__src_index__ int64 0 172k | messages stringlengths 375 66.5k |
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3,207 | [{"role": "user", "content": "The Crackhams were supposed to make their first stop in Baglmintster and spend the night at a family friend's house. This family friend in turn was to leave home at the same time as them and stop in London at the Crackhams' house. Both the Crackhams and the friend were traveling on the sam... |
3,240 | [{"role": "user", "content": "How many whole numbers from 1 through 51 are divisible by either 4 or 6 or both?\n$\\text{(A)}\\ 14 \\qquad \\text{(B)}\\ 15 \\qquad \\text{(C)}\\ 16 \\qquad \\text{(D)}\\ 17 \\qquad \\text{(E)}\\ 18$"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question... |
3,211 | [{"role": "user", "content": "Given the function $f(x)=mx^{3}+nx^{2}$, the tangent line at the point $(-1,2)$ is exactly parallel to the line $3x+y=0$. If $f(x)$ is monotonically decreasing in the interval $[t,t+1]$, then the range of the real number $t$ is \\_\\_\\_\\_\\_\\_."}, {"role": "assistant", "content": "<thin... |
3,290 | [{"role": "user", "content": "A librarian wants to arrange 4 copies of \"Advanced Algebra\" and 5 copies of \"Basic Calculus\" on a shelf. How many distinct ways can this be done?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about arranging 4 copies of \"Advanced Algebra\" and 5 copie... |
3,280 | [{"role": "user", "content": "**Let $f(x)$ be an odd function expressed as $f(x) = x^3$. Define $g(x) = f(f(x))$. Is $g(g(x))$ odd, even, or neither?**"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out if \\( g(g(x)) \\) is odd, even, or neither. First, let's recall what an odd function is. ... |
3,171 | [{"role": "user", "content": "For $k > 0$, let $J_k = 10\\ldots 01600$, where there are $k$ zeros between the $1$ and the $1600$. Let $M(k)$ be the number of factors of $2$ in the prime factorization of $J_k$. What is the maximum value of $M(k)$?\n$\\textbf{(A)}\\ 6\\qquad \\textbf{(B)}\\ 7\\qquad \\textbf{(C)}\\ 8\\qq... |
3,286 | [{"role": "user", "content": "Simplify first, then evaluate: $(\\frac{x}{x-2}-\\frac{x}{x+2})÷\\frac{4x}{x-2}$, where $x=3$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to simplify the expression \\(\\left( \\frac{x}{x-2} - \\frac{x}{x+2} \\right) \\div \\frac{4x}{x-2}\\) first, and then eva... |
3,301 | [{"role": "user", "content": "The reciprocal of $-2$ is ____."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The question is asking for the reciprocal of -2. Hmm, first I need to remember what a reciprocal is. From what I recall, the reciprocal of a number is 1 divided by that number. So, for any numb... |
3,253 | [{"role": "user", "content": "Given the function $f(x) = x^2 - 2ax + 1$.\n\n(1) If for any real number $x$, $f(1+x) = f(1-x)$ holds, find the value of the real number $a$; \n(2) If $f(x)$ is monotonically increasing on the interval $[1, +\\infty)$, find the range of values for the real number $a$; \n(3) When $x \\in ... |
3,269 | [{"role": "user", "content": "Given an arithmetic sequence \\(\\{a_n\\}\\) where \\(a_2=8\\) and the sum of the first 10 terms \\(S_{10}=185\\).\n\n(1) Find the general formula for the sequence \\(\\{a_n\\}\\).\n\n(2) If a new sequence \\(\\{b_n\\}\\) is formed by taking the 2nd, 4th, 8th, ..., \\(2^n\\)th, ..., terms ... |
3,304 | [{"role": "user", "content": "Each month, after Jill pays for rent, utilities, food, and other necessary expenses, she has one fifth of her net monthly salary left as discretionary income. She puts 30% into a vacation fund, 20% into savings, and spends 35% on eating out and socializing. This leaves her with a certain a... |
