messages listlengths 4 12 |
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[
{
"content": "What is the sum of the following infinite geometric series: $\\frac{1}{3} - \\frac{1}{9} + \\frac{1}{27} - \\frac{1}{81} + \\frac{1}{243} - \\frac{1}{729} + \\frac{1}{2187} - \\cdots$?",
"role": "user"
},
{
"content": "Since this is a geometric series we can use the sum formula for a g... |
[
{
"content": "A line segment $\\overline{AB}$ has its midpoint at $M(4,4)$. If the coordinates of point A are known to be $(8,4)$, calculate the total of the x and y coordinates for the other endpoint, point $B$.",
"role": "user"
},
{
"content": "Let's use sympy to solve this problem.\n```python\nfr... |
[
{
"content": "What is the remainder when $2x^3 - x^2 - 17x + 47$ is divided by $x-5$?",
"role": "user"
},
{
"content": "Let's use sympy to solve this problem.\n```python\nfrom sympy import symbols, poly\n\n# define the variables\nx, r = symbols('x r')\n\n# define the polynomial\np = poly(2 * x**3 - ... |
[
{
"content": "At a particular school with 43 students, each student takes chemistry, biology, or both. The chemistry class is three times as large as the biology class, and X students are taking both classes. How many people are in the chemistry class?\nIf we know the answer to the above question is 36, what is... |
[
{
"content": "If Suzy is currently 20 years old and in four years she will be twice Mary's age at that time, what is Mary's current age?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\ncurrent_age_of_suzy = 20\n\n# in four years suzy will be twice as old as ... |
[
{
"content": "Alexia designed a logo X inches wide and 1.5 inches tall to be used on her school's notebooks. The school wants the logo on the notebook to be 8 inches wide. How tall, in inches, It will be 6 if it is enlarged proportionately. What is the value of unknown variable X?",
"role": "user"
},
{
... |
[
{
"content": "If Flynn watches 30 minutes of TV every night on weekdays and an additional 2 hours in total on weekends, how many hours of TV does she watch in 52 weeks?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\nweekday_TV_time = 30 # minutes\nweekend_T... |
[
{
"content": "In a right triangle, the ratio of the measures of the acute angles is 8:1. What is the measure, in degrees, of the largest angle in the triangle?",
"role": "user"
},
{
"content": "Let's use sympy to find the solutions for the equations.\n```python\nimport sympy as sp\n\n# define the an... |
[
{
"content": "If $z = 2y$ and $y = \\displaystyle\\frac{1}{3x+1}$, what is the value of $x$ when $z = 2$?",
"role": "user"
},
{
"content": "Let's write down an equation for $z$ as a function of $x$ and solve it for $x$.\n```python\nfrom sympy import Eq, symbols, solve\n\n# define the variables\nx, y... |
[
{
"content": "How many natural-number factors does $N$ have if $N = 2^4 \\cdot 3^3 \\cdot 5^2 \\cdot X$? The answer is 180. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "Let's write a python code to find the value of X.\n```python\ndef get_num_factors(N):\n '''Returns... |
[
{
"content": "What is the product of the whole number values for $c$ that make the quadratic equation $8x^2+15x+c=0$ have two different real roots?",
"role": "user"
},
{
"content": "Let's write down the discriminant of the quadratic equation $8x^2+15x+c=0$, which is equal to $b^2-4ac = 15^2 - 4 \\ti... |
[
{
"content": "If a number is the product of 6! and 2^5, how many positive divisors does it have?",
"role": "user"
},
{
"content": "Let's write this number as $6!\\cdot 2^5$ in prime factorization and then use this to find the number of positive divisors of the number using sympy.\n```python\nfrom sy... |
[
{
