__src_index__ int64 0 172k | messages stringlengths 375 66.5k |
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3,066 | [{"role": "user", "content": "Clive opens a box full of different colored balls. The box contains 6 blue balls, 4 red balls, 3 times as many green balls as blue ones and twice as many yellow ones as red ones. How many balls are in the box Clive opens?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Cli... |
3,054 | [{"role": "user", "content": "The sum of the smallest natural number, the smallest prime number, and the smallest composite number is 6. (Judge true or false)"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says: \"The sum of the smallest natural number, the smallest prime number, and the s... |
3,063 | [{"role": "user", "content": "Let $\\overline{z}$ be the conjugate of the complex number $z$. If $z + \\overline{z} = 3$ and $(z - \\overline{z}) = 3i$ (where $i$ is the imaginary unit), then the sum of the real part and imaginary part of $z$ is ( )\nA: 0\nB: 3\nC: $-3$\nD: 2"}, {"role": "assistant", "content": "<thin... |
2,999 | [{"role": "user", "content": "Given a positive integer \\( n > 1 \\) and a set \\( S \\) with \\( n \\) elements, find the smallest positive integer \\( k \\) such that there exists a collection of subsets \\( A_{1}, A_{2}, \\cdots, A_{k} \\) of \\( S \\) with the property: for any two distinct elements \\( a \\) and \... |
3,064 | [{"role": "user", "content": "Jackson and Brandon both invest $500 in the stock market. Jackson's investment increases in value, while Brandon's is reduced to 20% of the initial value. Jackson has $1900 more than Brandon now. What is the ratio of Jackson's final investment value to his initial investment value?"}, {"ro... |
3,029 | [{"role": "user", "content": "Let the complex number $Z = (m^2 + 3m - 4) + (m^2 - 10m + 9)i$ where $m \\in \\mathbb{R}$,\n1. Calculate the modulus of the complex number $Z$ when $m=0$.\n2. For what values of the real number $m$ is the complex number $Z$ purely imaginary?\n3. For what values of the real number $m$ does ... |
3,044 | [{"role": "user", "content": "Simplify $$\\sqrt {1-2\\sin(π+4)\\cos(π+4)}$$ and choose the correct option:\nA: $\\cos 4 - \\sin 4$\nB: $\\sin 4 - \\cos 4$\nC: $-\\sin 4 - \\cos 4$\nD: $\\sin 4 + \\cos 4$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to simplify this square root expression: √[1 - 2 sin... |
3,069 | [{"role": "user", "content": "Which of the following functions is an odd function?\nA: $y = x + 1$\nB: $y = e^x$\nC: $y = x^2 + x$\nD: $y = x^3$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The question is asking which of the given functions is an odd function. I need to remember what an odd functio... |
3,001 | [{"role": "user", "content": "The number $15!$ ($15$ written in base $10$), when written in the base $16$ system, ends with exactly $k$ zeros. Determine the value of $k$.\nA) 1\nB) 2\nC) 3\nD) 4\nE) 5"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provi... |
3,058 | [{"role": "user", "content": "Given the function $f\\left(x\\right)=x^{3}-ax^{2}$ is not a monotonic function on $\\left[2,4\\right]$, the range of real number $a$ is ____."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about finding the range of real number \\( a \\) such that the func... |
3,065 | [{"role": "user", "content": "The sequence $\\{a_n\\}$ satisfies $a_1=3$, $a_{n+1}= \\frac {a_n-1}{a_n}$. Then $a_{2015}=$ ()\nA: $ \\frac {1}{2}$\nB: $3$\nC: $- \\frac {1}{2}$\nD: $ \\frac {2}{3}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a sequence where the first term is ... |
2,948 | [{"role": "user", "content": "For real numbers \\( x > y > 0 \\) and natural numbers \\( n > k \\), prove the inequality \\(\\left( x^k - y^k \\right)^n < \\left( x^n - y^n \\right)^k\\)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct a... |
3,025 | [{"role": "user", "content": "Marcella has 20 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left?"}, {"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 ... |
3,073 | [{"role": "user", "content": "Given a real number $a > 0$, the expression $\\int_{0}^{a} (a^{2} - x^{2}) \\, dx$ represents ( )\nA: Half the volume of a sphere with radius $a$\nB: Half the surface area of a sphere with radius $a$\nC: Half the area of a circle with radius $a$\nD: The area of the shape formed by the func... |
