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{
"content": "If there are 4 peanuts in the first box, and Mary puts 6 more peanuts inside, resulting in 10 peanuts in the first box. Meanwhile, there are 7 peanuts in the second box, and John adds 5 more peanuts. How many peanuts are in both boxes combined?",
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"content": "After M... |
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{
"content": "What is the best way to get from one place to another?",
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},
{
"content": "The term \"best\" is relative to your individual preferences and circumstances. \n\nIn general, how to get from one place to another depends on several key factors, such as the distance between the... |
[
{
"content": "In the Cartesian coordinate system, the coordinates of the point $P(-2,1)$ with respect to the $x$-axis are ( ).\n\nA: $(2,1)$\n\nB: $(1,-2)$\n\nC: $(-2,-1)$\n\nD: $(2,-1)$",
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"content": "To find the coordinates of the point $P(-2,1)$ with respect to the $x$-axis, we... |
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{
"content": "What is an operating model for AI?",
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},
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"content": "It refers to the processes put in place to work with AI, from use case definition, to development to deployment and operation. Ultimately the objective of an operating model for AI is to streamline the value generatio... |
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{
"content": "Points $P$, $Q$, and $R$ lie on the surface of a sphere with center $O$ and radius $25$. It is given that $PQ=15$, $QR=20$, $RP=25$, and that the distance from $O$ to $\\triangle PQR$ is $\\frac{x\\sqrt{y}}{z}$, where $x$, $y$, and $z$ are positive integers, $x$ and $z$ are relatively prime, and $... |
[
{
"content": "Why is Brazilian jiu jitsu an excellent martial art?",
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{
"content": "Brazilian jiu jitsu (BJJ) is an excellent martial art for a number of reasons. BJJ is, first and foremost, a generally safe martial art. BJJ does not emphasize or focus on striking techniques like ... |
[
{
"content": "Given this article, what is the largest size for a dead man zone?\n\nContext: The dead man zone is the area directly around a bushfire that is likely to burn within five minutes given the current wind conditions or an anticipated change in wind direction. The distance this zone extends from the fi... |
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{
"content": "Given the function $f(x)=\\cos (2x+\\varphi)$, where $(-\\pi\\leqslant \\varphi < \\pi)$, its graph is shifted to the right by $\\frac{\\pi}{2}$ units and overlaps with the graph of the function $y=\\sin x\\cos x + \\frac{\\sqrt{3}}{2}\\cos x$. What could be the value(s) of $|\\varphi|$?\n\nA: $\\... |
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{
"content": "A certain stock yields 8%. The market value of the stock is $150. What is the percentage of the stock's original value?",
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{
"content": "To determine the percentage of the stock's original value, we need to know the original value of the stock. Without this information... |
[
{
"content": "What is Wimbledon?\n\nContext: The Wimbledon Championships, commonly known simply as Wimbledon, is the oldest tennis tournament in the world and is widely regarded as the most prestigious. It has been held at the All England Club in Wimbledon, London, since 1877 and is played on outdoor grass cour... |
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{
"content": "In a class of 94 students, 41 are taking French, 22 are taking German. Of the students taking French or German, some are taking both courses. There are 40 students not enrolled in either course. How many students are taking both French and German?",
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{
"content": "Let'... |
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{
