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gt stringlengths 1 43	rej listlengths 1 1	chosen listlengths 4 12	rejected listlengths 4 12
70	[ "\\frac{5}{3}" ]	[ { "content": "Tony loved to solve difficult pen and paper puzzles. He did a warm-up puzzle that only took 10 minutes and after that he did 2 puzzles that each took 3 times as long. How long did he spend solving puzzles?", "role": "user" }, { "content": "The total time taken can be computed as the ...	[ { "content": "Tony loved to solve difficult pen and paper puzzles. He did a warm-up puzzle that only took 10 minutes and after that he did 2 puzzles that each took 3 times as long. How long did he spend solving puzzles?", "role": "user" }, { "content": "Let's solve this problem using Python's symp...
103	[ "0" ]	[ { "content": "If $6543_{10}$ is converted to base 8, then each digit of the result is squared, and finally, the squared digits are summed, what is the final result?", "role": "user" }, { "content": "I will find the answer by writing a computer program to perform the following steps:\n1. Convert $654...	[ { "content": "If $6543_{10}$ is converted to base 8, then each digit of the result is squared, and finally, the squared digits are summed, what is the final result?", "role": "user" }, { "content": "Let's write a python script to convert the number to base 8, square each digit and sum it.\n```python...
10.5	[ "12" ]	[ { "content": "The sum of three numbers is $66$. The first number is $3$ times the third number, and the second number is $24$. What is the third number?", "role": "user" }, { "content": "Define the three numbers as $x$, $y$ and $z$ where the third number is $z$.\nBased on the conditions given in the...	[ { "content": "The sum of three numbers is $66$. The first number is $3$ times the third number, and the second number is $24$. What is the third number?", "role": "user" }, { "content": "Let's find the answer by solving the equations \\[\nx + y + z = 66 \\quad \\text{and} \\quad z = \\frac{1}{3} x \...
3	[ "1" ]	[ { "content": "$f (x) = x + X and $g(x) = x^2 -6$, The value of $f(g(2))$ is 1. What is the value of unknown variable X?", "role": "user" }, { "content": "Let's first substitute 2 for x into the $g(x)$ function:\n```python\nfrom sympy import symbols, Eq, solve\n\n# Define the variables\nx, X = symbol...	[ { "content": "$f (x) = x + X and $g(x) = x^2 -6$, The value of $f(g(2))$ is 1. What is the value of unknown variable X?", "role": "user" }, { "content": "First let's substitute $g(2)$ into $f(x)$ and solve for $X$.\n```python\nimport sympy as sp\n\n# define the variables\nx, y, X = sp.symbols('x y X...
1	[ "94" ]	[ { "content": "The line segment connecting $(-2,7)$ and $(3,11)$ can be parameterized by the equations\n\\begin{align}\nx &= at + b, \\\\\ny &= ct + d,\n\\end{align}where $0 \\le t \\le X and $t = 0$ corresponds to the point $(-2,7).$ Find $a^2 + b^2 + c^2 + d^2. 94. What is the value of unknown variable X?",...	[ { "content": "The line segment connecting $(-2,7)$ and $(3,11)$ can be parameterized by the equations\n\\begin{align}\nx &= at + b, \\\\\ny &= ct + d,\n\\end{align}where $0 \\le t \\le X and $t = 0$ corresponds to the point $(-2,7).$ Find $a^2 + b^2 + c^2 + d^2. 94. What is the value of unknown variable X?",...
5	[ "6" ]	[ { "content": "I have X marbles numbered 1 through 5 in a bag. Suppose I take out two different marbles at random. What is the expected value of the sum of the numbers on the marbles?\nIf we know the answer to the above question is 6, what is the value of unknown variable X?", "role": "user" }, { "...	[ { "content": "I have X marbles numbered 1 through 5 in a bag. Suppose I take out two different marbles at random. What is the expected value of the sum of the numbers on the marbles?\nIf we know the answer to the above question is 6, what is the value of unknown variable X?", "role": "user" }, { "...
30	[ "100" ]	[ { "content": "Sasha made x chocolate muffins for her school bake sale fundraiser. Melissa made 4 times as many muffins as Sasha, and Tiffany made half of Sasha and Melissa's total number of muffins. If one muffin sold for $4, how much money did Sasha, Melissa, and Tiffany contribute to the fundraiser?\nIf we kn...	[ { "content": "Sasha made x chocolate muffins for her school bake sale fundraiser. Melissa made 4 times as many muffins as Sasha, and Tiffany made half of Sasha and Melissa's total number of muffins. If one muffin sold for $4, how much money did Sasha, Melissa, and Tiffany contribute to the fundraiser?\nIf we kn...
