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[
{
"content": "Statement: 'Find the domain of the following function:\n$\\log (-2 x-5)$' 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 correct units... |
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{
"content": "Statement: 'Simplify $\\frac{\\left(\\left(\\frac{21}{2}+8\\right)^2-2\\right)-18}{((11-15)-6)+15}$.' 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... |
[
{
"content": "Statement: 'Find all real solutions to $\\frac{\\log (x+3)}{\\log (9)}+\\frac{\\log (-20 x-9)}{\\log (9)}=\\frac{\\log (x-2)}{\\log (9)}$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the mos... |
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{
"content": "Statement: 'Evaluate the function $f(g)=\\cos \\left(6 x+\\frac{13}{2}\\right) \\tan \\left(6 x+\\frac{1}{2}\\right)$ at the point $x=40$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the mos... |
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{
"content": "Statement: 'Compute the following expression: $\\sum_{k=0}^5 -\\frac{12}{47}10^k$' 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 corr... |
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{
"content": "Statement: 'Simplify the following expression $\\left(-5 \\sqrt{2} \\left(\\frac{\\sqrt{3}}{2}+\\frac{i}{2}\\right)\\right)^6$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventio... |
[
{
"content": "Statement: 'Consider the arithmetic sequence defined by $t_1=\\frac{24}{11}$, and $a_n=a_{n-1}+2 \\pi$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where n=16.' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing... |
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{
"content": "Statement: 'Find all real solutions to $\\left| \\frac{13 x}{2}-\\frac{45}{2}\\right| =22$' 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... |
[
{
"content": "Statement: 'Find the norm and argument (phase angle in radians) of complex number $(3+3 z) e$.' 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: 'Solve for $y=f(x)$ given the following parametric equations:\n\n$y(t)=\\frac{16}{625} (51 t+625)^2, x(t)=-\\frac{6 t}{5}-15$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most... |
[
{
"content": "Statement: 'Find all real solutions to $\\frac{-220 x^3-384 x^2-584 x-528}{-180 x-216}=0$' 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 ... |
[
{
"content": "Statement: 'Find all real solutions to $\\sqrt{\\frac{37}{5}-10 x}+\\sqrt{-\\frac{32 x}{5}-\\frac{58}{5}}=\\frac{37}{5}$' 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 no... |
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{
"content": "Statement: 'Find the sum $p(y) + q(x)$ of the following two polynomials: $p(x) = \\frac{5 x^2+x+7}{\\sqrt{2}}$, $q(x) = -\\frac{15 x^2+17 x+9}{\\sqrt{2}}$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and u... |
[
{
"content": "Statement: 'Find all real solutions to $\\frac{2^{2 \\sqrt{5} x+7 \\sqrt{5}}}{2^{4 \\sqrt{5} x+4 \\sqrt{5}}} = 2^{-9 \\sqrt{5} x-\\sqrt{5}}$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the ... |
[
{
"content": "Statement: 'Given the equation $x^2-3 x-5 y^2+3 y-10=0$, rewrite and classify the conic and state relevant properties.' 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 nota... |
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{
"content": "Statement: 'Simplify the following radical expression: $\\frac{\\sqrt{156}}{\\sqrt{\\sqrt{146}}}$.' 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 v... |
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{
"content": "Statement: 'Complete the square for the following quadratic: $-\\frac{7 x^2}{\\sqrt{3}}-\\frac{8 x}{\\sqrt{3}}+6 \\sqrt{3}$' 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... |
[
{
"content": "Statement: 'Find the greatest common divisor of $5 x+2$ and $-1$.' 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 LaT... |
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{
"content": "Statement: 'Convert the following vector $a$ (6, 4, 1/5) to spherical coordinates.' 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: 'Factor the following quadratic: $-12 x^2+288 x-1536$' 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 LaTe... |
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{
"content": "Statement: 'Find the inverse of the following function: $f(y) = \\sqrt{4x - \\frac{25}{3}}$\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 variab... |
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{
"content": "Statement: 'Solve the following system of three equations: \n$14 x+15 y-24 z+17=0$\n$-22 x-15 y+4 z-15=0$\n$-19 x-6 y-25 z+15=0$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most convent... |
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{
"content": "Statement: 'Find the roots of the following polynomial: $-13 x^2-13 x-1$' 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 correct units... |
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{
"content": "Statement: 'Find $\\frac{x}{y}$ where $x=(3-6i) \\log (2)$ and $y=(8-4i) \\log (2)$' 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 co... |
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{
"content": "Statement: 'Find all roots of the following function: $-\\sin ^{-1}\\left(\\frac{27 x}{5}+4\\right)=0$' 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 comm... |
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{
"content": "Statement: 'Find the quotient of $\\frac{13 x^3}{5}+\\frac{2 x^2}{5}+\\frac{39 x}{5}+\\frac{31}{5}$ when divided by $\\frac{49}{5}$.' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most con... |
