__src_index__ int64 0 172k | messages stringlengths 375 66.5k |
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2 | [{"role": "user", "content": "A farmer has a rectangular field with dimensions $3m+8$ and $m-3$ where $m$ is a positive integer. If the field has an area of 76 square meters, find the value of $m$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide ... |
54 | [{"role": "user", "content": "Compute\n\\[\n\\sum_{n=1}^\\infty \\frac{3n + 2}{n(n + 1)(n + 3)}.\n\\]"}, {"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 compute this infinite... |
158 | [{"role": "user", "content": "If $\\left(3x-y+5\\right)^{2}+|2x-y+3|=0$, then $x+y=\\_\\_\\_\\_\\_\\_$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is: If \\((3x - y + 5)^2 + |2x - y + 3| = 0\\), then find \\(x + y\\). Hmm, right. So, I need to solve for \\(x\\) and \\(y\\) first, proba... |
134 | [{"role": "user", "content": "$(1)$ Fill in the table and observe the pattern of the decimal point movement of the radicand and its arithmetic square root.<br/>| $a$ | $\\ldots $ | $0.000004$ | $0.0004$ | $0.04$ | $4$ | $400$ | $40000$ | $\\ldots $ |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| $\\sqrt{a... |
81 | [{"role": "user", "content": "Given the sequence $a_n$: $\\frac{1}{1}$, $\\frac{2}{1}$, $\\frac{1}{2}$, $\\frac{3}{1}$, $\\frac{2}{2}$, $\\frac{1}{3}$, $\\frac{4}{1}$, $\\frac{3}{2}$, $\\frac{2}{3}$, $\\frac{1}{4}$, ..., according to the pattern of its first 10 terms, the value of $a_{99}+a_{100}$ is \\_\\_\\_\\_\\_\\_... |
65 | [{"role": "user", "content": "Given that ( ( ( 13 ! ) ^ some_power ) - ( ( 13 ! ) ^ 8 ) ) / ( ( ( 13 ! ) ^ 8 ) + ( ( 13 ! ) ^ 4 ) ) = a, the units digit for a / ( ( 13 ! ) ^ 4 ) is 9. What is the value of some_power?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is di... |
135 | [{"role": "user", "content": "Given that $b > a > 0$ and $ab=2$, determine the range of values for $\\frac{a^2+b^2}{a-b}$.\n\nA: $(-\\infty, -4]$\nB: $(-\\infty, -4)$\nC: $(-\\infty, -2]$\nD: $(-\\infty, -2)$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem. The question says that \... |
145 | [{"role": "user", "content": "Find $89^{-1} \\pmod{90}$, as a residue modulo 90. (Give an answer between 0 and 89, inclusive.)"}, {"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... |
164 | [{"role": "user", "content": "The little league stadium has 92 seats. 47 people came to the game today. 38 people were holding banners. How many seats were empty?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a little league stadium with 92 seats. 47 people came to the game today... |
143 | [{"role": "user", "content": "How many four-digit positive integers are there with thousands digit $1$ and are even?"}, {"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 a... |
53 | [{"role": "user", "content": "Given $p$: $|4x-3|\\leqslant 1$ and $q$: $x^{2}-(2a+1)x+a^{2}+a\\leqslant 0$, find the range of values for $a$ if $p$ is a necessary but not sufficient condition for $q$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provi... |
146 | [{"role": "user", "content": "Verify that 2 is a solution of the equation:\n\n$$\n(x+1)^{3}+(x+2)^{3}+(x+3)^{3}=(x+4)^{3}\n$$\n\nDoes this equation have any other integer solutions?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to verify if 2 is a solution to the equation \\((x+1)^3 + (x+2)^3 ... |
160 | [{"role": "user", "content": "If a sum of money doubles itself in 10 years at compound interest, compounded semiannually, what is the annual interest rate?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about compound interest where a sum of money doubles in 10 years, compounded semiann... |
166 | [{"role": "user", "content": "6 persons standing in queue with different age group , after two years their average age will be 43 and seventh person joined with them . hence the current average age has become 45 . find the age of seventh person ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure... |
118 | [{"role": "user", "content": "Determine the smallest positive integer $n$ such that $7^n \\equiv n^7 \\pmod 4$."}, {"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 sm... |
