \\in \\mathbb{R}\\}\\), find the minimum value o",
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"prompt_preview": "Find the number of sets A that satisfy the condition {0, 1} \u222a A = {0, 1}. Express your answer as a whole number.",
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"prompt_preview": "Find the minimum value of the function $f(x) = -x^2 + 4x + 5$ within the closed interval $[1, 4]$. Express your answer as a single number.",
"answer_preview": "5",
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"prompt_preview": "Distribute 100 apples among several children, with each child receiving at least one apple and each child receiving a different number of apples. What is the maximum number of children that can receive apples? Express your answer as a whole",
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"prompt_preview": "After 10% of the inhabitants of a village disappeared, a panic set in during which 25% of the remaining inhabitants left the village. Some time later, 15% of the people who left during the panic decided to return to the village. At that tim",
"answer_preview": "7425",
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"prompt_preview": "Given that $\\xi$ is normally distributed with mean 0 and variance $6^2$, and $P(-2 \\leq \\xi \\leq 0) = 0.4$, find the value of $P(\\xi > 2)$.",
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"prompt_preview": "Given that the coefficient of the $x^3$ term in the expansion of $((ax-1)^{5})$ is $80$, find the coefficient of the $x^2$ term in the expansion.",
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"prompt_preview": "A certain unit has a total of 600 employees, of whom 250 are young employees, 200 are middle-aged employees, and 150 are elderly employees. A stratified sampling method is used to select a sample, and the sample contains 5 young employees. ",
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"prompt_preview": "Two trains, each a certain length, moving in opposite directions, cross each other in 20 sec. If one is moving twice as fast as the other, and the speed of the faster train is 24 m/s, what is the length of each train?",
"answer_preview": "360",
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"prompt_preview": "There are a total of 9 seats in a row. Three people, A, B, and C, are to be seated in such a way that each person has empty seats on both sides, and A must be seated between B and C. How many different seating arrangements are there? (Answe",
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"prompt_preview": "In a vast garden, there are 500 plants. On the first day, hungry bugs devoured 300 plants. The next day, they were still hungry and ate 5/7 of the remaining plants. After that, they consumed 12 more plants. How many plants remain?",
"answer_preview": "45",
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"prompt_preview": "I run a 15-mile route which consists of 5 miles at a pace of 7 minutes per mile, then 6 miles at a pace of 8 minutes per mile, and finally 4 miles at a pace of 6 minutes per mile. What is my average speed in kilometers per hour for the enti",
"answer_preview": "13.54",
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"prompt_preview": "In a geometric sequence where all terms are positive, if $6a_{1}$, $a_{3}$, and $4a_{2}$ form an arithmetic sequence, then find the value of the expression $\\frac{a_{11}+a_{13}+a_{16}+a_{20}+a_{21}}{a_{8}+a_{10}+a_{13}+a_{17}+a_{18}}$.",
"answer_preview": "27",
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"prompt_preview": "Skylar started donating 8k to an organization on Skylar's birthday when Skylar turned 17. Yesterday, Skylar turned a certain age. Skylar has donated 440k till now. How old is Skylar now?",
"answer_preview": "72",
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"prompt_preview": "In a football tournament, each team meets exactly twice with every other team. There are no draws, a victory earns two points and a defeat earns no points. One team won the tournament with 26 points, and there are two teams tied for last pl",
"answer_preview": "12",
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"prompt_preview": "Given two perpendicular lines, $2x + my - 1 = 0$ and $3x - 2y + n = 0$, with the foot of the perpendicular from the point $(2, p)$, find the value of $m + n + p$.",
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"prompt_preview": "Given \\\\(a \\in \\mathbb{R}\\\\) and \\\\(i\\\\) as the imaginary unit, if \\\\((1-i)(a+i)\\\\) is a pure imaginary number, then the value of \\\\(a\\\\) is \\_\\_\\_\\_\\_\\_",
"answer_preview": "-1",