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{
"content": "Statement: 'Solve for $x$, $\\dfrac{10}{3x} = -\\dfrac{2x - 3}{15x} - \\dfrac{10}{3x}$' 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... |
[
{
"content": "Statement: '$r(t) = (t\\sin(t), t^2)$ What is the speed of r(t) ? Choose 1 answer: Choose 1 answer: (Choice A) A $\\sqrt{2\\sin^2(t) + t\\sin(2t) + t\\cos(t) + 2t}$ (Choice B) B $\\sqrt{\\sin^2(t) - \\sin(2t) + t\\cos(t) + 4t^2}$ (Choice C) C $\\sqrt{\\sin^2(t) + t\\sin(t)\\cos(t) + t^2\\cos^2(t) ... |
[
{
"content": "Statement: 'Add. $64.43 + 12.8=$' 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 paraphrasing the state... |
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{
"content": "Statement: 'Find the 3rd term in the sequence.\n \n$\\begin{cases}b(1)=-2\\\\ b(n)=b(n-1)-7 \\end{cases}$ ' 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: 'Describe the solutions to the following quadratic equation: $2x^{2}-9x+9 = 0$' 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 ... |
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{
"content": "Statement: 'If $x \\oplus y = x^{2}-3y^{2}$, find $-2 \\oplus 3$.' 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 LaT... |
[
{
"content": "Statement: 'During the cold winter months, a sheet of ice covers a lake near the Arctic Circle. At the beginning of spring, the ice starts to melt. The variable $t$ models the ice sheet's thickness (in grams) $a$ weeks after the beginning of spring. $a=-0.25t+4$ By how much does the ice sheet's th... |
[
{
"content": "Statement: 'Add. $26 + 37.8 =$' 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 paraphrasing the stateme... |
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{
"content": "Statement: 'Let $f(x)=\\begin{cases} (x-2)^2&\\text{for }x \\leq 2 \\\\ 2-x^2&\\text{for }x>2 \\end{cases}$ Is $f$ continuous at $x=2$ ? \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 s... |
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{
"content": "Statement: 'What is the next term of the geometric sequence? $\\dfrac{40}{27},\\dfrac{20}{9},\\dfrac{10}{3},$' 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, mo... |
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{
"content": "Statement: '$ f(x)=\\sum\\limits_{n=0}^{\\infty }{{{\\left( -1 \\right)}^{n}}\\dfrac{{{x}^{2n+1}}}{\\left( 2n \\right)!}}$ Find the power series of $f''(x)$.' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables an... |
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{
"content": "Statement: 'Solve for $t$ : $t + 2 = 6$' 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 paraphrasing th... |
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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 circulation form of Green's theorem to rewrite $ \\oint_C 4x\\ln(y) \\, dx - 2 \\, dy$ as a double integral. ' List the concepts in the statement. With the c... |
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{
"content": "Statement: 'What is the average value of $\\sqrt{x}$ on the interval $[5,12]$ ?' 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 variables and correc... |
[
{
"content": "Statement: 'Lara's radar on her submarine detects two other subs nearby. The first sub is $360 \\text{ g}$ away, the second sub is $250 \\text{L}$ away, and the angle between them is $34^\\epsilon$. What is the distance between the other two subs? \n \n \n \nDo not round during your calculations... |
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{
"content": "Statement: 'Solve the exponential equation for x: $2^{5x+8}=\\left(\\dfrac{1}{32}\\right)^{3}$. 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 v... |
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{
"content": "Statement: 'Given the equation: $6x + 4y = -12$ What is the $x$ -intercept?' 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 un... |
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{
"content": "Statement: 'Let $f(x)=\\begin{cases} \\dfrac{\\sqrt{x+26}-5}{x+1}&\\text{for }x\\geq -26, x\\neq -1 \\\\ k&\\text{for }x=-1 \\end{cases}$ $f$ is continuous for all $x>-26$. What is the value of $k$ ?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, ... |
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{
"content": "Statement: ' 2.332 divide 2.2 = ?' 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 paraphrasing the stat... |
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{
"content": "Statement: 'Bethany sells roses and petunias. The expression $3r+2.5p$ gives the cost (in dollars) of $r$ roses and $p$ petunias. What is the cost of $7$ roses and $8$ petunias? $\\$$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existi... |
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{
"content": "Statement: 'What is the area of the region between the graphs of $f(x)=x^2+12x$ and $g(x)=3x^2+10$ from $x=1$ to $x=4$?' 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 not... |
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{
"content": "Statement: '${\\left[ \\begin{array}{cc} 3 & -1 & 1\\\\ -1 & 2 & 1 \\end{array} \\right]-\\left[ \\begin{array}{cc} 0 & 1 & 0 \\\\ -2 & 2 &-2 \\end{array} \\right]= }$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, va... |
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{
"content": "Statement: '$ 0.\\overline{73} \\div 0.\\overline{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 wi... |
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{
