__src_index__ int64 0 172k | messages stringlengths 375 66.5k |
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3,100 | [{"role": "user", "content": "Express the quotient $1302_5 \\div 23_5$ in base $5$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I need to divide two numbers in base 5: 1302 base... |
3,121 | [{"role": "user", "content": "Let \\\\(l\\\\) and \\\\(m\\\\) be different lines, and \\\\(\\alpha\\\\), \\\\(\\beta\\\\), \\\\(\\gamma\\\\) be different planes. Then, the correct proposition is __________. \n\\\\(①\\\\) If \\\\(l \\perp m\\\\) and \\\\(m \\perp \\alpha\\\\), then \\\\(l \\perp \\alpha\\\\) or \\\\(l ... |
3,178 | [{"role": "user", "content": "Cheyenne is a craftswoman making pots for sale. On a particular week, she made 80 clay pots. However, when she put them in the sun to dry, 2/5 of the pots cracked and could not be sold. Each pot costs her $15 to make, and she plans to sell each uncracked pot for $40. How much profit did Ch... |
3,175 | [{"role": "user", "content": "What is the sum of all of the solutions of the equation $\\frac{8x}{40} = \\frac{7}{x}$?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the sum of all the solutions to the equation (8x)/40 = 7/x. Hmm, first, maybe I should simplify the left side. Let's star... |
3,159 | [{"role": "user", "content": "Given the complex number $z=(m^{2}-8m+15)+(m^{2}-9m+18)i$, which is represented by point $A$ in the complex plane, find the values of the real number $m$ such that:\n1. $z$ is a real number?\n2. $z$ is a purely imaginary number?\n3. $A$ is located in the third quadrant?"}, {"role": "assist... |
3,091 | [{"role": "user", "content": "$(1)$ If the solution set of the inequality $mx^{2}+mx+m-6 \\lt 0$ with respect to $x$ is non-empty, find the range of real numbers $m$; <br/>$(2)$ If for all $x\\in \\left[-2,1\\right]$, the inequality $mx^{2}-mx \\lt -m+2$ always holds, find the range of real numbers $m$."}, {"role": "as... |
3,179 | [{"role": "user", "content": "Among the following statements, the correct one is ( )\nA: $| a-b | = \\frac{3}{}$ is a fraction\nB: A square has 2 axes of symmetry\nC: An isosceles triangle is an acute triangle\nD: An isosceles triangle is an axisymmetric figure"}, {"role": "assistant", "content": "<think>\n\nOkay, let... |
3,184 | [{"role": "user", "content": "A group of people contains men, women, and children. The number of men is related to the number of women, and the number of women is 3 times the number of children. The number of children is 30. The group contains 300 people. What is the ratio of the number of men to the number of women in... |
3,164 | [{"role": "user", "content": "The pages of a book are numbered consecutively from the first to the last. A troublemaker, Vasya, tore out 25 sheets from different parts of the book and added up the numbers of all 50 torn pages. He obtained the number 2020. When the top student, Kolya, found out about this, he claimed th... |
3,183 | [{"role": "user", "content": "Mariel is a dog walker. While walking her pack of dogs, she gets tangled up in the leashes of another dog walker and their dogs. There are 36 legs tangled up in leashes. Mariel is walking 5 dogs. How many dogs does the other dog walker have?"}, {"role": "assistant", "content": "<think>\n\n... |
3,144 | [{"role": "user", "content": "Max was born on Friday, March 5th, 2010. That Friday was the first day of his life. His parents organized an event for him on the $1500$th day of his life. On which day of the week was this event?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, an... |
3,161 | [{"role": "user", "content": "Prove that the number of partitions of a set, denoted by \\(S(n, k)\\), satisfies the recurrence relation \\(S(n+1, k) = S(n, k-1) + k \\cdot S(n, k)\\) for \\(1 \\leq k \\leq n\\). Use this relation to calculate \\(S(5, 3)\\)."}, {"role": "assistant", "content": "<think>\n\nOkay, let's tr... |