108 | [{"role": "user", "content": "Given a function $f(x) = 2\\sin^2x - \\cos(2x + \\frac{\\pi}{3})$.\n(Ⅰ) Find the smallest positive period of $f(x)$;\n(Ⅱ) Prove that when $x \\in [0, \\frac{\\pi}{2}]$, $f(x) \\geq -\\frac{1}{2}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's tackle this problem step by step.... |
92 | [{"role": "user", "content": "Let $T$ be a subset of $\\{1,2,3,...,100\\}$ such that no pair of distinct elements in $T$ has a sum divisible by $11$. What is the maximum number of elements in $T$?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a... |
148 | [{"role": "user", "content": "Find the derivative of the following functions:\n\n1. $y=\\sqrt[5]{x^{3}};$\n\n2. $y=\\dfrac{1}{x^{4}};$\n\n3. $y=-2\\sin \\dfrac{x}{2}\\left( 1-2\\cos^{2}\\dfrac{x}{4} \\right);$ \n\n4. $y=\\log _{2}x^{2}-\\log _{2}x.$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's tackle the... |
175 | [{"role": "user", "content": "Ruth goes to school 8 hours a day and 5 days a week. She is in math class 25% of this time. How many hours per week does she spend in math class?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about Ruth going to school 8 hours a day, 5 days a week, and she... |
10 | [{"role": "user", "content": "Given that $b$ is a multiple of $2373$, find the greatest common divisor of $b^2 + 13b + 40$ and $b + 5$."}, {"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, ... |
56 | [{"role": "user", "content": "Each edge of a cube is colored either red or black. Every face of the cube has at least two black edges. The smallest number possible of black edges is:\n$\\text{(A) } 5\\quad \\text{(B) } 6\\quad \\text{(C) } 7\\quad \\text{(D) } 8\\quad \\text{(E) } 9$"}, {"role": "assistant", "content":... |
113 | [{"role": "user", "content": "Justin has a box that is 12 inches in height. The length of the box is 3 times its height and 4 times its width. The diagonal length of the box is 60 inches. What is the volume of the box?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out the volume of Justin's ... |
173 | [{"role": "user", "content": "Find the function $F(x)$, whose graph passes through the point $M_{0}(3 ;-2)$, given that $F'(x) = 4x^{2} + 9x^{-2}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the function F(x) that passes through the point M₀(3, -2), and its derivative is given as F'... |
141 | [{"role": "user", "content": "Determine the value of\n\n$$\nz=a \\sqrt{a} \\sqrt[4]{a} \\sqrt[8]{a} \\ldots \\sqrt[2^{n}]{a} \\ldots\n$$\n\nif \\( n \\) is infinitely large."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct ans... |
154 | [{"role": "user", "content": "The positive number \\( b \\) is chosen such that the terms \\( 30, b, \\frac{3}{8} \\) are the first, second, and third terms, respectively, of a geometric sequence. What is the value of \\( b \\), if \\( b \\) is positive?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex... |
170 | [{"role": "user", "content": "The least integer that is greater than \\((2+\\sqrt{3})^{2}\\) is:\n(A) 13\n(B) 14\n(C) 15\n(D) 16\n(E) 17"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the least integer that's greater than (2 + √3)². So first, I need to compute (2 + √3) square... |
179 | [{"role": "user", "content": "Solve the equation: $\\frac{1}{x-2}=\\frac{3}{x}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to solve the equation 1 over (x minus 2) equals 3 over x. Hmm, so it's a rational equation. I remember that to solve these, I should probably cross-multiply to get rid... |
140 | [{"role": "user", "content": "Determine the number of solutions to the equation $\\frac{{x}^{2}-6x+9}{x-1}-\\frac{3-x}{{x}^{2}-1}=0$.\n\nA: $0$ solutions\nB: $1$ solution\nC: $2$ solutions\nD: $3$ solutions"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out how many solutions this equation ha... |
142 | [{"role": "user", "content": "Give the value of \\(0 - 1 + 2 - 3 + 4 - 5 + \\ldots - 49 + 50\\). Only a numerical answer is expected."}, {"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... |
112 | [{"role": "user", "content": "The graph of the function \\( g(x) \\) is defined as \\( g(x) = x^2 - 4x + 3 \\) for \\( -2 \\le x \\le 5 \\). How many values of \\( x \\) satisfy \\( g(g(x)) = 3 \\)?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide... |