-15	[ "-10" ]	[ { "content": "Given the functions $f(x) = 3x^2 - 7$, $g(t) = 4t + c$, $h(x) = g(f(x))$ and $j(y) = y^3 + h(y)$, if $h(2) = 5$ and $j(2) = 13$, what is the value of $c$?", "role": "user" }, { "content": "Let's first identify what we know from the information in the problem:\n<ul><li>$f(x) = 3x^2 - 7$...	[ { "content": "Given the functions $f(x) = 3x^2 - 7$, $g(t) = 4t + c$, $h(x) = g(f(x))$ and $j(y) = y^3 + h(y)$, if $h(2) = 5$ and $j(2) = 13$, what is the value of $c$?", "role": "user" }, { "content": "We can solve this problem by expressing $h(x)$ and $j(y)$ in terms of $c$ and then substituting t...
3108	[ "2332" ]	[ { "content": "What is the sum of the least common multiple and the greatest common divisor of the numbers 1332 and 888?", "role": "user" }, { "content": "First we can write 1332 and 888 as $$\n\\begin{align}\n1332 &= 2^3 \\cdot 3 \\cdot 11 \\\\\n888 &= 2^3 \\cdot 3^2 \\cdot 13\n\\end{align}\n$$\nWe ...	[ { "content": "What is the sum of the least common multiple and the greatest common divisor of the numbers 1332 and 888?", "role": "user" }, { "content": "Let's first check whether 1332 and 888 have a common factor.\n```python\nfrom sympy import gcd\n\n# finding the gcf of the two numbers\ngcf = gcd(...
60	[ "480" ]	[ { "content": "If a 40-foot tree is casting a 10-foot shadow, and Andrea is casting a 15-inch shadow at the same time, how tall is Andrea in inches?", "role": "user" }, { "content": "In this question, we want to use the information about the tree and its shadow to find the height of Andrea, who is ca...	[ { "content": "If a 40-foot tree is casting a 10-foot shadow, and Andrea is casting a 15-inch shadow at the same time, how tall is Andrea in inches?", "role": "user" }, { "content": "Let's denote Andrea's height in inches by $x$.\nLet $x_f$ denote the length of a foot in the units of inches, and $y_f...
3	[ "2" ]	[ { "content": "What is the value of the expression $\\left\\lceil\\left(-\\frac{5}{3}\\right)^2\\right\\rceil$ when evaluated?", "role": "user" }, { "content": "The syntax 'ceiling' is used to denote the ceiling function. The ceiling of a real number is the smallest integer that is greater than or eq...	[ { "content": "What is the value of the expression $\\left\\lceil\\left(-\\frac{5}{3}\\right)^2\\right\\rceil$ when evaluated?", "role": "user" }, { "content": "I am not sure what $\\lceil{x}\\rceil$ means so I will leave it as is.\n```python\nimport math\n\nM = 5\nN = 3\nP = -M / N\n\nprint(P, math....
1461	[ "369" ]	[ { "content": "If one were to begin counting from the start of 2001 to the end of 2004, how many days would have passed?", "role": "user" }, { "content": "To compute the number of days that have passed from the start of 2001 to the end of 2004, we can start by getting the number of days in each year,...	[ { "content": "If one were to begin counting from the start of 2001 to the end of 2004, how many days would have passed?", "role": "user" }, { "content": "Let's write a python script to find the days between the start of 2001 and end of 2004.\n```python\nimport calendar\n# get years 2001 to 2004\nsta...
63	[ "163" ]	[ { "content": "If Molly and her parents spent most of the day at the beach and were joined by 100 people, but then 40 people left at 5:00, what is the total number of people at the beach if everyone stayed until evening?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n`...	[ { "content": "If Molly and her parents spent most of the day at the beach and were joined by 100 people, but then 40 people left at 5:00, what is the total number of people at the beach if everyone stayed until evening?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n`...