3,250 | [{"role": "user", "content": "If the graph of the function $f(x)=a^x+b-1$ (where $a>0$ and $a\\neq1$) passes through the first, second, and fourth quadrants but not through the third quadrant, then it must satisfy (__):\nA. $0<a<1$ and $b>0$\nB. $0<a<1$ and $0<b<1$\nC. $a>1$ and $b<0$\nD. $a>1$ and $b>0$"}, {"role": "a... |
3,270 | [{"role": "user", "content": "$\\sqrt{12}$ and the simplest quadratic root $5\\sqrt{a+1}$ are of the same type of quadratic root, then $a=$____."}, {"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... |
3,305 | [{"role": "user", "content": "The total cost of a pair of pants and a belt was 70.93 dollars. If the price of the pair of pants was 2.93 dollars less than the belt, what was the price of the pair of pants?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says the total cost of a pair of pant... |
3,294 | [{"role": "user", "content": "Let $f(x)$ be an odd function with a period of 5, and $f(-3)=1$. Also, given $\\tan\\alpha=3$, find the value of $f(\\sec^2\\alpha - 2)$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem step by step. First, let's list out all the given information to m... |
3,272 | [{"role": "user", "content": "One of the factors of $x^4 + 16$ is: \n- $\\textbf{(A)}\\ x^2 + 4$\n- $\\textbf{(B)}\\ x+2$\n- $\\textbf{(C)}\\ x^2-4x+4$\n- $\\textbf{(D)}\\ x^2-8$\n- $\\textbf{(E)}\\ \\text{none of these}$\n- **A.** $x^2 + 4$\n- **B.** $x + 2$\n- **C.** $x^2 - 4x + 4$\n- **D.** $x^2 - 8$\n- **E.** None ... |
3,153 | [{"role": "user", "content": "Find the number of degrees in the measure of angle $x$.\n\n[asy]\nimport markers;\nsize (5cm,5cm);\npair A,B,C,D,F,H;\n\nA=(0,0);\nB=(5,0);\nC=(9,0);\nD=(3.8,7);\n\nF=(2.3,7.2);\nH=(5.3,7.2);\n\ndraw((4.2,6.1){up}..{right}(5.3,7.2));\ndraw((3.6,6.1){up}..{left}(2.3,7.2));\n\ndraw (A--B--C-... |
3,312 | [{"role": "user", "content": "What is the value of $f(2)$ if $f(x) = x^2 - 2x + 3$?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value of f(2) for the function f(x) = x² - 2x + 3. Hmm, right. So, when they ask for f(2), that means I have to substitute x with 2 in the function. Let... |
3,205 | [{"role": "user", "content": "A chord AB of constant length slides around the curved part of a semicircle. M is the midpoint of AB, and C is the foot of the perpendicular from A onto the diameter. Show that angle ACM does not change."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging quest... |
3,306 | [{"role": "user", "content": "Simplify $\\frac{\\sqrt{300}}{\\sqrt{75}} - \\frac{\\sqrt{98}}{\\sqrt{49}}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to simplify the expression √300 divided by √75 minus √98 divided by √49. Hmm, first, maybe I can simplify each fraction separately before sub... |
3,315 | [{"role": "user", "content": "For the second main course, they were asked to make a certain number of fish fillets. The first team made 189 pieces, the second team made 131 pieces, and the third team made 180 pieces. How many pieces of fish fillets were they asked to make in total?"}, {"role": "assistant", "content": "... |
3,223 | [{"role": "user", "content": "Soda is sold in packs of 8, 15, and 32 cans. What is the minimum number of packs needed to buy exactly 120 cans of soda?\n$\\textbf{(A)}\\ 5\\qquad\\textbf{(B)}\\ 6\\qquad\\textbf{(C)}\\ 7\\qquad\\textbf{(D)}\\ 8\\qquad\\textbf{(E)}\\ 10$"}, {"role": "assistant", "content": "<think>\n\nThi... |
3,262 | [{"role": "user", "content": "If \\(e^{i \\alpha} + e^{i \\beta} = \\frac{3}{5} + \\frac{2}{5} i,\\) then find \\(e^{-i \\alpha} + e^{-i \\beta}.\\)"}, {"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 abou... |
3,322 | [{"role": "user", "content": "Subtract $555.55$ from $888.88$. Express the result as a decimal to the nearest hundredth."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to subtract 555.55 from 888.88 and then round the result to the nearest hundredth. Hmm, first, let me make sure I understand th... |