3,155 | [{"role": "user", "content": "On a board, the numbers 1, 2, 3, ..., 19, 20 are written. It is allowed to erase any two numbers \\( a \\) and \\( b \\) and write the number \\( a + b - 1 \\) instead.\n\nWhat number can remain on the board after 19 such operations?"}, {"role": "assistant", "content": "<think>\n\nThis is ... |
3,154 | [{"role": "user", "content": "A zoo has six pairs of different animals, one male and one female for each. The zookeeper wishes to feed the animals in a specific pattern: each time he feeds a single animal, the next one he feeds must be a different gender. If he starts by feeding the female lion, how many ways can he fe... |
3,186 | [{"role": "user", "content": "Given a complex number $z$ satisfying $(z-2)i=1+i$ (where $i$ is the imaginary unit), find $|z|$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the modulus of a complex number z, given that (z - 2)i = 1 + i. Hmm, first, maybe I should solve for z and then ... |
3,180 | [{"role": "user", "content": "An equilateral triangle and a square both have perimeters of 60 inches. What is the ratio of the length of the side of the triangle to the length of the side of the square? Express your answer as a common fraction."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challe... |
3,192 | [{"role": "user", "content": "A warehouse store sells cartons of gum. Each carton contains 5 packs of gum, and there are 3 sticks of gum in each pack. Each brown box contains 4 cartons of gum. How many sticks of gum are there in 8 brown boxes?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem... |
3,190 | [{"role": "user", "content": "A random variable $X \\sim B(n,p)$ has a mean of $200$ and a standard deviation of $10$. Find the values of $n$ and $p$ respectively. \nA: $400$, $\\dfrac{1}{2}$ \nB: $200$, $\\dfrac{1}{20}$ \nC: $400$, $\\dfrac{1}{4}$ \nD: $200$, $\\dfrac{1}{4}$"}, {"role": "assistant", "content": "<t... |
3,201 | [{"role": "user", "content": "Because of the decision Sofia asked the students to suggest specific types of food. If 144 students suggested adding mashed potatoes 467 suggested adding bacon to the menu and 79 suggested adding tomatoes. How many more students suggested mashed potatoes than those that suggested tomatoes?... |
3,202 | [{"role": "user", "content": "A waiter had some customers. After 3 customers left, he still had 5 customers. Then he got 99 new customers. How many customers did the waiter have initially?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by step. So, the question is: A wai... |
3,150 | [{"role": "user", "content": "Let $P$ be the parabola with equation $y = x^2$ and let $Q = (20, 14)$ There are real numbers $r$ and $s$ such that the line through $Q$ with slope $m$ does not intersect $P$ if and only if $r < m < s$ . What is $r + s?$ $ \\textbf{(A)} 1 \\qquad \\textbf{(B)} 26 \\qquad... |
3,151 | [{"role": "user", "content": "If $\\dfrac{a^2+b}{b+c^2}=\\dfrac{c^2+d}{d+a^2}$, find the condition for which this equation holds.\nA) $a = c$\nB) $a^2 + d + 2b = 0$\nC) $b^2 + a^2 + c^2 = 0$\nD) $ab + cd = 0$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem. The question is: If (a² ... |
3,157 | [{"role": "user", "content": "Let $P = 2^a$ and $Q = 3^b$ for integers $a$ and $b$. Which of the following is equal to $18^{ab}$ for every pair of integers $(a, b)$?\n- $\\textbf{(A)}\\ P^aQ^{2b} \\qquad \\textbf{(B)}\\ P^{2a}Q^b \\qquad \\textbf{(C)}\\ P^bQ^{2a} \\qquad \\textbf{(D)}\\ P^{2b}Q^a \\qquad \\textbf{(E)}\... |
3,182 | [{"role": "user", "content": "In the sequence $1, \\frac{1}{2}, \\frac{2}{1}, \\frac{1}{3}, \\frac{2}{2}, \\frac{3}{1}, \\frac{1}{4}, \\frac{2}{3}, \\frac{3}{2}, \\frac{4}{1}, \\ldots$, the 50th term is ( )\n\nA: $\\frac{7}{4}$\n\nB: $\\frac{4}{7}$\n\nC: $\\frac{6}{5}$\n\nD: $\\frac{5}{6}$"}, {"role": "assistant", "co... |