120	[ "0.3" ]	[ { "content": "What is $\\frac{1}{4}\\%$ of X? Express your answer as a decimal. The answer is 0.3. What is the value of unknown variable X?", "role": "user" }, { "content": "First, let's recall that $\\frac{a}{b}\\%$ can be written as $a\\%\\times b$.\nFor this problem, we can write \\[\\frac{1}{4}\...	[ { "content": "What is $\\frac{1}{4}\\%$ of X? Express your answer as a decimal. The answer is 0.3. What is the value of unknown variable X?", "role": "user" }, { "content": "In math, percentages are often expressed as fractions with a denominator of 100. So we need to convert $\\frac{1}{4}\\%$ into ...
10	[ "600" ]	[ { "content": "A fan can create an airflow of x liters per second. If the fan works for 10 minutes each day, calculate the amount of airflow it will create in one week.\nIf we know the answer to the above question is 42000, what is the value of unknown variable x?", "role": "user" }, { "content": "Le...	[ { "content": "A fan can create an airflow of x liters per second. If the fan works for 10 minutes each day, calculate the amount of airflow it will create in one week.\nIf we know the answer to the above question is 42000, what is the value of unknown variable x?", "role": "user" }, { "content": "Le...
-12	[ "9" ]	[ { "content": "For $x=-3$, $y=5$, and $z=-4$, find the outcome of the algebraic expression $x^2+y^2-z^2+2xy$.", "role": "user" }, { "content": "We can compute the outcome of the given expression using sympy as follows.\n```python\nfrom sympy import symbols, simplify\n\n# define the variables\nx, y, z...	[ { "content": "For $x=-3$, $y=5$, and $z=-4$, find the outcome of the algebraic expression $x^2+y^2-z^2+2xy$.", "role": "user" }, { "content": "First, let's calculate each of the expressions and then use those to calculate the requested value.\n\nLet's write down some equations to calculate each expr...
58	[ "74" ]	[ { "content": "Find the value of $x + y + z + w$ if $x$, $y$, $z$, and $w$ are positive integers, $x + y + xy = 76$, $z$ is the greatest prime number less than $20$, and $w$ is the smallest prime number greater than $20$.", "role": "user" }, { "content": "Let's write down the information from the que...	[ { "content": "Find the value of $x + y + z + w$ if $x$, $y$, $z$, and $w$ are positive integers, $x + y + xy = 76$, $z$ is the greatest prime number less than $20$, and $w$ is the smallest prime number greater than $20$.", "role": "user" }, { "content": "I will find the answer by enumerating all sol...
5	[ "4" ]	[ { "content": "How many prime numbers with two digits have a ones digit of 1?", "role": "user" }, { "content": "I will find out this by enumerating all the two-digit numbers with ones digit as 1.\n```python\n# Two-digit numbers with ones digit as 1\nx = [n for n in range(10, 100) if n % 10 == 1]\nx\n...	[ { "content": "How many prime numbers with two digits have a ones digit of 1?", "role": "user" }, { "content": "Let's list out all primes up to 100 and count the number of 1's in the units digit.\n```python\nimport sympy\n\n# create a set of all primes up to 100\nprimes = sympy.primerange(1, 100)\npr...
8	[ "16" ]	[ { "content": "Let $a$, $b$, $c$, $m$, $n$, and $p$ be integers with $m$ and $n$ odd, $n < m$, $c$ even, and $p$ a prime number such that $a^2 + b^2 + c^2 + p = m^2 - n^2 + c^2 + p$. Find the largest integer that divides $a^2 + b^2 + c^2 + p$ for any such $m$, $n$, $c$, and $p$.\n$\\textbf{(A)}\\ 2\\qquad \\text...	[ { "content": "Let $a$, $b$, $c$, $m$, $n$, and $p$ be integers with $m$ and $n$ odd, $n < m$, $c$ even, and $p$ a prime number such that $a^2 + b^2 + c^2 + p = m^2 - n^2 + c^2 + p$. Find the largest integer that divides $a^2 + b^2 + c^2 + p$ for any such $m$, $n$, $c$, and $p$.\n$\\textbf{(A)}\\ 2\\qquad \\text...
45	[ "15" ]	[ { "content": "Three faucets fill a 100-gallon tub in 6 minutes. How long, in seconds, does it take six faucets to fill a 25-gallon tub? Assume that all faucets dispense water at the same rate.", "role": "user" }, { "content": "Assuming we are given the amount of time it takes to fill a 100 gallon ...	[ { "content": "Three faucets fill a 100-gallon tub in 6 minutes. How long, in seconds, does it take six faucets to fill a 25-gallon tub? Assume that all faucets dispense water at the same rate.", "role": "user" }, { "content": "Let's first check how much water in gallons each faucet fills in a minu...