159 | [{"role": "user", "content": "Elective 4-5: Special Lecture on Inequalities\n\nGiven that the solution set of the inequality $|x+3|-2x-1 < 0$ is $(x_0,+\\infty)$.\n\n$(1)$ Find the value of $x_0$;\n\n$(2)$ If the function $f(x)=|x-m|+|x+ \\frac{1}{m}|-x_0$ $(m > 0)$ has a zero, find the value of the real number $m$."},... |
177 | [{"role": "user", "content": "the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 19 greater than the actual number and the second number added is 13 instead of 31 . find the correct average ."}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to f... |
183 | [{"role": "user", "content": "In a certain time, a sum of money increases by a certain percentage at 4% per annum simple interest. The time it takes is 25 years. What is the ratio of the final amount to the initial amount?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about simple inte... |
122 | [{"role": "user", "content": "Let $S_{n}$ be the sum of the first $n$ terms of the positive sequence ${a_{n}}$, and $S_{n}= \\frac{1}{4}a_{n}^{2}+ \\frac{1}{2}a_{n}- \\frac{3}{4}$.\n(1) Find the value of $a_{1}$;\n(2) Find the general term formula for the sequence ${a_{n}}$;\n(3) Given $b_{n}=2^{n}$, find the value of ... |
98 | [{"role": "user", "content": "Find the sum of all positive real solutions \\(x\\) to the equation \\[3\\cos2x \\left(\\cos2x - \\cos{\\left( \\frac{2000\\pi^2}{x} \\right) } \\right) = \\cos4x - 1,\\] where \\(x\\) is measured in radians."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging ... |
184 | [{"role": "user", "content": "John purchased three dozen oranges for $\\$$28.80. At the same rate, how much would five dozen of these oranges cost?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about John buying three dozen oranges for $28.80, and we need to find out how much five doze... |
188 | [{"role": "user", "content": "The ratio of the number of students in the first, second, and third grades of a high school is $5:2:3$. If a stratified sampling of a sample size of $200$ is to be conducted, the number of students to be drawn from the third grade is (__).\n\nA: $20$\n\nB: $40$\n\nC: $60$\n\nD: $80$"}, {"r... |
182 | [{"role": "user", "content": "In the arithmetic sequence $\\{a_n\\}$, if $a_3+a_5+a_7+a_9+a_{11}=100$, then the value of $3a_9-a_{13}$ is ( )\nA: 20\nB: 30\nC: 40\nD: 50"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about an arithmetic sequence. First, I need to remember what an arithm... |
131 | [{"role": "user", "content": "If point $P(a, b)$ is on the graph of the function $y = -x^2 + 3\\ln x$ and point $Q(c, d)$ is on the graph of the function $y = x + 2$, find the minimum value of $|PQ|$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provi... |
178 | [{"role": "user", "content": "The coefficient of $x$ in the expansion of $(x^{2}+3x+2)^{6}$ is ( ).\n\nA: $92$\n\nB: $576$\n\nC: $192$\n\nD: $384$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the coefficient of \\( x \\) in the expansion of \\( (x^2 + 3x + 2)^6 \\). Hmm, so... |
189 | [{"role": "user", "content": "Malcolm works in a company where they normally pack 40 apples in a box, producing a certain number of full boxes per day. Operations went as normal in one week. But in the next week, they packed 500 fewer apples per day. The total number of apples packed in the two weeks is 24,500. How man... |
196 | [{"role": "user", "content": "In a bag, there are 100 balls of the same size, including red, white, and black balls. There are 45 red balls. The probability of drawing a white ball from the bag is 0.23. What is the probability of drawing a black ball?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The... |
100 | [{"role": "user", "content": "The arithmetic mean, geometric mean, and harmonic mean of $a$, $b$, $c$ are $7$, $6$, $5$ respectively. What is the value of $a^2+b^2+c^2$?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer.... |
169 | [{"role": "user", "content": "Heather compares the price of a new computer at two different stores. Store $A$ offers 20% off the sticker price followed by a $100 rebate, and store $B$ offers 30% off the same sticker price with no rebate. Heather saves $25 by buying the computer at store $A$ instead of store $B$. What i... |