"content": "There are 11 square formations, each consisting of the same number of soldiers. If 1 general is added, a larger square formation can be formed. What is the minimum number of soldiers in one of the original square formations?",
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{
"content": "\n1. **Define the variables... |
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{
"content": "Given a triangle \\(ABC\\) for which \\(\\angle BAC \\neq 90^\\circ\\), let \\(B_1, C_1\\) be variable points on \\(AB, AC\\), respectively. Let \\(B_2, C_2\\) be the points on line \\(BC\\) such that a spiral similarity centered at \\(A\\) maps \\(B_1C_1\\) to \\(C_2B_2\\). Denote the circumcircl... |
[
{
"content": "Let $a,$ $b,$ $c$ be distinct complex numbers such that\n\\[\\frac{a}{1 - b} = \\frac{b}{1 - c} = \\frac{c}{1 - a} = k.\\]Find the sum of all possible values of $k.$",
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"content": "From the given equation,\n\\begin{align*}\na &= k(1 - b), \\\\\nb &= k(1 - c), \\\\\nc... |
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{
"content": "Which episode does Jon Snow lead a battle where he is outnumbered by Ramsey Bolton?",
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{
"content": "\"Battle of the Bastards\" is the ninth episode of the sixth season of Game of Thrones which had the massive battle between Jon Snow and Ramsey Bolton. Ramsey Bolton ul... |
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{
"content": "When the greatest common divisor and least common multiple of two integers are multiplied, the product is 180. How many different values could be the greatest common divisor of the two integers?",
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{
"content": "We know that $\\gcd(a,b) \\cdot \\mathop{\\text{lcm}}[a,b... |
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{
"content": "In 1995, a village had a population that was a perfect square. Twelve years later, after an increase of 180 people, its population was 12 more than a perfect square. Twenty-four years after 1995, with an increase of another 180 people, the population once again equaled a perfect square. Determine ... |
[
{
"content": "What is a whiteboard?\n\nContext: A whiteboard (also known by the terms marker board, dry-erase board, dry-wipe board, and pen-board) is a glossy, usually white surface for making non-permanent markings. Whiteboards are analogous to blackboards, but with a smoother surface allowing for rapid marki... |
[
{
"content": "At a restaurant that serves only vegan food, tell me whether each of the following items could be found in the kitchen or not: Butter, Eggs, Tofu, Chicken, Kale, Spinach, Peppers, Steak, Bread, Chickpeas, Pork",
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"content": "Butter: Could not be found in the kitchen\... |
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{
"content": "If \\(7x = 28\\) and \\(x + w = 9\\), what is the value of \\(xw\\)?\n(A) 9\n(B) 20\n(C) 18\n(D) 52\n(E) -252",
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"content": "\n1. To determine the value of \\( x \\), we start by solving the equation \\( 7x = 28 \\).\n\n\\[\nx = \\frac{28}{7}\n\\]\n\n\\[\nx = 4\n\\]\... |
[
{
"content": "What is a, \"one-timer\" in ice hockey?",
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{
"content": "Ice hockey is a sport typically played with one goalie and five skaters on each of two opposing teams. A one-timer is an expression used to describe a shot taken by a player directly from a pass of another playe... |
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{
"content": "In the geometric sequence $\\{a_n\\}$, it is known that $a_1=1$, and $a_4=8$, then $a_5=$ （ ）\nA: 16\nB: 16 or -16\nC: 32\nD: 32 or -32",
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{
"content": "Solution: $$q^{3}= \\frac {a_{4}}{a_{1}}=8$$ \n∴ $q=2$ \n∴ $a_{5}=a_{1}\\cdot q^{4}=16$ \nTherefore, the correct... |
[
{
"content": "What are the four primary states of matter? Answer in bullet point list, and capitalize each words",
"role": "user"
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{
"content": "- Solid\n- Liquid\n- Gas\n- Plasma",
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] |
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{