\frac{3}{2}	[ "\\frac{-3}{2}" ]	[ { "content": "Find the value(s) of $x$ such that $8xy-12y+2x-3=0$ is true for all values of $y$.", "role": "user" }, { "content": "Let's first check whether there is a value of $x$ for which $8xy-12y+2x-3=0$ is true for all values of $y$.\n```python\nimport sympy as sp\n\n# define the symbols\nx, y ...	[ { "content": "Find the value(s) of $x$ such that $8xy-12y+2x-3=0$ is true for all values of $y$.", "role": "user" }, { "content": "Let's write down the equation $8xy-12y+2x-3=0$ and transform it to obtain an expression that does not depend on $y$.\nWe can divide by $2$ to obtain $(4x-6)y+x-3=0$. Now...
34	[ "5" ]	[ { "content": "If $a \\triangle b = 2a^2 + 4b^2$ for all $a$ and $b$, then what is the value of $3 \\triangle 2$?", "role": "user" }, { "content": "For this expression\n$a \\triangle b = 2a^2 + 4b^2$, we are trying to find $3 \\triangle 2$.\nLet's try to evaluate $a \\triangle b$ for specific values ...	[ { "content": "If $a \\triangle b = 2a^2 + 4b^2$ for all $a$ and $b$, then what is the value of $3 \\triangle 2$?", "role": "user" }, { "content": "Let's write down the definitions of the operation in the given expression.\n$a\\triangle b = 2a^2+4b^2$\nSo $3\\triangle 2$ is $2 \\times 3^2 + 4 \\times...
67	[ "57" ]	[ { "content": "In a classroom, there are blue chairs, green chairs, and white chairs. There are 10 blue chairs. The green chairs are 3 times as many as the blue chairs, and there are 13 fewer white chairs than the green and blue chairs combined. How many chairs are there in a classroom?", "role": "user" },...	[ { "content": "In a classroom, there are blue chairs, green chairs, and white chairs. There are 10 blue chairs. The green chairs are 3 times as many as the blue chairs, and there are 13 fewer white chairs than the green and blue chairs combined. How many chairs are there in a classroom?", "role": "user" },...
50	[ "450" ]	[ { "content": "When Jo calculates the sum of all whole numbers from 1 through 100, and Kate also tallies up the first 100 whole numbers, but rounds each number to the closest ten before summing (with 5 rounding up), what is the difference in their totals?", "role": "user" }, { "content": "Let's write...	[ { "content": "When Jo calculates the sum of all whole numbers from 1 through 100, and Kate also tallies up the first 100 whole numbers, but rounds each number to the closest ten before summing (with 5 rounding up), what is the difference in their totals?", "role": "user" }, { "content": "Let's write...
7	[ "1.16666666666667" ]	[ { "content": "Find the number that when added to the numerator and denominator of the fraction $\\frac{3}{5}$ will make it equal to $\\frac{5}{6}$. What is this number?", "role": "user" }, { "content": "Let's say that adding this number $n$ to both numerator and denominator changes the fraction to $...	[ { "content": "Find the number that when added to the numerator and denominator of the fraction $\\frac{3}{5}$ will make it equal to $\\frac{5}{6}$. What is this number?", "role": "user" }, { "content": "Let $n$ be the number that we are looking for.\nThe original fraction is $3/5$.\nIf we add $n$ to...
19	[ "29" ]	[ { "content": "The average of three positive integers is 26, with the central number being 27. Knowing that the largest of these numbers is 5 greater than the median, determine the smallest integer in the sequence.", "role": "user" }, { "content": "Let the three numbers be $x$, $y$, and $z$ ($x \\leq...	[ { "content": "The average of three positive integers is 26, with the central number being 27. Knowing that the largest of these numbers is 5 greater than the median, determine the smallest integer in the sequence.", "role": "user" }, { "content": "Let's say the three integers are $a, b, c$ where $a ...
\frac{1}{16}	[ "0.0044" ]	[ { "content": "What is the value of $\\sin 6^\\circ \\sin 42^\\circ \\sin 66^\\circ \\sin 78^\\circ$?", "role": "user" }, { "content": "We can use the following property of sine and cosine to simplify the expression:\n$\\sin(a)\\sin(b) = \\frac{1}{2}(\\cos(a-b) - \\cos(a+b))$\nSo\n```python\nimport m...	[ { "content": "What is the value of $\\sin 6^\\circ \\sin 42^\\circ \\sin 66^\\circ \\sin 78^\\circ$?", "role": "user" }, { "content": "Let's use that $\\sin(n \\cdot \\theta) = 2 \\sin(\\theta) \\cos(n-1 \\cdot \\theta) - 2 \\sin((n-1) \\cdot \\theta) \\cos(\\theta)$.\nWe can thus rewrite the produc...
