Datasets:
id stringlengths 25 29 | source stringclasses 1
value | question stringlengths 13 3.12k | steps listlengths 3 45 | answer stringlengths 3 2.73k |
|---|---|---|---|---|
Llama-3.1-70B-Instruct_36 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | If a task requires a force of 50 N and the worker applies a force of 60 N, what is the % efficiency of the worker's action? | [
"First, I need to understand the problem. The task requires a force of 50 N, and the worker applied a force of 60 N. I need to calculate the efficiency of the worker's action.",
"Efficiency is generally calculated as the ratio of the useful output to the total input. In this context, the useful force is 50 N, and... | To determine the **efficiency** of the worker's action, we can use the following approach:
**Efficiency** is generally defined as the ratio of the **useful output** to the **total input**. In this context:
- **Useful Output**: The force required by the task, which is **50 N**.
- **Total Input**: The force applied by ... |
Llama-3.1-70B-Instruct_51 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | How many possible outcomes are there when you roll two six-sided dice? | [
"To determine the number of possible outcomes when rolling two six-sided dice, I start by considering each die individually. Each die has 6 faces, so there are 6 possible outcomes for the first die and 6 possible outcomes for the second die.",
"Next, I use the multiplication principle, which states that if there ... | To determine the number of possible outcomes when rolling two six-sided dice, we can use the **multiplication principle** of counting. Here's a step-by-step solution:
1. **Understand the Problem:**
- Each die has 6 faces, numbered from 1 to 6.
- When rolling two dice, each die operates independently of the other... |
Llama-3.1-70B-Instruct_70 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | Solve the equation $\frac{3}{4}x + 2 = 10$. | [
"First, I need to isolate the term with \\( x \\) on one side of the equation. To do this, I'll subtract 2 from both sides of the equation.",
"This will eliminate the constant term on the left side, leaving me with \\(\\frac{3}{4}x = 8\\).",
"Next, to solve for \\( x \\), I'll multiply both sides of the equatio... | To solve the equation:
\[
\frac{3}{4}x + 2 = 10
\]
**Step 1: Subtract 2 from both sides**
\[
\frac{3}{4}x + 2 - 2 = 10 - 2
\]
Simplifying:
\[
\frac{3}{4}x = 8
\]
**Step 2: Multiply both sides by the reciprocal of \(\frac{3}{4}\) to solve for \(x\)**
The reciprocal of \(\frac{3}{4}\) is \(\frac{4}{3}\).
\[
\frac... |
Llama-3.1-70B-Instruct_89 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The total number of integers from 1 to 100 that are not divisible by 7 and not divisible by 5 is how many? | [
"First, I need to determine the total number of integers from 1 to 100, which is 100.",
"Next, I'll calculate how many of these integers are divisible by 5. This is done by dividing 100 by 5, resulting in 20 numbers.",
"Then, I'll find out how many integers are divisible by 7 by dividing 100 by 7, which gives a... | To determine the number of integers from 1 to 100 that are **not** divisible by 7 and **not** divisible by 5, we can use the principle of inclusion and exclusion.
**Step 1: Calculate the total number of integers from 1 to 100.**
\[
\text{Total numbers} = 100
\]
**Step 2: Find the number of integers divisible by 5.**... |
Llama-3.1-70B-Instruct_93 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | A food truck is traveling along a straight road. It starts at a speed of 25 miles per hour. Every 30 minutes, the truck accelerates by 5 miles per hour. If the food truck travels for 2 hours, how many miles will it travel? | [
"First, I need to determine how many times the food truck accelerates during the 2-hour journey. Since it accelerates every 30 minutes, there are 2 intervals of acceleration.",
"The initial speed of the truck is 25 miles per hour. In the first 30 minutes, it travels at this speed. In the second 30 minutes, the sp... | To determine how many miles the food truck will travel in 2 hours, we'll break down the journey into intervals based on the acceleration schedule.
**Given:**
- **Initial Speed:** 25 miles per hour (mph)
- **Acceleration:** 5 mph every 30 minutes
- **Total Time:** 2 hours
**Step 1: Determine the Number of Acceleration... |
Llama-3.1-70B-Instruct_97 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | After the lab investigation, you have two solutions: Solution A and Solution B. They contain the same solute and same solvent. However, Solution A has a 10% concentration of solute while Solution B has a 20% concentration of solute. What is the volume percentage concentration of a mixture that contains 60 mL of Solutio... | [
"First, I need to determine the amount of solute in each solution. Solution A has a 10% concentration, so in 60 mL, the solute is 6 mL. Solution B has a 20% concentration, so in 40 mL, the solute is 8 mL.",
"Next, I'll calculate the total amount of solute in the mixture by adding the solute from both solutions, w... | To determine the volume percentage concentration of the mixture, follow these steps:
1. **Calculate the amount of solute in each solution:**
- **Solution A:**
\[
\text{Solute in Solution A} = 10\% \times 60\,\text{mL} = 0.10 \times 60 = 6\,\text{mL}
\]
- **Solution B:**
\[
\text{S... |
Llama-3.1-70B-Instruct_110 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | A high school has a total of 300 students. The students are divided into 5 classes, and each class has an equal number of students. What is the number of students in each class? | [
"First, I need to determine the number of students in each class when 300 students are divided equally among 5 classes.",
"To find this, I'll divide the total number of students by the number of classes.",
"So, 300 divided by 5 equals 60.",
"Therefore, each class has 60 students."
