BitZone910/SFT-Qwen2.5-3B
Text Generation • 3B • Updated • 20
Datasets:
instruction stringclasses 1
value | input stringlengths 10 2.46k | output stringlengths 269 47.3k |
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You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | The angle bisector of the acute angle formed at the origin by the graphs of the lines \(y = x\) and \(y=3x\) has equation \(y=kx.\) The original answer is in the form \(\frac{k+\sqrt{m}}{n}\). Please find the value of \(k + m + n\). | <think>Okay, so I need to find the equation of the angle bisector of the acute angle formed at the origin by the lines y = x and y = 3x. The answer is supposed to be in the form (k + sqrt(m))/n, and then find k + m + n. Hmm, angle bisector... right. So angle bisector is a line that divides the angle between two lines i... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Jan's three-eyed lizard has 3 times more wrinkles than eyes, and seven times more spots than wrinkles. How many fewer eyes does the lizard have than the combined number of spots and wrinkles? | <think> Let's break down the problem step by step and use Python to ensure our calculations are accurate.
1. The lizard has 3 eyes.
2. The lizard has 3 times more wrinkles than eyes. So, if the lizard has 3 eyes, then it has \(3 \times 3 = 9\) wrinkles.
3. The lizard has 7 times more spots than wrinkles. So, if the l... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Consider the triangular array of numbers with $0,1,2,3,\ldots$ along the sides and interior numbers obtained by adding the two adjacent numbers in the previous row. Rows $1$ through $6$ are shown.
\[
\begin{array}{ccccccccccc}
& & & & & 0 & & & & & \\
& & & & 1 & & 1 & & & & \\
& & & 2 & & 2 & & 2 & & & \\
& & 3 &... | <think> To solve the problem, we need to understand the structure of the triangular array and the function \( f(n) \), which represents the sum of the numbers in row \( n \). We can derive a pattern or formula for \( f(n) \) by analyzing the structure of the array.
First, let's observe the pattern in the sums of the r... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Lao is farming chickens. He can sell each chicken for $1.50. A bag of chicken feed weighs 20 pounds and costs $2. Each chicken will need 2 pounds of feed from the time it hatches to the time he sells it. If he makes $65 profit from selling chickens, how many did he sell? | <think> To determine how many chickens Lao sold, we need to consider both the revenue from selling the chickens and the cost of feeding them. Here's a step-by-step breakdown of the problem:
1. **Revenue from Selling Chickens**: If Lao sells each chicken for $1.50, and he sold \(x\) chickens, his total revenue is \(1.... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | A company has a tank that is already filled at a maximum capacity of 350,000 gallons of water. One day the tank starts losing 32,000 gallons/hour for 5 hours, after that time the company repaired the tank but it wasn't enough because the tank was still losing 10,000 gallons/hour. It stayed like that for 10 hours. In th... | <think> Let's break down the problem step by step and use Python to ensure accuracy.
1. **Initial Condition**: The tank starts with 350,000 gallons.
2. **First Leak**: The tank loses 32,000 gallons/hour for 5 hours.
3. **Second Leak**: After the first leak, the tank loses 10,000 gallons/hour for 10 hours.
4. **Fillin... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | A pool has 48 blue tiles and 32 red tiles. If the pool needs 100 tiles to be completed, how many more tiles are needed? | <think> To determine how many more tiles are needed to complete the pool, we can follow these steps:
1. Calculate the total number of tiles currently available.
2. Subtract this total from the required number of tiles (100) to find out how many more tiles are needed.
Let's use Python to perform these calculations.
... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | A certain series of books was published at intervals of seven years. When the seventh book was released, the sum of all the years in which the books in this series were published was 13,524. When was the first book of the series published? | <think> Let's break down the problem step-by-step.