360	[ "39300" ]	[ { "content": "Stan drove 300 miles in 5 hours, 20 minutes. Next, he drove X miles in 6 hours, 40 minutes. What was Stan's average speed in miles per hour for the total trip?\nIf we know the answer to the above question is 55, what is the value of unknown variable X?", "role": "user" }, { "content": ...	[ { "content": "Stan drove 300 miles in 5 hours, 20 minutes. Next, he drove X miles in 6 hours, 40 minutes. What was Stan's average speed in miles per hour for the total trip?\nIf we know the answer to the above question is 55, what is the value of unknown variable X?", "role": "user" }, { "content": ...
343	[ "219.75" ]	[ { "content": "Calculate the volume of a cube that has a surface area of 294 square inches.", "role": "user" }, { "content": "The surface area of a cube is $6(side)^2$, where $(side)$ is a side length of a cube. \nWe know that for a cube surface area of 294, the side is $\\sqrt{294/6} = \\sqrt{49} = ...	[ { "content": "Calculate the volume of a cube that has a surface area of 294 square inches.", "role": "user" }, { "content": "A cube is a 3-D object with 6 sides. So we can simply use the fact that the surface area is $A = 6s^2$, where $s$ is the length of one of the sides. In order to calculate the ...
12	[ "36" ]	[ { "content": "Adam and Tom are brothers. Adam is 8 years old and Tom is x years old. Their combined age will be 44 years old in 12 years. What is the value of unknown variable x?", "role": "user" }, { "content": "Let's write this out as two equations. The first one is the combined age of the two bro...	[ { "content": "Adam and Tom are brothers. Adam is 8 years old and Tom is x years old. Their combined age will be 44 years old in 12 years. What is the value of unknown variable x?", "role": "user" }, { "content": "Let's use sympy to solve this.\n```python\nimport sympy as sp\n\n# let's denote Adam's ...
3	[ "\\sqrt{5}+\\frac{3}{2}" ]	[ { "content": "Determine the maximum value possible for the expression $x+\\frac{1}{x}$ provided that $7=x^2+\\frac{1}{x^2}$.", "role": "user" }, { "content": "The given expression can be rewritten as $x^2+\\frac{1}{x^2}+2$.\nWe can rewrite $x^2+\\frac{1}{x^2}$ as $\\left(x-\\frac{1}{x}\\right)^2 + 2...	[ { "content": "Determine the maximum value possible for the expression $x+\\frac{1}{x}$ provided that $7=x^2+\\frac{1}{x^2}$.", "role": "user" }, { "content": "We can use Python's sympy library to solve this problem. Let's put the expression $x^2+\\frac{1}{x^2}$ into the equality and solve for x to g...
20	[ "1302" ]	[ { "content": "Given that $f(x) = 3x^2-2$ and we have another function $g(f(x))$ which equals $x^2 + x +1$, evaluate and sum up all the possible values for $g(25)$.", "role": "user" }, { "content": "Let's first check when $f(x)=3x^2-2$ equals 25.\n```python\nfrom sympy import symbols, solve\n\n# defi...	[ { "content": "Given that $f(x) = 3x^2-2$ and we have another function $g(f(x))$ which equals $x^2 + x +1$, evaluate and sum up all the possible values for $g(25)$.", "role": "user" }, { "content": "To solve this problem, we need to find $g(25)$.\nBased on the given information, we know that \\[g(f(x...
28	[ "7" ]	[ { "content": "If there exists an integer $p$ in the range $0 < 4p < 30$, can you determine the sum of all the distinct integer values that $p$ could take?", "role": "user" }, { "content": "We can solve this problem by creating a set of possible values for $p$ and then summing up the elements.\nTo cr...	[ { "content": "If there exists an integer $p$ in the range $0 < 4p < 30$, can you determine the sum of all the distinct integer values that $p$ could take?", "role": "user" }, { "content": "Given $0 < 4p < 30$, we have that\n```python\nfrom sympy import symbols, Eq, solve\n\n# define the variables\np...
