__src_index__ int64 0 172k | messages stringlengths 375 66.5k |
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63 | [{"role": "user", "content": "Sally had 27 Pokemon cards. Dan has some new Pokemon cards. Sally bought 20 Pokemon cards. Now, Sally has 6 more Pokemon cards than Dan has. How many Pokemon cards does Dan have?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out how many Pokemon cards Dan has. L... |
29 | [{"role": "user", "content": "Jimmy decides to make sandwiches for a picnic. He makes 8 sandwiches in total, using two slices of bread each. How many packs of bread does he need to buy to make these sandwiches, assuming he starts with no bread and each pack has 4 slices of bread in it?"}, {"role": "assistant", "conte... |
39 | [{"role": "user", "content": "Dilan, Martha, Phillip, and Veronica went to the park together to have some fun. They all had a different number of marbles. At the end of the day, they redistributed the marbles so they each had 15 marbles. If Dilan had 14 marbles, Martha had 20 marbles, and Veronica had 7 marbles, how ma... |
44 | [{"role": "user", "content": "David obtained 96 marks in English, 98 in Mathematics, 99 in Physics, some marks in Chemistry, and 98 in Biology. His average marks are 98.2. What are his marks in Chemistry?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. David has marks in five subjects: English, Mathema... |
46 | [{"role": "user", "content": "Given that an interior angle of a regular polygon is $144^{\\circ}$, then the number of sides of this regular polygon is ( )\n\nA: $12$\n\nB: $10$\n\nC: $8$\n\nD: $6$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that an interior angle of a regular polyg... |
15 | [{"role": "user", "content": "Factorize: $x^{3}-6x^{2}+9x=\\_\\_\\_\\_\\_\\_.$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to factorize the polynomial \\( x^3 - 6x^2 + 9x \\). Hmm, first, I remember that when factoring polynomials, the first step is usually to look for a greatest common fact... |
4 | [{"role": "user", "content": "Find all solutions to the equation $\\displaystyle\\sqrt[3]{3 - \\frac{x}{3}} = -2$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to solve the equation cube root of (3 minus x over 3) equals negative 2. Hmm, cube roots can be tricky, but I remember that to solve ... |
45 | [{"role": "user", "content": "What is the least positive multiple of 25 that is greater than 500?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the least positive multiple of 25 that is greater than 500. Hmm, first, I need to remember what a multiple of 25 is. A multiple of ... |
42 | [{"role": "user", "content": "Casey is going to stay at a motel while she works her summer job as a ski instructor. The hotel charges a certain amount per week or $1000/month. Casey will be staying 3 months, each with exactly 4 weeks. She saves $360 by paying monthly. What is the weekly charge for the motel?"}, {"role"... |
9 | [{"role": "user", "content": "Compute $\\cos 225^\\circ$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to compute cos 225 degrees. Hmm, 225 degrees. First, I should figure out where 225 degrees is on the unit circle. I know that 180 degrees is the angle pointing to the left along the x-axis, ... |
60 | [{"role": "user", "content": "Jason drives past 3 convenience stores on his way to work. The distance between the first store and the second store is 6 miles. The distance between the second store and third store is 2/3rds longer than the distance between the first two stores. The distance from his house to the first s... |
22 | [{"role": "user", "content": "At its Grand Opening, the Guthrie Market distributed two different types of souvenirs. One type cost 20 cents each, and the other type cost a certain amount. One thousand souvenirs were distributed in all, and the cost of these souvenirs was 220 dollars. They distributed 400 of the souveni... |
6 | [{"role": "user", "content": "Julian is writing a comic book. On average, his story has 280 frames per page. In his 25-page book, 10 pages have 305 frames, 7 pages have 250 frames, and the remaining pages have the average number of frames. How many frames will there be in total in his comic book?"}, {"role": "assistant... |