1. Let's denote the year in which the first book was published as \( y \).
2. The years in which the books were published are \( y, y+7, y+14, y+21, y+28, y+35, y+42 \).
3. The sum of these years is \( y + (y+7) + (y+14) + (y+21) + (y+28) + (y+35) + (y+42) = 7y + 7 \... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | A number in the form of $7777 \cdots 77$ is written on the blackboard. Each time the last digit is erased, the remaining number is multiplied by 3, and then the erased digit is added back. This operation is continued repeatedly. What is the final number obtained? | <think> To solve this problem, we need to simulate the described process. We start with a number consisting of a series of 7's. Let's denote this number as \( N \). The steps are as follows:
1. Erase the last digit of \( N \).
2. Multiply the remaining number by 3.
3. Add the erased digit back to the result of the mul... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Let $a_n$ be the integer obtained by writing all the integers from $1$ to $n$ from left to right. For example, $a_3 = 123$ and $a_{11} = 1234567891011$. Compute the remainder when $a_{44}$ is divided by $45$. | <think> To solve the problem, we need to construct the number \(a_{44}\) by concatenating all the integers from 1 to 44, and then find the remainder when this large number is divided by 45.
First, let's construct the number \(a_{44}\) as a string by concatenating all integers from 1 to 44. Then, we will convert this s... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Calculate the indefinite integral:
$$
\int (4 - 3x) e^{-3x} \, dx
$$ | <think>
To solve the indefinite integral \(\int (4 - 3x) e^{-3x} \, dx\) using Python and SymPy, we can follow these steps:
1. Define the variable \(x\).
2. Define the integrand \((4 - 3x) e^{-3x}\).
3. Use SymPy's `integrate` function to compute the indefinite integral.
4. Print the result.
Here is the Python code... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Find all the roots of the equation
\[ 1 - \frac{x}{1} + \frac{x(x-1)}{2!} - \frac{x(x-1)(x-2)}{3!} + \frac{x(x-1)(x-2)(x-3)}{4!} - \frac{x(x-1)(x-2)(x-3)(x-4)}{5!} + \frac{x(x-1)(x-2)(x-3)(x-4)(x-5)}{6!} = 0 \]
(Where \( n! = 1 \cdot 2 \cdot 3 \cdots n \))
In the answer, specify the sum of the found roots. | <think> Let's start by defining the polynomial equation and then find its roots using Python. The given equation is:
\[ 1 - \frac{x}{1} + \frac{x(x-1)}{2!} - \frac{x(x-1)(x-2)}{3!} + \frac{x(x-1)(x-2)(x-3)}{4!} - \frac{x(x-1)(x-2)(x-3)(x-4)}{5!} + \frac{x(x-1)(x-2)(x-3)(x-4)(x-5)}{6!} = 0 \]
This can be written in a... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | The expression \((1+2+3)\left(1+\frac{1}{2}+\frac{1}{3}\right)\) is equal to:
(A) 3
(B) 11
(C) 6
(D) \(\frac{11}{6}\)
(E) 12 | <think>
To solve the expression \((1+2+3)\left(1+\frac{1}{2}+\frac{1}{3}\right)\), we can break it down into two parts and compute each part separately before multiplying them together.
1. Compute the value of \(1 + 2 + 3\).
2. Compute the value of \(1 + \frac{1}{2} + \frac{1}{3}\).
3. Multiply the results from the ... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Given two spheres with radii $2R$ and $R$, the volume ratio of the larger sphere to the smaller sphere is __________. | <think> To find the volume ratio of the larger sphere to the smaller sphere, we can use the formula for the volume of a sphere, which is given by:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere. Let's denote the radius of the larger sphere as \( 2R \) and the radius of the smaller sphere as ... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | An investor invested some money in 2 separate schemes: A and B. Scheme A will yield 30% of the capital within a year, and scheme B will yield 50% of the capital within a year. If he invested $300 in scheme A and $200 in B, how much more money will he have in scheme A than in B after a year, provided he does not withdra... | <think> Let's break down the problem step-by-step and then use Python code to verify the result.
1. Calculate the yield from scheme A after one year.
2. Calculate the yield from scheme B after one year.
3. Compute the total amount of money the investor will have in each scheme after one year.
4. Find the difference b... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | A random walk is a process in which something moves from point to point, and where the direction of movement at each step is randomly chosen. Suppose that a person conducts a random walk on a line: he starts at $0$ and each minute randomly moves either $1$ unit in the positive direction or $1$ unit in the negativ... | <think> To solve this problem, we need to calculate the expected distance of a random walk after 6 moves. Let's break down the problem step-by-step.