20	[ "25" ]	[ { "content": "Mary is going on a business trip. It takes 10 minutes for her Uber to get to her house and 5 times longer to get to the airport. It takes 15 minutes to check her bag and three times as long to get through security. Then she has to wait for x minutes for her flight to start boarding and twice as lo...	[ { "content": "Mary is going on a business trip. It takes 10 minutes for her Uber to get to her house and 5 times longer to get to the airport. It takes 15 minutes to check her bag and three times as long to get through security. Then she has to wait for x minutes for her flight to start boarding and twice as lo...
2304	[ "768" ]	[ { "content": "There are 192 soaps in a package. They put them in 2 big boxes. If each box contains 6 packages, how much soap do the 2 boxes contain in total?", "role": "user" }, { "content": "The number of soaps in a package is 192.\nLet's solve this problem using Python code.\n```python\nnumber_of_...	[ { "content": "There are 192 soaps in a package. They put them in 2 big boxes. If each box contains 6 packages, how much soap do the 2 boxes contain in total?", "role": "user" }, { "content": "Let's solve this problem using Python's sympy library.\n```python\nimport sympy as sp\n\n# 192 soaps in 1 pa...
3	[ "7" ]	[ { "content": "In a school garden, there are flowers in different colors. In total there are 96 flowers of four colors: green, red, blue, and yellow. There are 9 green flowers and x times more red flowers. Blue flowers make up to 50% of the total flower count. There are 12 yellow flowers. What is the value of un...	[ { "content": "In a school garden, there are flowers in different colors. In total there are 96 flowers of four colors: green, red, blue, and yellow. There are 9 green flowers and x times more red flowers. Blue flowers make up to 50% of the total flower count. There are 12 yellow flowers. What is the value of un...
4	[ "1" ]	[ { "content": "At the zoo, there are 5 different types of animals. Seeing each animal type takes around 6 minutes. How much time would it take to see each animal type if the zoo decided to import x new species?\nIf we know the answer to the above question is 54, what is the value of unknown variable x?", "ro...	[ { "content": "At the zoo, there are 5 different types of animals. Seeing each animal type takes around 6 minutes. How much time would it take to see each animal type if the zoo decided to import x new species?\nIf we know the answer to the above question is 54, what is the value of unknown variable x?", "ro...
18	[ "150" ]	[ { "content": "When you take the square root of $\\frac{y}{50}$ you get $\\frac{3}{5}$. What does $y$ equal?", "role": "user" }, { "content": "Taking the square root of $\\frac{y}{50}$ is the same as taking the square root of $y$ and dividing by $\\sqrt{50}$.\nSo we have:\n$\\sqrt{y}/\\sqrt{50} = \\f...	[ { "content": "When you take the square root of $\\frac{y}{50}$ you get $\\frac{3}{5}$. What does $y$ equal?", "role": "user" }, { "content": "Let's write down the given equation: $\\sqrt{\\frac{y}{50}} = \\frac{3}{5}$.\nLet's square both sides to get $\\frac{y}{50} = \\frac{9}{25}$.\nNow we can cros...
12	[ "16" ]	[ { "content": "Mr. and Mrs. Lopez have two children. When they get into their family car, two people sit in the front, and the other two sit in the back. Either Mr. Lopez or Mrs. Lopez must sit in the driver's seat. How many seating arrangements are possible?", "role": "user" }, { "content": "Let'...	[ { "content": "Mr. and Mrs. Lopez have two children. When they get into their family car, two people sit in the front, and the other two sit in the back. Either Mr. Lopez or Mrs. Lopez must sit in the driver's seat. How many seating arrangements are possible?", "role": "user" }, { "content": "In t...
10500	[ "32.8125" ]	[ { "content": "Determine the independent term of $x$ when expanding the binomial $\\left(\\sqrt{x} + \\frac{5}{x}\\right)^9$.", "role": "user" }, { "content": "In order to identify the independent term of $x$ in $\\left(\\sqrt{x} + \\frac{5}{x}\\right)^9$, we first need to expand the binomial and exp...	[ { "content": "Determine the independent term of $x$ when expanding the binomial $\\left(\\sqrt{x} + \\frac{5}{x}\\right)^9$.", "role": "user" }, { "content": "Let's first check the binomial coefficient in Sympy:\n```python\nfrom sympy import binomial\n\n# binomial coefficients\nprint(binomial(9, 0))...