32 | [{"role": "user", "content": "The molecular weight of a certain substance is 74. What is the molecular weight of Bleach?"}, {"role": "assistant", "content": "<think>\n\nOkay, the user is asking about the molecular weight of bleach, but they've given the molecular weight of \"a certain substance\" as 74. Hmm, that's con... |
13 | [{"role": "user", "content": "Tom decides to open a theater. He knows it will cost $5 per square foot of space that he needs and he needs 12 square feet for every seat in his theater. He wants a 500 seat theater. He also realizes construction will cost twice as much as the land. He has a partner who covers a certain pe... |
40 | [{"role": "user", "content": "The following line is parameterized, so that its direction vector is of the form \\(\\begin{pmatrix} b \\\\ 1 \\end{pmatrix}\\). Find $b$.\n\nConsider a line passing through the points \\(\\begin{pmatrix} -4 \\\\ 6 \\end{pmatrix}\\) and \\(\\begin{pmatrix} 3 \\\\ -3 \\end{pmatrix}\\)."}, {... |
57 | [{"role": "user", "content": "If $3x - y = 9$ and $x + 4y = 11$, what is the value of $x$?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value of x given these two equations: 3x - y = 9 and x + 4y = 11. Hmm, so it's a system of linear equations. I remember there are a couple of met... |
0 | [{"role": "user", "content": "Consider the terms of an arithmetic sequence: $-\\frac{1}{3}, y+2, 4y, \\ldots$. Solve for $y$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to solve for y in this arithmetic sequence: -1/3, y+2, 4y, ... Hmm, arithmetic sequence means the difference between conse... |
19 | [{"role": "user", "content": "A vessel of capacity 2 liters has a certain percentage of alcohol and another vessel of capacity 6 liters has 40% alcohol. The total liquid of 8 liters was poured out into a vessel of capacity 10 liters, and the rest of the vessel was filled with water. The new concentration of the mixture... |
67 | [{"role": "user", "content": "Given the sequence ${a_n}$, the sum of the first n terms, S<sub>n</sub>, is equal to $n^2$. Find the value of $a_3^2 - a_2^2$.\nA: 9\nB: 16\nC: 21\nD: 11"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that the sum of the first n terms of the sequence {a_n... |
33 | [{"role": "user", "content": "We flip a fair coin 12 times. What is the probability that we get heads in exactly 9 of the 12 flips?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is: We flip a fair coin 12 times. What's the probability of getting exactly 9 heads? Hmm, right. So, first, I n... |
80 | [{"role": "user", "content": "Eric has a chicken farm with some chickens. His chickens lay 3 eggs each day. After 3 days, Eric collected 36 eggs. How many chickens does Eric have on his farm?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about Eric's chicken farm. He has some chickens,... |
50 | [{"role": "user", "content": "Given the plane vectors $\\overrightarrow{a}$, $\\overrightarrow{b}$, $\\overrightarrow{c}$, where $\\overrightarrow{a}=(1,2)$\n\n(Ⅰ) If $|\\overrightarrow{c}|=3\\sqrt{5}$ and $\\overrightarrow{a} \\parallel \\overrightarrow{c}$, find the coordinates of $\\overrightarrow{c}$;\n\n(Ⅱ) If $|\... |
79 | [{"role": "user", "content": "To earn money for her new computer, Tina sells handmade postcards. In a day, she can make some postcards. For each postcard sold, Tina gets $5. Tina earned $900 if she managed to sell all the postcards she made every day for 6 days. How many postcards can Tina make in a day?"}, {"role": "a... |
47 | [{"role": "user", "content": "if p is the product of the integers from 1 to 35 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the greatest integer k such that 3^k is a factor of the product of int... |
70 | [{"role": "user", "content": "Alice's white water rafting class is composed of some students and 10 instructors, including herself. She has 20 life vests on hand. 20% of her students are bringing life vests. Alice will need to get 22 more life vests so that the entire class has one. How many students are in Alice's cla... |
66 | [{"role": "user", "content": "For the nonzero numbers $a$, $b$, and $c$, define $$\n\\text{{J}}(a,b,c) = \\frac{a}{b} + \\frac{b}{c} + \\frac{c}{a}.\n$$ Find $\\text{{J}}(3,18, 27)$."}, {"role": "assistant", "content": "<think>\n\nGot it, let's see. The problem is asking for J(3, 18, 27) where J(a, b, c) is defined as ... |
