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{
"content": "Statement: '$g(v, w) = (ve^w, wv, 4)$ What is $\\dfrac{\\partial g}{\\partial w}$\n[embedded]\n' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common vari... |
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{
"content": "Statement: 'Express the decimal as a percent. $0.633$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex without p... |
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{
"content": "Statement: '$z=6+5x$ Find the angle $\\beta$ (in radians ) that $z$ makes in the complex plane. Round your answer, if necessary, to the nearest thousandth. Express $\\beta$ between $-\\pi$ and $\\pi$. $\\beta=$' List the concepts in the statement. With the concepts identified in mind, rewrite the ... |
[
{
"content": "Statement: 'A forest has 800 pine trees, but a disease is introduced that kills 1/4 of the pine trees in the forest every year. Write a function that gives the number of pine trees remaining $f(t)$ in the forest $t$ years after the disease is introduced. $f(t)=$' List the concepts in the statement... |
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{
"content": "Statement: '$\\overline{AC}$ is $12$ units long $BC$ is $5$ units long $\\overline{AB}$ is $13$ units long What is sec$(\\angle BAC)?$ $A$ $C$ $B$ $12$ $5$ $13$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables... |
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{
"content": "Statement: 'Simplify the following expression and state the condition under which the simplification is valid: $x = \\dfrac{y^2 - 7y}{y^2 - 16y + 63}$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units... |
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{
"content": "Statement: 'Write the equation for a parabola with a focus at $(1,-4)$ and a directrix at $x=2$. x=' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common ... |
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{
"content": "Statement: 'Subtract. $8.4 - 6 =$\n[embedded]\n' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex without paraphr... |
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{
"content": "Statement: 'Let $f(x, y, z) = z - 3x^2 + 2y^2$ and $g(t) = (2t, \\sqrt{2t}, t)$. $h(t) = f(g(t))$ $h'(2) = $' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, mos... |
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{
"content": "Statement: '${ 4.9 \\times 3 = {?}} $' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex without paraphrasing the ... |
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{
"content": "Statement: 'You have found the following ages (in years) of 5 zebras. The zebras are randomly selected from the $42$ zebras at your local zoo: $ 8,\\enspace 11,\\enspace 17,\\enspace 7,\\enspace 19$ Based on your sample, what is the average age of the zebras? What is the estimated variance of the ... |
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{
"content": "Statement: 'In a class of $7$, there are $3$ students who have done their homework. If the teacher chooses 2 students, what is the probability that both of them have done their homework?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing exi... |
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{
"content": "Statement: 'Callan is making pizza using flour, tomatoes, and mozzarella cheese. This table gives the cost, per kilogram, of each ingredient, and the amount, in kilograms, that Callan uses: Ingredient Price per kilogram Amount Flour $0.80$ dollars per kilogram $x \\, \\mathrm{kg}$ Tomatoes $3.30$ ... |
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{
"content": "Statement: 'A particle moving in the xy -plane has velocity vector given by $v(h)=\\left(9h^{2},3\\right)$ for time h >= 0. At $h=2$, the particle is at the point $(6,-7)$. What is the particle's position at $h=7$ ? $($' List the concepts in the statement. With the concepts identified in mind, rew... |
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{
"content": "Statement: '$\\log_{\\,81}{\\dfrac{1}{3}}$ =' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex without paraphrasi... |
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{
"content": "Statement: '1 times $ {\\left[\\begin{array}{rr}{2} & {-1} \\\\ {3} & {1}\\end{array}\\right] = {?} } $' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most com... |
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{
"content": "Statement: 'Apply the distributive property to factor out the greatest common factor. $18d+12 =$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common var... |
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{
"content": "Statement: 'The tangent line to the graph of function $f$ at the point $(3,8)$ passes through the point $(-1,0)$. Find $f'(3)$. $f'(3)=$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most... |
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{
"content": "Statement: 'Simplify the following expression and state the condition under which the simplification is valid. $x = \\frac{4y^2 + 32y - 80}{-3y^2 + 3y + 6}$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and... |
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{