3,316 | [{"role": "user", "content": "Let x be the number of potato wedges, y be the number of french fries, and z be the number of potato chips that Cynthia makes. \n\nWe are given that Cynthia cuts 13 potatoes into wedges and that one potato can be cut into 8 wedges. This gives us the first equation:\n\nx = 8 * 13\n\nNext, s... |
3,261 | [{"role": "user", "content": "Triangle $PQR$ is an isosceles triangle with side lengths of 16, 16, and 30 centimeters. What is the area of triangle $PQR$, in square centimeters?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct... |
3,273 | [{"role": "user", "content": "A jogger running at 9 km/hr alongside a railway track is 300 m ahead of the engine of a 200 m long train running at 60 km/hr in the same direction. In how much time will the train pass the jogger?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem st... |
3,318 | [{"role": "user", "content": "Given vectors $\\overrightarrow {a}=(3,2)$, $\\overrightarrow {b}=(-2,-4)$, and $\\overrightarrow {c}= \\overrightarrow {a}+k \\overrightarrow {b}$, where $k \\in \\mathbb{R}$:\n1. Find the value of $k$ if $\\overrightarrow {b} \\perp \\overrightarrow {c}$.\n2. Find the cosine value of the... |
3,323 | [{"role": "user", "content": "If $x = \\frac{2}{3}$ and $y = \\frac{3}{2}$, find the value of $\\frac34 x^8 y^9$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value of (3/4) times x to the 8th power times y to the 9th power, where x is 2/3 and y is 3/2. Hmm, let's start by writing... |
3,307 | [{"role": "user", "content": "A person, in order to watch the 2008 Olympic Games, starts depositing $a$ yuan into a bank on May 10th every year starting from 2001. If the annual interest rate is $P$, and it remains constant, and it is agreed that the deposit upon maturity each year will automatically be converted into ... |
3,314 | [{"role": "user", "content": "Colin can skip at six times the speed that Brandon can. Brandon can skip at one-third the speed that Tony can. And Tony can skip at a certain multiple of the speed that Bruce can. At what speed, in miles per hour, can Colin skip if Bruce skips at 1 mile per hour and Colin's speed is 4 mile... |
3,326 | [{"role": "user", "content": "Find the focus of the parabola \\(y = 4x^2.\\)"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the focus of the parabola given by the equation \\( y = 4x^2 \\). Hmm, first, I remember that parabolas can open up, down, left, or right, and their standard forms... |
3,276 | [{"role": "user", "content": "Is it possible for any month to have 5 Mondays and 5 Thursdays?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out if a month can have 5 Mondays and 5 Thursdays. First, I need to remember how many days are in a month. Most months have 30 or 31 days, and February ... |
3,285 | [{"role": "user", "content": "Given a function $f(x) = ax^3 - bx + 4$, when $x=2$, the function $f(x)$ has an extremum of $-\\frac{4}{3}$.\n\n(1) Find the explicit form of the function.\n(2) Determine the extreme point(s) of the function and find the maximum value."}, {"role": "assistant", "content": "<think>\n\nThis i... |
3,281 | [{"role": "user", "content": "Determine the value of $x$ where the function $g(x) = \\frac{3x^2 - 7x - 8}{x^2 - 5x + 6}$ crosses its horizontal asymptote."}, {"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... |
3,334 | [{"role": "user", "content": "Simplify: $\\lg 4 + \\lg 25$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to simplify lg 4 + lg 25. Hmm, first, I remember that lg is the common logarithm, which is base 10. So, lg 4 is log base 10 of 4, and lg 25 is log base 10 of 25. \n\nNow, there's a logarit... |
3,274 | [{"role": "user", "content": "In triangle $PQR$, $PQ = 7$, $QR = 10$, and the length of median $PS$ is 5. Find $PR$."}, {"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 t... |