1. **Understanding the Random Walk:**
- The person starts at position 0.
- Each move, the person moves either +1 or -1 with equal probability (1/2).
- After 6 mo... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Two integers are in the ratio of 1 to 3. If 10 is added to the smaller number, the ratio becomes 1 to 1. What is the larger integer? | <think> Let's solve the problem step-by-step using Python and SymPy.
1. **Understand the Problem:**
- Let the two integers be \(x\) and \(3x\) (since they are in the ratio 1:3).
- When 10 is added to the smaller number \(x\), the new ratio becomes 1:1. This means \(x + 10 = 3x\).
2. **Set Up the Equation:**
... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | The area of rectangle $ABCD$ is $72$ units squared. If point $A$ and the midpoints of $\overline{BC}$ and $\overline{CD}$ are joined to form a triangle, what is the area of that triangle? | <think> To solve this problem, let's first understand the geometric configuration and then use Python to verify our reasoning.
1. **Understand the Problem:**
- We have a rectangle \(ABCD\) with area \(72\) square units.
- Let the coordinates of the vertices of the rectangle be \(A(0, 0)\), \(B(a, 0)\), \(C(a, b)... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Translate the following math problem from Chinese to English:
The graph of the function $f(x)=2\sin(\omega x-\dfrac{\pi }{3})$ (where $\omega > 0$) is shifted to the left by $\dfrac{\pi }{3\omega }$ units to obtain the graph of the function $y=g(x)$. If $y=g(x)$ is an increasing function on the interval $\left[0,\dfra... | <think> To solve this problem, we need to follow these steps:
1. **Understand the transformation**: When the function \( f(x) = 2\sin(\omega x - \frac{\pi}{3}) \) is shifted to the left by \( \frac{\pi}{3\omega} \) units, the new function \( g(x) \) becomes:
\[
g(x) = 2\sin\left(\omega \left(x + \frac{\pi}{3\om... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Katy makes some brownies to eat throughout the week. She eats 5 on Monday and twice as many on Tuesday. After she has eaten the brownies on Tuesday, all of the brownies she made are gone. How many brownies did Katy make? | <think> Let's break down the problem step by step. Katy eats 5 brownies on Monday and twice as many on Tuesday. If she eats 5 brownies on Monday, then she eats \(2 \times 5 = 10\) brownies on Tuesday. Therefore, the total number of brownies she made is the sum of the brownies she ate on Monday and Tuesday.
We can exp... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | At time $t=0,$ a ball is thrown downward at 24 feet per second from a height of 160 feet above the ground. The equation $h = -16t^2 - 24t +160$ describes the height (in feet) of the ball. In how many seconds will the ball hit the ground? Express your answer as a decimal. | <think> To determine when the ball hits the ground, we need to find the time \( t \) when the height \( h \) is 0. This involves solving the quadratic equation:
\[ 0 = -16t^2 - 24t + 160 \]
We can solve this quadratic equation using the quadratic formula:
\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
where \( a = -... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Given $ \triangle{ABC}$ , where $ A$ is at $ (0,0)$ , $ B$ is at $ (20,0)$ , and $ C$ is on the positive $ y$ -axis. Cone $ M$ is formed when $ \triangle{ABC}$ is rotated about the $ x$ -axis, and cone $ N$ is formed when $ \triangle{ABC}$ is rotated about the $ y$ -axis. If the volume of cone $ M$... | <think> Let's solve the problem step-by-step.
1. **Determine the coordinates of point \( C \)**:
- Since \( C \) is on the positive \( y \)-axis, its coordinates are \( (0, h) \) where \( h \) is the height of the triangle.