82 | [{"role": "user", "content": "Nine families have an average of 3 children per family. If exactly three of these families are childless, what is the average number of children in the families with children?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by step. So, the q... |
55 | [{"role": "user", "content": "Solve the inequality\n\\[ -8x^2 + 6x - 1 < 0. \\]"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to solve the inequality -8x² + 6x - 1 < 0. Hmm, quadratic inequalities can be tricky, but I remember that first, I should probably find the roots of the corresponding e... |
87 | [{"role": "user", "content": "The reciprocal of the real number $-2$ is ( )\n\nA: $2$\n\nB: $-2$\n\nC: $\\frac{1}{2}$\n\nD: $-\\frac{1}{2}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The question is asking for the reciprocal of the real number -2. Hmm, reciprocal... I remember that the reciprocal ... |
69 | [{"role": "user", "content": "Given a complex number $z$ satisfying $\\frac {2i}{z}=- \\sqrt {3}-i$ (where $i$ is the imaginary unit), then $z$ equals\n\nA: $1$\n\nB: $-1$\n\nC: $- \\frac {1}{2}- \\frac { \\sqrt {3}}{2}i$\n\nD: $- \\frac {1}{2}+ \\frac { \\sqrt {3}}{2}i$"}, {"role": "assistant", "content": "<think>\n\n... |
75 | [{"role": "user", "content": "If the tangent line to the curve $y=e^{x}$ at $x=1$ is perpendicular to the line $2x+my+1=0$, then $m=$ .\nA: $-2e$\nB: $2e$\nC: $-\\dfrac{2}{e}$\nD: $\\dfrac{2}{e}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about finding the value of \\( m \\) such t... |
7 | [{"role": "user", "content": "If an arc of $60^{\\circ}$ on circle $C$ has the same length as an arc of $40^{\\circ}$ on circle $D$, what is the ratio of the area of circle $C$ to the area of circle $D$? Express your answer as a common fraction."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or chall... |
64 | [{"role": "user", "content": "The correct statement is \\_\\_\\_\\_\\_\\_ (only fill in the number of the correct statement)\n$①$ If set $A={y|y=x-1}$, $B={y|y=x^{2}-1}$, then $A∩B={(0,-1)}$, $((1,0))$;\n$②$ $y= \\sqrt {x-3}+ \\sqrt {2-x}$ is a function expression;\n$③$ $y= \\dfrac { \\sqrt {1-x^{2}}}{3-|3-x|}$ is a fu... |
28 | [{"role": "user", "content": "Given \\\\(f(x)=2a-\\sin x\\\\), then \\\\(f''(x)=\\\\) \nA: \\\\(\\cos x\\\\) \nB: \\\\(-\\cos x\\\\) \nC: \\\\(2+\\cos x\\\\) \nD: \\\\(2-\\cos x\\\\)"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the second derivative of the function f(x)... |
73 | [{"role": "user", "content": "The greatest prime number that is a divisor of $16,385$ is $3$ because $16,385 = 3 \\times 5 \\times 1093$. What is the sum of the digits of the greatest prime number that is a divisor of $16,385$?\n$\\textbf{(A)} \\: 5\\qquad\\textbf{(B)} \\: 8\\qquad\\textbf{(C)} \\: 9\\qquad\\textbf{(D)... |
68 | [{"role": "user", "content": "In acute triangle $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. If $a=4$, $b=5$, and the area of $\\triangle ABC$ is $5 \\sqrt {3}$, find $|AB|$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about an... |
74 | [{"role": "user", "content": "If the circle $(x-a)^2+(x+4)^2=9$ is tangent to the y-axis, then $a=$ ___."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a circle given by the equation \\((x - a)^2 + (x + 4)^2 = 9\\), and it's tangent to the y-axis. We need to find the value of \\(a... |
1 | [{"role": "user", "content": "Suppose that $g(x) = 5x - 3$. What is $g^{-1}(g^{-1}(14))$?"}, {"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 inverse of g inverse of 14... |
24 | [{"role": "user", "content": "When \\( a < -1 \\), the nature of the roots for the equation\n$$\n\\left(a^{3}+1\\right) x^{2}+\\left(a^{2}+1\\right) x-(a+1)=0\n$$\nis:\n(A) Two negative roots.\n(B) One positive root and one negative root, with the absolute value of the negative root being larger.\n(C) One positive root... |
34 | [{"role": "user", "content": "How many distinct, positive factors does $1320$ have?"}, {"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 number of distinct positive fa... |
