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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": "In the series A Song of Ice and Fire, who is the founder of House Blackfyre?",
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"content": "House Blackfyre, a branch that separated from House Targaryen, was founded by Daemon I Targaryen",
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] |
[
{
"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": "Let the ellipse $$\\frac {x^{2}}{a^{2}}+ \\frac {y^{2}}{b^{2}}=1(a＞b＞0)$$ have its left focus at F, its top vertex at A, and a line through point A perpendicular to AF intersects the ellipse and the positive x-axis at points P and Q, respectively, with AP:PQ = 8:5. \n(1) Find the eccentricity of ... |
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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": "Best place to visit for a day from Bangalore",
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},
{
"content": "1. Myshore\n2. Coorg\n3. Ooty",
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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... |
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{
"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": "Let \\( \\mathbf{a}, \\mathbf{b}, \\) and \\( \\mathbf{c} \\) be unit vectors such that \\( \\mathbf{a} \\cdot \\mathbf{b} = \\mathbf{a} \\cdot \\mathbf{c} = 0, \\) and the angle between \\( \\mathbf{b} \\) and \\( \\mathbf{c} \\) is \\( \\frac{\\pi}{3} \\). Then\n\\[\n\\mathbf{a} = k (\\mathbf{b}... |
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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": "What sport did Troy Stradford play in college?",
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{
"content": "Troy Stradford played football at Boston College in the 1980s and went on to play professionally for the Miami Dolphins in the NFL.",
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] |
[
{
"content": "Is it safe for dogs to eat chocolate?",
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},
{
"content": "No, chocolate is considered dangerous for dogs to consume.",
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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 $P$ be a point outside of circle $O.$ A segment is drawn from $P$ such that it is tangent to circle $O$ at point $T.$ Meanwhile, a secant from $P$ intersects $O$ at $A$ and $B,$ such that $PA < PB.$ If $PA = 3$ and $PT = AB - PA,$ then what is $PB$?",
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{
"content":... |
[
{
"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... |
[
{
"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 are the FAANG companies?",
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{
"content": "Five of the best performing tech stocks of the last decade are Facebook, Amazon, Apple, Netflix, and Google. Those five stocks have been pulled together into an the acronym FAANG.",
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] |
[
{
"content": "The graph below shows a portion of the curve defined by the quartic polynomial $P(x)=x^4+ax^3+bx^2+cx+d$.\n\n[asy]\nunitsize(0.8 cm);\n\nint i;\n\nreal func (real x) {\n return(0.5*(x^4/4 - 2*x^3/3 - 3/2*x^2) + 2.7);\n}\n\ndraw(graph(func,-4.5,4.5));\ndraw((-4.5,0)--(4.5,0));\ndraw((0,-5.5)--(0,5... |
[
{
"content": "In an election with only two candidates, a candidate secured 70% of the valid votes and won by a certain majority. The total number of valid votes was 435. What was the majority of votes by which the candidate won?",
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{
"content": "Let's denote the winning candidate's ... |
[
{
"content": "In the plane, the triangles $ABD$ and $BCE$ are outside the triangle $ABC$ and are also isosceles triangles right at $D$ and $C$ respectively. The point $H$ is the intersection of $CD$ and $AE$ . Show that $BH$ and $AE$ are perpendicular.",
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{
"conte... |
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{
"content": "Each term of a sequence, after the first term, is inversely proportional to the term preceding it, and the constant of proportionality stays the same. If the first term is 2 and the second term is 5, what is the 12th term?",
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{
"content": "Recall that two quantities ar... |
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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... |
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{
"content": "Compute\n\\[\\prod_{n = 1}^{20} \\frac{n + 3}{n}.\\]",