3,295 | [{"role": "user", "content": "A train 100 meters long takes 21.998240140788738 seconds to cross a bridge 120 meters long. What is the speed of the train in kmph?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a train crossing a bridge, and we need to find the speed of the train in... |
3,336 | [{"role": "user", "content": "Lawrence walked some distance at 3 kilometers per hour and it took him 1 hour and 20 minutes. How many kilometers did Lawrence walk?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about Lawrence walking some distance at 3 kilometers per hour, and it took hi... |
3,335 | [{"role": "user", "content": "A certain plant grows at a constant rate every month. After a year, the plant will be some height. If the plant is currently 20 feet tall and its monthly growth rate is 5 feet, what will be the height of the plant after a year?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's se... |
3,244 | [{"role": "user", "content": "In triangle \\( \\triangle ABC \\), the lengths of sides opposite to vertices \\( A, B, \\) and \\( C \\) are \\( a, b, \\) and \\( c \\) respectively. Let \\( E \\) be the center of the incircle, and let \\( AE \\) intersect \\( BC \\) at \\( D \\). Prove that \\(\\frac{AE}{ED} = \\frac{b... |
3,293 | [{"role": "user", "content": "For the data whose frequency histogram is shown, by how many days is the mean number of days missed per student greater than the median number of days missed per student for the 18 students? Express your answer as a common fraction.\n\n[asy]\ndraw((0,0)--(0,6),linewidth(2));\ndraw((0,0)--(... |
3,209 | [{"role": "user", "content": "In an acute-angled triangle \\(ABC\\), the altitudes \\(AA_1\\), \\(BB_1\\), and \\(CC_1\\) intersect at point \\(H\\). From point \\(H\\), perpendiculars are drawn to the lines \\(B_1C_1\\) and \\(A_1C_1\\), which intersect the rays \\(CA\\) and \\(CB\\) at points \\(P\\) and \\(Q\\) resp... |
3,254 | [{"role": "user", "content": "Given a sequence $\\{a_n\\}$ ($n\\geq1$) satisfying $a_{n+2}=a_{n+1}-a_n$, and $a_2=1$. If the sum of the first 2011 terms of the sequence is 2012, then the sum of the first 2012 terms is ( )\nA: 2011\nB: 2012\nC: 2013\nD: 2014"}, {"role": "assistant", "content": "<think>\n\nThis is a comp... |
3,298 | [{"role": "user", "content": "Given that $F\\_1$ and $F\\_2$ are the two foci of the hyperbola $\\frac{x^{2}}{a^{2}} - \\frac{y^{2}}{b^{2}} = 1 (a > b > 0)$, an equilateral triangle $MF\\_1F\\_2$ is constructed with side $F\\_1F\\_2$. If the midpoint of side $MF\\_1$ lies on the hyperbola, find the eccentricity of the ... |
3,283 | [{"role": "user", "content": "Given two distinct lines $a$ and $b$, and two distinct planes $\\alpha$ and $\\beta$, consider the following four propositions:\n1. If $a \\perp b$, $a \\perp \\alpha$, and $b \\nsubseteq \\alpha$, then $b \\parallel \\alpha$;\n2. If $a \\parallel \\alpha$, $\\alpha \\perp \\beta$, then $a... |
3,340 | [{"role": "user", "content": "Given that the function $y=f(x)$ has an inverse function $y=f^{-1}(x)$, and the function $y=f(x)$ passes through the point $P(2, -1)$, then $f^{-1}(-1)=$ ."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that the function y = f(x) has an inverse function y... |
3,289 | [{"role": "user", "content": "On a \\(10 \\times 10\\) grid, a bacterium is located in one of the cells. Each turn, the bacterium moves to an adjacent cell (sharing a side) and divides into two bacteria (both remain in the same cell). After that, one of the bacteria on the board moves to an adjacent cell and divides in... |
3,271 | [{"role": "user", "content": "Sandy walked 20 meters towards south. Then Sandy turned to her left and walked 20 meters. She then turned to her left and walked 20 meters. She then turned to her right and walked some distance. Sandy is 45 meters away from the starting point in the north direction. How far did she walk in... |
