conversations listlengths 2 2 | sft_template_type_idx stringclasses 1
value |
|---|---|
[
{
"content": "# 5.1. Condition:\n\nPolina came to the cafeteria and saw that 2 puff pastries cost 3 times more than 2 pies. Polina didn't have enough money for 2 puff pastries, but she did have enough for 1 pie and 1 puff pastry. After the purchase, she wondered how many times more money she spent buying 1 puff... | 5C |
[
{
"content": "## Problem Statement\n\nCalculate the definite integral:\n\n$$\n\\int_{0}^{1 / \\sqrt{2}} \\frac{d x}{\\left(1-x^{2}\\right) \\sqrt{1-x^{2}}}\n$$\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by... | 5C |
[
{
"content": "## Task 1.\n\nLet $a, b, c, d$ be real numbers such that\n\n$$\n\\begin{gathered}\na+b+c+d=10 \\\\\nab+bc+cd+da=25 \\\\\nabc+bcd+cda+dab=50\n\\end{gathered}\n$$\n\nProve that then $a^{2}+b^{2}+c^{2}+d^{2}=30$.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question makin... | 5C |
[
{
"content": "## Task 11/88\n\nDetermine all natural numbers $n$ for which $n^{4}+4$ is a prime number!",
"role": "user"
},
{
"content": "<think>\n<sample>\nFirst, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\n### Und... | 5C |
[
{
"content": "## Task 3 - 300513\n\nFritz, Hans, and Petra have collected a bag full of shells on the Baltic Sea beach. They do not know how many shells they have in the bag.\n\nFritz says: \"If you take 12 shells out of the bag seven times in a row, more than 6 shells will remain.\"\n\nHans says: \"But if you ... | 5C |
[
{
"content": "## Task 4 - 100934\n\nWe are looking for all ordered triples of real numbers $(x, y, z)$ that are solutions to the system of equations:\n(1) $x+y=2$\n(2) $x y-z^{2}=1$\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve ... | 5C |
[
{
"content": "## Task 6 - 070836\n\nA two-digit natural number is sought with the following properties:\n\n1) The difference between its digits is three.\n2) If its digits are swapped, the new number is nine less than twice the original number.\n\nBegin your response with \"Rewritten Question: \" and by rewriti... | 5C |
[
{
"content": "## Task B-3.1.\n\nDetermine the value of the expression $A=1+\\operatorname{tg} 35^{\\circ}+\\operatorname{tg} 10^{\\circ}+\\operatorname{tg} 35^{\\circ} \\cdot \\operatorname{tg} 10^{\\circ}$.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain onl... | 5C |
[
{
"content": "$1,1,2,3,5,8,13, ?, 34, \\cdots \\ldots$\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and then give your resulting equation or number as the answer in the \"<answer>\n(your answer)\n</a... | 5C |
[
{
"content": "$16(x-1)-(x-1)^{2}+(x-1)^{3}-(x-1)^{4}+(x-1)^{5}$ The coefficient of the $x^{2}$ term in the expanded form is $\\qquad$\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and then give your r... | 5C |
[
{
"content": "$18t = 18000kg$． (Judge True or False)",
"role": "user"
},
{
"content": "<think>\n<sample>\nFirst, I'll try to understand the problem better by writing out a plan and going really deep into detail about how I should solve this.\n\nStep 1: Understand the given equation.\nThe equation pr... | 5C |
[
{
"content": "$2 \\cdot 131$ The number of roots of the equation $\\sqrt{x^{2}+12 x+36}+x+6=0$ is\n(A) 0.\n(B) 2.\n(C) 4.\n(D) Infinitely many.\n(3rd \"Five Sheep Cup\" Junior High School Mathematics Competition, 1991)\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it ... | 5C |
[
{
"content": "$7.30 \\lg (\\lg x)+\\lg \\left(\\lg x^{3}-2\\right)=0$.\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.\n\n$7.30 \\lg (\\lg x)+\\lg \\left(\\lg x^{3}-2\\right)=0$.\n\nBegin your response with \"Rewritt... | 5C |
[
{
"content": "0.35 \\cdot 160+0.1 x=0.2 \\cdot 160+0.2 x, 0.15 \\cdot 160=0.1 x, x=240 \\text {. }\n$$\n\nIn total, it results in $160+240=400$ g of solution.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by ... | 5C |
[
{
"content": "1. For every pair of real numbers $x, y$, the function $f$ satisfies the equation\n$$\nf(x+y)-f(x)-f(y)=1+xy,\n$$\n\nand $f(1)=1$. Then, the number of integers $n$ for which $f(n)=n (n \\neq 1)$ is ( ) .\n(A) 0\n(B) 1\n(C) 2\n(L) 3\n\nBegin your response with \"Rewritten Question: \" and by rewrit... | 5C |