102 | [{"role": "user", "content": "Jessa needs to make cupcakes for 3 fourth-grade classes that each have 30 students and a P.E. class with a certain number of students. She needs to make 140 cupcakes. How many students are in the P.E. class?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Jessa needs to ma... |
71 | [{"role": "user", "content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given that $b=3$, $c=2\\sqrt{3}$, and $A=30^{\\circ}$, find the values of angles $B$, $C$, and side $a$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find a... |
35 | [{"role": "user", "content": "Observe the pattern of the following equations and answer the following questions: \nThe first equation: $1^{2}+2^{2}-3^{2}=1\\times a-b$, \nThe second equation: $2^{2}+3^{2}-4^{2}=2\\times 0-b$, \nThe third equation: $3^{2}+4^{2}-5^{2}=3\\times 1-b$, \nThe fourth equation: $4^{2}+5^{2... |
99 | [{"role": "user", "content": "If \\( f(x) = 5 - 4x \\) and \\( g(x) = x^2 + 2 \\), find \\( f(g(2)) \\)."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find f(g(2)). Hmm, first, I remember that when you have composite functions like f(g(x)), you have to evaluate the inner function first and ... |
76 | [{"role": "user", "content": "The value range of the function $f(x)=\\sin x-\\cos \\left(x+ \\frac {\\pi }{6}\\right)$ is ( )\nA: $[-2,2]$\nB: $[- \\sqrt {3}, \\sqrt {3}]$\nC: $[-1,1]$\nD: $[- \\frac { \\sqrt {3}}{2}, \\frac { \\sqrt {3}}{2}]$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to ... |
93 | [{"role": "user", "content": "In a class of 50 students, numbered from 1 to 50, the class is equally divided into 5 groups according to their numbers in ascending order. Using systematic sampling, 5 students are selected for a survey. If the student with number 4 is selected from the first group and the student with nu... |
106 | [{"role": "user", "content": "Find the value of adding 3 to the number of diagonals in the rectangle."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the value of adding 3 to the number of diagonals in a rectangle. First, I need to remember how many diagonals a rectangle has. ... |
103 | [{"role": "user", "content": "In the arithmetic sequence $\\{a_n\\}$, $a_2 = -5$ and $d = 3$. Find $a_1$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the first term \\( a_1 \\) of an arithmetic sequence where the second term \\( a_2 \\) is -5 and the common difference \\( d \\) is 3.... |
104 | [{"role": "user", "content": "If the linear function is $y=2x-3$, and it is shifted $3$ units upwards, the new equation of the graph is ______."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about shifting a linear function upwards. The original function is y = 2x - 3, and we need to sh... |
23 | [{"role": "user", "content": "Let \\( p = 2^{3009}, q = 3^{2006}, \\) and \\( r = 5^{1003} \\). Which of the following statements is true?\n(A) \\( p < q < r \\)\n(B) \\( p < r < q \\)\n(C) \\( q < p < r \\)\n(D) \\( r < p < q \\)\n(E) \\( q < r < p \\)"}, {"role": "assistant", "content": "<think>\n\nThis is a complex ... |
30 | [{"role": "user", "content": "How many two-digit positive integers are congruent to 1 (mod 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 the problem is asking: how many two-di... |
97 | [{"role": "user", "content": "Given vectors $\\overrightarrow{a}, \\overrightarrow{b}$ that satisfy $|\\overrightarrow{a}| = 1, |\\overrightarrow{b}| = 2$, and $\\overrightarrow{a} \\cdot \\overrightarrow{b} = -\\frac{1}{2}$, find:\n\n1. The value of $|\\overrightarrow{a} + \\overrightarrow{b}|$;\n2. The cosine value o... |
3 | [{"role": "user", "content": "Given the functions $f(x) = \\log_a(1+x)$ and $g(x) = \\log_a(1-x)$, where $a>0$ and $a \\neq 1$.\n1. Find the domain of the function $f(x) - g(x)$.\n2. Determine the parity of the function $f(x) - g(x)$.\n3. Find the range of $x$ for which $f(x) - g(x) > 0$."}, {"role": "assistant", "cont... |
25 | [{"role": "user", "content": "Three vertices of a cube are $A = (5, 9, 6)$, $B = (5, 14, 6)$, and $C = (5, 14, 11)$. What is the surface area of the cube?"}, {"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 thin... |
115 | [{"role": "user", "content": "Find the largest whole number such that eight times the number is less than 120.\n$\\text{(A)} \\ 12 \\qquad \\text{(B)} \\ 13 \\qquad \\text{(C)} \\ 14 \\qquad \\text{(D)} \\ 15 \\qquad \\text{(E)} \\ 16$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is aski... |