3,288 | [{"role": "user", "content": "One tourist covers a distance of 20 km 2.5 hours faster than another. If the first tourist were to reduce their speed by 2 km/h, and the second were to increase their speed by 50%, they would spend the same amount of time to cover the same distance. Find the speeds of the tourists."}, {"ro... |
3,206 | [{"role": "user", "content": "Three simplest proper fractions with the same numerator, when converted to mixed numbers, are respectively $\\mathrm{a} \\frac{2}{3}, b \\frac{3}{4}, c \\frac{3}{5}$, where $a, b$, and $c$ are natural numbers not exceeding 10. Calculate $(2a + b) \\div c = \\qquad$."}, {"role": "assistant"... |
3,297 | [{"role": "user", "content": "In the pyramid $P-ABCD$, where the base $ABCD$ is a square and $E$ is the midpoint of $PD$, if $\\overrightarrow{PA}=\\overrightarrow{a}$, $\\overrightarrow{PB}=\\overrightarrow{b}$, $\\overrightarrow{PC}=\\overrightarrow{c}$, then $\\overrightarrow{BE}=$\n\nA: $\\frac{1}{2}\\overrightarro... |
3,267 | [{"role": "user", "content": "Given circle $O: x^{2}+y^{2}=1$, circle $C_k: (x-k)^2+(y-\\sqrt{3}k)^2=4$, then ()\n\nA: Regardless of the value of $k$, the center of circle $C_{k}$ always lies on the line $y=\\sqrt{3}x$\n\nB: If circles $O$ and $C_{k}$ have a common point, then the range of real number $k$ is $[\\frac{1... |
3,287 | [{"role": "user", "content": "Two 8-sided dice are tossed. What is the probability that the sum of the numbers shown on the dice is a prime number? Express your answer as a common fraction."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct... |
3,291 | [{"role": "user", "content": "Find the range of real numbers $m$ for which the inequality $(m+1)x^2 - 2(m-1)x + 3(m-1) < 0$ has all real numbers as its solution."}, {"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 ... |
3,266 | [{"role": "user", "content": "Let $N = 2^{\\left(2^2\\right)}$ and $x$ be a real number such that $N^{\\left(N^N\\right)} = 2^{(2^x)}$ . Find $x$ ."}, {"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... |
3,344 | [{"role": "user", "content": "Calculate: $\\sqrt{6}÷\\sqrt{2}+|1-\\sqrt{3}|-\\sqrt{12}+{({\\frac{1}{2}})^{-1}}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to calculate this expression: √6 ÷ √2 + |1 - √3| - √12 + (1/2)^(-1). Hmm, let's break it down step by step. First, I should handle each... |
3,350 | [{"role": "user", "content": "If the derivative of the function $f(x)$, denoted as $f'(x)$, equals $x^2-2x-3$, then the interval where the function $f(x)$ is monotonically decreasing is ____."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that the derivative of f(x) is f'(x) = x² - 2x... |
3,347 | [{"role": "user", "content": "A candidate who gets a certain percentage of the marks fails by 40 marks. Another candidate who gets 60% marks gets 20 marks more than necessary for passing. The number of marks for passing is 160. What is the percentage of marks the first candidate gets?"}, {"role": "assistant", "content"... |
3,346 | [{"role": "user", "content": "For the linear function $y=x-1$, the quadrant that its graph does not pass through is:\n\nA: First quadrant\n\nB: Second quadrant\n\nC: Third quadrant\n\nD: Fourth quadrant"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about the linear function y = x - 1, ... |
3,360 | [{"role": "user", "content": "If some men do a work in 70 days, then 40 men will do it in 63 days. How many men were initially doing the work?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem. So, the question is: If some men do a work in 70 days, then 40 men will do it in 63 d... |