] | To determine the number of students in each class, follow these steps:
1. **Total Number of Students:**
The high school has a total of **300 students**.
2. **Number of Classes:**
The students are divided into **5 classes**.
3. **Equal Distribution:**
To find the number of students in each class, divid... |
Llama-3.1-70B-Instruct_112 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | If $x$ and $y$ are real numbers, such that $x + y = 3$ and $x - y = 1$, then what is $xy$? | [
"First, I have the two equations: \\( x + y = 3 \\) and \\( x - y = 1 \\).",
"I can add these two equations together to eliminate \\( y \\). Adding the left sides gives \\( x + y + x - y = 2x \\), and adding the right sides gives \\( 3 + 1 = 4 \\). So, \\( 2x = 4 \\), which means \\( x = 2 \\).",
"Next, I subst... | To find the value of \( xy \) given the equations:
\[
\begin{cases}
x + y = 3 \\
x - y = 1
\end{cases}
\]
**Step 1: Add the two equations**
\[
(x + y) + (x - y) = 3 + 1
\]
Simplifying the left side:
\[
x + y + x - y = 2x
\]
So,
\[
2x = 4
\]
**Step 2: Solve for \( x \)**
\[
x = \frac{4}{2} = 2
\]
**Step 3: Sub... |
Llama-3.1-70B-Instruct_113 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | After a 60% discount, a shirt is on sale for $20. What was the original price of the shirt? | [
"First, I recognize that the sale price of the shirt is $20 after a 60% discount.",
"This means that $20 represents 40% of the original price, since 100% minus 60% is 40%.",
"To find the original price, I can set up the equation: 40% of the original price equals $20.",
"Mathematically, this is 0.40 multiplied... | To determine the original price of the shirt before the discount, follow these steps:
1. **Understand the Discount:**
- The shirt is on sale for **60% off**, which means you're paying **40%** of the original price.
- The sale price is **\$20**.
2. **Set Up the Equation:**
- Let \( P \) be the original price ... |
Llama-3.1-70B-Instruct_119 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | A sailor's distance from a lighthouse is 500 meters. If the sailor is sailing directly towards the lighthouse at a constant speed of 10 m/s, how far will the sailor be from the lighthouse after 200 seconds? | [
"First, I need to determine the distance the sailor covers by multiplying the speed by the time traveled. The speed is 10 meters per second, and the time is 200 seconds, so the distance covered is 10 * 200 = 2000 meters.",
"Next, I'll subtract the distance covered from the initial distance to find the remaining d... | To determine how far the sailor will be from the lighthouse after 200 seconds, follow these steps:
1. **Calculate the distance covered by the sailor:**
The sailor is moving at a constant speed of 10 meters per second (m/s) for 200 seconds.
\[
\text{Distance covered} = \text{Speed} \times \text{Time} = 10\, ... |
Llama-3.1-70B-Instruct_135 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | If the height of the space station is increased by 26% and then decreased by 16%, what is the overall change in the height of the space station? | [
"First, I need to determine the overall change in the height of the space station when its height is first increased by 26% and then decreased by 16%.",
"I'll start by letting the original height of the space station be represented by \\( h \\).",
"When the height is increased by 26%, the new height becomes \\(... | To determine the overall change in the height of the space station after a 26% increase followed by a 16% decrease, follow these steps:
1. **Let the original height be \( h \).**
2. **Increase the height by 26%:**
\[
\text{New height} = h + 26\% \text{ of } h = h \times (1 + 0.26) = 1.26h
\]
3. **Decrease t... |
Llama-3.1-70B-Instruct_141 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | There are two random variables, $X$ and $Y$. The probability of the event $X$ is 0.5 and the probability of the event $Y$ is 0.7. The probability of the joint event $X \cap Y$ is 0.3. What is the probability of the event $X \cup Y$? | [
"First, I recognize that to find the probability of the union of two events, \\( P(X \\cup Y) \\), I can use the formula:",
"\\[ P(X \\cup Y) = P(X) + P(Y) - P(X \\cap Y) \\]",
"Given the probabilities:\n- \\( P(X) = 0.5 \\)\n- \\( P(Y) = 0.7 \\)\n- \\( P(X \\cap Y) = 0.3 \\)",
"I substitute these values into... | To find the probability of the union of two events \( X \) and \( Y \), denoted as \( P(X \cup Y) \), we can use the following formula:
\[
P(X \cup Y) = P(X) + P(Y) - P(X \cap Y)
\]
**Given:**
- \( P(X) = 0.5 \)
- \( P(Y) = 0.7 \)
- \( P(X \cap Y) = 0.3 \)
**Step-by-Step Solution:**
1. **Substitute the given probab... |
Llama-3.1-70B-Instruct_148 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | A school is giving its students a scholarship to attend a study abroad program. The scholarship will cover all expenses except for a registration fee of $X. The registration fee is 25% of the total expenses. What is the total cost of the study abroad program if the registration fee is $25? | [
"First, I need to determine the total cost of the study abroad program based on the given information.",
"The registration fee is $25, which represents 25% of the total expenses. To find the total cost, I can set up an equation where 25% of the total cost equals $25.",
"Let’s denote the total cost as \\( T \\).... | To determine the total cost of the study abroad program, let's break down the information provided:
1. **Registration Fee (X):** \$25
2. **Percentage of Total Expenses Covered by Registration Fee:** 25%
Let the total cost of the study abroad program be \( T \).