[
{
"content": "1. Given real numbers $a$, $b$, $x$, $y$ satisfy $x y=2008^{2008}$,\n$$\n\\frac{1}{1+2008^{a} x}+\\frac{1}{1+2008^{b-2009} y}=1 \\text {. }\n$$\n\nThen the value of $2008^{a+b}$ is\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is nee... | 5C |
[
{
"content": "1. Given that the total surface area of a rectangular prism is 11, and the sum of its 12 edges is 24, find the length of the diagonal of the rectangular prism.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then... | 5C |
[
{
"content": "1. Pleasant Goat, Pretty Goat, and Warm Goat represent the Sheep Village in a mental relay race, with each match having 100 questions. In the first match, Pleasant Goat plays, and his accuracy rate is $91 \\%$; in the second match, Pretty Goat plays, and she answers 85 questions correctly; in the ... | 5C |
[
{
"content": "10. (10 points) Xiao Ming and Xiao Hua are in Class 6 (1), which has between 20 and 30 students, and each student has a unique birthday. Xiao Ming says: “The number of students older than me is twice the number of students younger than me.” Xiao Hua says: “The number of students older than me is t... | 5C |
[
{
"content": "10. Given the sequence $\\left\\{a_{n}\\right\\}$ satisfies: $a_{1}=1, a_{n+1}=a_{n}+a_{n}^{2}\\left(n \\in \\mathbf{N}^{*}\\right)$. Let\n$$\nS_{n}=\\frac{1}{\\left(1+a_{1}\\right)\\left(1+a_{2}\\right) \\cdots\\left(1+a_{n}\\right)}, \\quad T_{n}=\\sum_{k=1}^{n} \\frac{1}{1+a_{k}}\n$$\n\nFind th... | 5C |
[
{
"content": "11. $[8]$ Let $A_{10}$ denote the answer to problem 10. Two circles lie in the plane; denote the lengths of the internal and external tangents between these two circles by $x$ and $y$, respectively. Given that the product of the radii of these two circles is $15 / 2$, and that the distance between... | 5C |
[
{
"content": "118. The random variable $X$ is given by the distribution function:\n\n$$\nF(x)=\\left\\{\\begin{array}{ccc}\n0 & \\text { if } & x \\leq -c \\\\\n\\frac{1}{2}+\\frac{1}{\\pi} \\arcsin \\frac{x}{c} & \\text { if } & -c < x \\leq c \\\\\n1 & \\text { if } & x > c\n\\end{array}\\right.\n$$\n\n( arcs... | 5C |
[
{
"content": "12 Find the maximum value of $\\sqrt{x-144}+\\sqrt{722-x}$.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and then give your resulting equation or number as the answer in the \"<answer>\... | 5C |
[
{
"content": "12. (10 points) The sum of three-digit numbers $n$ for which $\\frac{3 \\mathrm{n}+2}{5 \\mathrm{n}+1}$ is not in its simplest form is equal to what,\n\n\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think... | 5C |
[
{
"content": "12. 10 consecutive natural numbers are arranged in ascending order. If the sum of the last 6 numbers is 15 more than twice the sum of the first 4 numbers, then the smallest number among these 10 numbers is . $\\qquad$\n\nBegin your response with \"Rewritten Question: \" and by rewriting the questi... | 5C |
[
{
"content": "13. (3 points) A math competition has 10 questions, with a rule that each correct answer earns 5 points, and each wrong answer or no answer deducts 2 points. $A$ and $B$ each answer the questions, and their total score is 58 points, with $A$ scoring 14 points more than $B$. Then $A$ answered $\\qq... | 5C |
[
{
"content": "13. Define $n!=1 \\times 2 \\times \\ldots \\times n$, for example, $5!=1 \\times 2 \\times 3 \\times 4 \\times 5$. If $\\frac{n!\\times(n+1)!}{2}$ (where $\\mathbf{n}$ is a positive integer, and $1 \\leq n \\leq 100$) is a perfect square, for example, when $n=7$,\n$\\frac{n!\\times(n+1)!}{2}=\\fr... | 5C |
[
{
"content": "13. Find the value of\n$$\n\\frac{2007^{2}+2008^{2}-1993^{2}-1992^{2}}{4}\n$$\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and then give your resulting equation or number as the answer ... | 5C |
[
{
"content": "13. Ordered pairs of positive integers $(a, b)(a<b)$ satisfy $a+b=2008$, and $a, b$ are coprime. Then the number of pairs $(a, b)$ that satisfy the condition is $\\qquad$.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to so... | 5C |
