index int64 20k 20.2k | text stringlengths 735 3.8k |
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20,000 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Simplify $\sqrt5-\sqrt{20}+\sqrt{45}$.<|eot_id|><|start_header_id|>assistant<|end_heade... |
20,001 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Find the value of $x$ in the equation:$\frac{17^6-17^5}{16}=17^x$<|eot_id|><|start_head... |
20,002 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Compute the product of $\sqrt{54}$, $\sqrt{32}$, and $\sqrt{6}$, i.e., $\sqrt{54}\cdot\... |
20,003 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
At constant temperature, the pressure $p$ of a sample of gas is inversely proportional ... |
20,004 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
As shown in the figure below, a circular park consists of an outer-ring path for walker... |
20,005 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
In a 8 fluid ounce bottle of Vitamin Water, there are 125 calories. The problem is to d... |
20,006 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given the inequality $-4 \le 2x+1 \le 6$, determine the number of integers that satisfy... |
20,007 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Evaluate the expression $a^3 \cdot a^2$ if $a = 5$.<|eot_id|><|start_header_id|>assista... |
20,008 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given the mathematical expression $3 \times (7 - 5) - 5$, find its value.<|eot_id|><|st... |
20,009 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given the function $f(x) = \sqrt{x^2}$, we need to compute the range of this function. ... |
20,010 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given two right triangles $ABC$ and $ABD$, find the length of segment $BC$ in units.[as... |
20,011 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Find one-fourth of 6 times 8.<|eot_id|><|start_header_id|>assistant<|end_header_id|>
T... |
20,012 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given the equation $(2x+5)(x-3)=14$, the task is to find the sum of the possible values... |
20,013 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Mrs. Crabapple's British Literature class has 11 students, and the class meets four tim... |
20,014 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Find all positive integer values of $c$ such that the equation $x^2-7x+c=0$ only has ro... |
20,015 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Find the least four-digit positive integer, with all different digits, that is divisibl... |
20,016 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given the quadratic equation $x^{2} - 5x + 9 = 0$, let $a$ and $b$ be its solutions. Th... |
20,017 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
During the first year, ABC's stock price starts at $\$100$ and increases by $100\%$. Du... |
20,018 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Polina's Pizza offers five different toppings for their pizzas. The problem is to deter... |
20,019 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given the quadratic equation $x^2+bx+48=0$, the two solutions are in the ratio of 3 to ... |
20,020 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given a square with an area of $\frac{1}{4}$, find the side length of the square.<|eot_... |
20,021 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
The problem is to find the cost of five pounds of feathers and five ounces of gold, giv... |
20,022 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Simplify the expression $\frac{x+1}{3}+\frac{2-3x}{2}$ and express the result as a sing... |
20,023 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
John is working with the set $\{1,2,3,4,5,6\}$. He computes the sum of the elements of ... |
20,024 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
To make pizza dough, Luca mixes 50 mL of milk for every 250 mL of flour. How many mL of... |
20,025 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Let $M$, $N$, and $X$ be variables defined as follows:- $M = 2007 \div 3$- $N = M \div ... |
20,026 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given a table of points $(x, y)$ that lie on a straight line:$$\begin{array}{c|c}x & y ... |
20,027 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
I flip a fair coin once and roll a regular six-sided die. What is the probability the c... |
20,028 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given a geometric sequence $\frac{125}{9}, \frac{25}{3}, 5, 3, \ldots$, find the eighth... |
20,029 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
In the Olympic 100-meter finals, there are 8 sprinters, of which three are Americans. T... |
20,030 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given the equation $9^{18n} = 27^{24}$, find the value of $n$.<|eot_id|><|start_header_... |
20,031 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Moore's law states that the number of transistors that can be placed inexpensively on a... |
20,032 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
The problem is to find the real values of $x$ that satisfy the inequality $-4 < x^{4} +... |