Since the registration fee is 25% of the total expenses... |
Llama-3.1-70B-Instruct_167 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | There are 10 people in a room, and each person is either a left-hander or a right-hander. If 60% of the people in the room are right-handers, and if no two people in the room have the same handedness as their neighbor to the immediate right or left, then the maximum number of left-handers in the room is what percent of... | [
"First, I need to determine the total number of right-handers and left-handers in the room. With 10 people and 60% being right-handers, there are 6 right-handers and 4 left-handers.",
"Next, I need to arrange these individuals in a way that no two people with the same handedness are sitting next to each other. To... | To determine the maximum number of left-handers in the room under the given conditions, let's break down the problem step by step.
**Given:**
- Total people in the room: 10
- Percentage of right-handers: 60%
- No two people with the same handedness can sit next to each other.
**Step 1: Calculate the Number of Right-H... |
Llama-3.1-70B-Instruct_173 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | A car is traveling from City A to City B at a constant speed of 60 km/h. The car travels from City A to City C, which is 2/3 of the distance from City A to City B. How far is City C from City A? | [
"First, I need to determine the distance from City A to City B. Since the car is traveling at a constant speed of 60 km/h, but the time taken for the trip isn't provided, I'll assume the total distance from A to B is D kilometers.",
"Next, City C is located 2/3 of the way from City A to City B. To find the distan... | To determine the distance from City A to City C, let's follow these steps:
1. **Define the Total Distance:**
- Let the total distance from City A to City B be \( D \) kilometers.
2. **Determine the Distance to City C:**
- City C is located \( \frac{2}{3} \) of the way from City A to City B.
- Therefore, the ... |
Llama-3.1-70B-Instruct_175 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | If \(f(x) = 2x + 1\), what is the value of \(f(f(f(2)))\)? | [
"Okay, so I have this function f(x) = 2x + 1, and I need to find the value of f(f(f(2))). Hmm, that sounds like I have to apply the function f three times, each time using the result from the previous step. Let me break it down step by step.",
"First, I need to find f(2). Since f(x) is 2x + 1, plugging in 2 for x... | To find the value of \(f(f(f(2)))\) where \(f(x) = 2x + 1\), we proceed step by step.
First, we calculate \(f(2)\):
\[
f(2) = 2 \cdot 2 + 1 = 4 + 1 = 5
\]
Next, we use the result from the first step to find \(f(f(2))\), which is \(f(5)\):
\[
f(5) = 2 \cdot 5 + 1 = 10 + 1 = 11
\]
Finally, we use the result from the s... |
Llama-3.1-70B-Instruct_177 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The average price of a gallon of gasoline in the United States is $2.75 . If gas costs $2.25 a gallon in Tulsa and $3.00 a gallon in San Francisco, which city is closer to the national average? | [
"First, I need to determine how much each city's gas price deviates from the national average.",
"For Tulsa, the gas price is $2.25, which is $0.50 below the national average of $2.75.",
"For San Francisco, the gas price is $3.00, which is $0.25 above the national average.",
"Comparing the two deviations, San... | To determine which city's gasoline price is closer to the national average, we'll compare the difference between each city's price and the national average.
**Given:**
- **National Average Price:** \$2.75 per gallon
- **Tulsa Price:** \$2.25 per gallon
- **San Francisco Price:** \$3.00 per gallon
**Step 1: Calculate ... |
Llama-3.1-70B-Instruct_217 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | In a class of 30 students, a student is to be randomly selected to give a presentation. Find the probability that the student selected is a member of a club if there are 10 members of the club in the class. | [
"First, I need to determine the total number of students in the class, which is 30.",
"Next, I identify how many of these students are members of the club, and that number is 10.",
"To find the probability that a randomly selected student is a club member, I divide the number of club members by the total number... | To find the probability that a randomly selected student from the class is a member of the club, follow these steps:
1. **Determine the total number of students in the class:**
\[
\text{Total students} = 30
\]
2. **Identify the number of club members in the class:**
\[
\text{Club members} = 10
... |
Llama-3.1-70B-Instruct_235 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The school's chess club ordered 15 boxes of pizza with 12 slices in each box. If 48 students attended the meeting and each student ate \(\frac{3}{4}\) of a pizza, how many slices of pizza did they eat in total? | [
"First, I need to determine the total number of pizza slices available. There are 15 boxes of pizza, each containing 12 slices, so the total number of slices is 15 multiplied by 12, which equals 180 slices.",
"Next, I'll calculate the total number of pizzas consumed by the students. With 48 students attending and... | To determine how many slices of pizza the students ate in total, let's break down the problem step by step.