"content": "Name five NFL teams in the NFC.",
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"content": "Five NFL teams in the NFC are the Carolina Panthers, New Orleans Saints, Philadelphia Eagles, New York Giants, and Detroit Lions.",
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] |
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{
"content": "In the Cartesian coordinate system, if the line $ax-y+1=0$ passes through the focus of the parabola $y^2=4x$, then the real number $a=$ ____.",
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},
{
"content": "Firstly, the focus of the parabola $y^2=4x$ has the coordinates $(1,0)$, following the standard form of the pa... |
[
{
"content": "The opposite of $2023$ is\n\nA: $-\\frac{1}{{2023}}$\n\nB: $\\frac{1}{{2023}}$\n\nC: $-2023$\n\nD: $2023$",
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"content": "To find the opposite of a number, we simply change its sign. If the number is positive, its opposite is negative, and vice versa. For the number $... |
[
{
"content": "In town A, there are \\( n \\) girls and \\( n \\) boys, and each girl knows each boy. In town B, there are \\( n \\) girls \\( g_{1}, g_{2}, \\ldots, g_{n} \\) and \\( 2n-1 \\) boys \\( b_{1}, b_{2}, \\ldots, b_{2n-1} \\). The girl \\( g_{i}, i=1,2, \\ldots, n \\), knows the boys \\( b_{1}, b_{2}... |
[
{
"content": "Which company designed SoundBridge?\n\nContext: SoundBridge is a hardware device from Roku, Inc. designed to play internet radio or digital audio streamed across a home network, over either Wi-Fi or ethernet. SoundBridge devices directly browsed the Radio Roku guide. As of 2008 all Roku SoundBridg... |
[
{
"content": "In the series A Song of Ice and Fire, who is the founder of House Clegane?",
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{
"content": "The name of House Clegane's founder is unknown. He was a kennelmaster of Casterly Rock and saved Lord Tytos Lannister from a lionness. As a reward, Lord Lannister granted the un... |
[
{
"content": "Bill is stocking the kitchenware section of the Walmart. He needs to stack 60 pots. On each shelf, he can stack five pots vertically and a certain number of sets of vertically stacked pots side-by-side. He needs 4 shelves to stock all the pots. How many sets of vertically stacked pots can he place... |
[
{
"content": "The area of the smallest square that will contain a circle of radius 4 is what?",
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{
"content": "The smallest square has side 8 and area $8^2=\\boxed{64}$. [asy]\ndraw(Circle((12,12), 12));\ndraw((0,0)--(0,24)--(24,24)--(24,0)--cycle);\ndraw((0,12)--(24,12));\ndot((12,... |
[
{
"content": "The number $N$ is between $7$ and $15$. The average of $4$, $8$, and $N$ could be\n$\\text{(A)}\\ 6 \\qquad \\text{(B)}\\ 7 \\qquad \\text{(C)}\\ 9 \\qquad \\text{(D)}\\ 11 \\qquad \\text{(E)}\\ 13$\n$\\text{(A)}\\ 6 \\qquad \\text{(B)}\\ 7 \\qquad \\text{(C)}\\ 9 \\qquad \\text{(D)}\\ 11 \\qquad ... |
[
{
"content": "How do you plan a trip?",
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"content": "There are many different ways to plan a trip. In addition, there are many different factors to include in order to plan a trip. First of all, it is important to know the type of travel. Is this a business trip? Is this family tr... |
[
{
"content": "a can finish a piece of work in 4 days . b can do it in 14 days . they work together for two days and then a goes away . in how many days will b finish the work ?",
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{
"content": "Let's calculate the amount of work A and B can do together in one day.\n\nA can finish th... |
[
{
"content": "For any real numbers $x$ and $y$, find the minimum value of $|x-1|+|x|+|y-1|+|y+1|$.",
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{
"content": "To find the minimum value of the given expression, we will consider the properties of absolute values and the triangle inequality.\n\nWe have\n\\[\n|x-1|+|x|+|y-1|+|y+... |
[
{
"content": "The base six number $125_{6}$ is equal to the base $b$ number $221_{b}$. What is the positive value of $b$?",
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},
{