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"prompt_preview": "How many real number solutions exist for the equation $\\sqrt{x-1} \\cdot \\sqrt{x+1}=-\\sqrt{x^{2}-1}$, given that $x \\geq 1$? Express your answer as a single integer.",
"answer_preview": "1",
"source": "big_math"
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"prompt_preview": "A thin rectangular slab of potato was cut into two pieces for an osmosis lab. One piece is 50 mm greater than the other. If the original uncut slab is 600 mm, what is the length of the other piece of the potato after it is cut?",
"answer_preview": "325",
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"prompt_preview": "A high school has a total of $900$ students. A stratified sampling method is used to select a sample of $45$ students from the school, with $20$ students from Grade 10, and $10$ students from Grade 12. Determine the number of Grade 11 stude",
"answer_preview": "300",
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"prompt_preview": "Find the coefficient of $x^5y^2$ in the expansion of $(x^2+x+y)^5$. Express your answer as a numerical value in the form $\\boxed{[answer]}$.",
"answer_preview": "30",
"source": "big_math"
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"prompt_preview": "Given \u03b1\u2208({0,\u03c0/2}), solve the equation sin 2\u03b1 = cos(\u03c0/4-\u03b1) for cos 2\u03b1. Provide your answer as a single number.",
"answer_preview": "0",
"source": "big_math"
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"prompt_preview": "John uses the bathroom every 50 minutes, but each time he takes a break, it takes him an additional 5 minutes to walk to and from the bathroom. Also, the 2.5-hour movie has two 15-minute intermissions, during which John can use the restroom",
"answer_preview": "5",
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"prompt_preview": "The number \\( a^{100} \\) leaves a remainder of 2 when divided by 73, and the number \\( a^{101} \\) leaves a remainder of 69 when divided by the same number. Find the remainder when the number \\( a \\) is divided by 73.",
"answer_preview": "71",
"source": "olympiads"
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"prompt_preview": "A positive integer \\( n \\) is a multiple of 7. The square root of \\( n \\) is between 17 and 18. Determine the number of possible values of \\( n \\). Express your answer as a single integer.",
"answer_preview": "5",
"source": "big_math"
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"prompt_preview": "Among the real numbers $\\sqrt{4}$, $\\sqrt{3}$, $0$, $\\frac{22}{7}$, $\\sqrt[3]{0.125}$, $0.1010010001\\ldots$, $\\frac{\\pi}{2}$, how many are irrational? Express your answer as a whole number.",
"answer_preview": "3",
"source": "big_math"
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"prompt_preview": "Find the number of different values of integer n, such that one can find n different lines in the plane, where each line intersects exactly 2004 other lines. Express your answer as a single integer.",
"answer_preview": "1",
"source": "big_math"
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"prompt_preview": "Let $C$ be a hyperbola with equation $\\frac{x^2}{a^2}-\\frac{y^2}{b^2}=1$ $(a>0, b>0)$ and eccentricity $e$. Find a value of $e$ that satisfies the condition \"the line $y=2x$ has no common points with $C$.\"",
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"prompt_preview": "Hani said she would do 3 more situps per minute than Diana would. Diana then did some situps at a rate of 4 situps per minute. They did a total of 110 situps together. How many situps did Diana do?",
"answer_preview": "40",
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"prompt_preview": "Dorothy is a certain age and wants to go to a museum with her family. Her family consists of her, her younger brother, her parents, and her grandfather. The regular ticket cost is $10. People 18 years old or younger have a discount of 30%. ",
"answer_preview": "18",
"source": "orca_math"
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"prompt_preview": "Given the ellipse $C\\_1: \\frac{x^{2}}{9}+ \\frac{y^{2}}{5}=1$ and the hyperbola $C\\_2: x^{2}- \\frac{y^{2}}{3}=1$, let $P$ be the point of intersection of $C\\_1$ and $C\\_2$ in the first quadrant. The distance from point $P$ to the left focus ",
"answer_preview": "4",
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"prompt_preview": "In a $5 \\times 5$ square, some cells have been painted black as shown in the figure. Consider all possible smaller squares within this grid whose sides align with the grid lines. In how many of these smaller squares is the number of black c",