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"content": "We have that\n\\begin{align*}\n\\prod_{n = 1}^{20} &= \\frac{4}{1} \\cdot \\frac{5}{2} \\cdot \\frac{6}{3} \\cdot \\frac{7}{4} \\dotsm \\frac{20}{17} \\cdot \\frac{21}{18} \\cdot \\frac{22}{19} \\cdo... |
[
{
"content": "What are the four primary states of matter? Answer in bullet point list, and capitalize each words",
"role": "user"
},
{
"content": "- Solid\n- Liquid\n- Gas\n- Plasma",
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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": "Given that the polynomial $x^2-5x+t$ has only positive integer roots, find the average of all distinct possible values of $t$.",
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},
{
"content": "Let $r_1$ and $r_2$ be the roots of this polynomial. Since $-\\frac{b}{a}$ is the sum and $\\frac{c}{a}$ is the product of th... |
[
{
"content": "A group of science students went on a field trip along with their teachers and another group of language students. They took transportation using the following vehicles: 3 vans, 5 buses, and 2 minibuses. The vans had a capacity of 7 students each, the buses could hold 25 students and 2 teachers ea... |
[
{
"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 TV show features a team of teenagers that power up with powers given to them by Zordon to save the world from monsters?",
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{
"content": "The Mighty Morphin Power Rangers.",
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] |
[
{
"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": "Points $P_{1}(-1$,$y_{1})$, $P_{2}(\\frac{5}{2}$,$y_{2})$, $P_{3}(6$,$y_{3})$ are all on the graph of the quadratic function $y=mx^{2}-2mx+1\\left(m \\gt 0\\right)$. The relationship between $y_{1}$, $y_{2}$, and $y_{3}$ is ( ).\n\nA: $y_{1} \\gt y_{2} \\gt y_{3}$\n\nB: $y_{3} \\gt y_{2} \\gt y_{1... |
[
{
"content": "Given the exponential function $f(x) = a^x$ is always less than 2 for $x \\in [-2, 2]$, the range of the real number $a$ is \\_\\_\\_\\_\\_\\_.",
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{
"content": "When $a > 1$, $f(x) = a^x$ is an increasing function on $[-2, 2]$,\n\n∴ The maximum value of $f(x)$, $f(x)_{... |
[
{
"content": "In a $6 \\times 6$ chessboard, some $1 \\times 2$ dominoes are placed, each covering exactly two squares. If there are still 14 squares uncovered, determine if at least one more domino can be placed on the board.",
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{
"content": "\n1. **Strategy for approaching the pro... |
[
{
"content": "A picky princess is choosing a groom. One hundred grooms are courting her, each better than the last, and no two are equal. However, they propose in a random order. We will call a groom outstanding if the princess likes him more than all who have proposed before him. The first groom is also consid... |
[
{
"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 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$\\text{(A)}\\ 6 \\qquad \\text{(B)}\\ 7 \\qquad \\text{(C)}\\ 9 \\qquad \\text{(D)}\\ 11 \\qquad ... |
[
{
"content": "a can finish a piece of work in 4 days . b can do it in 14 days . they work together for two days and then a goes away . in how many days will b finish the work ?",
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{
"content": "Let's calculate the amount of work A and B can do together in one day.\n\nA can finish th... |
[
{
"content": "Find the number of square units in the area of the triangle.\n\n[asy]size(125);\ndraw( (-10,-2) -- (2,10), Arrows);\ndraw( (0,-2)-- (0,10) ,Arrows);\ndraw( (5,0) -- (-10,0),Arrows);\n\nlabel(\"$l$\",(2,10), NE);\nlabel(\"$x$\", (5,0) , E);\nlabel(\"$y$\", (0,-2) , S);\nfilldraw( (-8,0) -- (0,8) --... |
[
{
"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": "Petya has $n^{3}$ white $1 \\times 1 \\times 1$ cubes. He wants to assemble them into an $n \\times n \\times n$ cube that is completely white on the outside. What is the minimum number of cube faces Vasya needs to paint to prevent Petya from achieving this? Solve the problem for a) $n=2$; b) $n=3... |
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{
"content": "Given the polynomial \\( q(x) = x^5 - 4x^2 + 3 \\), find the coefficient of the \\( x^4 \\) term in the polynomial \\( (q(x))^2 \\).",
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},
{
"content": "First, analyze the polynomial \\( q(x) = x^5 - 4x^2 + 3 \\). To find the \\( x^4 \\) term in \\( (q(x))^2 \\), we consi... |
[
{
"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": "How many island does Hawaii have?",
"role": "user"
},
{
"content": "Hawaii has 8 islands in total,",
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] |
[
{