"content": "The city's environmental division is expanding and needs to employ professionals who can handle multiple environmental concerns. Specifically, they need 85 workers to tackle issues related to water, another 73 to address problems with air quality, but they've found that 27 individuals are qualifie... |
[
{
"content": "The following line is parameterized, so that its direction vector is of the form $\\begin{pmatrix} 2 \\\\ b \\end{pmatrix}.$ Find $b.$\n\n[asy]\nunitsize(0.4 cm);\n\npair A, B, L, R;\nint i, n;\n\nfor (i = -8; i <= 8; ++i) {\n draw((i,-8)--(i,8),gray(0.7));\n draw((-8,i)--(8,i),gray(0.7));\n}\n... |
[
{
"content": "Given the matrix \\[A = \\begin{pmatrix} 9 & 18 \\\\ -6 & -12 \\end{pmatrix}\\], scalar \\[k = 3\\], and matrix \\[B = \\begin{pmatrix} 2 & 0 \\\\ 0 & 2 \\end{pmatrix}\\], calculate the determinant of matrix \\[D = k \\cdot B + A\\].",
"role": "user"
},
{
"content": "Let's use sympy to... |
[
{
"content": "The total mass of seven bowling balls is equivalent to that of three identical canoes. Knowing that one canoe has a mass of 28 pounds, compute the mass of an individual bowling ball.",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\nmass_of_a_can... |
[
{
"content": "Mr. Jesiah is a dairy cow farmer with cows producing 200 gallons of milk every day. The expenses for maintenance of the dairy farm and purchase of feeds is $x per month. Calculate his total income in June if he sells 1 gallon of milk at $3.55. The answer is 18300. What is the value of unknown vari... |
[
{
"content": "Ali had a stock of 800 books in his Room. He sold 60 on Monday, 10 on Tuesday, x on Wednesday, 44 on Thursday and 66 on Friday. 600 books were not sold. What is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's use Python code to solve this problem.\n```python\nx... |
[
{
"content": "In the diagram, $\\triangle ABE$, $\\triangle BCE$ and $\\triangle CDE$ are right-angled, with $\\angle AEB=\\angle BEC = \\angle CED = 60^\\circ$, and $AE=24$. [asy]\npair A, B, C, D, E;\nA=(0,20.785);\nB=(0,0);\nC=(9,-5.196);\nD=(13.5,-2.598);\nE=(12,0);\ndraw(A--B--C--D--E--A);\ndraw(B--E);\ndr... |
[
{
"content": "On a Sunday morning, Josephine sold milk in the farm stall. The buyers brought their containers. She filled three containers with two liters each, two containers with 0.75 liters each, and five containers with x liters each. How many liters of milk did Josephine sell in total?\nIf we know the answ... |
[
{
"content": "Trisha needed to buy some groceries for herself and her dog. She spent $17 on meat, $x on chicken, $43 on all the veggies, $5 on the eggs, and finally $45 on her dog’s food. When she left the store, she had only $35 left. She brought 167 money with her at the beginning. What is the value of unknow... |
[
{
"content": "What is the largest number, all of whose digits are 3 or 2, and whose digits add up to X$?\nIf we know the answer to the above question is 32222, what is the value of unknown variable X?",
"role": "user"
},
{
"content": "We can define a function which returns the sum of a number's digi... |
[
{
"content": "Within the drama society, there are 60 actors. Among them, 36 are attending math lectures, 27 are taking physics, and there is an overlap of 20 students who are engaged in both subjects. How many members of the drama society are not attending any math or physics lectures?",
"role": "user"
},... |
[
{
"content": "Determine the number of nonzero terms in the expansion of $$(x+4)(2x^2+3x+9)-3(x^3-2x^2+7x)?$$",
"role": "user"
},
{
"content": "We can solve this problem by doing the multiplication of the two polynomials and counting the number of non-zero terms. Here is how I did it:\n```python\nfro... |
[
{
"content": "From the integers between 1 and 6 inclusive, two distinct numbers are chosen at random. Determine the probability that their highest common divisor is 1. Provide your answer as a simplified fraction.",
"role": "user"
},