[
{
"content": "Return your final response within <answer>...</answer>. 14 bags of candy have an average weight rounded to the nearest tenth of a gram equal to 90.2 grams. Given that the weight of each bag of candy is an integer, find the total weight of these 14 bags of candy.\n\nBegin your response with \"Rewri... | 5C |
[
{
"content": "14. Find the numerical value of the expression\n\n$$\n\\frac{1}{x^{2}+1}+\\frac{1}{y^{2}+1}+\\frac{2}{x y+1}\n$$\n\nif it is known that $x$ is not equal to $y$ and the sum of the first two terms is equal to the third.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the questi... | 5C |
[
{
"content": "14. Given the following equations\n\nI . $y=x-2$. II . $y=\\frac{x^{2}-4}{x+2}$.\nIII. $(x+2) y=x^{2}-4$. Which of the following represent the same graph? ( )\n(A) I and II.\n(B) I and III.\n(C) II and III.\n(D) I, II, and III.\n(E) None represent the same graph.\n\nBegin your response with \"Rewr... | 5C |
[
{
"content": "14. The lengths of the sides of a triangle are the integers $13, x, y$. It is given that $x y=105$. What is the length of the perimeter of the triangle?\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think ... | 5C |
[
{
"content": "15. Suppose that $x$ and $y$ are non-zero real numbers such that\n$$\n\\frac{x}{3}=y^{2} \\quad \\text { and } \\frac{x}{9}=9 y \\text {. }\n$$\n\nFind the value of $x+y$.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to so... | 5C |
[
{
"content": "2. (3 points) A student, while solving a calculation problem, was supposed to divide by 20 in the last step, but mistakenly added 20, thus obtaining an incorrect result of 180. What should the correct answer to this calculation problem be? $\\qquad$ .\n\nBegin your response with \"Rewritten Questi... | 5C |
[
{
"content": "2. Houses on the left side of the street have odd, and houses on the right side of the street have even house numbers. The sum of all house numbers on one side of the street is 1369, and on the other side 2162. How many houses are there on that street?\n\nBegin your response with \"Rewritten Quest... | 5C |
[
{
"content": "2. Prove: If $\\alpha, \\beta, \\gamma$ are acute angles, then\n$$\n\\tan \\alpha(\\cot \\beta+\\cot \\gamma)+\\tan \\beta(\\cot \\gamma+\\cot \\alpha)+\\tan \\gamma(\\cot \\alpha+\\cot \\beta) \\geqslant 6 .\n$$\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question ma... | 5C |
[
{
"content": "20. [11] There exist unique nonnegative integers $A, B$ between 0 and 9 , inclusive, such that\n$$\n(1001 \\cdot A+110 \\cdot B)^{2}=57,108,249 \\text {. }\n$$\n\nFind $10 \\cdot A+B$.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is... | 5C |
[
{
"content": "3. The two diagonals of a quadrilateral are perpendicular. The lengths of the diagonals are 14 and 30 . What is the area of the quadrilateral?\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by st... | 5C |
[
{
"content": "3. This year, the sum of Piplu and Luluxi's ages is 22 years old, 1 year later Piplu's age will be exactly twice Luluxi's age. This year, Luluxi is $\\qquad$ years old.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve... | 5C |
[
{
"content": "3.1. Alina and Masha wanted to create an interesting version of the school tour olympiad. Masha proposed several problems and rejected every second problem of Alina's (exactly half), Alina also proposed several problems and did not reject only every third problem of Masha's (exactly a third). In t... | 5C |
[
{
"content": "4. A sequence of integers $a_{1}, a_{2}, a_{3}, \\ldots$ is defined by\n$$\n\\begin{array}{c}\na_{1}=k, \\\\\na_{n+1}=a_{n}+8 n \\text { for all integers } n \\geq 1 .\n\\end{array}\n$$\n\nFind all values of $k$ such that every term in the sequence is a square.\n\nBegin your response with \"Rewrit... | 5C |
[
{
"content": "4. Calculate $\\sqrt{3+\\sqrt{5}}-\\sqrt{3-\\sqrt{5}}$.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and then give your resulting equation or number as the answer in the \"<answer>\n(yo... | 5C |