31 | [{"role": "user", "content": "Given the following four propositions: \n① The negation of the proposition \"For all $x \\in \\mathbb{R}, \\cos(x) > 0$\" is \"There exists an $x \\in \\mathbb{R}$ such that $\\cos(x) \\leq 0$\". \n② If $0 < a < 1$, then the equation $x^2 + a^x - 3 = 0$ has only one real root. \n③ For a... |
20 | [{"role": "user", "content": "Given that the sum of the first $n$ terms of a sequence $\\{a\\_n\\}$ is $S\\_n$, and $S\\_n=2^{n}a\\_n-1$, find the sum of the first $n$ terms of the sequence $\\{\\frac{a\\_n}{a_{n+1}}\\}$, denoted as $T\\_n=$ `____`."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or c... |
101 | [{"role": "user", "content": "Given that $\\sin ( \\frac {π}{6}+α)= \\frac {1}{3}$, find the value of $\\cos ( \\frac {2π}{3}-2α)$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that sin(π/6 + α) = 1/3, and we need to find cos(2π/3 - 2α). Hmm, trigonometric identities. Let me recall ... |
117 | [{"role": "user", "content": "sheela deposits rs . 2500 in bank savings account . if this is 25 % of her monthly income . what is her monthly income in ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says Sheela deposits Rs. 2500 in her bank savings account, and that amount is 25% of her ... |
17 | [{"role": "user", "content": "Consider the product of $x^5$, $x^2 + \\frac{1}{x^2}$, and $1 + \\frac{2}{x} + \\frac{3}{x^2}$. Determine the degree of the resulting polynomial.\n$\\textbf{(A)}\\ 3\\qquad \\textbf{(B)}\\ 5\\qquad \\textbf{(C)}\\ 6\\qquad \\textbf{(D)}\\ 7\\qquad \\textbf{(E)}\\ 8$"}, {"role": "assistant"... |
111 | [{"role": "user", "content": "Janice adds 2 tablespoons of koolaid powder and 16 tablespoons of water to a jug. She leaves it out long enough for 4 tablespoons of water to evaporate. Then she quadruples the amount of water in the jug. What percentage of the liquid in the jug is koolaid powder?"}, {"role": "assistant", ... |
43 | [{"role": "user", "content": "The sum of the first 3000 terms of a geometric sequence is 500. The sum of the first 6000 terms is 950. Find the sum of the first 9000 terms."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answe... |
119 | [{"role": "user", "content": "Below is the graph of $y = a \\sin (bx + c) + d$ for some positive constants $a, b, c,$ and $d$. The graph oscillates between 5 and -3. Find $d$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a sine function: y = a sin(bx + c) + d. They tell us it os... |
107 | [{"role": "user", "content": "A local store sells 9 pencils and 5 notebooks for $\\$3.45$. It also sells 6 pencils and 4 notebooks for $\\$2.40$. How much would 18 pencils and 9 notebooks cost?\nA) $\\$6.25$\nB) $\\$6.50$\nC) $\\$6.75$\nD) $\\$7.00$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I nee... |
61 | [{"role": "user", "content": "Given the function $f(x)=-x^{5}-3x^{3}-5x+3$, if $f(a)+f(a-2) > 6$, then the range of the real number $a$ is $(\\quad)$ \nA: $(-\\infty,3)$ \nB: $(3,+\\infty)$ \nC: $(1,+\\infty)$ \nD: $(-\\infty,1)$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem ... |
36 | [{"role": "user", "content": "Find the product of the solutions of the equation: $|z| = 3(|z| - 2)$."}, {"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.\nWell, so I need to find the product of th... |
123 | [{"role": "user", "content": "Every time Carl earned $0.50 he would go to the corner market and buy a candy bar. Carl's neighbor said he would pay him $0.75 every week for taking out his trash. At the end of four weeks, how many candy bars will Carl be able to buy?"}, {"role": "assistant", "content": "<think>\n\nOkay... |
121 | [{"role": "user", "content": "Among the following radicals, which one can be combined with $\\sqrt{3}$?\n\nA: $\\sqrt{30}$\n\nB: $\\sqrt{\\frac{1}{2}}$\n\nC: $\\sqrt{8}$\n\nD: $\\sqrt{27}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The question is asking which of the given radicals can be combined... |
94 | [{"role": "user", "content": "In triangle \\(ABC\\), the lengths are \\(AB = 6\\), \\(AC = 10\\). The point \\(M\\) is the midpoint of \\(BC\\), and \\(AM = 5\\). Determine the length of \\(BC\\).\n\\(\\textbf{(A)}\\ 2\\sqrt{45}\\)\n\\(\\textbf{(B)}\\ 2\\sqrt{43}\\)\n\\(\\textbf{(C)}\\ 9\\)\n\\(\\textbf{(D)}\\ 2\\sqrt{... |