20,033 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Find the least positive integer that is divisible by each of the first eight positive i... |
20,034 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Find the radius of the circle with equation $x^2 + 8x + y^2 - 6y = 0$.<|eot_id|><|start... |
20,035 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
The double-bar graph shows the number of home runs hit by McGwire and Sosa during each ... |
20,036 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given the expression $\sqrt{2}+\frac{1}{\sqrt{2}} + \sqrt{3} + \frac{1}{\sqrt{3}}$, we ... |
20,037 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Express the decimal number $1.45$ as a fraction.<|eot_id|><|start_header_id|>assistant<... |
20,038 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Let $(x,y)$ be an ordered pair of real numbers that satisfies the equation:$x^2+y^2=14x... |
20,039 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
The problem provides a chart showing the number of rounds of golf played by each golfer... |
20,040 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Expand the product of two polynomials: $(2x^5 + 3x^2)(x^4 - 4x^2 + 3x - 8)$.<|eot_id|><... |
20,041 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Joe wants to find all the four-letter words that begin and end with the same letter. Ho... |
20,042 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given a quadratic equation $2x^2+mx+8$, where $m$ is a real number, find the possible v... |
20,043 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
The problem is to find the value of $x$ given that the average of the numbers 12, 21, a... |
20,044 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Find the sum of all values of $x$ that satisfy the equation $|x-1| = 7$.<|eot_id|><|sta... |
20,045 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
In rectangle $ABCD$, $AB = 6$ cm and $BC = 8$ cm. Point $E$ is on $AD$ and point $F$ is... |
20,046 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
A bookstore is trying to determine the optimal price to charge for a certain book in or... |
20,047 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Solve for $x$ in the equation:$\frac{3}{5} \cdot \frac{1}{9} \cdot x = 6$The goal is to... |
20,048 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Solve for $w$ and express as a common fraction: $\frac{1\frac16}w=\frac{42}3$.<|eot_id|... |
20,049 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Two students are having a pie eating contest. The first student eats $\frac{6}{7}$ of o... |
20,050 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Evaluate the expression $(1+2i)6-3i$, where $i$ is the imaginary unit.<|eot_id|><|start... |
20,051 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given a point $(a, b)$ that lies on the line with the equation $3x + 2y = 12$, find the... |
20,052 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Find the arithmetic mean of the integers from $-4$ through $5$, inclusive. Express your... |
20,053 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
What is the positive difference between $120\%$ of 30 and $130\%$ of 20?<|eot_id|><|sta... |
20,054 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Find the greatest common factor (GCF) of the numbers 30, 90, and 75.<|eot_id|><|start_h... |
20,055 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Find the smallest integer $x$ that satisfies the inequality $x < 2x - 7$.<|eot_id|><|st... |
20,056 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Factor the following expression: $7x^2-63$.<|eot_id|><|start_header_id|>assistant<|end_... |
20,057 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given a set of five numbers $\{x, 2x, 3, 2, 5\}$, where $x$ is an integer, find the lar... |
20,058 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Let $f(y) = y^4 -3y^3 +y - 3$ and $g(y) = y^3 + 7y^2 -2$. Find $f(y) + g(y)$ and write ... |
20,059 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given the following information:- 24 lemons are required to make 32 gallons of lemonade... |
20,060 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Van was asked to add 46 to 37 and round the result to the nearest ten. He figured that ... |
20,061 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given the graphs of two functions, $f(x)$ and $g(x)$, defined on the domain $0 \le x \l... |
20,062 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
How many distinct arrangements of the letters in the word "monkey" are there?<|eot_id|>... |
20,063 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Let $f$ be an invertible function from $(-\infty,\infty)$ to $(-\infty,\infty)$ such th... |
20,064 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
In a right triangle, the lengths of the two legs are given as 40 inches and 42 inches. ... |
20,065 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Simplify the expression $(2-2i)(5+5i)$, where $i$ is the imaginary unit defined as $i^2... |
20,066 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Compute the result of dividing 0.18 by 0.003, i.e., find the value of $0.18 \div 0.003$... |