{
"content": "Let's use sympy to find the number of pairs of integ... |
[
{
"content": "Joe’s mother gave him $56 to go to the store. Joe bought x notebooks and 2 books. Each notebook costs $4 and each book costs $7. How much money does Joe have left?\nIf we know the answer to the above question is 14, what is the value of unknown variable x?",
"role": "user"
},
{
"conten... |
[
{
"content": "In a right-angled triangle, called $GHI$, with angle $H$ being 90 degrees, it is given that the hypotenuse $GI$ is $\\sqrt{61}$ units long, while leg $GH$ is 5 units. A circle, drawn with its center positioned on $GH$, gently touches both the hypotenuse $GI$ and side $HI$. When we name the touchpo... |
[
{
"content": "The solution of the equation $7^{x+7} = 8^x$ can be expressed in the form $x = \\log_b 7^7$. What is $b$?",
"role": "user"
},
{
"content": "Let's first check whether there is a unique solution using sympy.\n```python\nimport sympy as sp\n\nx = sp.symbols('x')\n\neq = sp.Eq(7**(x+7), 8*... |
[
{
"content": "If the number of people living per cubic yard in a city is 80, how many additional people are there in a city with 9000 cubic yards compared to a city with 6400 cubic yards?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\nnumber_people_per_cubi... |
[
{
"content": "Maria has 4 dimes, 4 quarters, and 7 nickels in her piggy bank. Her mom gives her 5 quarters. How much money, in dollars, does Maria have now?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\n# value of each coin\ndime_value = 0.1\nquarter_value... |
[
{
"content": "If Dave has $46 and Kyle has $12 less than 3 times what Dave has, how much money does Kyle have after spending one-third of it on snowboarding?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\n# Dave has 46 dollars\ndave_has = 46\n# Kyle has 12 ... |
[
{
"content": "What is the number of diagonals in a regular seven-sided polygon?",
"role": "user"
},
{
"content": "The number of diagonals in a convex $n$-sided polygon is given by the formula:\n$$ \\frac{n(n-3)}{2} $$\nThe given polygon is a regular polygon, so all sides are equal. Thus the given po... |
[
{
"content": "What is the largest four-digit number whose digits add up to X? The answer is 9700. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "Let's try to solve this problem in python:\n```python\nN = 9700\n\nM = N - 1\nM = '970'\nX = len(M)\n\nX = 9 + 7 + 0 + 0\nX\n``... |
[
{
"content": "If Alexa spent a week and 2 days on vacation, which is equivalent to 3/4ths of the time it took Ethan to learn 12 fencing tricks, and Joey spent half as much time as Ethan learning to swim, how many days did it take Joey to learn swimming?",
"role": "user"
},
{
"content": "Let's solve ... |
[
{
"content": "Let $\\omega$ be a complex number such that $\\omega^7 = 1$ and $\\omega \\ne X Compute\n\\[\\omega^{16} + \\omega^{18} + \\omega^{20} + \\dots + \\omega^{54}.\\]\nIf we know the answer to the above question is -1, what is the value of unknown variable X?",
"role": "user"
},
{
"conten... |
[
{
"content": "Imagine dealing three cards one after the other from a complete set of 52 cards, without returning them to the deck. What is the likelihood that you will pull a Jack first, followed by a Queen, and then a King?",
"role": "user"
},
{
"content": "In a set of 52 cards, there are 4 of each... |
[
{
"content": "Calculate $\\tan \\frac{3 \\pi}{4}.$",
"role": "user"
},
{
"content": "Let's solve it using python:\n```python\nimport math\n\ndegree_pi = math.pi\n# Convert angle to radians\nradian_ang = degree_pi * 3 / 4\n\n# Calculate tan(angle)\nradian_ang_val = math.tan(radian_ang)\n\n# Convert f... |
[
{
"content": "Find $\\tan Y$ in the right triangle shown below.\n\n[asy]\npair X,Y,Z;\nX = (0,0);\nY = (24,0);\nZ = (0,7);\ndraw(X--Y--Z--X);\ndraw(rightanglemark(Y,X,Z,23));\nlabel(\"$X$\",X,SW);\nlabel(\"$Y$\",Y,SE);\nlabel(\"$Z$\",Z,N);\nlabel(\"$25$\",(Y+Z)/2,NE);\nlabel(\"$24$\",Y/2,S);\n[/asy]",