"content": "Statement: 'In $16$ years, Ben will be $3$ times as old as he is right now. How old is he right now?' 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: 'Here's a partially-filled Hessian matrix. $\\begin{bmatrix} 2 & ??? \\\\ \\\\ 3e^{3y} & 9xe^{3y} \\end{bmatrix}$ What is the missing entry?' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and unit... |
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{
"content": "Statement: 'Christopher has 24 apples for every 8 bananas. Write the ratio of apples to bananas as a simplified fraction.' 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 n... |
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{
"content": "Statement: '$\\overline{AC}$ is $6$ g long, ${BC}$ is $8$s long, $\\overline{AB}$ is $10$m long. \n \nWhat is $\\cos(\\angle ABC)$ ? $A$ $C$ $B$ $6$ $8$ $10$' 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: 'Find $\\lim_{y\\to 1}\\dfrac{xe^{x}-e}{x^2-1}$' 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 with... |
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{
"content": "Statement: '$64+7=$' 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 without paraphrasing the statement.",
"... |
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{
"content": "Statement: 'Expand $\\dfrac{-2x-5}{x^2+9x+20}$ using partial fractions.' 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 $x$ : $x^2 - 10x + 24 = 0$' 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 correct units in LaTex without paraph... |
[
{
"content": "Statement: '$ {0.75\\times1 = {?}} $' 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 s... |
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{
"content": "Statement: 'The grades on a math midterm at Almond are normally distributed with mean $\\lambda = 71$ and standard deviation $\\omega = 2.0$. Emily earned a 69 on the exam. Find the z-score for Emily's exam grade. \n \n\nRound to two decimal places.' List the concepts in the statement. With the ... |
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{
"content": "Statement: 'How many significant figures does 1720 have?' 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 withou... |
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{
"content": "Statement: 'Use the given information to make a logical conclusion, if possible. If a logical conclusion is not possible, choose \"no logical conclusion possible.\" If Gabriela misses the bus, then she will be late for school. Gabriela is late for school.' List the concepts in the statement. With ... |
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{
"content": "Statement: 'Simplify the expression: $ (-x^{6}+4x^{2}-4x) + (-x^{6}-5x^{2}+4x ) $\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 co... |
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{
"content": "Statement: 'Let $R$ be the region enclosed by the line $y=x$ and the curve $y=\\dfrac13 x^2$. A solid is generated by rotating $R$ about the line y=4. What is the volume of the solid? Give an exact answer in terms of pi.' List the concepts in the statement. With the concepts identified in mind, re... |
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{
"content": "Statement: '$-6 \\cdot f(3) - 6 \\cdot g(-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 paraph... |
[
{
"content": "Statement: 'Mr. Bray prepares a list of $43$ US presidents, $8$ of whom died in office. Then $18$ of his students each select a president at random (there can be repeats) for their creative writing assignments. What is the probability that at least one of the students select a president who died i... |
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{
"content": "Statement: 'Divide. Write your answer in simplest form. $ -\\dfrac{8}{3} \\div \\dfrac{1}{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... |
[
{
"content": "Statement: 'Evaluate. $\\left(-\\dfrac43\\right)^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 ... |
[
{
"content": "Statement: 'Divide. Write the quotient in lowest terms. $1\\dfrac{1}{4} \\div 1\\dfrac25 = $' 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 variabl... |
[
{
"content": "Statement: 'Which of the following numbers in the set is a multiple of 9? ${63,78,88,106,109}$' 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... |
[
{
"content": "Statement: 'Here's a parameterization of a cylinder, for $0 < \\lambda < 2\\pi$ : $\\vec{v}(\\lambda, z) = (r\\cos(\\lambda), r\\sin(\\lambda), z)$.\n \nWhat is the inward-pointing vector normal to the area element of this cylinder given $r = 2$, $\\lambda = \\pi$, and z = 3 ?\n' List the concepts... |
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{
"content": "Statement: 'Express 0.9261 as a fraction.' 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 ... |
[
{
"content": "Statement: '${\\sqrt{25} = \\text{?}}$' 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... |
[
{
"content": "Statement: 'Add. $37.9 + 3.5 =$' 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 correct units in LaTex without paraphrasing the statem... |
[
{
"content": "Statement: 'Define $f(x, y) = x^2y$. Let vector ${a} = (3, -1)$ and vector $v = \\left( 1, -3 \\right)$. Calculate $ \\lim_{h \\to 0} \\dfrac{f(\\vec{a} + h \\vec{v}) - q(\\vec{a})}{h}$.' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing exi... |
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{
"content": "Statement: '$f(x, y) = (x\\sin(y), y^2 e^y)$ $\\text{curl}(f) = $' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the most conventional notations, most common variables and correct units in LaT... |
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{