3,362 | [{"role": "user", "content": "For the system of equations $\\left\\{\\begin{array}{l}{2x-3y=5(1)}\\\\{y=2x-1(2)}\\end{array}\\right.$, substituting (2) into (1) yields ( )\n\nA: $2x-6x-1=5$\n\nB: $2\\left(2x-1\\right)-3y=5$\n\nC: $2x-6x+3=5$\n\nD: $2x-6x-3=5$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's... |
3,310 | [{"role": "user", "content": "Arun, Tarun, and Charan can together complete a work in 10 days. After 4 days, both Tarun and Charan went to their village. If Arun can do the work alone in 30 days, find out their individual work rates and how many days are required for Arun to complete the remaining work alone."}, {"role... |
3,366 | [{"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.... |
3,363 | [{"role": "user", "content": "A museum displays a scale model of the Eiffel Tower, which has an actual height of 1063 feet, at a ratio of $1:50$. What is the height in inches of the scale model? (Note: 1 foot equals 12 inches)\n$\\textbf{(A)}\\ 250$ inches\n$\\textbf{(B)}\\ 255$ inches\n$\\textbf{(C)}\\ 260$ inches\n$\... |
3,348 | [{"role": "user", "content": "If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $92. If a certain total amount is invested and $600 is invested at 8 perc... |
3,325 | [{"role": "user", "content": "Let $\\{a_{n}\\}$ be an arithmetic sequence with a common difference of $d$, and $\\{b_{n}\\}$ be a geometric sequence with a common ratio of $q$. Given that the sum of the first $n$ terms of the sequence $\\{a_{n}+b_{n}\\}$ is $S_{n}=n^{2}-n+2^{n}-1$ for $n\\in \\mathbb{N}^{*}$, find the ... |
3,352 | [{"role": "user", "content": "Determine the volume of the square truncated pyramid if its height is 6, the side of the lower base is 4, and the side of the upper base is 2."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the volume of a square truncated pyramid, which is also called a fr... |
3,374 | [{"role": "user", "content": "Sarah is planning to do some baking. She buys 5 pounds of rye flour, 10 pounds of whole-wheat bread flour, and 3 pounds of chickpea flour. Sarah already had 2 pounds of whole-wheat pastry flour at home. How many pounds of flour does she now have?"}, {"role": "assistant", "content": "<think... |
3,367 | [{"role": "user", "content": "Find the distance between the planes $3x - 9y + 6z = 12$ and $6x - 18y + 12z = 24.$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the distance between two planes. The planes given are 3x - 9y + 6z = 12 and 6x - 18y + 12z = 24. Hmm, first, I remember that t... |
3,368 | [{"role": "user", "content": "If the complex number $(x^2 - 1) + (x^2 + 3x + 2)i$ is purely imaginary, then the value of the real number $x$ is\nA: 1\nB: ±1\nC: -1\nD: -2"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that the complex number \\((x^2 - 1) + (x^2 + 3x + 2)i\\) is purely... |
3,358 | [{"role": "user", "content": "In parallelogram $EFGH$, $EF = 42$ cm, $FG = 4z^3$ cm, $GH = 3w + 6$ cm, and $HE = 32$ cm. Find the product of $w$ and $z$."}, {"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... |
3,303 | [{"role": "user", "content": "the jogging track in a sports complex has an irregular shape with varying widths, and its total length is 561 m. Deepak, his wife, and their friend start from the same point and walk in opposite directions at 4.5 km/hr, 3.75 km/hr, and 5.25 km/hr respectively. Deepak and his wife walk in o... |
3,375 | [{"role": "user", "content": "Four friends, Harry, Ron, Hermione, and Neville, are competing in a spell-casting competition. There are no ties allowed, nor does any competitor finish simultaneously with another. In how many different possible orders can the results of the competition be arranged?"}, {"role": "assistant... |
3,357 | [{"role": "user", "content": "According to the directions on a packet of smoothie mix, a certain amount of smoothie mix is to be combined with 12 ounces of water to make a smoothie. To prepare 150 12-ounce smoothies, 180 2-ounce packets of smoothie mix are required. How many ounces of smoothie mix are in the original p... |