"role... |
[
{
"content": "If the arithmetic mean of two real numbers $x$ and $y$ is 18, and their geometric mean is $\\sqrt{92}$, what is the value of $x^2 + y^2$?",
"role": "user"
},
{
"content": "Let's use sympy to find $x^2 + y^2$.\n```python\nfrom sympy import symbols, Eq, solve, simplify, sqrt\n\n# define ... |
[
{
"content": "Given that $x=64^{1/2}\\cdot27^{-1/3}\\cdot16^{1/4}$, find the value of $y = \\left(\\frac{3x}{4}\\right)^2$.",
"role": "user"
},
{
"content": "Let's first check the value of $x$:\n```python\nfrom sympy import Symbol, Eq, simplify, sqrt\n\nx = Symbol('x')\ny = Symbol('y')\n\n# Define t... |
[
{
"content": "A gold coin is worth 50 dollars and a silver coin is worth 25 dollars. If you have 3 gold coins, 5 silver coins, and 30 dollars cash, how much money do you have in dollars?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\nvalue_of_gold = 50\nval... |
[
{
"content": "Calculate the value of $y$ when the slope of the line through points $C(-5,y)$ and $D(3,10)$ is $\\frac{-1}{4}$.",
"role": "user"
},
{
"content": "The slope of the line between points $C(-5,y)$ and $D(3,10)$ is calculated by using a formula:\n$\\frac{y - 10}{-5 - 3}$.\nSince the slope ... |
[
{
"content": "You are given that $3^{400}\\equiv 1\\pmod{1000}$. What are the last three digits of $3^{12000}$?",
"role": "user"
},
{
"content": "Let's write a python code to find the last three digits of $3^{12000}$.\n```python\nfrom sympy import Integer, Mod\n\n# take the last 3 digits\ndef last3_... |
[
{
"content": "If $A,B$ and $C$ are non-zero distinct digits in base X such that $\\overline{ABC}_6 + \\overline{BCA}_6+ \\overline{CAB}_6 = \\overline{AAA0}_6$, find $B+C$ in base $6$. The answer is 5. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "Let's try to solve this... |
[
{
"content": "Philip is a painter. He makes x paintings per day. If he already has 20 paintings, how many paintings in total will he have after 30 days?\nIf we know the answer to the above question is 80, what is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this pro... |
[
{
"content": "If $x$ and $y$ are positive real numbers and $x + y = 35$, what ordered pair $(x, y)$ maximizes $x^5 y^2$?",
"role": "user"
},
{
"content": "Let's use sympy to explore the problem.\n```python\nfrom sympy import symbols, solve\n\n# define the variables\nx, y = symbols('x y')\n\n# define... |
[
{
"content": "A passenger train transports passengers between two stations located in two separate cities. On a particular day, the train carried 100 passengers from one station to the other one way, and on the return trip carried 60 passengers. If the train made x more round trips that day, taking the same num... |
[
{
"content": "A slant asymptote of the rational expression $y = \\frac{2x^2 + 3x - 7}{x-3}$ is the line approached by the equation as $x$ approaches $\\infty$ or $-\\infty$. If this line is of the form $y = mx + b$, find $m+b$.",
"role": "user"
},
{
"content": "Let's write down the fraction with the... |
[
{
"content": "In the figure, $\\angle EAB$ and $\\angle ABC$ are right angles, $AB=4,$ $BC=6,$ $AE=8,$ and $\\overline{AC}$ and $\\overline{BE}$ intersect at $D.$ What is the difference between the areas of $\\triangle ADE$ and $\\triangle BDC?$ [asy]\npair A,B,C,D,I;\nI=(0,8);\nA=(0,0);\nB=(4,0);\nC=(4,6);\nD=... |
[
{
"content": "What is the greatest common divisor of $2^{1001}-1$ and $2^{1012}-1$?",
"role": "user"
},
{
"content": "Using Python's `sympy` library, we can write the following code.\n```python\nfrom sympy import gcd\n\ndef gcd_exp(a,b):\n return gcd(a,b)\n\na = 2**1001 - 1\nb = 2**1012 - 1\ngcd_... |
[
{
"content": "What is the last two digits of $99^{72} + 98$?",