"content": "First, convert the base six number $125_6$ to base ten:\n$$ 125_{6} = 1 \\cdot 6^2 + 2 \\cdot 6^1 + 5 \\cdot 6^0 = 1 \\cdot 36 + 2 \\cdot 6 + 5 ... |
[
{
"content": "Asia found a beautiful homecoming dress in a foreign online store. The dress was originally priced at €300. The store had a sale going on, offering a 20% discount on dresses. Then, Asia also had a special member coupon that granted her an additional 10% discount on the already reduced price. She b... |
[
{
"content": "In a sequence of positive integers, each term after the first is $\\frac{1}{3}$ of the sum of the term that precedes it and the term that follows it. What is the 6th term of this sequence if the 2nd term is 7 and the 3rd term is 20?",
"role": "user"
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{
"content": "Let $a_1, a_4, a_5,... |
[
{
"content": "Why is a pomegranate known as a hand grenade?",
"role": "user"
},
{
"content": "When pomegranates become overripe, they will literally burst on the tree, like a grenade. In Spanish, they are known as granadas for this reason.",
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] |
[
{
"content": "What are some physical activities I could do on a sunny day?",
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},
{
"content": "On a sunny day, you can take advantage of the nice weather by doing outdoor activities. For solo activities, you can go on a run, a hike or a bike ride. For group activities, consider playing... |
[
{
"content": "an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is l... |
[
{
"content": "Tell me whether these numbers are odd or even",
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},
{
"content": "10, 2, 7, 17, 777, 1284, 28, 57, 298, 102",
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] |
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{
"content": "A liter of cream contains a certain percentage of butterfat. To obtain one liter of mixture with 6.5 percent butterfat, 3 liters of skim milk containing 5.5 percent butterfat must be added to the mixture. What is the percentage of butterfat in the cream?",
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{
"content"... |
[
{
"content": "What is the smallest positive four-digit integer equivalent to 6 mod 7?",
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{
"content": "An integer that is equivalent to 6 mod 7 can be written in the form $7k+6$.\n\n$1000$ is the smallest four-digit integer, so we want to solve the inequality $7k+6 \\ge 1000$. This ... |
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{
"content": "Each day, Jenny ate $20\\%$ of the jellybeans that were in her jar at the beginning of that day. At the end of second day, 32 remained. How many jellybeans were in the jar originally?",
"role": "user"
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{
"content": "Since Jenny ate $20\\%$ of the jellybeans remaining each day, $80\\%... |
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{
"content": "How many ways can a four-cell polyomino in the shape of the letter $Z$ (see the figure) be placed on a chessboard (size $8 \\times 8$ cells) so that it fits exactly on the cells of the board and within its boundaries? The polyomino can be rotated and flipped. Justify your answer.",
"role": "us... |
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{
"content": "Two circles touch each other externally. Find the length of their common external tangent (between the points of tangency), given that the radii are 16 and 25.",
"role": "user"
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{
"content": ": \n1. Let's name the centers of the given circles $O$ and $O_2$, having radii 16 and 25, re... |
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{
"content": "Given the function $f(x)=x^{2}+\\\\ln x$, if the equation of the tangent line to the curve $y=f(x)$ at the point $(1,f(1))$ is $y=ax+b$, then $a+b=$ _____ .",
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{
"content": "Since $f(x)=x^{2}+\\\\ln x$,\n\nThen $f(1)=1^{2}+\\\\ln 1=1$, so the point of tangency is $(1,1... |
[
{
"content": "When did Felix Luna die?\n\nContext: Félix César Luna (30 September 1925 – 5 November 2009) was an Argentine writer, lyricist and historian.",
"role": "user"
},
{