3,195 | [{"role": "user", "content": "Let $[x]$ denote the greatest integer less than or equal to $x$. For example, $[1.7]=1$, $[-1.7]=-2$. Based on this definition, perform the following operations: \n(1) $[2.3]-[6.3]$ \n(2) $[4]-[-2.5]$ \n(3) $[-3.8]\\times[6.1]$ \n(4) $[0]\\times[-4.5]$．"}, {"role": "assistant", "conten... |
3,158 | [{"role": "user", "content": "Given the sets $A=\\{x|(x-1)(x-a)\\geqslant 0\\}$ and $B=\\{x|x\\geqslant a-1\\}$, if $A\\cup B=\\mathbb{R}$, find the maximum value of $a$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem step by step. The question is about finding the maximum value o... |
3,194 | [{"role": "user", "content": "The equation of the ellipse is given by\n\\[\\frac{(x - h)^2}{a^2} + \\frac{(y - k)^2}{b^2} = 1.\\]\nIn a Cartesian coordinate system, an ellipse is drawn with center at $(3, -5)$, a horizontal semi-major axis of length 6, and a vertical semi-minor axis of length 2. Calculate the sum $h + ... |
3,176 | [{"role": "user", "content": "If $\\alpha$ is in the third quadrant, then $\\frac{\\alpha}{2}$ must be in $\\text{( }\\ \\text{)}$.\nA. The first or second quadrant\nB. The first or third quadrant\nC. The third or fourth quadrant\nD. The second or fourth quadrant"}, {"role": "assistant", "content": "<think>\n\nOkay, le... |
3,147 | [{"role": "user", "content": "The function \\( g \\), defined on the set of integers, satisfies the following conditions:\n\n1) \\( g(1) > 1 \\)\n2) \\( g(x+y) + x g(y) + y g(x) = g(x) g(y) + x + y + xy \\) for any \\( x, y \\in \\mathbb{Z} \\);\n3) \\( 3 g(x) = g(x+1) + 2x - 1 \\) for any \\( x \\in \\mathbb{Z} \\).\n... |
3,119 | [{"role": "user", "content": "Given the function $F(x)=e^{x}$ satisfies: $F(x)=g(x)+h(x)$, and $g(x)$, $h(x)$ are even and odd functions on $\\mathbb{R}$, respectively. If for all $x\\in(0,2]$ the inequality $g(2x)-ah(x)\\geqslant 0$ always holds, then the range of the real number $a$ is \nA: $(-\\infty, \\sqrt{2}]$ ... |
3,185 | [{"role": "user", "content": "Given the following equations:\n\n\\\\(\\sqrt{2}=2\\cos \\frac{\\pi }{4}\\\\),\n\n\\\\(\\sqrt{2+\\sqrt{2}}=2\\cos \\frac{\\pi }{8}\\\\),\n\n\\\\(\\sqrt{2+\\sqrt{2+\\sqrt{2}}}=2\\cos \\frac{\\pi }{16}\\\\), ...\n\nPlease induce the $n^{th}$ $(n\\in \\mathbb{N}^{*})$ equation:\n\n\\\\(\\unde... |
3,197 | [{"role": "user", "content": "How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8.5 m x 6 m x 22.5 cm?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to figure out how many bricks are needed to build a wall. The bricks have dimensions 25 cm x 11.25 cm x ... |
3,109 | [{"role": "user", "content": "Gabrielle has a $3 \\times 3$ grid and L-shaped pieces that cover three squares each, as shown below. Can she cover her grid using these pieces?\n\n![L-shaped piece](https://cdn.mathpix.com/cropped/2024_05_10_a954a7760d797f08770eg-095.jpg?height=134&width=143&top_left_y=2297&top_left_x=959... |
3,215 | [{"role": "user", "content": "Seonwoo wants to combine 35 pencils and 5 erasers and hand them out to 5 friends in equal numbers. Find how many of them should he hand out to each friend."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Seonwoo has 35 pencils and 5 erasers, and he wants to give them out t... |
3,103 | [{"role": "user", "content": "Ron has 6 cousins whose average age is 10 years. The median age of these cousins is 9 years. Calculate the combined age of Ron's youngest and oldest cousins.\n$\\textbf{(A)}\\ 12\\qquad\\textbf{(B)}\\ 15\\qquad\\textbf{(C)}\\ 18\\qquad\\textbf{(D)}\\ 21\\qquad\\textbf{(E)}\\ 24$"}, {"role"... |
3,219 | [{"role": "user", "content": "A garden table and a bench cost 450 dollars combined. The price of the garden table is 2 times the price of the bench. What is the cost of the bench, in dollars?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says a garden table and a bench cost $450 combined.... |