2,995 | [{"role": "user", "content": "Gavriil saw a squirrel on a tree branch directly opposite him at a distance of 3.75 meters. He decided to feed the squirrel and threw a nut horizontally at a speed of 2.5 m/s directly towards the squirrel. Can the squirrel catch the nut if it can jump rapidly in any direction for a distanc... |
3,056 | [{"role": "user", "content": "Given the set $A=\\{x|-2\\leqslant x\\leqslant 5\\}$ and the set $B=\\{x|p+1\\leqslant x\\leqslant 2p-1\\}$, find the range of values for the real number $p$ such that $A\\cap B=B$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about finding the range of v... |
3,031 | [{"role": "user", "content": "\nKostya planted some number of tulip bulbs along a path. Then Tanya came and planted a new bulb between each pair of neighboring bulbs planted by Kostya. After that, Inna came and planted a new bulb between each pair of neighboring bulbs already planted. Finally, Dima came and did the sam... |
3,041 | [{"role": "user", "content": "A boat moves at a speed of 20 mph in still water. When traveling in a river with a current of 3 mph, it travels 24 miles downstream and then returns upstream to the starting point. Calculate the ratio of the average speed for the entire round trip to the boat's speed in still water.\nA) \\... |
3,076 | [{"role": "user", "content": "What is the remainder when $17^{53}$ is divided by 7?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the remainder when 17^53 is divided by 7. Hmm, modular arithmetic, right? Maybe I can use Fermat's Little Theorem here. Let me remember what that is. Fermat... |
3,038 | [{"role": "user", "content": "Graph the set of points in the coordinate plane whose coordinates satisfy the equation \\(4x^{2} y^{2}=4xy+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.\... |
3,086 | [{"role": "user", "content": "Given a quadratic equation in terms of $x$: $x^{2}-4x-3=0$, with two real roots denoted as $x_{1}$ and $x_{2}$, then $x_{1}+x_{2}=$____."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a quadratic equation: \\(x^2 - 4x - 3 = 0\\). They want the sum of ... |
3,080 | [{"role": "user", "content": "Which of the following numbers is not a perfect square?\n$\\textbf{(A) }6^{210}\\qquad\\textbf{(B) }7^{301}\\qquad\\textbf{(C) }8^{402}\\qquad\\textbf{(D) }9^{302}\\qquad \\textbf{(E) }10^{404}$\n$\\textbf{(A) }6^{210}\\qquad\\textbf{(B) }7^{301}\\qquad\\textbf{(C) }8^{402}\\qquad\\textbf{... |
3,087 | [{"role": "user", "content": "Alicia has some gumballs. Pedro has that many gumballs plus an additional number of gumballs equal to three times the number Alicia has. They put their gumballs in a bowl, and later Pedro takes out 40% of the gumballs to eat. There are 60 gumballs remaining in the bowl. How many gumballs d... |
3,035 | [{"role": "user", "content": "Two classes are planting trees. Each student in the first class plants 3 trees and each student in the second class plants 5 trees. A total of 115 trees are planted. The maximum total number of students in both classes combined is $\\qquad$."}, {"role": "assistant", "content": "<think>\n\n... |
3,081 | [{"role": "user", "content": "Emily's quiz scores so far are: 91, 94, 88, 90, and 101. What score does she need to get on the sixth quiz to make the arithmetic mean of the six scores equal 95?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Emily has taken five quizzes so far with scores 91, 94, 88, 90... |
3,090 | [{"role": "user", "content": "renu can do a piece of work in 6 days , but with the help of her friend suma , she can do it in 3 days . in what time suma can do it alone ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about Renu and Suma working together to do a piece of work. Renu can ... |
3,088 | [{"role": "user", "content": "Consider the quadratic function $f(x) = 2x^2 + 6x + 5$. Determine the minimum value of this function given that it passes through the point $(1, 13)$.\nA) 13\nB) 0.5\nC) -1.5\nD) 5"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says to consider the quadratic f... |
3,039 | [{"role": "user", "content": "For how many bases between three and eight inclusive does the representation of $784_{10}$ have a final digit of 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 i... |