"content": "If w is 40 percent less than u, u is 40 percent less than y, and z is 46 percent less than y, then z is greater than w by what percent of w?",
"role": "user"
},
{
"content": "Let's start by expressing the relationships between w, u, and y in terms of equations.\n\nIf w is 40 percent le... |
[
{
"content": "A function $f(x)$ satisfies the following conditions: ① $f(x)$ is a monotonically increasing function on the interval $\\left[a,b\\right]$; ② The range of $f(x)$ on $\\left[a,b\\right]$ is $\\left[ka,kb\\right]$. The interval $\\left[a,b\\right]$ is called a $k$-level \"harmonic interval\" of $y=f... |
[
{
"content": "Which team's have the most NCAA Division I men's basketball championships?",
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},
{
"content": "1. UCLA has 11 championship wins\n2. Kentucky has 8 championship wins\n3. North Carolina has 6 championship wins\n4. Due has 5 championship wins\n5. Indian has 5 championship wi... |
[
{
"content": "Use the bisection method to find an approximate solution to the equation $x^2-5=0$ within the interval (2, 3), after \\_\\_\\_\\_\\_\\_ bisections, the accuracy can reach 0.01.",
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{
"content": "Since the initial interval length is 1, and the accuracy requirement is 0.0... |
[
{
"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... |
[
{
"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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}
] |
[
{
"content": "Write a recipe for making garlic mashed potatoes which goes through step by step.",
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{
"content": "1) Wash and peel the potatoes\n2) Chop the potatoes into inch size pieces\n3) Fill a pot with enough water to cover the potatoes\n4) Bring the water to boil\n5) Boil unti... |
[
{
"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": "Find the remainder of the Euclidean division of \\( 2018^{2019^{2020}} \\) by 11.",
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},
{
"content": "1. Consider the given expression \\(2018^{2019^{2020}}\\) modulo 11. To simplify the problem, we will make use of Fermat's Little Theorem, which states that if \\(p\\) is... |
[
{
"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)}.\\]",
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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": "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": "Each subsequent number is chosen independently of the previous ones. If it matches one of the already chosen numbers, you should move clockwise to the first unchosen number.\n\nIn the end, $k$ different numbers are obtained.\n\na) Is it true that the appearance of each specific number in such a se... |
[
{
"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": "What is the greatest product obtainable from two integers whose sum is 2024?",
"role": "user"
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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 ... |
[
{
"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": "A regular octahedron is formed by joining the centers of adjoining faces of a cube. The ratio of the volume of the octahedron to the volume of the cube is\n$\\mathrm{(A) \\frac{\\sqrt{3}}{12} } \\qquad \\mathrm{(B) \\frac{\\sqrt{6}}{16} } \\qquad \\mathrm{(C) \\frac{1}{6} } \\qquad \\mathrm{(D) \\... |
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{
"content": "Solve the system of differential equations\n\n$$\n\\left\\{\\begin{array}{l}\nx^{\\prime}=2 x-4 y \\\\\ny^{\\prime}=x-3 y\n\\end{array}\\right.\n$$",
"role": "user"
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"content": "\nTo solve the system of differential equations\n\n\\[ \n\\left\\{\n\\begin{array}{l}\nx' = 2x - 4y \\\\... |
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{
"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": "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.... |
[
{
"content": "Given the expression $\\left(kx^{-1}+ky^{-1}\\right)^{-1}$, simplify it to its reduced form.\n$\\textbf{(A) \\ }\\frac{xy}{x+y} \\qquad \\textbf{(B) \\ }k(x+y) \\qquad \\textbf{(C) \\ }xy \\qquad \\textbf{(D) \\ }\\frac{xy}{k(x+y)} \\qquad \\textbf{(E) \\ }k\\frac{x+y}{xy}$",
"role": "user"
... |
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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": "Find the area of the triangle with vertices $(-1,4),$ $(7,0),$ and $(11,5).$",
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{
"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": "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... |
[
{