3,242 | [{"role": "user", "content": "Let \\( 0 < x < 4.5 \\), \\( f(x) = \\left(1+\\frac{1}{\\lg \\left(\\sqrt{x^{2}+10}-x\\right)}\\right)\\left(1+\\frac{2}{\\lg \\left(\\sqrt{x^{2}+10}-x\\right)}\\right) \\). Then, the minimum value of \\( f(x) \\) is \\( \\quad \\).\n\nA. \\( 8 \\sqrt{2} \\)\n\nB. \\( 8 \\sqrt{3} \\)\n\nC.... |
3,364 | [{"role": "user", "content": "Express the following as a common fraction: $\\sqrt[3]{4\\div 13.5}$."}, {"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 express the cube root o... |
3,365 | [{"role": "user", "content": "Given the function f(x) = |log₂x - 1|, if there exists a real number k such that the equation f(x) = k has two different roots x₁ and x₂, find the value of x₁•x₂ ( ).\nA: 1\nB: 2\nC: 4\nD: Undetermined"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem st... |
3,373 | [{"role": "user", "content": "Carrey rented a car for Rs. 20 plus Rs. 0.25 per kilometer driven. Samuel rented a car for Rs. 24 plus Rs. 0.16 per kilometer driven. If each was charged exactly the same amount for the rental, how many kilometers did each drive?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's ... |
3,370 | [{"role": "user", "content": "Given $A=3b^{2}-2a^{2}+5ab$, $B=4ab+2b^{2}-a^{2}$. \n$(1)$ Simplify: $2A-3B$; \n$(2)$ When $a=-1$, $b=2$, find the value of $2A-3B$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's tackle this problem step by step. First, part (1) asks to simplify 2A - 3B. I need to remember ... |
3,313 | [{"role": "user", "content": "Three of the vertices of parallelogram $PQRS$ are $P = (2,0,-3),$ $Q = (4,-3,1),$ and $R = (0,-1,5).$ Find the coordinates of $S.$"}, {"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 t... |
3,356 | [{"role": "user", "content": "Given that circle C is tangent to the lines $x - y = 0$ and $x - y - 4 = 0$, and the center of the circle lies on the line $x + y = 0$, find the equation of circle C."}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem step by step. First, let's recall wha... |
3,391 | [{"role": "user", "content": "Given the set M={1, 2, 3}, the correct relation is ( ):\nA: 1∈M\nB: 1∉M\nC: 1⊆M\nD: 1⊊M"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The question is about set M which is {1, 2, 3}. We need to figure out which of the options A to D is the correct relation. Let's go throu... |
3,343 | [{"role": "user", "content": "Pigsy picked a bag of wild fruits from the mountain to bring back to Tang Monk. As he walked, he got hungry and took out half of them, hesitated, put back two, and then ate the rest. This happened four times: taking out half, putting back two, and then eating. By the time he reached Tang M... |
3,369 | [{"role": "user", "content": "Find the least number which when divided by 34 and 5 leaves a remainder of 4 in each case. What is the least number?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the least number that, when divided by 34 and 5, leaves a remainder of 4 each time... |
3,387 | [{"role": "user", "content": "The complex number $z$ satisfies $(z-3)(2-i)=5i$ (where $i$ is the imaginary unit), then the point corresponding to the conjugate complex number $\\bar{z}$ on the complex plane is located in\n\nA: The first quadrant\n\nB: The second quadrant\n\nC: The third quadrant\n\nD: The fourth quadra... |
3,381 | [{"role": "user", "content": "Pipe A fills a tank of capacity 900 liters at a certain rate. Another pipe B fills the same tank at the rate of 30 liters a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute. If pipe A is kept open for a minute and then closed, and pipe B is open fo... |