### **Step 1: Calculate the Total Number of Pizza Slices Ordered**
The school ordered **15 boxes** of pizza, with each box containing **12 slices**.
\[
\text{Total slices} = 15 \text{ boxes} \times 12 \text{ s... |
Llama-3.1-70B-Instruct_240 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | Tom is training for a marathon. His current training regimen consists of running 30 miles one week, and then increasing that distance by 5 miles the following week. This pattern continues for 10 weeks, after which Tom will run his marathon. If Tom wants to determine how far he will run during the final week of his trai... | [
"First, I recognize that Tom's training follows an arithmetic sequence where he increases his weekly running distance by a constant difference each week.",
"Tom starts with 30 miles in the first week, and each subsequent week he increases his distance by 5 miles. This pattern continues for a total of 10 weeks.",
... | To determine how far Tom will run during the final week of his training, we can analyze his training pattern. Here's a step-by-step solution:
### **Understanding the Training Pattern**
- **Starting Point:** Tom begins by running **30 miles** in the first week.
- **Weekly Increase:** Each subsequent week, he increases ... |
Llama-3.1-70B-Instruct_250 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | A company makes a profit of $3 on each of its small boxes of cereal and $2 on each of its large boxes of cereal. How much profit will the company make in a day if it sells 140 small boxes and 90 large boxes of cereal? | [
"First, I need to determine the profit from selling small boxes of cereal. The company makes a $3 profit on each small box and sells 140 of them. So, the profit from small boxes is 3 multiplied by 140, which equals $420.",
"Next, I'll calculate the profit from selling large boxes of cereal. The company makes a $2... | To determine the total profit the company makes in a day from selling both small and large boxes of cereal, follow these steps:
1. **Calculate the profit from small boxes:**
- **Profit per small box:** \$3
- **Number of small boxes sold:** 140
\[
\text{Profit from small boxes} = 3 \times 140 = \$42... |
Llama-3.1-70B-Instruct_259 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The cost of making a certain type of garment is $2.50 per unit and the selling price is $4.75 per unit. Write an expression to represent the profit made from selling x units of the garment. | [
"First, I need to determine the profit from selling one unit of the garment. The selling price per unit is $4.75, and the cost per unit is $2.50.",
"To find the profit per unit, I subtract the cost from the selling price: $4.75 - $2.50, which equals $2.25.",
"Next, to find the total profit from selling x units,... | To determine the profit made from selling \( x \) units of the garment, follow these steps:
1. **Calculate the profit per unit:**
\[
\text{Profit per unit} = \text{Selling price per unit} - \text{Cost per unit}
\]
Given:
\[
\text{Selling price per unit} = \$4.75
\]
\[
\text{Cost per ... |
Llama-3.1-70B-Instruct_261 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | For the experiment of tossing a fair six-sided die, how many total outcomes are there? | [
"First, I recognize that a standard six-sided die has numbers from 1 to 6.",
"When the die is tossed once, each face represents a possible outcome.",
"Therefore, there are 6 possible outcomes in total."
] | To determine the total number of possible outcomes when tossing a fair six-sided die, follow these steps:
1. **Understand the Die:**
- A standard die has six faces.
- Each face is numbered from 1 to 6.
2. **Identify Possible Outcomes:**
- When you toss the die, each face has an equal chance of landing face u... |
Llama-3.1-70B-Instruct_280 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | In a triangle, the first angle is $x$ degrees and the third angle is 5 degrees more than the second angle. If the sum of the angles in the triangle is 180 degrees, what is the value of $x$? | [
"First, I recognize that the sum of the angles in any triangle is always 180 degrees.",
"Let's denote the first angle as \\( x \\) degrees. The second angle can be represented as \\( y \\) degrees, and the third angle is 5 degrees more than the second angle, so it is \\( y + 5 \\) degrees.",
"Setting up the equ... | To find the value of \( x \) in the triangle, let's follow these steps:
1. **Understand the Problem:**
- The first angle is \( x \) degrees.
- The third angle is 5 degrees more than the second angle.
- The sum of all angles in a triangle is 180 degrees.