3,210 | [{"role": "user", "content": "In the arithmetic sequence ${a_n}$, $a_2 + a_6 = 10$, find the value of $a_1 + a_2 + ... + a_7$ ( ).\nA: 15\nB: 35\nC: 50\nD: 70"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about an arithmetic sequence. We need to find the sum of the first 7 terms, giv... |
3,072 | [{"role": "user", "content": "From point \\( T \\), a tangent \\( TA \\) and a secant intersecting the circle at points \\( B \\) and \\( C \\) are drawn. The angle bisector of \\(\\angle ATC\\) intersects chords \\( AB \\) and \\( AC \\) at points \\( P \\) and \\( Q \\) respectively. Prove that \\( PA = \\sqrt{PB \\c... |
3,152 | [{"role": "user", "content": "Suppose that $\\sec x + \\tan x = \\frac{15}{4}$ and that $\\csc x + \\cot x = \\frac{p}{q},$ where $\\frac{p}{q}$ is in lowest terms. Find $p + q.$"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correc... |
3,222 | [{"role": "user", "content": "If $\\|\\mathbf{u}\\| = 7,$ then find $\\mathbf{u} \\cdot \\mathbf{u}.$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that the norm of vector u is 7, and we need to find the dot product of u with itself. Hmm, I remember that the norm of a vector is relat... |
3,216 | [{"role": "user", "content": "one night 19 percent of the female officers on a police force were on duty . if 152 police officers were on duty that night and half of these were female officers , how many female officers were on the police force ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure... |
3,189 | [{"role": "user", "content": "A farmer needs to buy 100 heads of livestock for 100 dollars. If each calf costs 10 dollars, each lamb 3 dollars, and each piglet 0.5 dollars, how many calves, lambs, and piglets does the farmer buy?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem... |
3,114 | [{"role": "user", "content": "Given that the positive real numbers $a$, $b$, and $c$ are the lengths of the sides of a triangle, prove that: $\\dfrac{c}{a+b}+ \\dfrac{a}{b+c}+ \\dfrac{b}{c+a} > 1$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide ... |
3,212 | [{"role": "user", "content": "A garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement of 1900 men arrives, and it is now found that the provisions will last for some more days. How many more days will the provisions last after the reinforcement arrives?"}, {"role": "assistant", "conten... |
3,167 | [{"role": "user", "content": "Let $S_{n}$ be the sum of the first $n$ terms of a geometric sequence $\\{a_{n}\\}$. If $S_{4}=-5$ and $S_{6}=21S_{2}$, then $S_{8}=\\left(\\ \\ \\right)$\n\nA: $120$\n\nB: $85$\n\nC: $-85$\n\nD: $-120$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem s... |
3,220 | [{"role": "user", "content": "a sum fetched a total simple interest of $ 4016.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about simple interest. I need to find the principal sum that, when invested at 9% per annum, gi... |
3,203 | [{"role": "user", "content": "Use the Horner's method to compute the value of $f(x)=x^{6}-12x^{5}+60x^{4}-160x^{3}+240x^{2}-192x+64$. When $x=2$, what is the value of $v_{4}$?\n\nA: $0$\nB: $80$\nC: $-80$\nD: $-32$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to use Horner's method to compute... |
3,214 | [{"role": "user", "content": "Find the equation of the line that passes through the point (1, 3) and is perpendicular to the line $x + 2y - 1 = 0$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the equation of a line that passes through (1, 3) and is perpendicular to the line x + 2y - ... |
3,224 | [{"role": "user", "content": "Three balls, colored red, black, and white, are randomly distributed to three people— A, B, and C—with each person receiving one ball. The event \"person A receives the white ball\" and the event \"person B receives the white ball\" are ( )\nA: Opposite events\nB: Impossible events\nC: Mut... |