78 | [{"role": "user", "content": "Given ellipse $C_{1}: \\dfrac {x^{2}}{a^{2}}+ \\dfrac {y^{2}}{b^{2}}=1(a > b > 0)$ and hyperbola $C_{2}: x^{2}-y^{2}=4$ have the same right focus $F_{2}$. Point $P$ is a common point of $C_{1}$ and $C_{2}$. If $|PF_{2}|=2$, then the eccentricity of the ellipse $C_{1}$ equals \\_\\_\\_\\_\\... |
127 | [{"role": "user", "content": "Sandy bought 65 books for $1080 from one shop and 55 books for $840 from another shop. What is the average price that Sandy paid per book?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the average price Sandy paid per book. So, first, I need to ... |
18 | [{"role": "user", "content": "The sum of three numbers $a$, $b$, and $c$ is 120. If we increase $a$ by 8, decrease $b$ by 3 and multiply $c$ by 3, the three resulting numbers are equal. What is the value of $b$?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficu... |
130 | [{"role": "user", "content": "A woman is 42 years of age and her daughter is 8 years old. In a certain number of years, the mother will be three times as old as her daughter. How many years will it take for the mother to be three times as old as her daughter?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's ... |
37 | [{"role": "user", "content": "Given that \\(1 \\leq x, y, z \\leq 6\\), how many cases are there in which the product of natural numbers \\(x, y, z\\) is divisible by 10?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer... |
132 | [{"role": "user", "content": "How many plums will balance one pear, given that 3 apples and one pear weigh as much as 10 plums, and one apple and 6 plums balance one pear? Assume that fruits of the same kind have the same weight."}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out how many plu... |
5 | [{"role": "user", "content": "In $\\triangle ABC$, the lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given that $\\cos \\frac{C}{2} = \\frac{\\sqrt{5}}{3}$ and $a \\cos B + b \\cos A = 2$, find the maximum area of $\\triangle ABC$."}, {"role": "assistant", "content": "<th... |
86 | [{"role": "user", "content": "Suppose $\\sin y = 0$ and $\\cos(y+w) = -\\frac{1}{2}$. What is the smallest possible positive value of $w,$ in radians?"}, {"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 ab... |
110 | [{"role": "user", "content": "the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 100 visitors who did... |
129 | [{"role": "user", "content": "Given that $\\sin(\\frac{\\pi}{6} + \\alpha) = \\frac{1}{3}$, find the value of $\\cos(\\frac{2\\pi}{3} - 2\\alpha)$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that sin(π/6 + α) = 1/3, and we need to find cos(2π/3 - 2α). Hmm, trigonometric identities... |
8 | [{"role": "user", "content": "Given that $P$ is any point on the circle $C$: $(x-2)^{2}+(y-2)^{2}=1$, and $Q$ is any point on the line $l$: $x+y=1$, find the minimum value of $| \\overrightarrow{OP}+ \\overrightarrow{OQ}|$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem step by st... |
26 | [{"role": "user", "content": "Suppose that $A, B, C, D$ are four points in the plane, and let $Q, R, S, T, U, V$ be the respective midpoints of $AB, AC, AD, BC, BD, CD$. If $QR = 2001$, $SU = 2002$, and $TV = 2003$, find the distance between the midpoints of $QU$ and $RV$."}, {"role": "assistant", "content": "<think>\n... |
89 | [{"role": "user", "content": "Find all real numbers $x$ so that the product $(x + i)((x + 1) + i)((x + 2) + i)$ is pure imaginary. Enter all the solutions, separated by commas."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct... |
139 | [{"role": "user", "content": "find the number of terms in an arithmetic progression with the first term 2 and the last term being 62 , given that common difference is 2 ."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the number of terms in an arithmetic progression where the first term... |
72 | [{"role": "user", "content": "Define a regular \\(n\\)-pointed star as described in the original problem, but with a modification: the vertex connection rule skips by \\(m\\) steps where \\(m\\) is coprime with \\(n\\) and \\(m\\) is not a multiple of \\(3\\). How many non-similar regular 120-pointed stars adhere to th... |