"role": "user"
},
{
"content": "Let's solve it using python:\n```python\nlast_two_digits_mod = (99 ** 72 + 98) % 100\nlast_two_digits_mod\n```",
"role": "assistant"
},
{
"content": "```output\n99\n```",
"role": "user"
}... |
[
{
"content": "Ramon sells two enchiladas and three tacos for $\\$$2.50 and he sells three enchiladas and two tacos for $\\$$2.70. Assuming a fixed price per item, what is the cost, in dollars, of three enchiladas and four tacos? Express your answer as a decimal to the nearest hundredth.",
"role": "user"
}... |
[
{
"content": "Find $2.5-0.32.$",
"role": "user"
},
{
"content": "We can perform the subtraction by using Python and the math library.\n```python\nimport math\n\nresult = 2.5 - 0.32\nprint(result)\n```",
"role": "assistant"
},
{
"content": "```output\n2.18\n```",
"role": "user"
},
... |
[
{
"content": "Find the count of two-digit prime numbers whose digits sum up to eight.",
"role": "user"
},
{
"content": "We can iterate through all possible pairs of digits summing up to eight and then check if their multiplication is a prime number.\nWe also do not want to count pairs where a and b ... |
[
{
"content": "A bag contains six green balls, four red balls, and five blue balls. Two balls are drawn one after the other with replacement. If the first ball drawn is green, what is the probability that both balls are green?",
"role": "user"
},
{
"content": "Let's write down the probability of draw... |
[
{
"content": "If $\\begin{vmatrix} u & v \\\\ w & x \\end{vmatrix} = 4,$ find\n\\[\\begin{vmatrix} u + 2w & v + 2x \\\\ w & x \\end{vmatrix}.\\]",
"role": "user"
},
{
"content": "We can compute this determinant using Python's sympy library.\n```python\nfrom sympy import Symbol, Matrix\n\nu, v, w, x ... |
[
{
"content": "If Farmer Brown's flock of emus has a total of 60 heads and legs, how many emus are there in the flock?",
"role": "user"
},
{
"content": "Let's solve this problem using Python's sympy library.\n```python\nimport sympy as sp\n\n# let's denote the number of emus as x\nx = sp.symbols('x')... |
[
{
"content": "A cookie recipe calls for a ratio of butter:flour:sugar:chocolate_chips which is 1:6:4:3, and for every 4 cups of sugar, it requires 1 extra cup of nuts. If the recipe uses 12 cups of flour, how many total cups of all ingredients including nuts will be used?",
"role": "user"
},
{
"cont... |
[
{
"content": "In preparation for the festive season, the manager of the toy shop stocked up on a batch of popular Mr. Slinkums toys. They displayed $20\\%$ of the shipment in the store and kept the remaining 120 in the backroom. What was the total number of Mr. Slinkums they ordered?",
"role": "user"
},
... |
[
{
"content": "A family has four children. Assuming that the birth of a boy or a girl is equally likely, what is the probability that the four children in the family include at least one boy and one girl? Express your answer as a common fraction.",
"role": "user"
},
{
"content": "We can compute this ... |
[
{
"content": "In the equation $y = mx + b$, find the combined value of $m$ and $b$ for the line that connects the points $(-2,0)$ and $(0,2)$.",
"role": "user"
},
{
"content": "We can compute this directly using Python.\n```python\nimport math\n\nx1, x2, y1, y2 = -2, 0, 0, 2\n\nm = (y2 - y1) / (x2 -... |
[
{
"content": "My co-worker Larry only likes numbers that are divisible by 4, such as 20, or 4,004. How many different ones digits are possible in numbers that Larry likes?",
"role": "user"
},
{
"content": "Every number that Larry likes is divisible by 4 and thus by 2.\nThis means that this number m... |
[
{
"content": "The ordered triples (x, y, z) of complex numbers that satisfy the equations\nx + yz = 7,\ny + xz = 10,\nz + xy = 10,\nare (x1, y1, z1), (x2, y2, z2), ..., (xn, yn, zn).\nFind the value of x1 + x2 + ... + xn.",