3,200 | [{"role": "user", "content": "Let GCF(a, b) be the abbreviation for the greatest common factor of a and b, and let LCM(c, d) be the abbreviation for the least common multiple of c and d. What is GCF(LCM(9, 21), LCM(10, 15))?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and ... |
3,230 | [{"role": "user", "content": "The town of Milburg has 5256 grown-ups and children. 2987 are children. How many adults live in Milburg?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that the town of Milburg has 5256 grown-ups and children total. Out of those, 2987 are children. We nee... |
3,196 | [{"role": "user", "content": "Given that the terms of the geometric sequence $\\\\{a\\_n\\\\}$ are all positive, the common ratio $q=2$, and $a\\_3 \\cdot a\\_{13}=16$, find $a\\_9$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find \\( a_9 \\) in a geometric sequence where all terms are p... |
3,234 | [{"role": "user", "content": "The slant height of a cone is 10, and its height is 8. Then, the surface area of this cone is ( )\nA: 60π\nB: 80π\nC: 96π\nD: 116π"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about finding the surface area of a cone. They gave the slant height as 10 and... |
3,239 | [{"role": "user", "content": " Mrs. Hilt bought an ice cream cone for 99 cents. How much would 2 ice cream cones cost?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says Mrs. Hilt bought an ice cream cone for 99 cents. We need to find out how much 2 ice cream cones would cost. Hmm, so fir... |
3,232 | [{"role": "user", "content": "In a family there are two cars. In a given week, the first car gets an average of 25 miles per gallon, and the second car gets 40 miles per gallon. The two cars combined drive a total of 1825 miles in that one week, for a certain amount of gas consumption. The first car consumed 30 gallons... |
3,243 | [{"role": "user", "content": "What is the quotient if the dividend is 149, the divisor is 16, and the remainder is 5?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the quotient when the dividend is 149, the divisor is 16, and the remainder is 5. Hmm, I remember that in divis... |
3,148 | [{"role": "user", "content": "What is the greatest number of Sundays that can occur in the first $84$ days of a year?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so the problem is ... |
3,236 | [{"role": "user", "content": "Safety Rent-a-Car rents an intermediate-size car at a daily rate of 21.95 dollars plus 0.19 per mile. City Rentals rent an intermediate-size car for 18.95 dollars plus 0.21 per mile. For what mileage is the cost the same?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I n... |
3,237 | [{"role": "user", "content": "a company has two models of computers , model x and model y . operating at a constant rate , a model x computer can complete a certain task in 72 minutes and a model y computer can complete the same task in 36 minutes . if the company used the same number of each model of computer to compl... |
3,233 | [{"role": "user", "content": "10% of people in a village in Sri Lanka died by bombardment, 20% of the remainder left the village on account of fear. The population is now reduced to 4554. How much was the population in the beginning?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this pro... |
3,165 | [{"role": "user", "content": "Find the minimum area of the part bounded by the parabola $ y\\equal{}a^3x^2\\minus{}a^4x\\ (a>0)$ and the line $ y\\equal{}x$ ."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need ... |
3,135 | [{"role": "user", "content": "Points $A,B,C,D,E$ and $F$ lie, in that order, on $\\overline{AF}$, dividing it into five segments, each of length 1. Point $G$ is not on line $AF$. Point $H$ lies on $\\overline{GD}$, and point $J$ lies on $\\overline{GF}$. The line segments $\\overline{HC}, \\overline{JE},$ and $\\overli... |