138 | [{"role": "user", "content": "The slope of the tangent line to $f(x) = x^3 + x^2 + 1$ at $x = 1$ is ( )\nA: 2\nB: 3\nC: 4\nD: 5"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the slope of the tangent line to the function f(x) = x³ + x² + 1 at x = 1. Hmm, right. I remember tha... |
136 | [{"role": "user", "content": "a positive integer , which when added to 1000 , gives a sum which is greater than when it is multiplied by 1000 . this positive integer is"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem. So, the question is: find a positive integer that, when add... |
88 | [{"role": "user", "content": "How many four-digit numbers satisfy the property that the second digit is the average of the first and the third digits?"}, {"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 ab... |
125 | [{"role": "user", "content": "The sum of the first three terms of a geometric sequence $\\{a_n\\}$ is equal to three times its first term. Then, the common ratio of this geometric sequence is __________."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that the sum of the first three te... |
109 | [{"role": "user", "content": "The number of positive integers $k$ for which the equation\n\\[kx-18=3k\\]\nhas an integer solution for $x$ is:\nA) 3\nB) 4\nC) 5\nD) 6\nE) 7"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answe... |
105 | [{"role": "user", "content": "In an examination, there are 100 questions divided into 3 groups A, B, and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in some group carries a certain number of marks. It is known... |
95 | [{"role": "user", "content": "Given that the sum of the first $n$ terms of the sequence ${a\\_n}$ is $S\\_n$, and $S\\_n = 2a\\_n - n$, find the maximum value of $n$ that satisfies $a\\_n \\leq 10n$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provid... |
120 | [{"role": "user", "content": "Find the ordered pair $(x, y)$ that satisfies the equations $7x - 50y = 3$ and $3y - x = 5$."}, {"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 ... |
58 | [{"role": "user", "content": "Consider a quadratic polynomial \\[x^2 - tx + q,\\] where the roots \\(r_1\\) and \\(r_2\\) satisfy \\[r_1 + r_2 = r_1^2 + r_2^2 = r_1^4 + r_2^4.\\] Determine the minimum possible value of \\[\\dfrac{1}{r_1^5} + \\dfrac{1}{r_2^5}.\\]"}, {"role": "assistant", "content": "<think>\n\nThis is ... |
149 | [{"role": "user", "content": "The negation of the statement \"All honor students receive scholarships\" is:\nA) All honor students do not receive scholarships\nB) Some honor students do not receive scholarships\nC) No honor students receive scholarships\nD) All honor students receive scholarships"}, {"role": "assistant... |
116 | [{"role": "user", "content": "Find all real numbers \\( x, y, z \\) such that\n\n\\[ x + y + z = 3, \\quad x^2 + y^2 + z^2 = 3, \\quad x^3 + y^3 + z^3 = 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 ... |
144 | [{"role": "user", "content": "Jenny decided to get a cat with her girlfriend. They agreed to split all the costs down the middle except for they would each buy their own toys for the cat. The adoption fee was $50, the vet visits cost $500 for the first year and the monthly cost of food was some amount. She bought $200 ... |
147 | [{"role": "user", "content": "Let $U=\\mathbb{R}$, and $M=\\{x|x^2-2x>0\\}$. Then, the complement of $M$ in $\\mathbb{R}$, denoted as $\\complement_{\\mathbb{R}}M$, is\n\nA: $[0,2]$\n\nB: $(0,2)$\n\nC: $(-\\infty,0)\\cup(2,+\\infty)$\n\nD: $(-\\infty,0]\\cup[2,+\\infty)$"}, {"role": "assistant", "content": "<think>\n\n... |
151 | [{"role": "user", "content": "If the one-variable quadratic equation $x^{2}+2x+2m=0$ has two distinct real roots with respect to $x$, then the range of values for $m$ is ______."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a quadratic equation \\( x^2 + 2x + 2m = 0 \\) having tw... |
133 | [{"role": "user", "content": "Given that $f(x)$ and $g(x)$ are both odd functions, and $F(x) = af(x) + bg(x) + 2$ has a maximum value of 5 on the interval $(0, +\\infty)$ (where $ab \\neq 0$), find the minimum value of $F(x)$ on the interval $(-\\infty, 0)$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's t... |
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