2. **Volume of cone \( M \)**:
- When \( \triangle ABC \) is rotated about the \( x \)-... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Given positive integers $a$, $b$, $c$ satisfying the inequality $a^2 + b^2 + c^2 + 43 \leq ab + 9b + 8c$, find the value of $a + b + c$. | <think> To solve the inequality \(a^2 + b^2 + c^2 + 43 \leq ab + 9b + 8c\), we can rearrange it to form a quadratic expression and analyze it. Let's rewrite the inequality as follows:
\[a^2 + b^2 + c^2 + 43 - ab - 9b - 8c \leq 0\]
We can complete the square for the terms involving \(a\), \(b\), and \(c\):
\[a^2 - a... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Given \( b = 3 \), evaluate the expressions in the set \( \{-2b, 5b, \frac{30}{b}, b^2 + 1, 2\} \) and determine which expression yields the largest number. | <think> To solve this problem, we need to evaluate each expression in the set \(\{-2b, 5b, \frac{30}{b}, b^2 + 1, 2\}\) given that \(b = 3\). We will then compare the results to determine which expression yields the largest number.
Let's break it down step-by-step:
1. Evaluate \(-2b\):
\[ -2b = -2 \cdot 3 = -6 \]
2.... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Solve the following: $\left(2\frac{1}{2} - 3\frac{1}{3}\right)^2 \div \left(4\frac{1}{4} + 1\frac{1}{6}\right)$. Express your answer as a mixed number. | <think> Let's break down the problem step-by-step and solve it using Python and SymPy.
1. Convert the mixed numbers to improper fractions.
2. Perform the subtraction inside the first set of parentheses.
3. Square the result of the subtraction.
4. Perform the addition inside the second set of parentheses.
5. Divide th... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | A retailer buys three electronic items - a radio, a television, and a speaker. He buys the radio for Rs 225, the television for Rs 4,500, and the speaker for Rs 1,500. His overhead expenses are Rs 30 for the radio, Rs 200 for the television, and Rs 100 for the speaker. He sells the radio for Rs 300, the television for ... | <think> To calculate the overall profit percentage for the retailer, we need to follow these steps:
1. Calculate the total cost price (CP) of all three items, including the overhead expenses.
2. Calculate the total selling price (SP) of all three items.
3. Determine the total profit by subtracting the total cost pric... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Given two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ in a plane with an angle of $60^{{∘}}$ between them, $\overrightarrow{a}$ = (2, 0), and $|\overrightarrow{b}|$ = 1, find the value of $| \overrightarrow{a} + 2\overrightarrow{b} |$. | <think> To find the value of \( | \overrightarrow{a} + 2\overrightarrow{b} | \), we can use the formula for the magnitude of a vector sum. The magnitude of the vector \(\overrightarrow{a} + 2\overrightarrow{b}\) is given by:
\[ | \overrightarrow{a} + 2\overrightarrow{b} | = \sqrt{(\overrightarrow{a} + 2\overrightarro... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Given a right triangle \( ABC \) with a right angle at vertex \( C \) and leg lengths in the ratio of \( 1:3 \). Points \( K \) and \( L \) are the centers of squares that share one side with leg \( AC \) and \( BC \) respectively, and these squares do not overlap with triangle \( ABC \). Point \( M \) is the midpoint ... | <think> To solve this problem, we will use both geometric reasoning and Python code to ensure the accuracy of our results.
### Part (a): Justifying that point \( C \) lies on the line segment \( KL \)
Given a right triangle \( ABC \) with a right angle at \( C \) and leg lengths in the ratio \( 1:3 \), let's assume \... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Certain integers, when divided by $\frac{3}{5}, \frac{5}{7}, \frac{7}{9}, \frac{9}{11}$, result in a mixed number where the fractional part is $\frac{2}{3}, \frac{2}{5}, \frac{2}{7}, \frac{2}{9}$, respectively. Find the smallest integer greater than 1 that satisfies these conditions. | <think> To solve this problem, we need to find an integer \( x \) such that when \( x \) is divided by \(\frac{3}{5}\), \(\frac{5}{7}\), \(\frac{7}{9}\), and \(\frac{9}{11}\), the fractional parts of the resulting mixed numbers are \(\frac{2}{3}\), \(\(\frac{2}{5}\), \(\frac{2}{7}\), and \(\frac{2}{9}\) respectively.
... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Given the complex number $z$ that satisfies $z= \frac {5}{1-2i}$ (where $i$ is the imaginary unit), find the value of $|z|$. | <think> To find the value of \( |z| \) for the complex number \( z = \frac{5}{1-2i} \), we can follow these steps:
1. **Rationalize the Denominator**: Multiply the numerator and the denominator by the complex conjugate of the denominator to get rid of the imaginary part in the denominator.
2. **Simplify the Expressio... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Points $A(11, 9)$ and $B(2, -3)$ are vertices of $\triangle ABC$ with $AB=AC$. The altitude from $A$ meets the opposite side at $D(-1, 3)$. What are the coordinates of point $C$? Provide your answer as an ordered pair \((m, n)\). Please give the value of m + n. | <think> To solve the problem, we need to find the coordinates of point \( C \) such that \( AB = AC \) and the altitude from \( A \) to \( BC \) intersects \( BC \) at point \( D(-1, 3) \). Let's break down the problem into manageable steps:
1. **Calculate the slope of \( AD \)**:
The slope of \( AD \) is given by:... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | $\log_{2}9 \cdot \log_{3}4 + 2^{\log_{2}3} = $ \_\_\_\_\_\_ ． | <think>
To solve the expression \(\log_{2}9 \cdot \log_{3}4 + 2^{\log_{2}3}\), we can break it down into smaller parts and use properties of logarithms and exponents.
1. First, we simplify \(\log_{2}9 \cdot \log_{3}4\):
- We know that \(\log_{2}9 = \log_{2}(3^2) = 2\log_{2}3\).
- We also know that \(\log_{3}4 ... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Given a triangle \(ABC\). On the extension of the side \(AC\) beyond point \(C\), point \(N\) is taken such that \(CN = AC\); point \(K\) is the midpoint of side \(AB\).
In what ratio does the line \(KN\) divide the side \(BC\)? | <think> To solve this problem, we can use coordinate geometry. Let's place the triangle \(ABC\) in a coordinate system for simplicity. Assume \(A = (0, 0)\), \(B = (2b, 0)\), and \(C = (2c_1, 2c_2)\).
1. **Find the coordinates of point \(N\)**:
Since \(N\) is on the extension of \(AC\) beyond point \(C\) and \(CN ... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | 在平面直角坐标系 xOy 中，动点 A 在圆 x^2+y^2=1 上，点 B 的坐标为 (3,0)，若点 C 使得三角形 ABC 是等边三角形，则 |OC| 的最大值为__________. | <think> To solve this problem, we need to find the maximum value of \( |OC| \) where \( C \) is a point such that \( \triangle ABC \) is an equilateral triangle, with \( A \) being a point on the unit circle \( x^2 + y^2 = 1 \) and \( B \) being the point \( (3, 0) \).
Let's break down the problem into manageable step... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | 已知向量 $\boldsymbol{a}, \boldsymbol{b}$ 满足 $|\boldsymbol{a}-\boldsymbol{b}|=3,|\boldsymbol{a}+2 \boldsymbol{b}|=6, \boldsymbol{a}^{2}+\boldsymbol{a} \cdot \boldsymbol{b}-2 \boldsymbol{b}^{2}=-9$, 则 $|b|=$ 的原始答案为 $\sqrt{m}$ 的形式，请给出 m 的值。 | <think> To solve the problem, we need to use the given conditions and vector properties. Let's denote the magnitudes of the vectors and their dot products to form a system of equations.
Given:
1. \( |\boldsymbol{a} - \boldsymbol{b}| = 3 \)
2. \( |\boldsymbol{a} + 2\boldsymbol{b}| = 6 \)
3. \( \boldsymbol{a}^2 + \bolds... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Alexis imagines a $2008 \times 2008$ grid of integers arranged sequentially in the following way:
\[
\begin{array}{r@{\hspace{20pt}}r@{\hspace{20pt}}r@{\hspace{20pt}}r@{\hspace{20pt}}r}
1, & 2, & 3, & \ldots, & 2008 \\
2009, & 2010, & 2011, & \ldots, & 4026 \\
4017, & 4018, & 4019, & \ldots, & 6024 \\
\vdots & & & & \... | <think> To solve this problem, let's first understand the structure of the grid and the process Alexis follows.