[
{
"content": "4. On a sheet of paper, 12 consecutive integers are written. After one of them is crossed out, the sum of the remaining numbers equals 325. Which number was crossed out?\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solv... | 5C |
[
{
"content": "4. On the table, there are 100 different cards with numbers $3, 6, 9, \\ldots 297, 300$ (each card has exactly one number, and each number appears exactly once). In how many ways can 2 cards be chosen so that the sum of the numbers on the selected cards is divisible by $5?$\n\nBegin your response ... | 5C |
[
{
"content": "4. Two boats departed from piers $A$ and $C$. The speed of the boat traveling from $A$ is 7 km per hour, and from $C$ is 3 km per hour. Determine after how much time the boats will meet, if the distance between the piers is 20 km, and the speed of the river current from $A$ to $C$ is 2 km per hour... | 5C |
[
{
"content": "4.35. How many zeros does the product of all integers from 1 to 100 inclusive end with?\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and then give your resulting equation or number as t... | 5C |
[
{
"content": "46 z+240=0$. The roots of this equation are numbers whose sum is $46 \\mathrm{e}$ and whose product is 240, that is, the roots are 6 and 40. Therefore, $z=6$ or $z=40$ (I). Similarly, substituting $y z=\\frac{240}{x}$ into $x+y z=64$ leads to $x=4$ or $x=60$ (II). From $x y z=240$, it follows that... | 5C |
[
{
"content": "5 (1133). For what value of $a$ does the sum of the squares of the roots of the quadratic trinomial $x^{2}-(a-2) x-a-1$ take the smallest value?\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by ... | 5C |
[
{
"content": "5. Solution. First, let's prove that building towers taller than 2 is meaningless.\n\nIndeed, suppose one of the towers has a height of \\( h > 2 \\). Let's remove the top floor from it, turning it into a new tower of height 1. How will this change the inspector's sum? The shortened tower no longe... | 5C |
[
{
"content": "5. The edge length of a wooden cube is a natural number greater than 2. We paint the cube and then cut it into unit cubes. The number of unit cubes that have exactly two painted faces is a divisor of the number of unit cubes that have no painted faces. Determine the smallest natural number that ca... | 5C |
[
{
"content": "5. The length of the diagonal $AC$ of the rhombus $ABCD$ with an acute angle at vertex $A$ is 12. Points $M$ and $N$ on sides $DA$ and $DC$ are the bases of the heights of the rhombus dropped from vertex $B$. The height $BM$ intersects the diagonal $AC$ at point $P$ such that $AP: PC = 2: 3$. Find... | 5C |
[
{
"content": "51. Little One eats a jar of jam in six minutes, while Karlson is twice as fast. How long will it take them to eat the jam together\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and then... | 5C |
[
{
"content": "53. In the Cartesian coordinate system, the area of the region that satisfies the inequality $|x|+|y| \\leq 7$ is\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and then give your resulti... | 5C |
[
{
"content": "6. $12 f(n)$ is a function defined on the set of positive integers, taking non-negative integer values, and for all $m, n$ we have:\n$$\\begin{array}{l}\nf(m+n)-f(m)-f(n)=0 \\text { or } 1 ; \\\\\nf(2)=0, f(3)>0, f(9999)=3333 .\n\\end{array}$$\n\nTry to find: $f(1982)$.\n\nBegin your response with... | 5C |
[
{
"content": "6. Find the sum of all even numbers from 10 to 31. Calculate in different ways.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and then give your resulting equation or number as the answe... | 5C |
[
{
"content": "6. Given: $20=20+18+16+\\ldots+x$. How many addends are there in the right side of the equation?\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and then give your resulting equation or nu... | 5C |
[
{
"content": "7. The number of sets $X$ that satisfy the condition $\\{1,2,3\\} \\subseteq X \\subseteq\\{1,2,3,4,5,6\\}$ is\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and then give your resulting ... | 5C |