3,199 | [{"role": "user", "content": "Find the number of complex solutions to\n\\[\\frac{z^3 - 1}{z^2 - 3z + 2} = 0.\\]"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I need to find the nu... |
3,252 | [{"role": "user", "content": "Thomas, Toby, and Rebecca worked a certain number of hours in one week. Thomas worked x hours. Toby worked 10 hours less than twice what Thomas worked, and Rebecca worked 8 hours less than Toby. Rebecca worked 56 hours. What is the total number of hours they worked in one week?"}, {"role":... |
3,246 | [{"role": "user", "content": "A man is trying to maximize the amount of money he saves each month. In particular, he is trying to decide between two different apartments. The first apartment costs $800 per month in rent and will cost an additional $260 per month in utilities. The second apartment costs $900 per month a... |
3,213 | [{"role": "user", "content": "Let the universal set be $\\mathbb{R}$, $A=\\{x|2\\leqslant x < 4\\}$, $B=\\{x|3x-7\\geqslant 8-2x\\}$. \n$(1)$ Find $A\\cup(\\complement_{\\mathbb{R}}B)$. \n$(2)$ If $C=\\{x|a-1\\leqslant x\\leqslant a+3\\}$ and $A\\cap C=A$, find the range of the real number $a$."}, {"role": "assistant... |
3,229 | [{"role": "user", "content": "Let $F_{1}$ and $F_{2}$ be the two foci of the ellipse $C$: $\\frac{x^2}{5}+y^{2}=1$. Point $P$ lies on $C$. If $\\overrightarrow{PF_{1}}\\cdot \\overrightarrow{PF_{2}}=0$, then $|PF_{1}|\\cdot |PF_{2}|$ is equal to:\n\nA: $1$\n\nB: $2$\n\nC: $4$\n\nD: $5$"}, {"role": "assistant", "content... |
3,225 | [{"role": "user", "content": "The Cookie Monster now encounters another cookie whose boundary is described by the equation $x^2 + y^2 + 10 = 6x + 12y$. Determine the radius of this cookie."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct ... |
3,173 | [{"role": "user", "content": "Two athletes start running simultaneously - the first from \\( A \\) to \\( B \\), and the second from \\( B \\) to \\( A \\). They run at different but constant speeds and meet at a distance of 300 meters from \\( A \\). After running the track \\( AB \\) to the end, each of them immediat... |
3,226 | [{"role": "user", "content": "Simplify: $$(x^{2}-4)\\left( \\frac {x+2}{x^{2}-2x}- \\frac {x-1}{x^{2}-4x+4}\\right)\\div \\frac {x-4}{x}$$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to simplify this expression: \\((x^{2}-4)\\left( \\frac {x+2}{x^{2}-2x}- \\frac {x-1}{x^{2}-4x+4}\\right)\\di... |
3,217 | [{"role": "user", "content": "Define an operation \"$\\ast$\" for positive integers that satisfies the following properties:\n(1) $2 \\ast 2006 = 1$; (2) $(2n+2) \\ast 2006 = 3 \\cdot [(2n) \\ast 2006]$, then the value of $2008 \\ast 2006$ is."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challen... |
3,256 | [{"role": "user", "content": "In civil engineering, the stability of cylindrical columns under a load is often examined using the formula \\( L = \\frac{50T^3}{SH^2} \\), where \\( L \\) is the load in newtons, \\( T \\) is the thickness of the column in centimeters, \\( H \\) is the height of the column in meters, and... |
3,231 | [{"role": "user", "content": "Let $p(x) = 3x - 8$ and $q(x) = 4x - c$. If $p(q(3)) = 10$, what is $c$?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I need to solve this problem w... |
3,191 | [{"role": "user", "content": "Calculate $75 \\cdot \\left(4\\frac{1}{3} - 5\\frac{1}{4}\\right) \\div \\left(3\\frac{1}{2} + 2\\frac{1}{5} \\right)$. Express your answer as a mixed number."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct ... |
3,115 | [{"role": "user", "content": "Find the condition of $a,b$ for which the function $f(x)\\ (0\\leq x\\leq 2\\pi)$ satisfying the following equality can be determined uniquely,then determine $f(x)$ , assuming that $f(x) $ is a continuous function at $0\\leq x\\leq 2\\pi$ .\r\n\r\n\\[f(x)=\\frac{a}{2\\pi}\\int_0^{2... |