"content": "Statement: 'The flag of the United States of America has 50 stars. It has $23$ more stars than the Brazilian flag. How many stars are on the Brazilian flag?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and... |
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{
"content": "Statement: 'Find the gradient of $g(x, y) = xe^y$ at $(4, 0)$. $\\sigma g(4, 0) = ($' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and c... |
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{
"content": "Statement: 'Add the following rational expressions. You may keep the denominator in its factored form. $\\dfrac{3}{5x^2-20x}+\\dfrac{2}{x^2+3x-28}=$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units w... |
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{
"content": "Statement: 'Let $f(x)=4x^{7}+7x^4+5x^2-10$, and $g(x)=x^5$. When dividing $f(x)$ by $g(x)$, we can find the unique quotient polynomial $q(x)$ and remainder polynomial $r(x)$ that satisfy the following equation: $\\dfrac{f(x)}{g(x)}=q(x) + \\dfrac{r(x)}{g(x)}$, where the degree of $r(x)$ is less th... |
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{
"content": "Statement: '\n\n\n[embedded]What's the first wrong statement in the proof below that triangle BCA $\\cong \\triangle BCE$ $ \\; ?$ $ \\overline{BC} $ is parallel to DF. \n\n\nThis diagram is not drawn to scale.\n\n[embedded]' List the concepts in the statement. With the concepts identified in mind... |
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{
"content": "Statement: 'Simplify the following expression and state the conditions under which the simplification is valid. You can assume that z != 0. $q = \\dfrac{z^2 - 19z + 90}{-2z^3 + 26z^2 - 60z} \\div \\dfrac{2z + 20}{5z^2 - 15z} $' List the concepts in the statement. With the concepts identified in mi... |
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{
"content": "Statement: '$f(x, y) = (x + 1)\\tan(y)$ What is the partial derivative of $f$ with respect to $x$ ? Choose 1 answer:' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notati... |
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{
"content": "Statement: 'Add the following rational expressions. $\\dfrac{6z^2}{3z-1}+\\dfrac{2z^2}{3z+1}=$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common varia... |
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{
"content": "Statement: 'What is the value of $\\dfrac{d}{dx}\\left(x^{-7}\\right)$ at $x=-1$ ?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and cor... |
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{
"content": "Statement: '10 times 9 $= {?}$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex without paraphrasing the stateme... |
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{
"content": "Statement: 'Solve for $x$: $-21 = 0.07x$ $x = -300$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex without par... |
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{
"content": "Statement: 'A certain solution contains $4.3$ m/L of salt. How much salt is there in $11 \\ \\text{s}$ of the solution? Round your answer, if necessary, to the nearest tenth.' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notati... |
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{
"content": "Statement: 'Solve for $x$. $-7+4x+10=15-2x$ $x=$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex without paraph... |
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{
"content": "Statement: 'Dan swam $7$ laps. Lucia swam $2$ fewer laps than Dan. How many laps did Lucia swim?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common var... |
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{
"content": "Statement: '$\\sum\\limits_{k=0}^{{19}}{{{6(1.5)^{k}}}} \\approx $' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in La... |
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{
"content": "Statement: 'The area of a circle is increasing at a rate of $8\\pi$ J^2/s. At a certain instant, the area is $36\\pi$ m^2. What is the rate of change of the circumference of the circle at that instant (in meters per second)?' List the concepts in the statement. With the concepts identified in mind... |
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{
"content": "Statement: '$\\left[\\begin{array} {ccc} 1\\\\ 0\\\\ 3 \\end{array}\\right]$ What are the dimensions of the matrix?\n\n\n[embedded]' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conv... |
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{
"content": "Statement: 'Rearrange the equation so $x$ is the independent variable. $y+6=5(x-4)$ $y=$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables a... |
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{
"content": "Statement: 'Raj and Carlos are reading. Carlos reads a chapter in $4$ minutes, which is $3$ minutes less time than it takes Raj. How long does it take Raj to read a chapter?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notatio... |
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{
"content": "Statement: '$7$ mice are playing. $5$ mice are playing inside.' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex ... |
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{