[
{
"content": "8. A rectangle with an area of 80, one of its diagonals has a length of $2 \\sqrt{41}$, the perimeter of this rectangle is $\\qquad$\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and the... | 5C |
[
{
"content": "8. Given $0<x<\\frac{\\pi}{2}, \\sin x-\\cos x=\\frac{\\pi}{4}$. If $\\tan x+\\frac{1}{\\tan x}$ can be expressed in the form $\\frac{a}{b-\\pi^{c}}$ ($a$, $b$, $c$ are positive integers), then $a+b+c=$ $\\qquad$\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question ma... | 5C |
[
{
"content": "88. A chocolate bar consists of 40 pieces. What is the minimum number of breaks required to get all 40 pieces, if breaking several pieces at once is not allowed?",
"role": "user"
},
{
"content": "<think>\n<sample>\nRewritten Question: \nA chocolate bar consists of 1 piece initially. Wh... | 5C |
[
{
"content": "89 If $f(x)=5x-3, x \\in\\{0,2,3,4,5\\}, g(x)=x^{2}-2x-3, x \\in\\{-2$, $-1,1,4,5\\}$, then the domain of the function $F(x)=\\lg f(x)+\\frac{1}{\\sqrt{g(x)}}$ is $\\qquad$\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to s... | 5C |
[
{
"content": "9. (5 points) As shown in the figure, the shaded part is a square with a side length of 6 cm. Around it are four rectangles. If the sum of the perimeters of the four rectangles is 92 cm, then the sum of the areas of the four rectangles is $\\qquad$ square centimeters.\n\nBegin your response with \... | 5C |
[
{
"content": "9. A chemistry student conducted an experiment: from a tank filled with syrup solution, he poured out several liters of liquid, refilled the tank with water, then poured out twice as much liquid and refilled the tank with water again. As a result, the amount of syrup in the tank decreased by $\\fr... | 5C |
[
{
"content": "92. Bicycle races. Two cyclists are participating in a race on a circular track. Brown completes a full lap in 6 minutes, while Robinson takes 4 minutes.\n\nHow many minutes will it take for Robinson to overtake Brown\n\nBegin your response with \"Rewritten Question: \" and by rewriting the questi... | 5C |
[
{
"content": "A certain type of rice must comply with the normal distribution of weight $(kg)$, denoted as $\\xi ～N(10,{σ}^{2})$, according to national regulations. Based on inspection results, $P(9.9≤\\xi≤10.1)=0.96$. A company purchases a bag of this packaged rice as a welfare gift for each employee. If the c... | 5C |
[
{
"content": "A coal store needs to transport 47,500 kilograms of coal to a factory. Each truck can carry 2,500 kilograms. How many trucks are needed to transport all the coal? (Set up an equation with the unknown $x$ and solve it.)",
"role": "user"
},
{
"content": "<think>\n<sample>\nTo determine h... | 5C |
[
{
"content": "A factory produces four different models of products: A, B, C, and D, with production volumes of 200, 400, 300, and 100 units, respectively. To inspect the quality of the products, a stratified sampling method is used to select 60 units from all the products for inspection. The number of units tha... | 5C |
[
{
"content": "A forestry farm has 3000 saplings, including 400 pine saplings. To investigate the growth of the saplings, a stratified sampling method is used to draw a sample of 150 saplings. The number of pine saplings in the sample is ______.\n\nBegin your response with \"Rewritten Question: \" and by rewriti... | 5C |
[
{
"content": "A four-digit number $2\\Box\\Box5$ is divisible by $45$. How many such four-digit numbers are there?\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and then give your resulting equation o... | 5C |
[
{
"content": "Return your final response within <answer>...</answer>. A large sewage pool contains a certain amount of sewage, with sewage continuously flowing in. If 4 sewage treatment devices are used, it takes 36 days to treat all the sewage in the pool. If 5 sewage treatment devices are used, it takes 27 da... | 5C |
[
{
"content": "A magpie cooked porridge and fed her chicks. The third chick received as much porridge as the first two combined. The fourth one received as much as the second and third. The fifth one received as much as the third and fourth. The sixth one received as much as the fourth and fifth. The seventh one... | 5C |