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"prompt_preview": "A cone has a surface area of $3\\pi$. Its lateral surface unfolds into a semicircle. The diameter of the base of the cone is ______.",
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"prompt_preview": "Given an arithmetic sequence ${{a_n}}$, let ${S_n}$ denote the sum of its first $n$ terms. If ${a_4 + a_6 + a_8 = 15}$, find the value of ${S_{11}}$. Express your answer as a single number.",
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"prompt_preview": "A person bought 118 glass bowls at a certain rate per bowl. He sold 102 of them at Rs. 15 and the remaining broke. The percentage gain for him is 8.050847457627118%. What was the rate at which he bought the glass bowls?",
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"prompt_preview": "Tom bought 10 packages of miniature racing cars. Each package contains five cars. He gave a certain number of nephews 1/5 of the cars. Tom has 30 miniature racing cars left. How many nephews did Tom give cars to?",
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"prompt_preview": "Triassic Discoglossus tadpoles have five legs each, and Sabertooth Frog tadpoles grow several tails (each has the same number). A Jurassic Park employee scooped up a few tadpoles along with some water. It turned out that the captured tadpol",
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"prompt_preview": "There were sweets on the table. Jack came and took half of all the candies and 4 more candies. Then Paul came and took some sweets. There were 22 sweets on the table at first. How many sweets did Paul take?",
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"prompt_preview": "A triangle has two medians of lengths 9 and 12. Find the largest possible area of the triangle. (Note: A median is a line segment joining a vertex of the triangle to the midpoint of the opposite side.)",
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"prompt_preview": "Given that X follows a normal distribution N(4, \u03c3^2) (\u03c3 > 0), and the probability of X taking values in the interval (0, 8) is 0.6, find the probability of X taking values in the interval (0, 4). Express your answer as a decimal value betwe",
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"prompt_preview": "Shelly writes down a vector $v=(a, b, c, d)$, where $0<a<b<c<d$ are integers. Let $\\sigma(v)$ denote the set of 24 vectors whose coordinates are $a, b, c$, and $d$ in some order. For instance, $\\sigma(v)$ contains $(b, c, d, a)$. Shelly not",
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"prompt_preview": "Three dogs need 7 hours to dig 9 holes. Five birds take 40 minutes to build 2 nests. Keeping these rates, how many more minutes does a dog take to dig a hole than a bird takes to build a nest?",
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"prompt_preview": "Consider an arithmetic sequence where the first term and the common difference are both non-negative integers, the number of terms is at least 3, and the sum of the terms is 97^2. How many such sequences are there? Express your answer as a ",
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"prompt_preview": "If \\( S = \\frac{1}{1 + 1^{2} + 1^{4}} + \\frac{2}{1 + 2^{2} + 2^{4}} + \\frac{3}{1 + 3^{2} + 3^{4}} + \\ldots + \\frac{200}{1 + 200^{2} + 200^{4}} \\), find the value of \\( 80402 \\times S \\).",
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"prompt_preview": "Let $a$ and $b$ be real numbers. One of the roots of $x^3 + ax + b = 0$ is $1 + i \\sqrt{3}.$ Find $a + b.$",
"answer_preview": "8",
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"prompt_preview": "If $2^x = 9$, and $\\log_{2} \\frac {8}{3} = y$, then $x + 2y = \\_\\_\\_\\_\\_\\_$.",
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"prompt_preview": "If the integer part of $\\sqrt[3]{a}$ is $2$, then the number of odd numbers $a$ that satisfy this condition is ____.",
"answer_preview": "9",
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"prompt_preview": "Ginger likes to make cakes for every holiday for people. She has 2 children, each of whom she bakes a cake for on their birthdays, Christmas, Easter, and Halloween. She has a husband for whom she makes a cake on these same holidays, as well",
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"prompt_preview": "How many parts at most can three planes divide space into?",
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"prompt_preview": "A woman is not good at weaving cloth, and the amount of cloth she weaves decreases by the same amount every day. She weaves 5 feet on the first day and 1 foot on the last day. Calculate the total amount of cloth she weaves in 30 days. Expre",