168 | [{"role": "user", "content": "Among the following functions, the one with the smallest positive period of $π$ and whose graph is symmetrical about the point $( \\frac {π}{3},0)$ is $\\(\\quad \\)$\nA: $y=sin ( \\frac {x}{2}+ \\frac {π}{6})$\nB: $y=cos (2x- \\frac {π}{3})$\nC: $y=cos (2x- \\frac {π}{6})$\nD: $y=sin (2x-... |
152 | [{"role": "user", "content": "The sequence $\\left\\{a_{n}\\right\\}$ is defined as follows: $a_{1}=\\frac{1}{2}$, and $a_{n+1}=\\frac{a_{n}^{2}}{a_{n}^{2}-a_{n}+1}$ for $n=1,2,\\ldots$. Prove that for every positive integer $n$, the inequality $a_{1}+a_{2}+\\cdots+a_{n}<1$ holds."}, {"role": "assistant", "content": "<... |
205 | [{"role": "user", "content": "Which of the following statements about algorithms and the three types of logical structures (sequential structure, conditional structure, loop structure) is correct?\nA: An algorithm can contain at most two types of logical structures.\nB: If the algorithms for the same problem are differ... |
202 | [{"role": "user", "content": "Given that the initial side of angle $\\alpha$ coincides with the positive half of the x-axis, and its terminal side lies on the ray defined by $3x-4y=0$ (where $x<0$), find the value of $\\sin\\alpha - \\cos\\alpha$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The pro... |
185 | [{"role": "user", "content": "Six socks, colored blue, brown, black, red, purple, and green are in a drawer. In how many different ways can we choose four socks from the drawer if the order of the socks does not matter, and at least one of the socks chosen must be blue?"}, {"role": "assistant", "content": "<think>\n\nT... |
114 | [{"role": "user", "content": "Points $M$ and $N$ are taken on the sides $AB$ and $BC$ respectively of triangle $ABC$. It turns out that the perimeter of $\\triangle AMC$ is equal to the perimeter of $\\triangle CNA$, and the perimeter of $\\triangle ANB$ is equal to the perimeter of $\\triangle CMB$. Prove that $\\tria... |
174 | [{"role": "user", "content": "Given $U=\\mathbb{R}$, $A=\\{x\\mid 1\\leqslant x\\leqslant 3\\}$, $B=\\{x\\mid 2 < x < 4\\}$, $C=\\{x\\mid a\\leqslant x\\leqslant a+1\\}$, where $a$ is a real number,\n(1) Find $A\\cap B$ and $A\\cup(\\lnot_{U}B)$;\n(2) If $B\\cap C=C$, find the range of values for $a$."}, {"role": "assi... |
195 | [{"role": "user", "content": "Given the universal set $U = \\mathbb{R}$, set $A=\\{x|\\log _{2}(x-1) \\lt 0\\}$, $B=\\left\\{{x|{\\frac{2}{x}≥1}}\\right\\}$, then ( ).\n\nA: $\\complement _{U}A=\\left[2,+\\infty \\right)$\n\nB: $B\\subseteq A$\n\nC: $A\\cap (\\complement _{U}B)=\\varnothing $\n\nD: $A\\cup B=\\left(-\\... |
187 | [{"role": "user", "content": "Last summer, $120$ students attended a basketball camp. Of those attending, $70$ were boys and $50$ were girls. The students were from three different middle schools: Jonas, Clay, and Pine. $50$ students were from Jonas Middle School, $40$ from Clay Middle School, and $30$ from Pine Middle... |
197 | [{"role": "user", "content": "There are twice as many cows in Devonshire as there are hearts on a standard deck of 52 playing cards. If there are 4 hearts on a card, calculate the total cost of the cows when they are sold at $200 each."}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this p... |
207 | [{"role": "user", "content": "What is the area enclosed by the region defined by the equation $x^2 + y^2 - 8x + 6y = -9$?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the area enclosed by the region defined by the equation \\( x^2 + y^2 - 8x + 6y = -9 \\). Hmm, first, I remember that ... |
153 | [{"role": "user", "content": "The blue parabola shown is the graph of the equation $x = ay^2 + by + c$. Find $c$. The grid lines are spaced one unit apart.\n\n[asy]\nsize(150);\nreal ticklen=3;\nreal tickspace=2;\n\nreal ticklength=0.1cm;\nreal axisarrowsize=0.14cm;\npen axispen=black+1.3bp;\nreal vectorarrowsize=0.2cm... |
171 | [{"role": "user", "content": "Initially, a full container holds water. One third of the water is poured out. Then, one fourth of the remainder is poured out. This process continues with one fifth of the remainder for the third pouring, one sixth for the fourth, and so forth. After how many pourings does exactly one fif... |
228 | [{"role": "user", "content": "Tom and Tim both brought 4, six-sided dice to school. How many total sides are there?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says Tom and Tim both brought 4, six-sided dice to school. We need to find the total number of sides. Hmm, first, let's break i... |