The grid is a \(2008 \times 2008\) matrix where the element in the \(i\)-th row and \(j\)-th column is given by:
\[ a_{ij} = (i-1) \cdot 2008 + j \]
where \(i\) and \(j\) range from 1 to 2008.
When Alexis p... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Stormi is saving up to buy a bicycle. She washes 3 cars for $10 each. She mows 2 lawns for $13 each. If the bicycle she wants costs $80, how much more money does Stormi need to make to afford the bicycle? | <think> Let's break down the problem step by step and use Python code to ensure accuracy.
1. Calculate the total money Stormi earns from washing cars.
2. Calculate the total money Stormi earns from mowing lawns.
3. Sum up the total earnings from both activities.
4. Subtract the total earnings from the cost of the bic... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Given the system of equations $\left\{\begin{array}{l}5x-2y=3\\ mx+5y=4\end{array}\right.$ and $\left\{\begin{array}{l}x-4y=-3\\ 5x+ny=1\end{array}\right.$ have the same solution, find the values of $m$ and $n$. | <think> To solve the problem, we need to find the values of \(m\) and \(n\) such that the two systems of equations have the same solution. Let's break down the problem into manageable steps:
1. **Solve the first system of equations for \(x\) and \(y\):**
\[
\begin{cases}
5x - 2y = 3 \\
mx + 5y = 4
\end... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Find the largest real number \(x\) such that
\[
\frac{x^{2} + x - 1 + \left|x^{2} - (x - 1)\right|}{2} = 35x - 250.
\] | <think> Let's start by analyzing the given equation:
\[
\frac{x^{2} + x - 1 + \left|x^{2} - (x - 1)\right|}{2} = 35x - 250.
\]
First, we need to consider the expression inside the absolute value, \(x^2 - (x - 1) = x^2 - x + 1\). Since \(x^2 - x + 1 = (x - \frac{1}{2})^2 + \frac{3}{4}\) is always positive for all rea... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | The first term of a sequence is $2005$. Each succeeding term is the sum of the cubes of the digits of the previous term. What is the ${2005}^{\text{th}}$ term of the sequence? | <think> To solve this problem, we need to generate the sequence iteratively until we reach the 2005th term. The first term of the sequence is given as 2005. Each succeeding term is the sum of the cubes of the digits of the previous term. Let's write a Python function to compute the next term in the sequence and then it... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Joey wants to buy the latest released pair of designer High Jump basketball sneakers. He plans to mow 3 neighbors’ lawns for $8 a lawn, sell 2 collectible figures to his friends for $9 each, and work an after-school job for 10 hours at $5 per hour. If his earnings just cover the price of the High Jump sneakers, how muc... | <think> Let's break down Joey's earnings from each activity:
1. Mowing 3 neighbors' lawns at $8 per lawn.
2. Selling 2 collectible figures at $9 each.
3. Working an after-school job for 10 hours at $5 per hour.
We can calculate the total earnings by summing up the earnings from each activity. Let's use Python to com... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Simplify first, then evaluate: $\left(a-b\right)^{2}+\left(a+3b\right)\left(a-3b\right)-a\left(a-2b\right)$, where $a=-1$ and $b=2$. | <think> Let's break down the problem step-by-step and use Python to ensure accuracy.
1. **Simplify the expression**:
\[
(a - b)^2 + (a + 3b)(a - 3b) - a(a - 2b)
\]
2. **Expand each term**:
- \((a - b)^2 = a^2 - 2ab + b^2\)
- \((a + 3b)(a - 3b) = a^2 - (3b)^2 = a^2 - 9b^2\)
- \(a(a - 2b) = a^2 - 2ab... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | James supercharges his car which increases his car's speed by 30%. He then cuts weight by 15% which increases the speed a further 10 mph. If his car's original speed was 150 mph what is the new speed? | <think> Let's break down the problem step by step and use Python to ensure accuracy.
1. **Initial Speed**: James' car starts at 150 mph.
2. **Supercharging**: This increases the speed by 30%. So the new speed after supercharging is \(150 \text{ mph} \times (1 + 0.30)\).