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"prompt_preview": "jenny can divide her sweets equally to 5 people and also to 6 people equally but not to 12 people . what could be the number ?",
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"prompt_preview": "the ratio of numbers is 4 : 5 and their h . c . f is 4 . their l . c . m is :",
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"prompt_preview": "The product of 6 consecutive odd numbers greater than zero is 135135. What is the largest of these 6 numbers? $\\qquad$",
"answer_preview": "13",
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"prompt_preview": "Nine positive real numbers \\( a_{1}, a_{2}, \\cdots, a_{9} \\) form a geometric sequence, and \\( a_{1}+a_{2}=\\frac{3}{4} \\), \\( a_{3}+a_{4}+a_{5}+a_{6}=15 \\). Find the value of \\( a_{7}+a_{8}+a_{9} \\).",
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"prompt_preview": "Li Jiang's average score for 5 math tests is 90, the median is 91, and the mode is 93. What is the sum of his lowest two test scores?",
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"prompt_preview": "Sylvia chose positive integers \\( a, b \\) and \\( c \\). Peter determined the value of \\( a+\\frac{b}{c} \\) and got an answer of 101. Paul determined the value of \\( \\frac{a}{c}+b \\) and got an answer of 68. Mary determined the value of \\( \\fr",
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"prompt_preview": "Nicholas bought six times as much fabric as Kenneth. If Kenneth paid $40 for an oz of fabric and bought 700oz, calculate the amount of money that Nicholas paid more than Kenneth for the fabric he bought.",
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"prompt_preview": "A cube of sides 9 is first painted red and then cut into smaller cubes of some side length. There are 12 smaller cubes with paint on exactly 2 sides. What is the side length of the smaller cubes?",
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"prompt_preview": "Martin owns a farm with some hens. These hens lay 80 eggs in 10 days. Martin decided to buy 15 more hens. All hens will lay 300 eggs in 15 days. How many hens did Martin initially have?",
"answer_preview": "25",
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"prompt_preview": "A sequence $\\\\{a_n\\\\}$ is defined by the formula $a_n=(-1)^{n+1}(2n-1)$. Compute the sum of the first $100$ terms.",
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"prompt_preview": "tough and tricky questions : remainders . 1 ^ 1 + 2 ^ 2 + 3 ^ 3 + . . . + 7 ^ 7 is divided by 7 . what is the remainder ?",
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"prompt_preview": "In the sequence $\\{a_n\\}$, $a_{n-1}=2a_n$. If $a_5=4$, then the product $a_4a_5a_6=$ _______.",
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"prompt_preview": "The problem involves the application of the laws of exponents and logarithms, and is of medium difficulty. Solve the following expression: $\\left({27}^{\\frac{2}{3}}-{2}^{{{\\log }\\_{2}}3}\\bullet {{\\log }\\_{2}}\\dfrac{1}{8}+{\\log }_{10} 4+{\\lo",
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"prompt_preview": "The speed of a boat in still water is some km/hr, and the rate of current is 6 km/hr. The distance travelled downstream in 44 minutes is 35.2 km. What is the speed of the boat in still water?",
"answer_preview": "42.0",
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"prompt_preview": "On the first day of school, Mrs. McGillicuddy had 25 students registered for the morning session of kindergarten, but 3 students were absent; and she had some students registered for the afternoon session, but 4 students were absent. Mrs. M",
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"prompt_preview": "Given a sequence $\\{a_n\\}$ satisfying $\\log_{2}a_{n+1}=1+\\log_{2}a_{n}$ $(n\\in\\mathbb{N}^*)$, and $a_{1}+a_{2}+a_{3}+\\ldots+a_{10}=1$, then $\\log_{2}(a_{101}+a_{102}+\\ldots+a_{110})=$ ______.",
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"prompt_preview": "Given that the terminal side of angle a passes through point P(1,-2), calculate the value of 2*sin(a)/cos(a). Express your answer as a single number.",
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"prompt_preview": "Jake's neighbors hire him to mow their lawn and plant some flowers. Mowing the lawn takes 1 hour and pays $15. If Jake wants to make $20/hour working for the neighbors, and planting the flowers takes a certain amount of time, Jake should ch",
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"prompt_preview": "Given that \\\\(k\\\\) is a constant, if the minimum value of the function \\\\(y=x^2+\\frac{k}{x} (x > 0, k > 0)\\\\) is \\\\(3\\\\), then the value of \\\\(k\\\\) at this time is.",