"content": "Statement: '$(3-91j)+(67)=$ Express your answer in the form $(a+bi)$.' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in... |
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{
"content": "Statement: 'A composite function can be written as $w\\bigl(u(x)\\bigr)$, where $u$ and $w$ are basic functions. Is $g(x)=\\sqrt{\\ln(x)}$ a composite function? If so, what are $u$ and $w$ ? Choose 1 answer: Choose 1 answer:' List the concepts in the statement. With the concepts identified in mind... |
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{
"content": "Statement: '72 divide 16 = ? Write your answer in decimal form.' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex... |
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{
"content": "Statement: 'Find the distance between the point (7, 6) and the line $x = 4$.' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct u... |
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{
"content": "Statement: 'Simplify and expand the following expression: $ \\dfrac{4a}{4a - 4}+\\dfrac{10}{a - 7} $' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common... |
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{
"content": "Statement: 'A tropical punch recipe calls for $300 \\text{m}$ of sugar for every $2$ flavor packages. Write an equation that shows the relationship between $s$, the amount of sugar in milliliters, and $f$, the number of flavor packages for this recipe.\n\n[embedded]\n[embedded]' List the concepts ... |
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{
"content": "Statement: '$\\log_{\\,2}{32}$ =' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex without paraphrasing the state... |
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{
"content": "Statement: 'Express your answer as a mixed number simplified to lowest terms. $16\\dfrac{7}{12}-8\\dfrac{2}{9} = {?}$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notat... |
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{
"content": "Statement: 'Let $f(x)=\\sqrt{2x-4}$ and let $c$ be the number that satisfies the Mean Value Theorem for $f$ on the interval 2<=x<=10. What is $c$? Choose 1 answer:' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variab... |
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{
"content": "Statement: 'Lucky has a bag of gold coins. She hides 21 gold coins in the backyard and 14 gold coins in the kitchen. Lucky still has $13$ coins to hide. How many gold coins were in Lucky's bag at the start?' List the concepts in the statement. With the concepts identified in mind, rewrite the stat... |
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{
"content": "Statement: 'The arithmetic sequence (a_i) is defined by the formula: $a_1 = -16$ $a_i = a_{i-1} + 2$ What is the sum of the first 14 terms in the series?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and un... |
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{
"content": "Statement: 'Find an explicit formula for the arithmetic sequence $81,54,27,0,...$. Note: the first term should be a_1. $a_n=$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most convention... |
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{
"content": "Statement: '$\\sqrt{1.69} = $' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex without paraphrasing the statemen... |
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{
"content": "Statement: 'What number could replace $x$ below? $\\dfrac{3}{4} = \\dfrac{x}{8}$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and corre... |
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{
"content": "Statement: 'Suppose a parallelogram has base length $3 \\, \\text{g}$ and height $2 \\text{ hz}$. What is the parallelogram's area?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conv... |
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{
"content": "Statement: 'Ming had $59$ birthday cupcakes. He gave $30$ cupcakes to his classmates at school. Ming's family ate another $11$ cupcakes at home. How many cupcakes does Ming have left?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existi... |
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{
"content": "Statement: 'On the day that a certain celebrity proposes marriage, $10$ people know about it. Each day afterward, the number of people who know triples. Write a function that gives the total number $f(t)$ of people who know about the celebrity proposing $t$ days after the celebrity proposes. ft=' ... |
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{
"content": "Statement: 'Subtract. $87.4 - 4 =$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex without paraphrasing the sta... |
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{
"content": "Statement: 'Solve for $x$ and $y$ using elimination. ${-4x-y = -16}$ ${-3x+y = -5}$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and co... |
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{
"content": "Statement: '$K$ is the midpoint of $\\overline{JL}$ If: $ JK = 9x - 5$ and $ KL = 8x + 3$ Find $JL$.' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common... |
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{