3,024 | [{"role": "user", "content": "Show that the number of paths in $\\mathbb{Z}^{2}$ making $2n$ steps from $(0, 0)$ to $(0, 0)$ is $\\binom{2n}{n}^2$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out how to show that the number of paths in ℤ² making 2n steps from (0, 0) to (0, 0) is (2n choose... |
3,068 | [{"role": "user", "content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given that $A=\\frac{\\pi}{6}$, $a=1$, and $b=\\sqrt{3}$, find the value of $c$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value of side \\( c \... |
3,085 | [{"role": "user", "content": "A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs. 306 less than the sum lent. What was the sum lent?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by step. So, the question i... |
3,079 | [{"role": "user", "content": "Given $\\sin\\alpha= \\frac {12}{13}$, $\\cos\\beta= \\frac {4}{5}$, and $\\alpha$ is an angle in the second quadrant, $\\beta$ is an angle in the fourth quadrant, then $\\sin(\\alpha-\\beta)$ equals to ( )\n\nA: $\\frac {33}{65}$\n\nB: $\\frac {63}{65}$\n\nC: $-\\frac {16}{65}$\n\nD: $... |
3,097 | [{"role": "user", "content": "An inspector rejects 0.08% of the meters as defective. He examined a certain number of meters and rejected 2. How many meters did he examine?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says an inspector rejects 0.08% of the meters as defective, and he reje... |
3,099 | [{"role": "user", "content": "Given $f(x) = \\begin{cases} x^{2}, & x<0 \\\\ 2^{x}-2, & x\\geq 0 \\end{cases}$, then $f(f(-2)) = \\_\\_\\_\\_\\_\\_$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find f(f(-2)). Hmm, first, I should probably figure out what f(-2) is, and then plug that resul... |
2,983 | [{"role": "user", "content": "In the positive sequence $\\{a_{n}\\}$, given that $a_{2}=8$, the point $({a}_{n+1},{a}_{n}^{2}+2{a}_{n})$ lies on the line $y=x$, $b_{n}=\\lg (a_{n}+1)$, where $n\\in N^{*}$. \n$(1)$ Prove that the sequence $\\{b_{n}\\}$ is a geometric sequence; \n$(2)$ Let $S_{n}$ be the sum of the fir... |
2,987 | [{"role": "user", "content": "Let\n\\[ f(x) = \\sqrt{x(80 - x)} + \\sqrt{x(3 - x)} \\]\nfor \\( 0 \\leq x \\leq 3 \\). Let \\( M \\) be the maximum value of \\( f(x) \\), and let \\( x = x_0 \\) be the point where the maximum value is attained. Determine the ordered pair \\( (x_0, M) \\)."}, {"role": "assistant", "cont... |
3,015 | [{"role": "user", "content": "Find the derivatives of the following functions:\n1) $y = x^{3} \\cdot 3^{x}$.\n2) $f(x) = \\sqrt[x]{3} + \\frac{1}{25^{5x}} + 6^{1/x}$; calculate $f^{\\prime}(1)$.\n3) $y = \\ln (\\cos(3x))$.\n4) $r = a^{4} b^{\\prime \\prime} c^{\\prime \\prime} + \\log_{10}(5p) - 4 \\log_{10}(\\sqrt{\\v... |
3,020 | [{"role": "user", "content": "Find the maximum value of:\n\\[2x^2 + 4xy + 5y^2 + 8x - 6y.\\]"}, {"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 of this... |
3,092 | [{"role": "user", "content": "A garrison of 2000 men has provisions for 62 days. After some days, a reinforcement of 2700 men arrives, and it is now found that the provisions will last only for 20 days more. How many days passed before the reinforcement arrived?"}, {"role": "assistant", "content": "<think>\n\nOkay, let... |
2,993 | [{"role": "user", "content": "Let $x$ and $z$ be nonzero real numbers. Determine the minimum value and maximum value of\n\\[\\frac{|3x + z|}{|x| + |z|},\\]\nand find the difference between these maximum and minimum values."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it... |
3,104 | [{"role": "user", "content": "Evaluate the expression: | 5 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to evaluate this expression: |5 - 8(3 - 12)| - |5 - 11|. Hmm, absolute values can be tricky, but I remember that I need to handle the operations inside the... |
2,966 | [{"role": "user", "content": "Let $ABCD$ be a square. Consider a variable point $P$ inside the square for which $\\angle BAP \\ge 60^\\circ.$ Let $Q$ be the intersection of the line $AD$ and the perpendicular to $BP$ in $P$ . Let $R$ be the intersection of the line $BQ$ and the perpendicular to $BP$ ... |
3,077 | [{"role": "user", "content": "A and B classes of a certain school jointly held a \"Classic Reading\" competition. $10$ students were randomly selected from class A and class B respectively, and the competition scores of these students were collected, organized, and analyzed. The following is some of the information pro... |