2. **Define the Angles:**
- Let the second angle be ... |
Llama-3.1-70B-Instruct_282 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The expression $x + y + (x + y) \cdot (x + y)$ can also be written in the form
$$a(x + y)^2 + bx + by + c,$$where $a$, $b$, and $c$ are constants. What is $a + b + c$? | [
"First, I'll start by expanding the original expression \\( x + y + (x + y) \\cdot (x + y) \\).",
"I know that \\( (x + y) \\cdot (x + y) \\) is the same as \\( (x + y)^2 \\), which expands to \\( x^2 + 2xy + y^2 \\).",
"So, the expression becomes:\n\\[\nx + y + x^2 + 2xy + y^2\n\\]",
"Next, I'll rearrange th... | To rewrite the expression \( x + y + (x + y) \cdot (x + y) \) in the form \( a(x + y)^2 + bx + by + c \), follow these steps:
1. **Expand the Expression:**
\[
x + y + (x + y) \cdot (x + y)
\]
First, expand \( (x + y) \cdot (x + y) \):
\[
(x + y)^2 = x^2 + 2xy + y^2
\]
So, the expression becomes... |
Llama-3.1-70B-Instruct_307 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | When the average price of a kilogram of carrots was 28 pence per kilogram, how much did 200 kilograms of carrots cost? | [
"First, I need to determine the cost of 200 kilograms of carrots when the average price is 28 pence per kilogram.",
"To find the total cost, I will multiply the number of kilograms by the price per kilogram.",
"So, 200 kg multiplied by 28 pence per kg equals 5,600 pence.",
"Therefore, 200 kilograms of carrots... | To determine the cost of 200 kilograms of carrots when the average price is 28 pence per kilogram, follow these steps:
1. **Understand the Given Information:**
- **Price per kilogram of carrots:** 28 pence
- **Quantity of carrots:** 200 kilograms
2. **Set Up the Calculation:**
The total cost can be calcu... |
Llama-3.1-70B-Instruct_321 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | In a survey of 200 workers, 110 of them said that they were not satisfied with their jobs. How many workers are satisfied with their jobs? | [
"First, I note that there are 200 workers in total.",
"Out of these, 110 workers are not satisfied with their jobs.",
"To find the number of satisfied workers, I subtract the number of dissatisfied workers from the total number of workers: 200 minus 110 equals 90.",
"Therefore, 90 workers are satisfied with t... | To determine how many workers are satisfied with their jobs, follow these steps:
1. **Total number of workers surveyed:**
\[
200
\]
2. **Number of workers not satisfied with their jobs:**
\[
110
\]
3. **Calculate the number of satisfied workers:**
Subtract the number of dissatisfied worker... |
Llama-3.1-70B-Instruct_331 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | If $x$ is a positive integer and $x^2+2x+1=64$, what is the value of $x$? | [
"First, I notice that the equation \\( x^2 + 2x + 1 = 64 \\) can be rewritten by completing the square. This simplifies the equation to \\( (x + 1)^2 = 65 \\).",
"Next, I take the square root of both sides to solve for \\( x + 1 \\), which gives me \\( x + 1 = \\sqrt{65} \\) or \\( x + 1 = -\\sqrt{65} \\).",
"S... | To find the value of \( x \) in the equation \( x^2 + 2x + 1 = 64 \), follow these steps:
1. **Rewrite the Equation:**
Start by recognizing that the left side of the equation is a perfect square trinomial.
\[
x^2 + 2x + 1 = (x + 1)^2
\]
2. **Set Up the Equation:**
Substitute the perfect squa... |
Llama-3.1-70B-Instruct_332 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | One month after a large earthquake, a relief agency has established a refugee camp with 100 tents, and is providing medical care, food, and shelter to the refugees. The agency has budgeted equally for the first 3 months to provide this care. However, 10% of the tents are uninhabitable, and the agency can only provide f... | [
"First, I need to determine the number of uninhabitable tents. With 100 tents in total and 10% uninhabitable, that leaves 90 tents that are usable.",
"Next, the agency can only provide food and medical care to 90% of the refugees. This means they will only need to budget for 90% of the original food and medical c... | To determine the new total budget for the 3-month period, let's break down the problem step by step.
### **Given:**
- **Total Tents:** 100
- **Uninhabitable Tents:** 10%
- **Refugees Receiving Food and Medical Care:** 90%
- **Original Monthly Budget:** \$500,000
- **Budget Period:** 3 months
### **Step 1: Calculate t... |
Llama-3.1-70B-Instruct_338 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | An outpatient surgical center needs to stock Cephalexin antibiotic tablets, which come in a bottle of 50, 20, or 10. The center currently has a need for 250 tablets. What size bottles should the center order? | [
"First, I need to determine how to combine bottles of 50, 20, and 10 tablets to meet the requirement of 250 tablets.",
"I'll start by using as many 50-tablet bottles as possible. Dividing 250 by 50 gives 5 bottles, which provide exactly 250 tablets. This combination meets the requirement without any excess.",
"... | To determine the most efficient way for the outpatient surgical center to stock 250 Cephalexin antibiotic tablets using bottles of 50, 20, or 10 tablets, we can follow these steps:
### **Step 1: Identify the Goal**
We need to find the combination of bottle sizes (50, 20, or 10 tablets) that adds up to exactly 250 tabl... |
Llama-3.1-70B-Instruct_358 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | A trader buys 2000 eggs at $0.50 each and sells them at $1.00 each. If 10 eggs were broken, how much profit did the trader make? | [
"First, I need to calculate the total cost the trader incurred by multiplying the number of eggs by the cost per egg. So, 2000 eggs at $0.50 each amounts to $1000.",
"Next, I'll determine the total revenue by multiplying the number of eggs sold by the selling price per egg. Since 10 eggs were broken, the trader s... | **Solution:**
1. **Calculate the total cost:**
The trader buys 2000 eggs at \$0.50 each.