3,251 | [{"role": "user", "content": "Two trains of equal length are running on parallel lines in the same direction. One train is running at 42 km/hr, and the other train is running at a certain speed. The faster train passes the slower train in 36 seconds. The length of each train is 30 meters. What is the speed of the slowe... |
3,245 | [{"role": "user", "content": "What is the range of the function $$r(x) = \\frac{1}{(1-x)^2}~?$$ Express your answer in interval notation."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the range of the function \\( r(x) = \\frac{1}{(1 - x)^2} \\). Hmm, first, let me recall what the rang... |
3,263 | [{"role": "user", "content": "On dividing 122 by a number, the quotient is 6 and the remainder is some value. The divisor is 20. What is the remainder?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says: On dividing 122 by a number, the quotient is 6 and the remainder is some value. The d... |
3,249 | [{"role": "user", "content": "In the arithmetic sequence $\\{a_n\\}$, $a_7=8$, and the sum of the first 7 terms $S_7=42$, then its common difference is ______."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the common difference of an arithmetic sequence where the 7th term is 8 and the ... |
3,227 | [{"role": "user", "content": "What is the least positive integer divisible by each of the first eight positive integers?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the least positive integer divisible by each of the first eight positive integers. So, first eight positive ... |
3,218 | [{"role": "user", "content": "Given that the domain of the function $f(x) = \\ln(2+x) - \\ln(2-x)$ is $A$, and the range of $g(x) = x^2 + 2x + m$ is $B$, if $A \\subseteq B$, determine the range of values for the real number $m$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question,... |
3,257 | [{"role": "user", "content": "Jordan ran 2 miles in half the time it took Steve to run 3 miles. If it took Steve 24 minutes to run 3 miles, using the same rates, how many minutes would it take Jordan to run 8 miles?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by step.... |
3,248 | [{"role": "user", "content": "What is the remainder of \\(3^{2028}\\) when it is divided by 8?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the remainder when \\(3^{2028}\\) is divided by 8. Hmm, remainders when divided by 8... Maybe I can use modular arithmetic here. I remember that ... |
3,258 | [{"role": "user", "content": "Find the area of a quadrilateral with one of its diagonals being 10 cm and one of its off sets being 7 cm and the other off set being some length. The area of the quadrilateral is 50 cm². What is the length of the second off set?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's ... |
3,105 | [{"role": "user", "content": "As shown in the diagram, the distance between any two adjacent points in a row is 1, and the distance between any two adjacent points in a column is also 1. Every second, a green point can turn any point that is at a distance of no more than 1 into green. Given the initial state shown in t... |
3,238 | [{"role": "user", "content": "The maximum value of the function $f(x) = x^2 - 4x + 5$ in the interval $[0, m]$ is 5, and the minimum value is 1. Then, the range of $m$ is ( )\n\nA: $[2, +\\infty)$\n\nB: $[2,4]$\n\nC: $(-\\infty, 2]$\n\nD: $[0,2]$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figur... |
3,188 | [{"role": "user", "content": "A palindrome between $1000$ and $10,000$ is chosen at random. What is the probability that it is divisible by $11$?\n$\\textbf{(A)}\\ \\dfrac{1}{11} \\qquad \\textbf{(B)}\\ \\dfrac{1}{10} \\qquad \\textbf{(C)}\\ \\dfrac{1}{9} \\qquad \\textbf{(D)}\\ \\dfrac{1}{8} \\qquad \\textbf{(E)}\\ 1$... |