[
{
"content": "A pile of balls consists of red and white balls. It is known that the number of white balls is less than the number of red balls, but twice the number of white balls is more than the number of red balls. If each white ball is marked with \"2\" and each red ball is marked with \"3\", the total sum ... | 5C |
[
{
"content": "A point $(a,b)$ in the plane is called [i]sparkling[/i] if it also lies on the line $ax+by=1$. Find the maximum possible distance between two sparkling points.\n\n[i]Proposed by Evan Chen[/i]\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only... | 5C |
[
{
"content": "A school conducted a survey on the extracurricular physical exercise situation of 1,000 students. Using stratified sampling by gender, a sample of 100 students was selected. It is known that 51 of the sampled students are female. What is the total number of male students in the school?\n\nBegin yo... | 5C |
[
{
"content": "A shooting athlete shoots $10$ times in a row. Among them, $1$ shot hits the target with $10$ points, $4$ shots hit the target with $9$ points, $3$ shots hit the target with $8$ points, and $2$ shots hit the target with $7$ points. The average number of points this shooting athlete hits in this ro... | 5C |
[
{
"content": "Return your final response within <answer>...</answer>. A soccer ball is stitched using black and white pieces of leather. The black pieces are regular pentagons, and the white pieces are regular hexagons, with the side lengths of both shapes being equal. Each black pentagon is stitched to five wh... | 5C |
[
{
"content": "Return your final response within <answer>...</answer>. A square and an equilateral triangle are filled with the same number of equal circles that touch each other and the sides of these shapes. How many circles are required if there are 14 more circles along the side of the triangle than along th... | 5C |
[
{
"content": "A taxi fare standard in a certain city is as follows: The flag-down fare is $8, and the flag-down distance is $3km$ (if not exceeding $3km$, the fare is charged at the flag-down rate); for distances exceeding $3km$ but not exceeding $8km$, the fare for the excess part is charged at $2.15$ per kilo... | 5C |
[
{
"content": "A3. Solve the inequality $\\frac{10}{x^{2}+4} \\leq 0$. Which numbers are solutions?\n(A) $x \\in[-2,2]$\n(B) $x_{1}=2, x_{2}=-2$\n(C) $x \\in(-\\infty, 2)$\n(D) $x \\in(0,5)$\n(E) The inequality has no solutions.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question m... | 5C |
[
{
"content": "According to the equation $5=3x-2$, it can be transformed into which of the following?\n\nA: $-3x=2-5$\n\nB: $-3x=-2+5$\n\nC: $5-2=3x$\n\nD: $5+2=3x$\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think ste... | 5C |
[
{
"content": "Ada is younger than Darwyn. Max is younger than Greta. James is older than Darwyn. Max and James are the same age. Which of the five people is the oldest?\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then thin... | 5C |
[
{
"content": "Among the following four functions, which one is not a monotonic function on its domain?\\\\((\\\\) \\\\()\\\\)\nA: \\\\(y=-2x+1\\\\)\nB: \\\\(y=x^{3}\\\\)\nC: \\\\(y=\\\\lg x\\\\)\nD: \\\\(y= \\\\dfrac {1}{x}\\\\)\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question... | 5C |
[
{
"content": "Ana has $22$ coins. She can take from her friends either $6$ coins or $18$ coins, or she can give $12$ coins to her friends. She can do these operations many times she wants. Find the least number of coins Ana can have.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the ques... | 5C |
[
{
"content": "Arrange $4$ people in a row, if person A and person B must be together, then there are ______ different ways to arrange them.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and then give ... | 5C |
[
{