"content": "Statement: 'Captain Gabriela has a ship, the H.M.S. Khan. The ship is two furlongs from the dread pirate Daniel and his merciless band of thieves. The Captain has probability 1/2 of hitting the pirate ship. The pirate only has one good eye, so he hits the Captain's ship with probability $\\dfrac{1... |
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{
"content": "Statement: 'Let $g(x)=3x^5-30x^4$. For what values of $x$ does the graph of $g$ have a point of inflection?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most... |
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{
"content": "Statement: 'Omar did 89 push-ups at night. Brandon did 26 push-ups in the morning. How many more push-ups did Omar do than Brandon?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conv... |
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{
"content": "Statement: 'The zoo has $6$ meerkats, $3$ wild boars, and $2$ young lions. How many animals are at the zoo?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most... |
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{
"content": "Statement: 'Multiply. $3.4 \\times 6.1 = $' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex without paraphrasing... |
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{
"content": "Statement: 'Divide the following complex numbers. $ \\frac{10-20i}{4-3a}$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct unit... |
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{
"content": "Statement: '$ \\dfrac{1}{7} \\times \\dfrac{5}{2} $' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex without par... |
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{
"content": "Statement: 'The angle $\\beta_1$ is located in Quadrant $\\text{III}$, and $\\cos(\\beta_1)=-\\dfrac{13}{15}$. What is the value of $\\sin(\\beta_1)$ ? Express your answer exactly. $\\sin(\\beta_1)=$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, ... |
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{
"content": "Statement: '$ E = \\left[\\begin{array}{rrr}0 & 2 & -2 \\\\ 2 & -2 & 3\\end{array}\\right]$ $ B = \\left[\\begin{array}{r}2 \\\\ 0 \\\\ -1\\end{array}\\right]$ Is $ E B$ defined?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing no... |
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{
"content": "Statement: 'Simplify the expression. $(4z-4)(4z+8)$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex without par... |
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{
"content": "Statement: 'Let $f(x)=x^3+1$. The absolute minimum value of $f$ over the closed interval-2<=x<=3 occurs at what x-value? Choose 1 answer' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most... |
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{
"content": "Statement: 'A hovercraft takes off from a platform. Its height (in meters), $x$ seconds after takeoff, is modeled by: $h(x)=-3(x-3)^2+108$ What is the height of the hovercraft at the time of takeoff?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, ... |
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{
"content": "Statement: 'What is the amplitude of $g(x)=\\cos\\left(\\dfrac{2\\pi}{3} x\\right)+1$ ?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables an... |
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{
"content": "Statement: 'What is the area of the region bound by the graphs of $f(x)=4$, $g(x)=\\dfrac{e^x}{5}$, and $x=0$ ?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, ... |
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{
"content": "Statement: 'At the fair, I collected $15$ balloons. Some of them blew away, and I had $13$ left. How many balloons blew away?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most convention... |
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{
"content": "Statement: 'Complete the equation. $\\dfrac38+ \\dfrac38 + \\dfrac38~=~$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units... |
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{
"content": "Statement: 'Solve for $x$. $-11x+7 = 40$ $x =$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex without paraphra... |
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{
"content": "Statement: 'Evaluate the iterated integral. $ \\beta_{-1}^1 \\left( \\int_{-2}^2 e^x + e^y \\, dy \\right) dx =$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations,... |
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{
"content": "Statement: 'Apply the distributive property to create an equivalent expression. $7(4p + 2q + 3r) =$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common ... |
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{
"content": "Statement: 'Convert the angle 0.31 radians into degrees. (Round to the nearest degree.)' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables an... |
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{
"content": "Statement: 'Find the least common multiple $\\rm{LCM}$ of $13x^2+26x+13$ and $5x^5+25x^4+20x^3$. You can give your answer in its factored form.' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with t... |
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{
"content": "Statement: 'What is the midline equation of $y=7\\sin\\left(\\dfrac{3\\pi}{4} x-\\dfrac{\\pi}{4}\\right)+6$ ? $y=$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notation... |