3,221 | [{"role": "user", "content": "Petya and Vasya ride bicycles at constant speeds around a circle. Petya's speed is 8 km/h, and Vasya's speed is 10 km/h. Initially, they rode in opposite directions (Petya clockwise and Vasya counterclockwise), and then Petya changed his direction (started moving counterclockwise) and simu... |
3,198 | [{"role": "user", "content": "There were equal amounts of water in two glasses. The amount of water in the first glass initially increased by $1\\%$, then by $2\\%$, then by $3\\%$, and so on up to $27\\%$. In the second glass, the amount of water initially increased by $27\\%$, then by $26\\%$, then by $25\\%$, and so... |
3,264 | [{"role": "user", "content": "a man buys rs . 48 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is :"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by step. First, let's make sure I understand the ques... |
3,241 | [{"role": "user", "content": "A jogger running at 10 km/hr alongside a railway track is a certain distance ahead of the engine of a 120 m long train running at 46 km/hr in the same direction. It takes 46 seconds for the train to pass the jogger. How far ahead is the jogger from the engine of the train in meters?"}, {"r... |
3,208 | [{"role": "user", "content": "Suppose \\(x, y,\\) and \\(z\\) are three positive numbers that satisfy the equations \\(xyz = 1,\\) \\(x + \\frac{1}{z} = 7,\\) and \\(y + \\frac{1}{x} = 20.\\) Find \\(z + \\frac{1}{y}.\\)"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it i... |
3,278 | [{"role": "user", "content": "Jan is making candy necklaces for herself and a few friends. Everyone receives a candy necklace each and each candy necklace is made up of 10 pieces of candies. The pieces of candies come from blocks of candy, which each produce 30 pieces of candy. Jan breaks down some blocks of candy and ... |
3,279 | [{"role": "user", "content": "Given the sets $A={1,2,3,4,5}$ and $B={1,3,5,7,9}$, let $C=A\\cap B$. Determine the number of subsets of set $C$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about finding the number of subsets of set C, where C is the intersection of sets A and B. First... |
3,268 | [{"role": "user", "content": "For the one-variable linear equation $x^{2}+2x-8=0$ with roots $x_{1}$ and $x_{2}$, find $\\frac{{x}_{2}}{{x}_{1}}+\\frac{{x}_{1}}{{x}_{2}}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a quadratic equation, but wait, it says \"one-variable linear ... |
3,193 | [{"role": "user", "content": "Given three numbers $22^{44}$, $33^{33}$, $44^{22}$, connect these three numbers with \">\"."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I need to ... |
3,204 | [{"role": "user", "content": "Given vectors $\\overrightarrow{a}=(\\cos x,\\sin x)$, $\\overrightarrow{b}=( \\sqrt {3}\\sin x,\\sin x)$, where $x\\in R$, define the function $f(x)= \\overrightarrow{a}\\cdot \\overrightarrow{b}- \\dfrac {1}{2}$.\n(1) Find the smallest positive period of the function $f(x)$;\n(2) Find th... |
3,137 | [{"role": "user", "content": "On a 3x3 grid of evenly spaced points (each unit distance apart), how many different rectangles can be formed by using these points as vertices?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct an... |
3,275 | [{"role": "user", "content": "In a study investigating the relationship between smoking and lung cancer, data was collected, organized, and analyzed, resulting in the conclusion that \"there is more than a 99% level of confidence that smoking is related to developing lung cancer.\" Evaluate the correctness of the follo... |
3,235 | [{"role": "user", "content": "Let \\(a, b,\\) and \\(c\\) be three distinct numbers. Solve the system\n\n$$\n\\left\\{\\begin{aligned}\nz + ay + a^{2}x + a^{3} &= 0 \\\\\nz + by + b^{2}x + b^{3} &= 0 \\\\\nz + cy + c^{2}x + c^{3} &= 0\n\\end{aligned}\\right.\n$$"}, {"role": "assistant", "content": "<think>\n\nThis is a... |
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