"content": "Aunt Wang went to buy apples. If she buys 2.5 kg, she is short of 1.6 yuan. If she buys 2 kg, she has an excess of 0.9 yuan. How much money does she have?",
"role": "user"
},
{
"content": "<think>\n<sample>\nLet's denote the price per kilogram of apples as \\( p \\) yuan and the amount... | 5C |
[
{
"content": "B2. The difference in the perimeters of two squares is $8 \\mathrm{~cm}$, and the difference in their areas is $16 \\mathrm{~cm}^{2}$. Calculate the sum of their areas.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve... | 5C |
[
{
"content": "Calculate the number of methods for placing 3 different balls into boxes numbered 1 through 6, such that box number 6 contains at least one ball.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by... | 5C |
[
{
"content": "Calculate: $$\\lim_{n \\to \\infty} \\frac { C_{ n }^{ 2 }}{1+2+3+\\ldots+n}$$\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and then give your resulting equation or number as the answer... | 5C |
[
{
"content": "Return your final response within <answer>...</answer>. Calculate: \\(0.2 \\times 63 + 1.9 \\times 126 + 196 \\times 9 =\\) \n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and then give y... | 5C |
[
{
"content": "Return your final response within <answer>...</answer>. Claudia and Adela are betting to see which one of them will ask the boy they like for his telephone number. To decide they roll dice. If none of the dice are a multiple of 3, Claudia will do it. If exactly one die is a multiple of 3, Adela wi... | 5C |
[
{
"content": "Convert the binary number $101101_{(2)}$ to an octal number. The result is\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and then give your resulting equation or number as the answer in ... | 5C |
[
{
"content": "Return your final response within <answer>...</answer>. Ctibor marked a square land plot on a map with a scale of 1:50000 and calculated that its side corresponds to $1 \\mathrm{~km}$ in reality. He then resized the map on a copier such that the marked square had an area $1.44 \\mathrm{~cm}^{2}$ s... | 5C |
[
{
"content": "Define the even function $f(x)$ on $[-2a+3, a]$. When $x \\in [0, a]$, $f(x) = \\log_a(2x + 3)$. Determine the range of $f(x)$.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and then giv... | 5C |
[
{
"content": "Define the operation $\\oplus$ on real numbers $x$ and $y$ as $x\\oplus y=x(2-y)$. If the inequality $\\left(t-a\\right)\\oplus \\left(t+a\\right) \\lt 1$ holds for any real number $t$, then the range of real number $a$ is ______.\n\nBegin your response with \"Rewritten Question: \" and by rewriti... | 5C |
[
{
"content": "Definition: The function f(x) is defined as the largest integer not exceeding x, denoted as [x]. For example, f(1.6) = [1.6] = 1, f(-2.4) = [-2.4] = -3. Determine the value of f(lg81).\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is... | 5C |
[
{
"content": "Determine the domain of the function $f(x)= \\frac {\\log (x+2)}{ \\sqrt {-x^{2}-x+6}}$.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is needed to solve it, then think step by step and then give your resulting equation or number as ... | 5C |
[
{
"content": "Return your final response within <answer>...</answer>. Determine the smallest integer \\( n \\) whose unit digit is 5, such that \\( \\sqrt{n} \\) is an integer whose digit sum is 9.\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only what is ... | 5C |
[
{
"content": "Return your final response within <answer>...</answer>. Each number from 1 to 6 replaces one of the letters \\(P, Q, R, S, T\\), and \\(U\\). The sum of \\(P\\) and \\(Q\\) is 5 and the difference between \\(R\\) and \\(S\\) is 5. If \\(T\\) is greater than \\(U\\), what number replaces the letter... | 5C |
[
{
"content": "Example 13. Let $a, b, c$ be distinct integers from 1 to 9. What is the largest possible value of $\\frac{a+b+c}{a b c}$? (1992, 1st Dannevirke-Shanghai Friendship Correspondence Competition)\n\nBegin your response with \"Rewritten Question: \" and by rewriting the question making it contain only ... | 5C |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.