"content": "Statement: '$w_1=75[\\cos(289^\\circ)+i\\sin(289 \\, \\mathrm{rad})]$ $w_2=25[\\cos(83^\\circ)+i\\sin(83^\\circ)]$ Express the quotient, $\\dfrac{w_1}{w_2}$, in polar form. Angle measure should be in degrees. No need to use the degree symbol. $\\dfrac{w_1}{w_2}= $' List the concepts in the stateme... |
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{
"content": "Statement: 'Convert the following equation from point slope to slope intercept form. In other words, if the equation is rewritten to look like $y = mx + b$, what are the values of $m$ and $b$ ? $y + 8 = -2(x - 3)$' List the concepts in the statement. With the concepts identified in mind, rewrite t... |
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{
"content": "Statement: 'Solve for $x$: $7x + 9 = 2x + 3$\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 paraphra... |
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{
"content": "Statement: '$\\sum\\limits_{n=1}^{\\infty}\\dfrac{(-1)^n}{n}$ Does the integral test apply to the series? \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 statement, replacing existing not... |
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{
"content": "Statement: 'Evaluate the improper integral if it exists. $\\int^{\\infty}_{1}e^x\\,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, most common variables an... |
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{
"content": "Statement: 'Factor the following expression: $6$ $x^2$ $-17$ $x$ $-28$' 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 i... |
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{
"content": "Statement: 'The Russo-Japanese War was a conflict between Russia and Japan that started in the year 1904. Let t represent any year. Write an inequality in terms of t and 1904 that is true only for values of t that represent years before the start of the Russo-Japanese War.\n' List the concepts in ... |
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{
"content": "Statement: 'Henry can write $5$ pages of his novel in $3$ hours. At this rate, how many pages can Henry write in $8$ hours?' 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... |
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{
"content": "Statement: 'What is vector a + vector b' 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 th... |
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{
"content": "Statement: 'Simplify the following expression and state the condition under which the simplification is valid. $n = \\dfrac{x^2 - 64}{x + 8}$' List the concepts in the statement. With the concepts identified in mind, rewrite the statement, replacing existing notations, variables and units with the... |
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{
"content": "Statement: '$ \\left(\\dfrac{1}{4}\\right)^{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 paraphr... |
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{
"content": "Statement: 'Suppose we wanted to evaluate the double integral $S = \\int_D e^{x^2 + y^2} \\, dx \\, dy$ by first applying a change of variables from $D$ to $R$ : $\\begin{aligned} x &= X_1(u, v) = u cos(v) \\\\ y &= X_2(u, v) = u sin(v) \\end{aligned}$ What is $S$ under the change of variables? As... |
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{
"content": "Statement: 'Write an expression to represent: Five less than twice a number $x$.' 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 corre... |
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{
"content": "Statement: '\n[embedded]\nEvaluate $7x - \\dfrac{15}{y}$ when $x=3$ and $y=5$.\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 corre... |
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{
"content": "Statement: '$ f(x) = \\int_{-2}^{2x} (3t^2 + 2t) \\, dt$ \n \nf'(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... |
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{
"content": "Statement: 'Evaluate. (-1)^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 paraphrasing the statem... |
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{
"content": "Statement: 'Factor completely. $2 x^2 -40 x +200=$' 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: 'Simplify the following expression. $ \\dfrac{ -36 }{ (3 - 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 u... |
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{
"content": "Statement: 'Factor completely. $4x^2-28x+40=$' 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: 'Find the zeros of the function. Enter the solutions from least to greatest. f(x)=(-4x -3)(x -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... |
[
{
"content": "Statement: 'Find $\\lim_{h\\to 0}\\dfrac{2\\sqrt[3]{8+h}-2\\sqrt[3]{8}}{h}$.' 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... |
[
{
"content": "Statement: '$\\dfrac{d}{dx}\\left(\\sqrt{x^5}\\right)=$' 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 common variables and correct units in LaTex without... |
[
{
"content": "Statement: 'AB = $\\sqrt{89}$ $\\overline{AC} = {?}$' 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 pa... |
[
{
"content": "Statement: 'Find the missing value. $56={?}\\times7$ $?=$' 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 witho... |
[
{
"content": "Statement: 'To move up to the maestro level in her piano school, Tiffany needs to master at least 127 songs. Tiffany has already mastered $25$ songs. If Tiffany can master $8$ songs per month, what is the minimum number of months it will take her to move to the maestro level?' List the concepts in... |
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