3,026 | [{"role": "user", "content": "A square is inscribed in a circle, and another square is inscribed in the segment of the circle that is cut off by one of the sides of the first square. Find the ratio of the side lengths of these squares."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging que... |
3,009 | [{"role": "user", "content": "Consider the quadratic equation $5x^2 - 13x - 6 = 0$. Determine the absolute value of the difference between its roots. If this difference can be expressed as $\\frac{\\sqrt{p}}{q}$, where $p$ and $q$ are integers, and $p$ is not divisible by the square of any prime, find the sum $p + q$."... |
3,093 | [{"role": "user", "content": "If $l, m, n$ are non-identical straight lines in space, and $\\alpha, \\beta$ are non-coincident planes, then the correct option among the following is ( )\nA: If $\\alpha \\parallel \\beta$, $l \\subset \\alpha$, $n \\subset \\beta$, then $l \\parallel n$\nB: If $\\alpha \\perp \\beta$, ... |
3,111 | [{"role": "user", "content": "Jacob is now some years younger than Michael. If 3 years from now Michael will be twice as old as Jacob, Jacob will be 13 years old in 4 years. How many years younger is Jacob than Michael?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by s... |
3,083 | [{"role": "user", "content": "As is well known, balance scales reach equilibrium when both pans have the same weight. On one pan of the scales lie 9 identical diamonds, and on the other - 4 identical emeralds. If one more of the same emerald is added to the side with the diamonds, the scales will balance. How many diam... |
3,117 | [{"role": "user", "content": "Bingley has some bracelets. Kelly gives Bingley a fourth of her 16 bracelets. Then Bingley gives a third of his bracelets to his little sister. Now, Bingley has 6 bracelets remaining. How many bracelets did Bingley have initially?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's... |
2,994 | [{"role": "user", "content": "$10$ students are doing queue training, with $3$ students in the front row and $7$ students in the back row. Now the physical education teacher wants to draw $2$ students from the back row to move to the front row. If the relative order of the other students remains unchanged, then there a... |
3,125 | [{"role": "user", "content": "While shopping, Maria bought 35 green towels and 21 white towels. She gave her mother some of them and ended up with 22 towels. How many towels did Maria give to her mother?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Maria bought some towels, right? She got 35 green a... |
3,116 | [{"role": "user", "content": "Given the universal set $U=\\mathbb{R}$, and the set $M=\\{x\\,|\\,|x-1|\\leq2\\}$, then $C_{U}M=$ （ ）\nA: $\\{x\\,|\\,-1<x<3\\}$\nB: $\\{x\\,|\\,-1\\leq x\\leq 3\\}$\nC: $\\{x\\,|\\,x<-1 \\text{ or } x>3\\}$\nD: $\\{x\\,|\\,x\\leq-1 \\text{ or } x\\geq3\\}$"}, {"role": "assistant", "cont... |
3,061 | [{"role": "user", "content": "Given the function $f(x) = \\cos 2x - 2\\sin\\left(\\frac{\\pi}{2} - x\\right)\\cos\\left(\\frac{\\pi}{2} + x\\right)$, then ()\n\nA: The maximum value of $f(x)$ is 3\n\nB: The smallest positive period of $f(x)$ is $\\pi$\n\nC: The graph of $f(x)$ is symmetric about the line $x = \\frac{\\... |
3,102 | [{"role": "user", "content": "Mitya is 11 years older than Shura. When Mitya was as old as Shura is now, he was twice as old as she was. How old is Mitya?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by step. So, the problem says: Mitya is 11 years older than Shura. Wh... |
2,984 | [{"role": "user", "content": "Construct a rectangle on one side of a regular quadrilateral. On one non-adjacent side of the rectangle, construct a regular pentagon. Continue this pattern by constructing a regular hexagon on a non-adjacent side of the pentagon, followed by a regular heptagon, and finally, conclude with ... |
3,113 | [{"role": "user", "content": "Xiao Ming has 9 medals that look exactly the same, among which only one is real, and the rest 8 are replicas. It is known that the real gold medal is heavier than any of the replicas. Xiao Ming only has a balance scale. How many times at least does Xiao Ming need to weigh to find the real ... |
3,132 | [{"role": "user", "content": "Julia played tag with 5 kids on tuesday. She had played tag with 6 kids on monday.. How many more kids did she play with on monday than on tuesday?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says Julia played tag with 5 kids on Tuesday and 6 kids on Monday... |