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"prompt_preview": "How many pieces of 85 cm length can be cut from a rod of 34 meters long?",
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"prompt_preview": "Define a new operation \"\u203b\" with the rule: $a\u203bb=ab-a-b$. For instance, $1\u203b2=1\u00d72-1-2=-1$. If the two roots of the equation $x^2+x-1=0$ are $x_1$ and $x_2$, then $x_1\u203bx_2 =$ __________.",
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"prompt_preview": "If a = 105 and a ^ 3 = some number * 25 * 35 * 63, what is the value of that number?",
"answer_preview": "7",
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"prompt_preview": "Find the value of 72516 x 9999. What is the product of these two numbers?",
"answer_preview": "724987484",
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"prompt_preview": "By the time Anne is two times as old as Emile, Emile will be six times as old as Maude. If Anne will be 96 years old, how old will Maude be at that time?",
"answer_preview": "96",
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"prompt_preview": "Find the number of positive integer solutions for the equation 3x + 5y = 501. Express your answer as a single integer.",
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"prompt_preview": "What are the last two digits of \\(1 \\times 2 \\times 3 \\times 4 \\times \\cdots \\times 2004 \\times 2005 \\times 2006\\)?",
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"prompt_preview": "Given that in the expansion of $(1+x)^n$, the binomial coefficients of the third and the eighth terms are equal, the sum of the binomial coefficients of the odd terms is \\_\\_\\_\\_\\_\\_.",
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"prompt_preview": "Given an arithmetic sequence $\\{a_n\\}$, the sum of the first $m$ terms is 30, and the sum of the first $2m$ terms is 100. Find the sum of the first $3m$ terms.",
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"prompt_preview": "Given the function $f(x) = mx^3 + nx + 1$ (where $mn \\neq 0$), and $f(-1) = 5$, then $f(1) = \\_\\_\\_\\_\\_\\_$.",
"answer_preview": "7",
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"prompt_preview": "Truck X is some miles ahead of Truck Y, which is traveling the same direction along the same route as Truck X. If Truck X is traveling at an average speed of 47 miles per hour and Truck Y is traveling at an average speed of 53 miles per hou",
"answer_preview": "23",
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"prompt_preview": "Sangita is required to fly a certain number of hours to earn an airplane pilot certificate. She has already completed 50 hours of day flying, 9 hours of night flying, and 121 hours flying cross-country. To meet her goal in exactly 6 months,",
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"prompt_preview": "Worker A takes some hours to do a job. Worker B takes 6 hours to do the same job. Working together but independently, it takes both A and B 3.428571428571429 hours to do the same job. How long does it take for Worker A to do the job alone?",
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"prompt_preview": "Solve the equation for x: 19(x + y) + 17 = 19(-x + y) - 21. What is the solution for x?",
"answer_preview": "-2",
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"prompt_preview": "Annie calculated she has three times more toys than Mike, and a certain difference less than Tom. Mike has 6 toys. Annie, Mike, and Tom have a total of 56 toys. What is the difference between the number of toys Annie has and the number of t",
"answer_preview": "2",
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"prompt_preview": "a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 4 litres a minute . when the tank is full , the inlet is opened and due to the leak the tank is empty in 8 hours . the capacity of ",
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"prompt_preview": "A train 100 m long running at a certain speed takes 10.889128869690424 seconds to cross a bridge 142 m in length. What is the speed of the train in km/hr?",
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"prompt_preview": "For what value of the parameter \\( m \\) is the sum of the squares of the roots of the equation \\[ x^{2}-(m+1) x+m-1=0 \\] the smallest?",
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"prompt_preview": "A sum was put at simple interest at a certain rate for 10 years. Had it been put at a 5% higher rate, it would have fetched Rs. 200 more. What was the sum?",
"answer_preview": "2000",