221 | [{"role": "user", "content": "Ray writes a two-digit number. He sees that the number exceeds 4 times the sum of its digits by a certain value. If the number is increased by 18, the result is the same as the number formed by reversing the digits. The number is 57. What is the value by which the number exceeds 4 times th... |
203 | [{"role": "user", "content": "Calculate: \n\\\\((1) \\sqrt{48}+ \\sqrt{8}- \\sqrt{18}- \\sqrt{12} \\\\) \\\\((2) 2( \\sqrt{2}+ \\sqrt{3})-( \\sqrt{3}- \\sqrt{2})^{2} \\\\)."}, {"role": "assistant", "content": "<think>\n\nOkay, let's tackle these two problems one by one. Starting with problem (1): √48 + √8 - √... |
217 | [{"role": "user", "content": "Given that the graph of a linear function passes through the points (3, 5) and (-4, -9),\n(1) Find the equation of this linear function;\n(2) Determine whether the point (-1, -3) is on the graph of this linear function."}, {"role": "assistant", "content": "<think>\n\nOkay, let's tackle thi... |
214 | [{"role": "user", "content": "Let set $U = \\{ x \\mid x \\text{ is a positive integer less than } 9\\}$, set $A = \\{1, 2, 3\\}$, and set $B = \\{3, 4, 5, 6\\}$. Then the intersection of the complements of $A$ and $B$ with respect to $U$, denoted $\\complement_U A \\cap \\complement_U B$, equals to ( )\n\nA: $\\{3\\}$... |
222 | [{"role": "user", "content": "Find the length of the longest pole that can be placed in a room 12 m long, 8 m broad, and 9 m high."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is to find the length of the longest pole that can be placed in a room that's 12 meters long, 8 meters broad, an... |
215 | [{"role": "user", "content": "Simplify first, then evaluate: $3(a^{2}-ab+7)-2(3ab-a^{2}+1)+3$, where $a=2$ and $b=\\frac{1}{3}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to simplify the expression first and then evaluate it with a=2 and b=1/3. The expression is 3(a² - ab + 7) - 2(3ab - a²... |
223 | [{"role": "user", "content": "$a=0$ is the condition for the complex number $z=a+bi$ ($a, b \\in \\mathbb{R}$) to be a purely imaginary number ( ).\n\nA: Sufficient but not necessary condition \nB: Necessary but not sufficient condition \nC: Necessary and sufficient condition \nD: Neither sufficient nor necessary co... |
230 | [{"role": "user", "content": "Evaluate $\\cos 420^{\\circ} + \\sin 330^{\\circ}$.\n\nA: $1$\n\nB: $-1$\n\nC: $\\dfrac{1}{2}$\n\nD: $0$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to evaluate cos 420 degrees plus sin 330 degrees. Hmm, first, I remember that trigonometric functions are periodi... |
236 | [{"role": "user", "content": "In the book \"Nine Chapters on the Mathematical Art,\" there is a mathematical problem stated as follows: During the Qingming Festival outing to the park, a total of eight boats were taken. Each large boat holds six people, each small boat holds four people. There were thirty-eight student... |
234 | [{"role": "user", "content": "Two pipes A and B can fill a tank in 10 hours and some hours respectively. If both the pipes are opened simultaneously, the tank will be filled in approximately 6 hours. How much time will pipe B take to fill the tank alone?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. ... |
241 | [{"role": "user", "content": "Jackson is making dinner. He makes a salad out of lettuce (50 calories), carrots (twice the calories of the lettuce) and dressing (210 calories). He also makes a pizza with 600 calories for the crust, 1/3 the crust's calories for the pepperoni, and 400 calories for the cheese. If Jackson e... |
226 | [{"role": "user", "content": "Two stations p and q are 200 km apart on a straight track. One train starts from p at 7 a.m. and travels towards q at 20 kmph. Another train starts from q at a certain time and travels towards p at a speed of 25 kmph. They meet at 12. At what time did the second train start from station q?... |
176 | [{"role": "user", "content": "To traverse a straight path 10 meters long, a flea uses the following strategy: each day, it covers half of the remaining distance. Thus, it covers 5 meters on the first day, 2.5 meters on the second, and so on (the size of the flea can be disregarded).\n\n(a) How many meters will it have ... |