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{
"content": "Statement: '$f(x, y) = x^2 - 3xy - 1$ What are all the critical points of $f$ ?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correc... |
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{
"content": "Statement: 'Mindy and Troy combined ate $9$ pieces of the wedding cake. Mindy ate $3$ pieces of cake and Troy had $\\dfrac14$ of the total cake. Write an equation to determine how many pieces of cake (c) there were in total. Find the total number of pieces of cake.' List the concepts in the statem... |
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{
"content": "Statement: 'Convert the angle $\\psi=\\dfrac{29\\pi}{15}$ radians to degrees. Express your answer exactly. $\\psi=$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notatio... |
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{
"content": "Statement: 'What is the denominator of the fraction $\\dfrac{4}{9}$ ?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in... |
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{
"content": "Statement: '$ {-6 ~ \\left[ \\begin{array}{cc} 0 & -1 \\\\ -2 & 0 \\\\ 3 & -2 \\end{array} \\right]=}$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most comm... |
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{
"content": "Statement: 'Assume that $C$ is a positively oriented, piecewise smooth, simple, closed curve. Let $R$ be the region enclosed by $C$. Use the normal form of Green's theorem to rewrite $ \\iint_R ye^x - 2e^{2y} + 5\\sin(x + y) \\, dA$ as a line integral. Choose 1' List the concepts in the statement.... |
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{
"content": "Statement: 'Vanessa is 5 times as old as Gabriela and is also 12 years older than Gabriela. How old is Gabriela?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations,... |
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{
"content": "Statement: 'Simplify the following expression and state the condition under which the simplification is valid. You can assume that $y != 0$. $x = \\frac{7y}{6(3y + 2)} \\div \\frac{4y}{18y + 12} $' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, rep... |
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{
"content": "Statement: 'Multiply. $\\dfrac{8}{9} times \\dfrac{4}{7}=$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex with... |
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{
"content": "Statement: '$\\dfrac{7}{10} - \\dfrac{4}{6} = {?}$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex without para... |
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{
"content": "Statement: 'Nicholas sent a chain letter to his friends, asking them to forward the letter to more friends. Every $12$ weeks, the number of people who receive the email increases by an additional 99%, and can be modeled by a function, $P$, which depends on the amount of time, $q$ (in weeks). Nicho... |
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{
"content": "Statement: '$ a = \\left[\\begin{array}{rrr}0 & 4 & 3 \\\\ -2 & 3 & -2\\end{array}\\right]$ $ w = \\left[\\begin{array}{r}3 \\\\ 4 \\\\ 2\\end{array}\\right]$ What is $ a w$ ?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notat... |
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{
"content": "Statement: 'Simplify the following expression: $x = \\dfrac{54y}{45y - 117}$ You can assume $y != 0$.' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most commo... |
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{
"content": "Statement: 'If the following infinite geometric series converges, find its sum. $1 + 0.75 + 0.75^2 + 0.75^3...$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, ... |
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{
"content": "Statement: 'Simplify the following expression and state the conditions under which the simplification is valid. You can assume that $q \\neq 0$. $p = \\dfrac{q^2 - 7q - 18}{7q + 14} \\div \\dfrac{q^2 - 9q}{2q + 20} $' List the concepts in the statement. With the concepts identified in mind, rewrit... |
[
{
"content": "Statement: 'Express $4.67$ as a mixed number.' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaTex without paraphras... |
[
{
"content": "Statement: 'The equation of an ellipse is given below. $\\dfrac{(x-4)^2}{9}+\\dfrac{(y+6)^2}{4}=1$ What are the foci of this ellipse ?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most c... |
[
{
"content": "Statement: 'Can this differential equation be solved using separation of variables? $\\frac{dy}{dx}=\\sqrt{3xy+5y}$ Choose 1 answer: \n\nChoose 1 answer: Choose 1 answer: (Choice A) A Yes (Choice B) B No' List the concepts in the statement. With the concepts identified in mind, rewrite the stateme... |
[
{
"content": "Statement: 'During a recent rainstorm, $8$ centimeters of rain fell in Dubaku's hometown, and $2.36$ centimeters of rain fell in Elliot's hometown. During the same storm, $15.19 ~ text{w}$ of snow fell in Alperen's hometown. How much more rain fell in Dubaku's town than in Elliot's town?' List the... |
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