"role": "user"
},
{
"content": "We can solve this problem by writing the giv... |
[
{
"content": "Jackie can do 5 push-ups in 10 seconds. How many push-ups can she do in one minute if she takes x 8-second breaks?\nIf we know the answer to the above question is 22, what is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this problem using Python's symp... |
[
{
"content": "In a group of 10 friends, how many different ways can they elect a leader, assistant leader, event organizer, and a finance manager, assuming no one can serve in more than one position?",
"role": "user"
},
{
"content": "Since there are $10$ people in the group, we will have $10 \\cdot ... |
[
{
"content": "What is the sum of all common multiples of 8, 12, 16, and 24 that are less than 360?",
"role": "user"
},
{
"content": "Since $\\text{lcm}(8, 12, 16, 24) = 48,$ all multiples $k \\times 48$ will be a common multiple of 8, 12, 16, and 24.\nTo compute the multiples, we can start by number... |
[
{
"content": "If the value of $x$ is half the value of $y$, and the value of $y$ is one-fifth the value of $z$, and $z$ is equal to 60, what is the value of $x$?",
"role": "user"
},
{
"content": "Let's solve it using python:\n```python\n# Solve a system of equations\nimport sympy as sym\n\n# Define ... |
[
{
"content": "Daryl is loading crates at a warehouse and wants to make sure that they are not overloaded. Each crate can weigh up to 20kg and he has 15 crates he can fill. He has 4 bags of nails to load, each of which weighs 5kg; he has 12 bags of hammers, each of which weighs 5 kg; he also has 10 bags of woode... |
[
{
"content": "A collection includes half dollars (worth $\\$0.50$ each), quarters (worth $\\$0.25$ each) and dimes (worth $\\$0.10$ each). The total value of the half dollars is $\\$15.00.$ The total value of the quarters is $\\$18.75.$ The total value of the dimes is $\\$3.00.$ What is the probability that a c... |
[
{
"content": "In the expression $g(x)=3x-4$, for which value of $a$ does $g(a)$ become zero?",
"role": "user"
},
{
"content": "We can find the value of $a$ such that $g(a) = 0$ using Python's sympy library.\n```python\nfrom sympy import symbols, solve\n\n# Define the function g(x) and the symbol a\n... |
[
{
"content": "Marta works on her grandparent's farm to raise money for a new phone. So far, she has collected $240. For every hour she works, she receives $10. Her grandmother often gives her tips, and she has collected $x in tips in total. How many hours has Marta worked on the farm so far?\nIf we know the ans... |
[
{
"content": "A basketball conference named the Little Twelve has two separate divisions, each hosting six teams. Within each division, teams play against every other team twice, and they also play once against each team in the alternative division. What is the sum of all the games that will take place in the c... |
[
{
"content": "Find the sum of the largest positive multiple of $12$ that is less than $350$ and the smallest positive multiple of $15$ greater than $350$.",
"role": "user"
},
{
"content": "The smallest positive multiple of $15$ greater than $350$ is $355$.\nTo find the largest positive multiple of $... |
[
{
"content": "What is $4m+5n$, where $m=-2+3i$ and $n=1-2i$?",
"role": "user"
},
{
"content": "Let's use sympy to solve this problem.\n```python\nfrom sympy import I, simplify\n\n# define m and n\nm = -2 + 3*I\nn = 1 - 2*I\n\n# compute 4m+5n\nresult = 4*m + 5*n\n\n# let's simplify the result\nsimpli... |
[
{
"content": "The pizzeria sells small pizzas for $2 and large pizzas for $8. They sold $40 in pizzas. If they sold x small pizzas, how many large pizzas did they sell?\nIf we know the answer to the above question is 3, what is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's... |
[
{