20,067 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given the arithmetic sequence $1000, ~987, ~974, ~961, \ldots ,$ find the least positiv... |
20,068 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
A square is divided into five congruent rectangles, as shown in the diagram below. If t... |
20,069 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Find the smallest three-digit number that is a multiple of 13.<|eot_id|><|start_header_... |
20,070 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Evaluate the expression $\log_28\sqrt{2}$.<|eot_id|><|start_header_id|>assistant<|end_h... |
20,071 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Find the value of $r$ that satisfies the equation:$$3(r-7) = 4(2-2r) + 4$$<|eot_id|><|s... |
20,072 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
An amusement park offers a bulk discount for tickets. The price for each ticket is $\$7... |
20,073 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Evaluate the logarithmic expression $\log_{\sqrt8}(64\sqrt{8})$.<|eot_id|><|start_heade... |
20,074 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Find the value of the following expression:$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\ri... |
20,075 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Find the domain of the function $k(y) = \frac{1}{2y+1}$. Express the answer using inter... |
20,076 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given a three-digit integer $63\underline{\hphantom{0}}$, where the units digit is unkn... |
20,077 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given a randomly chosen integer $n$ between $1$ and $10$ inclusive, we need to find the... |
20,078 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
A school needs to transport 411 students to an event. Each bus can hold a maximum of 38... |
20,079 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
A sign painter is tasked with painting individual numerals for a row of 50 houses. The ... |
20,080 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given a function $f(x)$ with the following properties:- $f(1) = 2$- $f(4) = 3$- $f(7) =... |
20,081 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
A coin is flipped eight times, and the sequence of heads and tails occurring is recorde... |
20,082 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Simplify the complex number multiplication:$$(3-i)(6+2i)$$where $i$ is the imaginary un... |
20,083 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Solve the following equation for $c$:\[\frac{c-23}{2} = \frac{2c +5}{7}.\]<|eot_id|><|s... |
20,084 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Simplify the following expression:$\root 3 \of {x \root 3 \of {x \root 3 \of {x \sqrt{x... |
20,085 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Subtract $111.11$ from $333.33$. Express the result as a decimal to the nearest hundred... |
20,086 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given the equation $x(x-3)=1$, express the solutions in the form $\frac{a+\sqrt{b}}{c}$... |
20,087 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Express the following sum of fractions as a common fraction:$\cfrac{ \frac{2}{5}+\frac{... |
20,088 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given the quadratic equation $2x^2 + 13x + 6 = 0$, find the product of the squares of i... |
20,089 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Find the value of $x$ that minimizes the quadratic expression $x^2- 14x + 3$.<|eot_id|>... |
20,090 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given a regular octagon $ABCDEFGH$, sides $\overline{AH}$ and $\overline{CD}$ are exten... |
20,091 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Find the smallest composite number that has no prime factors less than 10.<|eot_id|><|s... |
20,092 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Let $m$ and $n$ be two numbers that satisfy the following equations:\begin{align*}mn &=... |
20,093 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Find the sum of the distinct prime factors of the number 315.<|eot_id|><|start_header_i... |
20,094 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given the graph of the function $y=\frac{1}{2}x^2-9$, find the square of the smallest d... |
20,095 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Find the smallest two-digit prime number such that reversing the digits of the number p... |
20,096 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given a square and a circle with equal perimeter and circumference respectively, find t... |
20,097 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Given two points $P(5,3)$ and $Q(-3,6)$, find the midpoint of the line segment $\overli... |
20,098 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
Consider this pattern where the positive, proper fractions with denominator $(n+1)$ ar... |
20,099 | <|begin_of_text|><|start_header_id|>system<|end_header_id|>You are a expert mathematician, solve the problems accordingly
using relevant mathematical techniques<|eot_id|><|begin_of_text|><|start_header_id|>user<|end_header_id|>
What is the probability that a randomly chosen positive integer less than or equal to 2... |
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