"content": "Felix Luna died on November 5th, 2009",
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] |
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{
"content": "A circle centered at $A$ with a radius of $1$ and a circle centered at $B$ with a radius of $4$ are externally tangent. A third circle is tangent to the first two and to one of their common external tangents as shown. What is the radius of the third circle? [asy]\ndraw((-3,0)--(7.5,0));\ndraw(Circ... |
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{
"content": "Two circles of radius $r$ are externally tangent to each other and internally tangent to the ellipse $x^2 + 5y^2 = 6,$ as shown below. Find $r.$\n[asy]\nsize(7cm);\ndraw(scale(sqrt(6), sqrt(6)/sqrt(5))* unitcircle);\ndraw((0,-1.5)--(0,1.7),EndArrow);\ndraw((-3,0)--(3,0),EndArrow);\ndraw(Circle( (s... |
[
{
"content": "What are good native plants for a garden in Ohio?",
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},
{
"content": "Native plants that will grow well in Ohio include Purple Coneflower, Thin Leaf Mountain Mint, Sawtooth Sunflower, and Little Bluestem Grass. There's quite a few plants that grow well in Ohio and are nat... |
[
{
"content": "For integers $a$ and $T,$ $T \\neq 0,$ a parabola whose general equation is $y = ax^2 + bx + c$ passes through the points $A = (0,0),$ $B = (2T,0),$ and $C = (2T + 1,28).$ Let $N$ be the sum of the coordinates of the vertex point. Determine the largest value of $N.$",
"role": "user"
},
{... |
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{
"content": "What is the Fallout game?\n\nContext: Fallout: A Post Nuclear Role Playing Game is a 1997 role-playing video game developed and published by Interplay Productions. In a mid-22nd century post-apocalyptic and retro-futuristic world, decades after a global nuclear war between the United States and Ch... |
[
{
"content": "Let $F(0) = 0,$ $F(1) = \\frac{3}{2},$ and\n\\[F(n) = \\frac{5}{2} F(n - 1) - F(n - 2)\\]for $n \\ge 2.$ Find\n\\[\\sum_{n = 0}^\\infty \\frac{1}{F(2^n)}.\\]",
"role": "user"
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{
"content": "We claim that $F(n) = 2^n - \\frac{1}{2^n}$ for all nonnegative integers $n.$ We prove this ... |
[
{
"content": "Give me some strategies to prevent procrastination",
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{
"content": "Procrastination is a huge problem for individuals in today's society. Though there are many strategies to beat procrastination, the effectiveness of these strategies is largely dependent on the individ... |
[
{
"content": "Let $\\mathbf{a},$ $\\mathbf{b},$ $\\mathbf{c},$ $\\mathbf{d}$ be four distinct unit vectors in space such that\n\\[\\mathbf{a} \\cdot \\mathbf{b} = \\mathbf{a} \\cdot \\mathbf{c} = \\mathbf{b} \\cdot \\mathbf{c} =\\mathbf{b} \\cdot \\mathbf{d} = \\mathbf{c} \\cdot \\mathbf{d} = -\\frac{1}{11}.\\... |
[
{
"content": "Let $f$ be a function taking the nonnegative integers to the nonnegative integers, such that\n\\[2f(a^2 + b^2) = [f(a)]^2 + [f(b)]^2\\]for all nonnegative integers $a$ and $b.$\n\nLet $n$ be the number of possible values of $f(25),$ and let $s$ be the sum of the possible values of $f(25).$ Find $... |
[
{
"content": "After spending some amount on rent, Rs. 1500 on milk, Rs. 4500 on groceries, Rs. 2500 on children's education, Rs. 2000 on petrol, and Rs. 5200 on miscellaneous expenses, Mr. Kishore saved 10% of his monthly salary. He saved Rs. 2300. How much did he spend on rent?",
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{
... |
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{
"content": "What is the greatest product obtainable from two integers whose sum is 2024?",
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{
"content": "Let the two integers be $x$ and $2024-x$. The product we want to maximize is $2024x - x^2$. To find the maximum, we can complete the square:\n\n1. Rewrite the expression: $202... |
[
{
"content": "Let $A = (-4, 0),$ $B = (-3, 2),$ $C = (3, 2),$ and $D = (4, 0).$ Suppose that point $P$ satisfies \\[PA + PD = 10,\\] and \\[PB + PC = 8.\\] Find the $y-$coordinate of $P$, which can be expressed in the form $\\frac{-a + b \\sqrt{c}}{d},$ where $a, b, c, d$ are positive integers. Find $a + b + c ... |