\[
\text{Total Cost} = 2000 \text{ eggs} \times \$0.50/\text{egg} = \$1000
\]
2. **Determine the number of eggs sold:**
Out of 2000 eggs, 10 eggs were broken. Therefore, the number of eggs sold is:
... |
Llama-3.1-70B-Instruct_362 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well? | [
"First, I need to understand the snail's daily progress. Each day, the snail climbs 3 feet, but it slips back 2 feet at night. This means the snail makes a net gain of 1 foot each day.",
"The well is 20 feet deep. However, on the final day, when the snail reaches or surpasses the top, it won't slip back. So, I sh... | To determine how many days it will take for the snail to reach the top of the 20-foot well, let's break down the problem step by step.
### **Understanding the Snail's Progress**
- **Daily Climb:** The snail climbs **3 feet** during the day.
- **Nightly Slip:** The snail slips back **2 feet** at night.
- **Net Gain:**... |
Llama-3.1-70B-Instruct_384 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The sum of the interior angles of any polygon can be found using the formula 180(n-2), where n is the number of sides. How many sides does a polygon have if the sum of its interior angles is 900 degrees? | [
"Okay, so I have this problem here: I need to find out how many sides a polygon has if the sum of its interior angles is 900 degrees. Hmm, I remember that there's a formula for the sum of interior angles in a polygon. Let me try to recall... I think it's something like 180 times (n minus 2), where n is the number o... | To find the number of sides of a polygon given that the sum of its interior angles is 900 degrees, we use the formula for the sum of the interior angles of a polygon, which is \(180(n-2)\) degrees, where \(n\) is the number of sides.
We start with the given sum of the interior angles:
\[
180(n - 2) = 900
\]
Next, we ... |
Llama-3.1-70B-Instruct_389 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The owner of a small bakery decided to increase the price of a chocolate cake from $8 to $9. At the same time, the bakery started to offer a 10% discount on all chocolate cakes sold. How did the price change for each chocolate cake sold compare to before the increase and the discount? | [
"First, I need to determine the original price of the chocolate cake, which is $8.",
"Next, the price was increased by $1, making the new price $9.",
"Then, a 10% discount is applied to the new price of $9. To calculate the discount amount, I multiply $9 by 10%, which equals $0.90.",
"Subtracting the discount... | To determine how the price of each chocolate cake has changed after the increase and the discount, follow these steps:
1. **Original Price:**
\[
\$8
\]
2. **New Price After Increase:**
\[
\$8 + \$1 = \$9
\]
3. **Discount Calculation:**
\[
10\% \text{ of } \$9 = 0.10 \times \$9 = \$0.90
\]
... |
Llama-3.1-70B-Instruct_404 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | A $1000 loan has an annual interest rate of 9% and a loan period of 1 year. What is the total amount that will be paid back to the loan shark at the end of the year? | [
"First, I need to determine the type of interest calculation method. Since the problem doesn't specify, I'll assume it's simple interest.",
"With simple interest, the interest is calculated only on the principal amount. The formula for simple interest is I = P × r × t, where P is the principal, r is the annual in... | To determine the total amount to be paid back on a \$1000 loan with an annual interest rate of 9% over a period of 1 year, we'll use the **simple interest** formula.
**Simple Interest Formula:**
\[
\text{Interest} = P \times r \times t
\]
Where:
- \( P \) = Principal amount (\$1000)
- \( r \) = Annual interest rate (... |
Llama-3.1-70B-Instruct_406 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The area of a rectangle is 40 square units. The length is 5 units. What is the width? | [
"To determine the width of the rectangle, I start with the formula for the area of a rectangle, which is the product of its length and width.",
"Given that the area is 40 square units and the length is 5 units, I can set up the equation 5 multiplied by the width equals 40.",
"Solving for the width, I divide bot... | To find the width of the rectangle, we can use the formula for the area of a rectangle:
\[
\text{Area} = \text{Length} \times \text{Width}
\]
Given:
- Area = 40 square units
- Length = 5 units
Let \( w \) be the width of the rectangle. Plugging the known values into the formula:
\[
40 = 5 \times w
\]
To solve for ... |
Llama-3.1-70B-Instruct_418 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | If we assume a 4.5% annual growth rate of the global economy, what is the projected number of years before the global economy doubles in size based on the rule of 72? | [
"First, I recognize that the Rule of 72 is a quick method to estimate how long it will take for an investment or the economy to double in size at a given annual growth rate.",
"The formula for the Rule of 72 is:",
"Number of Years = 72 / Annual Growth Rate Percentage",
"Given an annual growth rate of 4.5%, I ... | To determine how many years it will take for the global economy to double in size with an annual growth rate of 4.5%, we can use the **Rule of 72**. This rule provides a quick estimate for doubling time by dividing 72 by the annual growth rate percentage.