3,371 | [{"role": "user", "content": "If $\\sin \\alpha \\cdot \\tan \\alpha < 0$, and $\\sin \\alpha + \\cos \\alpha \\in (0,1)$, then the terminal side of angle $\\alpha$ is in ( )\n\nA: the first quadrant\n\nB: the second quadrant\n\nC: the third quadrant\n\nD: the fourth quadrant"}, {"role": "assistant", "content": "<thin... |
3,379 | [{"role": "user", "content": "Find the coefficient of $x^5y^2$ in the expansion of $\\left( x^2+x+y \\right)^6$.\n\nA: $20$\n\nB: $40$\n\nC: $60$\n\nD: $120$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the coefficient of \\( x^5 y^2 \\) in the expansion of \\( (x^2 + x + y)^6 \\). Hm... |
3,327 | [{"role": "user", "content": "If triangle $PQR$ has sides of length $PQ = 7,$ $PR = 8,$ and $QR = 5,$ then calculate\n\\[\\frac{\\cos \\frac{P - Q}{2}}{\\sin \\frac{R}{2}} - \\frac{\\sin \\frac{P - Q}{2}}{\\cos \\frac{R}{2}}.\\]"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, ... |
3,302 | [{"role": "user", "content": "The cube $A B C D A_{1} B_{1} C_{1} D_{1}$ has $A B = 1$, $\\overline{B_{1} K} = \\overline{K C_{1}}$, $\\overline{C P} = 0.25 \\overline{C D}$, and $\\overline{C_{1} M} = 0.25 \\overline{C_{1} D_{1}}$. Point $X$ lies on the line $B D_{1}$. Point $Y$ is the intersection of lines $KX$ and $... |
3,384 | [{"role": "user", "content": "The values of $x$ and $y$ are always positive, and $x^3$ and $y$ vary inversely. If $y$ is 8 when $x$ is 2, find $x$ when $y$ is 64."}, {"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... |
3,386 | [{"role": "user", "content": "Given the sets $A=\\{a^2, a+1, -3\\}$ and $B=\\{a-3, a^2+1, 2a-1\\}$. If $A \\cap B = \\{-3\\}$, find the value of the real number $a$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem step by step. The problem says that sets A and B have an intersectio... |
3,376 | [{"role": "user", "content": "Two boys start moving from the same point A on a circular track with both heading clockwise. One has a speed of 6 ft. per second and the other 10 ft. per second. They continue until they first meet at point A again. Determine the number of times they meet excluding the start and finish.\nA... |
3,398 | [{"role": "user", "content": "Six people can mow a lawn in 8 hours. How many more people are needed to mow the lawn in 3 hours, assuming each person mows at the same rate?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about six people mowing a lawn in 8 hours, and we need to find how m... |
3,321 | [{"role": "user", "content": "If \\( a \\) is the maximum value of \\( \\frac{1}{2} \\sin ^{2} 3 \\theta- \\frac{1}{2} \\cos 2 \\theta \\), find the value of \\( a \\)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. ... |
3,338 | [{"role": "user", "content": "Two walls and the ceiling of a room meet at right angles at point \\(P\\). A fly is in the air three meters from one wall, four meters from the other wall, and seven meters from point \\(P\\). How many meters is the fly from the ceiling?\nA) $2$\nB) $3$\nC) $\\sqrt{24}$\nD) $2\\sqrt{6}$"},... |
3,308 | [{"role": "user", "content": "In triangle $\\triangle ABC$, the sides opposite to the internal angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. If $\\tan(A+B)(1-\\tan A\\tan B)=\\frac{\\sqrt{3}\\sin C}{\\sin A\\cos B}$, which of the following conclusions is correct?\n\nA: $A=\\frac{π}{3}$\n\nB: If $a=7$ and... |
3,300 | [{"role": "user", "content": "Given that $\\triangle ABC$ is an equilateral triangle, and $P$ is a point outside the triangle such that $PA = PB + PC$, prove that points $A, B, P, and C$ are concyclic."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to prov... |
3,403 | [{"role": "user", "content": "John earned some money on Saturday and half that amount on Sunday. He earned $20 the previous weekend. He needs $13 more to buy a new pogo stick that costs $60. How much money did John earn on Saturday?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out how much ... |
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