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{
"content": "Extract the names from the cast of the film Replikator, and separate them with a comma.\n\nContext: Replikator is a 1994 science fiction film directed by G. Philip Jackson and starring Michael St. Gerard, Brigitte Bako, Ned Beatty and Ilona Staller.\n\nCast\n\n Michael St. Gerard as Ludo Ludovi... |
[
{
"content": "Mari made 4 more than a certain multiple of decorated buttons as Kendra. Sue made half as many as Kendra. Sue made 6 buttons. Mari made 64 buttons. What is the multiple of Kendra's buttons that Mari made?",
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},
{
"content": "Let's denote the certain multiple of decorated ... |
[
{
"content": "James has a rainwater collection barrel with a maximum capacity of 80 gallons. For each inch of rain, he collects 15 gallons. On Monday it rained 4 inches, on Tuesday it rained 3 inches, and on Wednesday it rained 2.5 inches. James can sell water for $1.2 per gallon on Monday, $1.5 per gallon on T... |
[
{
"content": "Mongolia TST 2011 Test 1 #2\n\nLet $p$ be a prime number. Prove that: $\\sum_{k=0}^p (-1)^k \\dbinom{p}{k} \\dbinom{p+k}{k} \\equiv -1 (\\mod p^3)$ (proposed by B. Batbayasgalan, inspired by Putnam olympiad problem)\n\nNote: I believe they meant to say $p>2$ as well.",
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... |
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{
"content": "In a modified walking game, I stand still on move 1, and for each subsequent move $n$ where $2 \\le n \\le 30$, I take two steps forward if $n$ is prime and three steps backward if $n$ is composite. After completing move 30, I walk directly back to my original starting point. How many steps long i... |
[
{
"content": "Each square in the grid shown is 1 cm by 1 cm. What is the area of the shaded figure, in cm²?",
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{
"content": "\n1. **Determine the total area of the grid:**\n\n The grid is composed of squares measuring \\(1 \\, \\text{cm} \\times 1 \\, \\text{cm}\\). There are \\(3... |
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{
"content": "A circle of radius 1 is tangent to a circle of radius 2. The sides of $\\triangle ABC$ are tangent to the circles as shown, and the sides $\\overline{AB}$ and $\\overline{AC}$ are congruent. What is the area of $\\triangle ABC$?\n\n[asy]\nunitsize(0.7cm);\npair A,B,C;\nA=(0,8);\nB=(-2.8,0);\nC=(2.... |
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{
"content": "Construct a parallelogram given its perimeter, one diagonal, and the angle between the given diagonal and one side of the parallelogram.",
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{
"content": "\n1. **Given Data and Definitions:**\n - Let \\( P \\) be the perimeter of the parallelogram.\n - Let \\( d \\)... |
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{
"content": "Add $4_6 + 14_6.$ Express your answer in base $6.$",
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{
"content": "When adding the numbers, we notice that $4+4$ leaves a residue of $2$ when divided by $6.$ Thus, the sum will have a rightmost digit of $2,$ and we must carry-over. This yields that $$\\begin{array}{c@... |
[
{
"content": "It is known that $\\sin y = 2 \\cos x + \\frac{5}{2} \\sin x$ and $\\cos y = 2 \\sin x + \\frac{5}{2} \\cos x$. Find $\\sin 2x$.",
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{
"content": "\n1. Given the equations:\n\n \\[\n \\sin y = 2 \\cos x + \\frac{5}{2} \\sin x\n \\]\n \\[\n \\cos y = 2 \\sin x ... |
[
{
"content": "Find the area of the triangle with vertices $(-1,4),$ $(7,0),$ and $(11,5).$",
"role": "user"
},
{
"content": "Let $A = (-1,4),$ $B = (7,0),$ and $C = (11,5).$ Let $\\mathbf{v} = \\overrightarrow{CA} = \\begin{pmatrix} -1 - 11 \\\\ 4 - 5 \\end{pmatrix} = \\begin{pmatrix} -12 \\\\ -1 \... |
[
{
"content": "Five rays $\\overrightarrow{OA}$ , $\\overrightarrow{OB}$ , $\\overrightarrow{OC}$ , $\\overrightarrow{OD}$ , and $\\overrightarrow{OE}$ radiate in a clockwise order from $O$ forming four non-overlapping angles such that $\\angle EOD = 2\\angle COB$ , $\\angle COB = 2\\angle BOA$ , while... |
[
{