238 | [{"role": "user", "content": "Calculate the volume of the body bounded above by the surface \\(z = xy^2\\) and below by the rectangle \\(0 \\leq x \\leq 1\\), \\(0 \\leq y \\leq 2\\)."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the volume of the body bounded above by z = xy² and belo... |
248 | [{"role": "user", "content": "The slope angle of the tangent line to the graph of the function $f(x) = \\ln(x^2+1)$ at the point $(1, f(1))$ is \nA: 0\nB: $\\frac{\\pi}{2}$\nC: $\\frac{\\pi}{3}$\nD: $\\frac{\\pi}{4}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the slope an... |
198 | [{"role": "user", "content": "Compute $\\gcd(37^{11} + 1, 37^{11} + 37^3 + 1)$."}, {"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 compute the greatest common divisor of two ... |
225 | [{"role": "user", "content": "Find the variance of the discrete random variable $X$ that is distributed according to the Poisson distribution:\n\n$$\n\\begin{array}{ccccccc}\nX & 0 & 1 & 2 & \\cdots & k & \\cdots \\\\\nP & \\mathrm{e}^{-\\lambda} & \\lambda \\mathrm{e}^{-\\lambda} / 1! & \\lambda^{2} \\mathrm{e}^{-\\la... |
235 | [{"role": "user", "content": "The line $y=kx-2$ intersects the parabola $y^2=8x$ at points A and B, and the x-coordinate of the midpoint of AB is 2. Find the value of $k$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that the line y = kx - 2 intersects the parabola y² = 8x at points... |
204 | [{"role": "user", "content": "Let $f(x) = x^3 - 1$ and $g(x) = 3x^2 + 3x + 1$. What is $g(f(-3))$?"}, {"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 g(f(-3)), which mea... |
256 | [{"role": "user", "content": "Given sets $M=\\{2, 4\\}$, $N=\\{1, 2\\}$, and $P=\\{x|x= \\frac{a}{b}, a\\in M, b\\in N\\}$, then the number of subsets of set $P$ is ( )\n\nA: 3 \nB: 4 \nC: 8 \nD: 16"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about finding the number of subsets o... |
242 | [{"role": "user", "content": "A unit has 200 employees. Now, 40 employees need to be selected as a sample using the systematic sampling method. All employees are randomly numbered from 1 to 200 and evenly divided into 40 groups according to their numbers in order (1-5, 6-10, ..., 196-200). If the number drawn from the ... |
247 | [{"role": "user", "content": "A team of 60 workers constructed a bridge in 5 days working at the same efficiency. If the subsequent team worked at 80% efficiency and consisted of 40 workers, how many days would it have taken this team to complete an identical bridge?"}, {"role": "assistant", "content": "<think>\n\nOkay... |
191 | [{"role": "user", "content": "Flatville modifies its bicycle license plates which initially contain three letters: the first from $\\{B, F, K, S, Z\\}$, the second from $\\{E, U, Y\\}$, and the third from $\\{G, J, Q, V\\}$. To increase the number of plates, they add two new letters. These new letters can either be bot... |
213 | [{"role": "user", "content": "The expression $2y^2 - 5y - 12$ can be written as $(2y + a)(y + b),$ where $a$ and $b$ are integers. What is $a - b$?"}, {"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... |
224 | [{"role": "user", "content": "Let $a$ and $b$ be the roots of the equation $x^2 - 6x + 8 = 0$. Compute:\n\\[a^2 + a^5 b^3 + a^3 b^5 + b^2.\\]"}, {"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.\n... |
156 | [{"role": "user", "content": "If the integer \\( n \\) is neither a multiple of 2 nor a multiple of 5, prove that \\( n \\) must be able to divide a number composed entirely of the digit 1."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct... |
260 | [{"role": "user", "content": "Jim spends 8 hours scuba diving. In that time he finds a treasure chest with 100 gold coins in it. He also finds some smaller bags that have half as much gold each. He finds 25 gold coins per hour. How many smaller bags did he find?"}, {"role": "assistant", "content": "<think>\n\nOkay, let... |
254 | [{"role": "user", "content": "m = { - 9 , - 7 , - 5 , - 3 , 0, 5 , 7 } \nt = { - 8 , - 6 , - 2 , 0, 3 , 4 , 6 , 7 }\n\nIf an integer is to be randomly selected from set m above and an integer is to be randomly selected from set t above, what is the probability that the product of the two integers will be negative?"}, {... |