3,089 | [{"role": "user", "content": "A ship 150 km from the shore springs a leak which admits 13 / 3 tonnes of water in 5 / 2 minutes. 180 tonnes of water would sink it. However, the pumps can only throw out 9 tonnes of water per hour. Find the minimum average rate of sailing so that the ship may just reach the shore as it be... |
3,067 | [{"role": "user", "content": "Solve the following inequalities: \n(1) $\\frac {2-x}{x+4}\\leq0$; \n(2) $x^2-3ax+2a^2\\geq0$."}, {"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... |
3,107 | [{"role": "user", "content": "Find the phase shift, vertical shift, and the maximum and minimum values of the graph of \\( y = 3\\sin\\left(3x - \\frac{\\pi}{4}\\right) + 1 \\)."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the phase shift, vertical shift, and the maximum and minimum v... |
3,112 | [{"role": "user", "content": "How many multiples of 5 are between 100 and 400?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking how many multiples of 5 are between 100 and 400. Hmm, first, I need to make sure I understand what \"between\" means here. Does it include 100 and 400? We... |
3,138 | [{"role": "user", "content": "Joan grew 29 carrots and 14 watermelons. Jessica grew 11 carrots, and Michael grew 37 carrots. How many carrots did they all grow in total?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the total number of carrots that Joan, Jessica, and Michael... |
3,120 | [{"role": "user", "content": "Given that point P is outside the plane of the parallelogram ABCD, if $$\\overrightarrow {AB}$$\\=(2，-1，-4), $$\\overrightarrow {AD}$$\\=(4，2，0), $$\\overrightarrow {AP}$$\\=(-1，2，-1). Determine the correct statement(s) among the following:\n① AP ⊥ AB;\n② AP ⊥ AD;\n③ $$\\overrightarrow {AP... |
3,133 | [{"role": "user", "content": "A courtyard is some meters long and 14 meters wide and is to be paved with bricks of dimensions 25 cm by 15 cm. The total number of bricks required is 8960. How long is the courtyard?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out how long the courtyard is. F... |
3,118 | [{"role": "user", "content": "Prove that if a natural number is equal to half the sum of all its divisors, then the sum of the reciprocals of the divisors is equal to 2."}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem. The question says: If a natural number is equal to half th... |
3,142 | [{"role": "user", "content": "What are the coordinates of the intersection point between the lines $2x + 3y - 7 = 0$ and $5x - y - 9 = 0$?\n\nA: $(1, 2)$\n\nB: $(2, 1)$\n\nC: $(3, 1)$\n\nD: $(1, 3)$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the intersection point of the two lines g... |
3,127 | [{"role": "user", "content": "Cherry put up a delivery service. She charges $2.50 for a 3-5 kilograms cargo, $4 for a 6-8 kilograms cargo, $6 for a 9-12 kilograms cargo, and $8 for a 13-15 kilograms cargo on weekdays. On weekends, the rates are $3 for a 3-5 kilograms cargo, $5 for a 6-8 kilograms cargo, $7.50 for a 9-1... |
3,141 | [{"role": "user", "content": "Find the value of $({1}+\\sqrt{{3}}{i})^{{3}}$. The options are:\nA: $-8$\nB: $8$\nC: $-8i$\nD: $8i$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value of (1 + √3 i)^3. Hmm, complex numbers raised to a power. Maybe I can use De Moivre's Theorem? Or ma... |
3,130 | [{"role": "user", "content": "Given that the random variable $X$ follows a normal distribution $N(3, \\sigma^2)$, and $P(X < 5) = 0.8$, find the probability of $1 < X < 3$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that X is a normal random variable with mean 3 and variance σ², s... |
3,096 | [{"role": "user", "content": "Express the value of the following as a common fraction:\n\\[\n\\left(1-\\frac{1}{3}\\right)\\cdot\\left(1-\\frac{1}{4}\\right)\\cdot\\left(1-\\frac{1}{5}\\right) \\dotsm \\left(1-\\frac{1}{51}\\right)\\cdot\\left(1-\\frac{1}{52}\\right)\n\\]"}, {"role": "assistant", "content": "<think>\n\... |
3,078 | [{"role": "user", "content": "A play has two different male roles, two different female roles, and three different roles that can be either gender. Only a man can be assigned to a male role, and only a woman can be assigned to a female role. If six men and seven women audition, in how many ways can the seven roles be a... |