"content": "How much time violinist Ling Ling spent practicing each day?\n\nContext: In 2017, TwoSet Violin made a comedic reference to Ling Ling, a fictional violinist who \"practices 40 hours a day\". In an interview with Yle Uutiset, they described Ling Ling as the final boss of a video game: the Chuck Nor... |
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{
"content": "A truncated cone has horizontal bases with radii 24 and 5. A sphere is tangent to the top, bottom, and lateral surface of the truncated cone. What is the radius of the sphere?",
"role": "user"
},
{
"content": "Let's denote the radii of the bottom and top bases of the truncated cone as ... |
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{
"content": "The sides of rectangle $ABCD$ have lengths $10$ and $11$. An equilateral triangle is drawn so that no point of the triangle lies outside $ABCD$. The maximum possible area of such a triangle can be written in the form $p\\sqrt{q}-r$, where $p$, $q$, and $r$ are positive integers, and $q$ is not div... |
[
{
"content": "\nConsider an arithmetic sequence $\\left\\{a_{n}\\right\\}$ with the sum of the first $n$ terms denoted as $S_{n}$. Given that $S_{2}=10$ and $S_{5}=55$, the coordinates of a direction vector for the line passing through the points $P\\left(n, a_{n}\\right)$ and $Q\\left(n+2, a_{n+2}\\right)$ cou... |
[
{
"content": "What is the period of $y = \\tan \\frac{x}{2}$?",
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{
"content": "The graph of $y=\\tan \\frac{x}{2}$ passes through one full period as $\\frac{x}{2}$ ranges from $-\\frac{\\pi}{2}$ to $\\frac{\\pi}{2},$ which means $x$ ranges from $-\\pi$ to $\\pi.$ Thus, the period i... |
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{
"content": "What is the least common multiple of 18 and 30?",
"role": "user"
},
{
"content": "Firstly, we factorize each number:\n- \\(18 = 2 \\cdot 3^2\\)\n- \\(30 = 2 \\cdot 3 \\cdot 5\\)\n\nTo find the LCM, we take the highest power of all prime factors present:\n- The highest power of 2 presen... |
[
{
"content": "What is the EU compensation regulation EU261 for cancelled flights?\n\nContext: The Flight Compensation Regulation 2004 (EC) No 261/2004 is a regulation in EU law establishing common rules on compensation and assistance to passengers in the event of denied boarding, flight cancellations, or long d... |
[
{
"content": "Given $ \\sin \\alpha = \\frac{2}{3} $, find the value of $ \\cos^2\\left( \\frac{\\alpha}{2} - \\frac{\\pi}{4} \\right) $.",
"role": "user"
},
{
"content": "We have been given that $ \\sin \\alpha = \\frac{2}{3} $. Firstly, let's find the cosine of $ \\alpha $. Since $\\sin^2 \\alpha ... |
[
{
"content": "Why Linux fails as a desktop?",
"role": "user"
},
{
"content": "Linux has been criticized for a number of reasons, including lack of user-friendliness and having a steep learning curve, being inadequate for desktop use, lacking support for some hardware, having a relatively small games... |
[
{
"content": "What is SAP?",
"role": "user"
},
{
"content": "SAP is a multinational software vendor headquartered in Walldorf, Germany. SAP stands for \"System Analyse und Programmentwicklung\" which are the German words for System Analysis and Program Development. SAP was founded in 1972 by Dietmar... |
[
{
"content": "Let $A_1A_2,B_1B_2, C_1C_2$ be three equal segments on the three sides of an equilateral triangle. Prove that in the triangle formed by the lines $B_2C_1, C_2A_1,A_2B_1$ , the segments $B_2C_1, C_2A_1,A_2B_1$ are proportional to the sides in which they are contained.",
"role": "user"
},... |
[
{
"content": "Find the integer $n$, $0 \\le n \\le 6$, such that \\[n \\equiv 100000 \\pmod{7}.\\]",
"role": "user"
},
{
"content": "Since $100000 \\equiv 5 \\pmod{7}$, the integer $n$ we seek is $n = \\boxed{5}$.",
"role": "assistant"
}
] |
[
{
"content": "The length of 3 ropes are in a certain ratio. The sum of the weights of the longest and the shortest rope is 100 meters more than the length of the third rope. The length of the shortest rope is 80 meters. What is the ratio of the lengths of the ropes?",
"role": "user"
},
{
"content": ... |
[
{
"content": "Rachel is some years older than Leah. The sum of their ages is 34. Rachel is 19 years old. How many years older is Rachel than Leah?",