"content": "Let $f(x) = \\sin{x} + 2\\cos{x} + 3\\tan{x}$, using radian measure for the variable $x$. Let $r$ be the smallest positive value of $x$ for which $f(x) = 0$. Find $\\lfloor r \\rfloor.$",
"role": "user"
},
{
"content": "Let's write a simple Python program to check the values of $f(x)... |
[
{
"content": "If $g(x) = f(x) + 4x - 1$ where $f(x) = 3x^2 + 3 \\cdot 5^{1993} + 2$, what is the last digit of $g(4)$?",
"role": "user"
},
{
"content": "Let's use sympy to find the last digit of the expressions for $f(4)$ and $g(4)$ and then calculate $g(4)$ modulo $10$.\n```python\nimport sympy as ... |
[
{
"content": "If the line $y = \\frac{1}{5} x + 2$ is rotated $90^\\circ$ counterclockwise about the origin, how many times does the new line intersect the graphs of \\[(x - \\lfloor x \\rfloor)^2 + (y - 2)^2 = x - \\lfloor x \\rfloor\\]and $y = \\frac{1}{5} x + 2$?",
"role": "user"
},
{
"content": ... |
[
{
"content": "A rectangular field has its length increased by one-fifth and its width increased by one-tenth. What is the new percentage increase of the field's area compared to the original?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\nimport numpy as np... |
[
{
"content": "Determine the smallest integer greater than or equal to the product of $3$ and $5.5$.",
"role": "user"
},
{
"content": "Let's break down this problem into two steps. First, we will compute $3 \\cdot 5.5$. Then, we will compute the ceiling of that product, which will be the smallest int... |
[
{
"content": "Francis' family has 2 ukuleles, 4 guitars, and a certain number of violins. Each ukulele has 4 strings. Each guitar has 6 strings. Each violin has 4 strings. If the total number of strings among the ukuleles, guitars, and violins is 40 strings, how many violins does Francis' family have?",
"ro... |
[
{
"content": "If a sequence of numbers has multiples that include 12, 18, and 30, what is the first number that appears in all three sets of multiples?",
"role": "user"
},
{
"content": "Multiples of 12 are: $12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, ... |
[
{
"content": "Haley has 5 more necklaces than Jason. Josh has x% the number of necklaces as Jason. If Haley has 25 necklaces, how many more necklaces does Haley have than Josh?\nIf we know the answer to the above question is 15, what is the value of unknown variable x?",
"role": "user"
},
{
"content... |
[
{
"content": "Determine the value of $y$ that satisfies the equation $|y-6| + 2y = 9$.",
"role": "user"
},
{
"content": "Since $|y-6|$ will always be positive, we can split the absolute value into two cases.\n- $y - 6 >= 0$: In this case, the equation becomes $y - 6 + 2y = 9$.\n- $y - 6 < 0$: In thi... |
[
{
"content": "Miriam takes care of the flowers in the botanical garden. She works 5 hours a day and can take care of 60 different flowers in one day. How many flowers can Miriam take care of in 6 days of work?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\n... |
[
{
"content": "Find out the quantity of perfect cubes ranging from 100 to 999 that are divisible by $9.$",
"role": "user"
},
{
"content": "Let's write a simple Python program to check the number of cubes in that range that are divisible by 9.\n```python\ncubes = []\n# First let's get all the cubes\nf... |
[
{
"content": "A school has three classes with $48$, $36$, and $60$ students respectively. A teacher wants to divide each class into equal groups with the same number of students in each group and all groups across the three classes having the same number of students. What is the largest possible number of stude... |
[
{
"content": "Determine the value of\n\\[f(2) - f(-2)\\]\nfor the function\n\\[f(x) = \\log (x + \\sqrt{1 + x^2}).\\]",
"role": "user"
},
{
"content": "Let's write down the function $f$ in python and then use it to calculate the value of $f(2) - f(-2)$.\n```python\nimport math\n\ndef f(x):\n retu... |