3,128 | [{"role": "user", "content": "What is the value of $a$ if the lines $2y - 2a = 6x$ and $y + 1 = (a + 6)x$ are parallel?"}, {"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 fin... |
3,140 | [{"role": "user", "content": "According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 4 cans of water to make orange juice. To prepare 120 servings of orange juice, 12 12-ounce cans of concentrate are required. What is the size of each serving in ounces?"}, {"ro... |
3,145 | [{"role": "user", "content": "A compound has 1 Cu, 1 C, and a certain number of O atoms. The molecular weight of the compound is 124. How many O atoms are in the compound?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about finding the number of oxygen atoms in a compound that has 1 co... |
3,149 | [{"role": "user", "content": "Write down the function expression of a parabola that opens downwards and intersects the $y$-axis at the point $\\left(0,1\\right)$: ____."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the function expression of a parabola that opens downwards a... |
3,106 | [{"role": "user", "content": "A new window design consists of a rectangle topped with a semi-circle at both ends. The ratio of the length $AD$ of the rectangle to its width $AB$ is $4:3$. If $AB$ is 36 inches, what is the ratio of the area of the rectangle to the combined area of the semicircles?\n$\\textbf{(A)}\\ \\fr... |
3,129 | [{"role": "user", "content": "Determine the value of $r$ if $8 = 3^{4r-2}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value of \\( r \\) in the equation \\( 8 = 3^{4r - 2} \\). Hmm, so this is an exponential equation where the variable is in the exponent. I remember that to sol... |
3,008 | [{"role": "user", "content": "Let $(a_n)_1^{\\infty}$ be a sequence such that $a_n \\le a_{n+m} \\le a_n + a_m$ for all positive integers $n$ and $m$ . Prove that $\\frac{a_n}{n}$ has a limit as $n$ approaches infinity."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question... |
3,131 | [{"role": "user", "content": "I apologize for including the answer in that response. Here is the corrected problem without the solution:\n\nIn a company with three office branches, there are varying total numbers of employees and percentages of males working in each branch. Given the following information:\n\nBranch A:... |
3,156 | [{"role": "user", "content": "Seokjin, Taehyung, and Eunji's math test average score is 92. Also, Min-young and Hoseok's scores are 90 and 95, respectively. Find the average score of these five students on the math test, including decimal points."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The prob... |
3,074 | [{"role": "user", "content": "Can the numbers $1, 1, 2, 2, \\dots, 1986, 1986$ be arranged in a row such that there is one number between the two 1's, two numbers between the two 2's, $\\cdots$, and 1986 numbers between the two 1986's?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging que... |
3,028 | [{"role": "user", "content": "One line is parameterized by\n\\[\\begin{pmatrix} 2 + s \\\\ 4 - ks \\\\ 3 + ks \\end{pmatrix}.\\]\nAnother line is parameterized by\n\\[\\begin{pmatrix} t/3 \\\\ 2 + t \\\\ 5 - t \\end{pmatrix}.\\]\nIf the lines are coplanar, then find \\(k\\)."}, {"role": "assistant", "content": "<think>... |
3,049 | [{"role": "user", "content": "Three real numbers are given. Fractional part of the product of every two of them is $ 1\\over 2$ . Prove that these numbers are irrational.\r\n\r\n*Proposed by A. Golovanov*"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to ... |
3,163 | [{"role": "user", "content": "Nina did a running drill to get in shape for soccer season . First , Nina ran 0.08 mile . Then she ran 0.08 mile and 0.67 mile. In total , Nina ran _____ miles ."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about Nina running some miles, and we need to fi... |
3,126 | [{"role": "user", "content": "If the equation $x^{m+n}+5y^{m-n+2}=8$ with respect to $x$ and $y$ is a linear equation in two variables, then the value of $mn$ is ______."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer.... |
3,166 | [{"role": "user", "content": "A grocery store had some apples, 80 bottles of regular soda, and 54 bottles of diet soda. They had 98 more bottles than apples. How many apples did they have?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by step. So, the grocery store has ... |