**Step-by-Step Solution:**
1. **Understand the Rule of 72 Form... |
Llama-3.1-70B-Instruct_421 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | There are 10 people at a party, and they all shake hands with each other. How many handshakes are there? | [
"To determine the number of handshakes at the party, I start by considering that each of the 10 people can shake hands with 9 others.",
"This gives a total of 10 multiplied by 9, which equals 90 handshakes.",
"However, this count includes each handshake twice since each interaction involves two people.",
"To ... | To determine the number of handshakes that occur when 10 people at a party each shake hands with one another, we can use a combinatorial approach.
**Step 1: Understanding the Problem**
Each person at the party shakes hands with every other person exactly once. We need to count the total number of unique handshakes.
... |
Llama-3.1-70B-Instruct_446 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | A man is on a mission to check the integrity of the books in his bookcase. He notes that there are 5 shelves. The following books are placed on each shelf:
- Shelf 1: 2 books
- Shelf 2: 5 books
- Shelf 3: 3 books
- Shelf 4: 1 book
- Shelf 5: 4 books
How many books are on his bookcase in total? | [
"First, I need to identify the number of books on each shelf. Shelf 1 has 2 books, Shelf 2 has 5 books, Shelf 3 has 3 books, Shelf 4 has 1 book, and Shelf 5 has 4 books.",
"Next, I will add the number of books on each shelf together to find the total number of books in the bookcase. So, I add 2 + 5 + 3 + 1 + 4.",... | To determine the total number of books on the bookcase, we'll add the number of books on each shelf together.
**Given:**
- **Shelf 1:** 2 books
- **Shelf 2:** 5 books
- **Shelf 3:** 3 books
- **Shelf 4:** 1 book
- **Shelf 5:** 4 books
**Calculation:**
\[
\text{Total books} = \text{Shelf 1} + \text{Shelf 2} + \text{Sh... |
Llama-3.1-70B-Instruct_451 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The total population of a small town is 50000 people. 1/5 of the population are men, and 2/3 of the men are married. What is the number of married men in the town? | [
"First, I need to determine the total number of men in the town. Since the population is 50,000 and 1/5 of them are men, I can calculate the number of men by multiplying 50,000 by 1/5.",
"Next, to find out how many of these men are married, I'll take the number of men and multiply it by 2/3, as 2/3 of the men are... | **Solution:**
1. **Calculate the total number of men in the town:**
\[
\text{Number of men} = \frac{1}{5} \times \text{Total population} = \frac{1}{5} \times 50,000 = 10,000
\]
2. **Determine the number of married men:**
\[
\text{Number of married men} = \frac{2}{3} \times \text{Number of men} ... |
Llama-3.1-70B-Instruct_460 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The discovery of hidden patterns among seemingly unrelated phenomena is a hallmark of science. One example is the relation between the time it takes for a cup of coffee to cool down and the time it takes for a person to forget a newly learned poem. Although the specific numerical values of these times may differ greatl... | [
"First, I need to understand the problem. The coffee cools down by 50% every 10 minutes, which means it follows an exponential decay pattern. I can model this with the formula:",
"T(t) = T₀ * (1/2)^(t/10)",
"where T(t) is the temperature at time t, T₀ is the initial temperature, and t is the time in minutes.",
... | To determine how long it takes for the coffee to cool down to \( \frac{1}{4} \) of its original temperature, we can use the principle of exponential decay. Here's a step-by-step solution:
### **Step 1: Understand the Decay Pattern**
The coffee cools down by **50% every 10 minutes**. This means that every 10 minutes, ... |
Llama-3.1-70B-Instruct_465 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The hypotenuse of a right-angled triangle is 10 inches long. One of the other sides is 6 inches long. What is the length of the third side? | [
"Okay, so I have this problem here about a right-angled triangle. The hypotenuse is 10 inches long, and one of the other sides is 6 inches. I need to find the length of the third side. Hmm, right-angled triangles... I remember something about the Pythagorean theorem. Let me think.",
"The Pythagorean theorem is a ... | Given a right-angled triangle with a hypotenuse of 10 inches and one of the other sides being 6 inches, we need to find the length of the third side.
We use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the other two sides.