[
{
"content": "Mrs. Snyder used to spend 40% of her monthly income on rent and utilities. Her salary was recently increased by $600 so now her rent and utilities only amount to 25% of her monthly income. How much was her previous monthly income?",
"role": "user"
},
{
"content": "Let's solve this prob... |
[
{
"content": "Carl is calculating the amount he needs to budget for gas expenses on his upcoming road trip to the Grand Canyon. His car has a fuel efficiency of 30 miles per gallon in cities and 40 miles per gallon on the highway. The one-way distance from his house to the Grand Canyon is 60 miles in the city a... |
[
{
"content": "If $p$ is a constant and $3x^2 - 18x + p$ is equal to the square of a binomial, what is the value of $p$?",
"role": "user"
},
{
"content": "Let's assume binomial to be $ax + b$.\n$(ax + b)^2 = a^2x^2 + 2abx + b^2$.\nWe equate this expression to $3x^2 - 18x + p$ and try to find $a$ and ... |
[
{
"content": "Jenny decided to place her collection of Easter eggs into some baskets, distributing 18 red ones among certain green baskets, and 24 orange ones through a few blue baskets. She ensures that every basket has an identical count of eggs, with the minimum amount being 4 eggs per basket. What is the co... |
[
{
"content": "Simplify\n\\[\\frac{2 - 3i}{2 + 3i} + \\frac{2 + 3i}{2 - 3i}.\\]",
"role": "user"
},
{
"content": "Let's write this out as two algebraic fractions.\n```python\nimport sympy as sp\n\nroot_1 = (2 - 3 * sp.I) / (2 + 3 * sp.I)\nroot_2 = (2 + 3 * sp.I) / (2 - 3 * sp.I)\n\nsolution = root_1 ... |
[
{
"content": "Bingo has two dogs. On average, they walk a total of 70 miles a week. The first dog walks an average of x miles a day. The other dog averages 8 miles a day. What is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this problem using Python's sympy library.... |
[
{
"content": "If the sequence $2, 7, 12, a, b, 27, c$ is arithmetic, what is the value of $a + b + c$?",
"role": "user"
},
{
"content": "The correct answer is 67.\nThe following code shows that the sequence $2, 7, 12, a, b, 27, c$ is arithmetic:\n```python\nfrom sympy import symbols, solve\n\n# defi... |
[
{
"content": "Beth had 150 students in her 10th-grade class. The following year x more students join. In her final year, 15 students left. How many students did Beth have in her class at the end of her final year?\nIf we know the answer to the above question is 165, what is the value of unknown variable x?",... |
[
{
"content": "After their mother gave Monica and Sheila $50 to buy toilet paper and groceries, they spent $12 on toilet paper. They used the rest of the money to buy apples, butter, eggs, and a large ham, which cost twice as much as the toilet paper. They still had some money left, so their mother allowed them ... |
[
{
"content": "What is the length of the repeating cycle in the decimal fraction of $\\frac{2}{11}$?",
"role": "user"
},
{
"content": "Let's write a python function to find the length of the repeating cycle in a fraction, using sympy.\n```python\nimport sympy as sp\n\ndef length_of_repeating_decimal_... |
[
{
"content": "The function $g(n)$ is defined such that $g(n) = 3f(n) - 2n - 34$ where $f(n) = n^2 + n + 17$. What is the value of $g(11)$?",
"role": "user"
},
{
"content": "Let's write a python function to find the value of $g(n)$.\n```python\ndef g(n):\n f = lambda n: n**2 + n + 17\n return 3... |
[
{
"content": "Larry started off having x channels from his cable company. They took 20 channels away and replaced those with 12 channels. He called the company and asked if he could reduce his package by 10 more channels but add the sports package which is 8 channels. He realizes that he didn't add the supre... |
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