3. **Weight Reduction**: This further increases... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Hongfu Supermarket purchased a batch of salt. In the first month, 40% of this salt was sold. In the second month, 420 bags of this salt were sold. At this point, the ratio of the amount of salt sold to the amount remaining is 3:1. How many bags of salt did Hongfu Supermarket purchase? | <think> Let's break down the problem step by step and use Python to find the solution.
1. Let's assume the total number of bags of salt purchased is \( x \).
2. In the first month, 40% of the salt was sold, so \( 0.4x \) bags were sold.
3. In the second month, 420 bags were sold.
4. After two months, the total number... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Real numbers $x$ and $y$ satisfy the equations $2^x=16^{y+1}$ and $27^y=3^{x-2}$. Find the product $xy$. | <think> Let's start by expressing the given equations in terms of the same base for the exponents.
The first equation is:
\[2^x = 16^{y+1}\]
Since \(16 = 2^4\), we can rewrite the equation as:
\[2^x = (2^4)^{y+1} \implies 2^x = 2^{4(y+1)} \implies x = 4(y+1) \implies x = 4y + 4\]
The second equation is:
\[27^y = 3^{... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Calculate the value of $(\log_2 3 + \log_2 27) \times (\log_4 4 + \log_4 \frac{1}{4})$. | <think> To solve the expression \((\log_2 3 + \log_2 27) \times (\log_4 4 + \log_4 \frac{1}{4})\), we can break it down into smaller parts and use properties of logarithms.
1. First, simplify \(\log_2 3 + \log_2 27\):
\[
\log_2 3 + \log_2 27 = \log_2 (3 \times 27) = \log_2 81
\]
Since \(81 = 3^4\), we hav... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | A basketball player made the following number of free throws in 8 successive games: 6, 18, 15, 14, 19, 12, 19, and 15. What is the median number of successful free throws? | <think> To find the median number of successful free throws, we need to follow these steps:
1. Arrange the data in ascending order.
2. Identify the middle value(s) of the ordered data set. Since there are 8 games (an even number), the median will be the average of the 4th and 5th values in the ordered list.
Let's do... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Jack and Jill are marathon runners. Jack can finish a marathon (43 km) in 4.5 hours and Jill can run a marathon in some time. The ratio of their average running speed is 0.9555555555555555 (Jack : Jill). How long does it take for Jill to finish the marathon? | <think> To determine how long it takes for Jill to finish the marathon, we can use the given ratio of their average running speeds. The ratio of their speeds is given as approximately 0.9555555555555555, which can be expressed as a fraction. Let's denote the time it takes for Jill to finish the marathon as \( t \) hou... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Let $f$ be a linear function with the properties that $f(1) \leq f(2)$, $f(3) \geq f(4)$, and $f(5) = 5$. What is the value of $f(0)$? | <think> To solve this problem, we need to determine the form of the linear function \( f(x) \). A linear function can be written in the form \( f(x) = ax + b \). We are given three conditions:
1. \( f(1) \leq f(2) \)
2. \( f(3) \geq f(4) \)
3. \( f(5) = 5 \)
First, let's substitute \( x = 5 \) into the linear functio... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | A group of science students went on a field trip. They took 9 vans and 10 buses. There were 8 people in each van and 27 people on each bus. How many people went on the field trip? | <think> To determine the total number of people who went on the field trip, we need to calculate the number of people in the vans and the number of people in the buses, and then sum these two amounts.
1. Calculate the total number of people in the vans:
\[ \text{Total people in vans} = 9 \text{ vans} \times 8 \text{ ... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | The rules for a race require that all runners start at $A$, touch any part of the 1500-meter wall, touch any part of the opposite 1500-meter wall, and stop at $B$. What is the minimum distance a participant must run? Assume that $A$ is 400 meters directly south of the first wall, and that $B$ is 600 meters directly nor... | <think> To solve this problem, we can use a method that involves reflecting the positions of points and using the properties of straight lines to find the minimum distance. Here's the step-by-step approach:
1. **Understand the Problem:**
- Point \(A\) is 400 meters south of the first wall.