263 | [{"role": "user", "content": "The price of rice falls by 20%. With the money that was sufficient to buy a certain amount of rice previously, now 25 kg of rice can be bought. How much rice could be bought previously with the same amount of money?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure ... |
237 | [{"role": "user", "content": "Find the maximum value of $3 \\cos x + 4 \\sin x$ over all angles $x$."}, {"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 to think about it.\nWell, so I need to find the maximum value... |
266 | [{"role": "user", "content": "Among the following numbers, the positive integers are:\n\nA: $3$\n\nB: $2.1$\n\nC: $0$\n\nD: $-2$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The question is asking which of the given numbers are positive integers. The options are A: 3, B: 2.1, C: 0, D: -2. \n\nFirst,... |
261 | [{"role": "user", "content": "The zero of the function $f(x) = 1 - \\log_{2}x$ is ( ) \nA: $(1, 1)$ \nB: $1$ \nC: $(2, 0)$ \nD: $2$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the zero of the function \\( f(x) = 1 - \\log_{2}x \\). Hmm, first, I need to remember what ... |
210 | [{"role": "user", "content": "Buratino calculated the time accurately and left Papa Carlo's house at 13:40 to reach the Field of Miracles and plant 4 coins exactly at sunset. If he had walked $25 \\%$ faster, he would have arrived at the Field of Miracles 1.5 hours earlier and waited. At what time did Buratino arrive a... |
244 | [{"role": "user", "content": "At North High School, 2200 students have choices among basketball, football, and baseball. At South Academy, there are 2600 students. In the two schools combined, the percentage of students who prefer basketball is:\n$\\text{(A)}\\ 26\\% \\qquad \\text{(B)}\\ 28\\% \\qquad \\text{(C)}\\ 30... |
157 | [{"role": "user", "content": "As shown in the figure, the side length of square $\\mathrm{ABCD}$ is $10$, and $O$ is its center. $O E \\perp O F$. Find the area of the shaded region."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and co... |
192 | [{"role": "user", "content": "In an isosceles trapezoid with bases \\(a = 21\\), \\(b = 9\\) and height \\(h = 8\\), find the radius of the circumscribed circle."}, {"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 ... |
271 | [{"role": "user", "content": "One fourth of one third of two fifth of a number is 16. What is the value of two fifth of that number?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem step by step. The question says: \"One fourth of one third of two fifth of a number is 16. What is th... |
269 | [{"role": "user", "content": "Given the sets $A=\\{-2,-1,0,1,2\\}$ and $B=\\{x|x^{2}\\leqslant 1\\}$, find the intersection $A\\cap B=$ .\n\nA: $\\{-2,-1,0,1\\}$\n\nB: $\\{-1,1\\}$\n\nC: $\\{-1,0\\}$\n\nD: $\\{-1,0,1\\}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the intersection o... |
267 | [{"role": "user", "content": "In the plane rectangular coordinate system $xOy$, it is known that the initial side of angle $\\alpha$ is the non-negative half-axis of the $x$-axis, and the terminal side passes through the point $P(-1,2)$. Then $\\cos(\\pi -\\alpha)=$\n\nA: $\\frac{\\sqrt{5}}{5}$\n\nB: $\\frac{2\\sqrt{5}... |
193 | [{"role": "user", "content": "Given two linear functions \\( f(x) \\) and \\( g(x) \\) such that the graphs \\( y = f(x) \\) and \\( y = g(x) \\) are parallel lines that are not parallel to the coordinate axes. Find the minimum value of the function \\( 3(g(x))^2 + 2 f(x) \\), given that the minimum value of the functi... |
262 | [{"role": "user", "content": "A student was asked to find 4 / 5 of a number. But the student divided the number by 4 / 5, thus the student got a certain amount more than the correct answer. The number is 60.00000000000002. How much more did the student get than the correct answer?"}, {"role": "assistant", "content": "<... |
199 | [{"role": "user", "content": "Given that $x_{1}, x_{2}$ are two adjacent zeros of the function $f(x) = 4\\cos{\\omega x}\\sin(\\omega x + \\frac{\\pi}{6}) + 1$, and it satisfies $|x_{1} - x_{2}| = \\pi$, where $\\omega > 0$.\n\n(Ⅰ) Find the value of $\\omega$;\n\n(Ⅱ) Find the maximum and minimum values of $f(x)$ in the... |
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