3,168 | [{"role": "user", "content": "There are some pigs in the barn. 22 more come to join them. Now there are 86 pigs. How many pigs were in the barn initially?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says there are some pigs in the barn, then 22 more come to join them, and now there are ... |
3,016 | [{"role": "user", "content": "In triangle \\( \\triangle ABC \\), it is given that \\( \\angle C=90^\\circ \\), \\( \\angle A=60^\\circ \\), and \\( AC=1 \\). Points \\( D \\) and \\( E \\) are on sides \\( BC \\) and \\( AB \\) respectively such that triangle \\( \\triangle ADE \\) is an isosceles right triangle with ... |
3,134 | [{"role": "user", "content": "Three dice with faces numbered 1 through 6 are stacked. Five of the eighteen faces are visible. The visible numbers are 1, 2, 3, 3, and 4. What is the total number of dots NOT visible in this view?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, a... |
3,162 | [{"role": "user", "content": "Given the functions f(x) and g(x) defined on R, where g(x) = f(|x - 1|), the graph of the function y = g(x) is symmetric about:\n\nA: The line x = -1\nB: The line x = 1\nC: The origin\nD: The y-axis"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem.... |
3,052 | [{"role": "user", "content": "Sarah's birthday is on Friday, June 16, in the year 2017. In what year will her birthday next fall on a Monday?\n$\\mathrm{(A)}\\ 2021 \\qquad \\mathrm{(B)}\\ 2022 \\qquad \\mathrm{(C)}\\ 2023 \\qquad \\mathrm{(D)}\\ 2024 \\qquad \\mathrm{(E)}\\ 2025$"}, {"role": "assistant", "content": "<... |
3,123 | [{"role": "user", "content": "Find the coefficient of $x$ in the expansion of ${(1-x)}^{4}{{(1-\\sqrt{x})}^{3}}$."}, {"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 the ... |
3,108 | [{"role": "user", "content": "Jerry has ten distinguishable coins, each of which currently has heads facing up. He chooses one coin and flips it over, so it now has tails facing up. Then he picks another coin (possibly the same one as before) and flips it over. How many configurations of heads and tails are possible af... |
3,160 | [{"role": "user", "content": "Mr. Callen decided to diversify his business by investing in various artisanal items. He bought the following items to resell at a profit:\n\n1. 18 paintings at $75 each\n2. 25 wooden toys at $30 each\n3. 12 handmade hats at $20 each\n4. 10 leather wallets at $50 each\n5. 35 ceramic mugs a... |
3,062 | [{"role": "user", "content": "Jack and Bill are two friends whose ages have digits reversed in each other's. Seven years from now, Jack's age will be three times Bill's age. What is the difference in their current ages?\nA) 18\nB) 27\nC) 36\nD) 54\nE) 45"}, {"role": "assistant", "content": "<think>\n\nThis is a complex... |
3,174 | [{"role": "user", "content": "Neil baked 20 cookies. He gave some fraction of the cookies to his friend and has 12 cookies left. What fraction of the cookies did Neil give to his friend?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Neil baked 20 cookies and gave some to his friend, then has 12 left.... |
3,070 | [{"role": "user", "content": "For which values of \\(a\\) does the equation \\(|x-3| = a x - 1\\) have two solutions? Enter the midpoint of the interval of parameter \\(a\\) in the provided field. Round the answer to three significant digits according to rounding rules and enter it in the provided field."}, {"role": "a... |
3,169 | [{"role": "user", "content": "A train running at a certain speed crosses a pole in 2 seconds. The length of the train is 3.3333333333333335 meters. What is the speed of the train in km/hr?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a train crossing a pole, and we need to find ... |
3,071 | [{"role": "user", "content": "The quadratic equation $ax^2 - 30x + c = 0$ has exactly one solution. Given that $a+c=41$, and $a < c$, find the ordered pair $(a, c)$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I n... |
3,082 | [{"role": "user", "content": "Consider the function $f(x) = \\tan\\left( \\frac{x}{2} - \\frac{\\pi}{3} \\right)$.\n(1) Determine the domain of $f(x)$, its smallest positive period, intervals of monotonicity, and centers of symmetry.\n(2) Find the solution set for the inequality $-1 \\leq f(x) \\leq \\sqrt{3}$."}, {"ro... |
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