"role": "user"
},
{
"content": "If Rachel is 19 years old and the sum of Rachel and Leah's ages is 34, then we can find Leah's age by subtracting Rache... |
[
{
"content": "A circular dartboard is divided into regions with various central angles, as shown. The probability of a dart randomly landing in a particular region is $\\frac16$. What is the corresponding measure, in degrees, of the central angle of this section of the dartboard? [asy]\nunitsize(1.5cm);\ndefaul... |
[
{
"content": "Given $x>0$, $y>0$, and $x+8y-xy=0$,\n(1) What are the values of $x$ and $y$ when $xy$ is minimized?\n(2) What are the values of $x$ and $y$ when $x+y$ is minimized?",
"role": "user"
},
{
"content": "(1) Since $x>0$ and $y>0$, and given that $x+8y-xy=0$, we can rearrange the equation t... |
[
{
"content": "A box with a volume of 24 $\\text{cm}^3$ can hold 75 paperclips. How many paperclips could a box with a volume of 60 $\\text{cm}^3$ hold, assuming the number of paperclips scales directly with the volume?",
"role": "user"
},
{
"content": "1. Let $x$ be the number of paperclips that the... |
[
{
"content": "What is the difference between a putter and a driver in golf?",
"role": "user"
},
{
"content": "In golf, a driver is generally used from the tee box to hit the ball as far as possible at the beginning of a hole. A putter is used when on the green to hit the ball short distances on the ... |
[
{
"content": "Given proposition $p$: All exponential functions are monotonic, then the negation of $p$, $\\neg p$, is\n\nA: All exponential functions are not monotonic.\nB: All monotonic functions are not exponential functions.\nC: There exists an exponential function that is not monotonic.\nD: There exists a m... |
[
{
"content": "Given that the random variable $X$ follows a binomial distribution $X \\sim B(6, \\frac{1}{3})$, find the probability $P(X=2)$.",
"role": "user"
},
{
"content": "Given that the random variable $X$ follows a binomial distribution, the probability of getting exactly $k$ successes in $n$ ... |
[
{
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. Given the vectors $m=(b+c,a^{2}+bc)$ and $n=(b+c,-1)$, and $m\\cdot n=0$.\n\n(1) Find the measure of angle $A$;\n\n(2) If $a=3$, find the maximum perimeter of $\\triangle ABC$.",
"role": "u... |
[
{
"content": "What is the sum of the number of faces, edges and vertices of a triangular prism?\n\n[asy]\ndraw((0,0)--(10,0)--(5,8.7)--cycle);\ndraw((0,0)--(20,20),dashed);\ndraw((10,0)--(30,20));\ndraw((5,8.7)--(25,28.7));\ndraw((25,28.7)--(30,20)--(20,20)--cycle,dashed);\ndraw((25,28.7)--(30,20));\n[/asy]",
... |
[
{
"content": "Corn costs 99 cents per pound, and beans cost 45 cents per pound. If Shea buys 24 total pounds of corn and beans, and it costs $\\$18.09$, how many pounds of corn did Shea buy? Express your answer as a decimal to the nearest tenth.",
"role": "user"
},
{
"content": "Let $c$ and $b$ be t... |
[
{
"content": "The railway department stipulates that the sum of the length, width, and height of a passenger's luggage must not exceed $160cm$. A manufacturer produces luggage that meets this requirement. It is known that the height of the luggage is $30cm$, and the ratio of the length to the width is $3:2$. Wh... |
[
{
"content": "Find all real values of $x$ that satisfy $x + \\frac{45}{x-4} = -10.$\n\nEnter all the solutions, separated by commas.",
"role": "user"
},
{
"content": "Multiplying both sides by $x-4,$ we get $x(x-4) + 45 = -10(x-4),$ or $x^2-4x+45 = -10x+40,$ which simplifies to $x^2+6x + 5 = 0.$ Thi... |
[
{
"content": "Compute: $8 + 6(3-8)^2$.",
"role": "user"
},
{
"content": "We tackle the parentheses, then the exponent, then the product, then the sum: \\begin{align*}\n8+6(3-8)^2 &= 8 + 6(-5)^2\\\\\n&= 8+6\\cdot 25\\\\\n&= 8+150\\\\\n&=\\boxed{158}.\n\\end{align*}",
"role": "assistant"
}
] |
[
{
"content": "From the passage provided, extract where Java was developed\n\nContext: Java is a high-level, class-based, object-oriented programming language that is designed to have as few implementation dependencies as possible. It is a general-purpose programming language intended to let programmers write on... |
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