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"prompt_preview": "Use the Horner's method to calculate the polynomial $f(x) = x^5 + 4x^4 + 3x^3 + 2x^2 + 1$ when $x=5$. The sum of the number of multiplication operations and addition operations is \\_\\_\\_\\_\\_\\_.",
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"prompt_preview": "There are 2 red balls, 3 yellow balls, and 4 white balls, with balls of the same color being indistinguishable. How many different ways can these 9 balls be arranged in a row? (Answer with a number)",
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"prompt_preview": "January 1, 2015 was a Thursday. What day of the week was June 1, 2015?",
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"prompt_preview": "Given that point A $(a, 4)$ is symmetric to point B across the y-axis, and the coordinates of point B are $(-2, b)$, find the value of $a+b$.",
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"prompt_preview": "In Kylie's class of 50 students, their test scores are distributed in the following manner: - The first 10 students scored 90, 85, 88, 92, 80, 94, 89, 91, 84, and 87 marks. - The second 15 students scored 5 marks fewer than their respect",
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"prompt_preview": "Dave had 24 files and 13 apps on his phone. After deleting some apps and files, he had 17 apps and some files left. He deleted 3 files. How many files did he have left?",
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"prompt_preview": "Jackson wants to improve his endurance running. His goal is to start by running 3 miles on the first day, and then increase his daily running distance by doubling the distance every week for the next four weeks. How many miles is Jackson ru",
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"prompt_preview": "Find the limit of the function \\( f(x, y) = (x^2 + y^2)^2 x^2 y^2 \\) as \\( x \\rightarrow 0 \\) and \\( y \\rightarrow 0 \\).",
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"prompt_preview": "Excluding stoppages, the speed of a bus is some kmph, and including stoppages, it is 35 kmph. The bus stops for 18 minutes per hour. What is the speed of the bus excluding stoppages?",
"answer_preview": "35",
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"prompt_preview": "The graph of the function $y = x^2$ ($x > 0$) has a tangent at the point $(a_k, a_k^2)$, which intersects the x-axis at the point with the x-coordinate $a_{k+1}$, where $k$ is a positive integer. Given $a_1 = 16$, find the sum $a_1 + a_3 + ",
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"prompt_preview": "12 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?",
"answer_preview": "264",
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"prompt_preview": "A bookseller has two display windows. She plans to display 3 new fiction books in the left window, and some new non-fiction books in the right window. Assuming she can put the 4 fiction books in any order, and separately, a certain number o",
"answer_preview": "2",
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"prompt_preview": "The coefficient of the term $x^3$ in the expansion of $({\\sqrt{x}-\\frac{2}{{\\sqrt{x}}}})^8$ is _______. (Provide your answer as a number)",
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"prompt_preview": "Some chess players take part in a tournament. Every player plays twice with each of his opponents. There are 380 games to be played. How many players are participating in the tournament?",
"answer_preview": "19",
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"prompt_preview": "There are 3 boxes of cereal. One box holds some ounces of cereal. Another box holds half the amount of the first box and 5 ounces less than the third box. There is a total of 33 ounces of cereal in all 3 cereal boxes. How many ounces of cer",
"answer_preview": "19",
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{
"sample_id": 19336,
"sample_count": 3,
"error_ema": 0.1524374932050705,
"priority_score": 1.0653303861618042,
"sampling_probability": 2.996958210133016e-05,
"seen": 1,
"prompt_preview": "What is the sum of the first some natural numbers (starting from 1) if the sum is 276?",
"answer_preview": "276",
"source": "orca_math"
},
{
"sample_id": 20184,
"sample_count": 3,
"error_ema": 0.1524374932050705,
"priority_score": 1.0653303861618042,
"sampling_probability": 2.996958210133016e-05,
"seen": 1,
"prompt_preview": "A rectangular tiled patio is composed of 30 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 30 tiles, and ",
"answer_preview": "3",
"source": "orca_math"
}
]
}
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