"content": "Where can I find Yukigassen tournaments?\n\nContext: Yukigassen (雪合戦) is a snowball fighting-competition from Japan. Today there are annual tournaments in Sōbetsu, Hokkaidō in Japan, Kemijärvi in Finland, Vardø in Norway, Murmansk in Russia, Mount Buller, Victoria in Australia, Luleå in Sweden, An... |
[
{
"content": "What number is a multiple of every integer?",
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},
{
"content": "For every integer $x$, $\\boxed{0} = 0 \\cdot x$ is a multiple of $x$.",
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] |
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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": "Consider a problem where hexagonal tiles are arranged such that each subsequent hexagon has an additional band of dots, with each side of a layer containing one more dot than its previous layer. The first hexagon in the sequence has 2 dots, and the pattern extends outwards uniformly. How many dots... |
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{
"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... |
[
{
"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": "In the Cartesian coordinate system $xOy$, for point $P(x,y)$, we call the point ${P'}(-y+1,x+1)$ the conjugate point of point $P$. Given that the conjugate point of point $A_{1}$ is $A_{2}$, the conjugate point of point $A_{2}$ is $A_{3}$, the conjugate point of point $A_{3}$ is $A_{4}$, and so on... |
[
{
"content": "Let $S$ be the set of all rational numbers $r$, $0<r<1$, that have a repeating decimal expansion in the form $0.abcabcabc\\ldots=0.\\overline{abc}$, where the digits $a$, $b$, and $c$ are not necessarily distinct. To write the elements of $S$ as fractions in lowest terms, how many different numera... |
[
{
"content": "How do you make a simple green salsa?",
"role": "user"
},
{
"content": "Blend the following ingredients in a blender:\n \n8 Jalapeños or 4 Serrano Peppers (your heat pref)\n4 Tomatillos\n½ Small Onion\n1 Garlic Clove\n½ Bunch of Cilantro\n1 Big Avocado \n\nAfter it's blended well pour... |
[
{
"content": "The tax on a commodity is diminished by 16%, and its consumption increased by 15%. What is the effect on revenue in percentage?",
"role": "user"
},
{
"content": "Let's assume the original tax on the commodity is T and the original consumption is C. The revenue generated from the tax is... |
[
{
"content": "Three positive integers add to 93 and have a product of 3375. The integers are in the ratio 1: k: k². What are the three integers?",
"role": "user"
},
{
"content": "\nLet the three positive integers be \\( A \\), \\( Ak \\), and \\( Ak^2 \\), where \\( A \\) is a positive constant.\n\n... |
[
{
"content": "Triangle $ABC$ has $BC=20.$ The incircle of the triangle evenly trisects the median $AD.$ If the area of the triangle is $m \\sqrt{n}$ where $m$ and $n$ are integers and $n$ is not divisible by the square of a prime, find $m+n.$\n",
"role": "user"
},
{
"content": "[asy] size(300); poin... |
[
{
"content": "In rectangle ABCD, AC = 10, AB = 8, then the area of $\\triangle ABC$ is ____.",
"role": "user"
},
{
"content": "**Solution**: Since all the interior angles of rectangle ABCD are right angles, $\\triangle ABC$ is a right-angled triangle. \nGiven AC = 10, AB = 8, \nthus, BC = $\\sqrt{... |
[
{
"content": "A bakery sells three kinds of rolls. How many different combinations of rolls could Jack purchase if he buys a total of six rolls and includes at least one of each kind?",
"role": "user"
},
{
"content": "We don't have to worry about three of the rolls since there will be one of each ki... |
[
{
"content": "A band has 72 members who will all be marching during halftime. They need to march in rows with the same number of students per row. If there must be between 5 and 20 students per row, in how many possible row-lengths can the band be arranged?",
"role": "user"
},
{
"content": "If $x$ m... |
[
{
"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": "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": "What is the Capitol",
"role": "user"
},
{
"content": "The United States Capitol, often called The Capitol or the Capitol Building, is the seat of the United States Congress, the legislative branch of the federal government. It is located on Capitol Hill at the eastern end of the Nation... |
[
{
"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": "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": "Extract what previous provinces Kardzhali a part of in the past\n\nContext: The territory of Kardzhali province was acquired by Bulgaria during the First Balkan War in 1912. In 1913 the region was organized as the district (окръг, okrăg in Bulgarian) of Mestanli. This district was part of Stara Za... |
[
{
"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... |
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