- Point \(B\) is 600 m... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | What is the largest number of points that can be arranged on a given circle such that in all the triangles they form, none of the angles is less than $25^\circ$? | <think> To solve this problem, we need to determine the maximum number of points that can be arranged on a circle such that in all the triangles formed by these points, none of the angles is less than \(25^\circ\).
When points are arranged on a circle, the angles of the triangles formed are related to the arc lengths ... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | The average score on last week's Spanish test was 90. Marco scored 10% less than the average test score and Margaret received 5 more points than Marco. What score did Margaret receive on her test? | <think> Let's break down the problem step by step and use Python to ensure our calculations are accurate.
1. The average score on the Spanish test is 90.
2. Marco scored 10% less than the average test score.
3. Margaret received 5 more points than Marco.
First, we calculate Marco's score:
\[ \text{Marco's score} = \... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | A rectangular garden 60 feet long and 20 feet wide is enclosed by a fence. To make the garden larger, while using the same amount of fencing, its shape is changed to a square. By how many square feet does this enlarge the garden? | <think> To solve this problem, we need to follow these steps:
1. **Calculate the perimeter of the original rectangular garden.**
2. **Determine the side length of the square garden using the same perimeter.**
3. **Calculate the area of the original rectangular garden.**
4. **Calculate the area of the new square garde... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | If the ratio of \( b \) to \( a \) is 4, then what is the value of \( a \) when \( b = 15 - 7a \)? | <think> Given that the ratio of \( b \) to \( a \) is 4, we can write this as:
\[
\frac{b}{a} = 4 \implies b = 4a
\]
We are also given that:
\[
b = 15 - 7a
\]
Since both expressions equal \( b \), we can set them equal to each other:
\[
4a = 15 - 7a
\]
Now, we solve for \( a \):
\[
4a + 7a = 15 \implies 11a = 1... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | Find constants $A,$ $B,$ $C,$ and $D$ so that
\[\frac{x^3 + 3x^2 - 12x + 36}{x^4 - 16} = \frac{A}{x - 2} + \frac{B}{x + 2} + \frac{Cx + D}{x^2 + 4}.\] Enter the ordered quadruple $(k, m, n, p)$ for constants $A$, $B$, $C$, and $D$, and then find the sum $k + m + n + p$. | <think> To solve the given problem, we need to perform partial fraction decomposition on the expression \(\frac{x^3 + 3x^2 - 12x + 36}{x^4 - 16}\). The denominator can be factored as \(x^4 - 16 = (x^2 - 4)(x^2 + 4) = (x - 2)(x + 2)(x^2 + 4)\). Thus, we can write:
\[
\frac{x^3 + 3x^2 - 12x + 36}{(x - 2)(x + 2)(x^2 + 4)... |
You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to s... | A $9 \times 9$ square consists of $81$ unit squares. Some of these unit squares are painted black, and the others are painted white. Each $2 \times 3$ rectangle and each $3 \times 2$ rectangle contain exactly 2 black unit squares and 4 white unit squares. Determine the number of black unit squares. | <think> To solve this problem, we need to determine the number of black unit squares in a $9 \times 9$ grid, given that each $2 \times 3$ and $3 \times 2$ rectangle contains exactly 2 black and 4 white unit squares. Let's break down the problem and use reasoning along with Python code to find the solution.
### Step-by... |
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sft_math_tir
The 30,438-example mathematical tool-integrated reasoning SFT file used by the Trace-OPSD project's SFT-Qwen2.5-3B.
Each record follows the Alpaca/LlamaFactory format:
| Field | Type | Meaning |
|---|---|---|
instruction |
string | Tool-use/system instruction |
input |
string | Mathematical problem |
output |
string | Demonstration with reasoning, tool actions/feedback, and answer |
from datasets import load_dataset
data = load_dataset("BitZone910/sft_math_tir", split="train")
To use the downloaded JSON with LlamaFactory, register sft_math_tir.json as an
Alpaca-format dataset in that installation's dataset_info.json.
Source and license
Adapted from the Tool-Star-SFT-54K dataset, whose dataset card declares MIT. The original Tool-Star authors retain their attribution.
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