Here, \( c = 10 \)... |
Llama-3.1-70B-Instruct_495 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | A car increases in speed from 20 km/h to 60 km/h in 6 seconds. What is the average acceleration of the car? | [
"First, I need to identify the initial and final speeds of the car. The initial speed is 20 km/h, and the final speed is 60 km/h.",
"Next, I'll convert these speeds from kilometers per hour to meters per second to ensure the units are consistent with the time given in seconds. To do this, I'll multiply each speed... | To determine the average acceleration of the car, we'll use the formula for acceleration:
\[
\text{Acceleration} = \frac{\text{Change in Speed}}{\text{Time Taken}}
\]
**Given:**
- **Initial Speed (\(v_i\))** = 20 km/h
- **Final Speed (\(v_f\))** = 60 km/h
- **Time (\(t\))** = 6 seconds
**Step 1: Convert Speeds to m/... |
Llama-3.1-70B-Instruct_505 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The magnetic dipole moment of a circular coil is given by the formula $m = IA$, where $I$ is the current flowing through the coil and $A$ is the area of the coil. The current through the coil is given by the formula $I = \frac{E}{R}$, where $E$ is the electromotive force (EMF) and $R$ is the resistance of the coil. Usi... | [
"Okay, so I have this problem where I need to find the magnetic dipole moment of a circular coil in terms of EMF, area, and resistance. Hmm, let me think about what I know.",
"First, the magnetic dipole moment, usually denoted by m, is given by the formula m = IA. I remember that I is the current flowing through ... | The magnetic dipole moment \( m \) of a circular coil is given by the formula \( m = IA \), where \( I \) is the current and \( A \) is the area of the coil. The current \( I \) can be expressed using Ohm's Law as \( I = \frac{E}{R} \), where \( E \) is the electromotive force (EMF) and \( R \) is the resistance of the... |
Llama-3.1-70B-Instruct_513 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The area of a rectangle is 50 square centimeters and the width is 5 centimeters. What is the length of the rectangle? | [
"First, I recognize that the area of a rectangle is calculated by multiplying its length by its width.",
"Given that the area is 50 square centimeters and the width is 5 centimeters, I can set up the equation: 50 = length × 5.",
"To find the length, I divide both sides of the equation by 5, which gives me the l... | To find the length of the rectangle, we can use the formula for the area of a rectangle:
\[
\text{Area} = \text{Length} \times \text{Width}
\]
Given:
- Area = 50 cm²
- Width = 5 cm
Let \( L \) be the length of the rectangle. Plugging the known values into the formula:
\[
50 = L \times 5
\]
To solve for \( L \), di... |
Llama-3.1-70B-Instruct_516 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | Norbert has been saving money for a new bike and has $120 in his savings account. He wants to buy a bike that costs $216. What fraction of the cost of the bike has Norbert already saved? | [
"First, I need to determine the fraction of the bike's cost that Norbert has already saved. He has $120 in his savings account, and the bike costs $216.",
"To find the fraction, I will divide the amount he has saved by the total cost of the bike. So, I calculate 120 divided by 216.",
"Next, I will simplify the ... | To determine what fraction of the bike's cost Norbert has already saved, follow these steps:
1. **Identify the Amount Saved and the Total Cost:**
- **Amount Saved:** \$120
- **Total Cost of the Bike:** \$216
2. **Set Up the Fraction:**
The fraction of the cost that Norbert has saved is the amount he has ... |
Llama-3.1-70B-Instruct_517 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | If an object’s weight is 30 N in air, and it is submerged in water, it experiences an upward buoyant force of 20 N. What is its apparent weight in the water? | [
"Okay, so I have this physics problem here. It says that an object's weight is 30 N in air, and when it's submerged in water, it experiences an upward buoyant force of 20 N. I need to find its apparent weight in the water. Hmm, let me think about how to approach this.",
"First, I remember that apparent weight is ... | The object's weight in air is 30 N, which is its actual weight. When submerged in water, it experiences an upward buoyant force of 20 N. The apparent weight is calculated by subtracting the buoyant force from the actual weight.
Apparent Weight = Actual Weight - Buoyant Force
Apparent Weight = 30 N - 20 N = 10 N
The ... |
Llama-3.1-70B-Instruct_545 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well? | [
"First, I need to understand the snail's daily progress. Each day, the snail climbs 3 feet but slips back 2 feet at night, resulting in a net gain of 1 foot per day.",
"However, on the final day when the snail reaches or surpasses the top of the 20-foot well, it won't slip back. This means I should consider the p... | To determine how many days it will take for the snail to reach the top of the 20-foot well, let's break down the problem step by step.
### Understanding the Snail's Progress:
- **Daily Climb:** The snail climbs **3 feet** during the day.
- **Nightly Slip:** The snail slips back **2 feet** at night.
- **Net Gain:** Eac... |
Llama-3.1-70B-Instruct_562 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | A manufacturer produces 2,500 units of a product every day. It produces units at a rate of 10 units per minute. How many minutes does the manufacturer take to produce 2,500 units? | [
"First, I need to determine how many minutes it takes for the manufacturer to produce 2,500 units when the production rate is 10 units per minute.",
"To find the time, I'll divide the total number of units by the production rate.",
"So, 2,500 units divided by 10 units per minute equals 250 minutes.",
"Therefo... | To determine how many minutes the manufacturer takes to produce 2,500 units at a rate of 10 units per minute, follow these steps:
1. **Understand the Given Information:**
- **Total Units to Produce:** 2,500 units
- **Production Rate:** 10 units per minute
2. **Set Up the Equation:**
\[
\text{Time} = \... |
Llama-3.1-70B-Instruct_565 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | This problem is about the composition of water molecules. A water molecule is made up of two hydrogen atoms and one oxygen atom, and its formula is H2O. How many hydrogen atoms are contained in one mole of water? | [
"To determine the number of hydrogen atoms in one mole of water, I start by identifying the chemical composition of a water molecule, which is H₂O. This means each water molecule contains 2 hydrogen atoms.",
"Next, I recall that one mole of any substance contains Avogadro's number of particles, which is approxima... | To determine the number of hydrogen atoms in one mole of water, follow these steps:
1. **Understand the Composition of Water:**
- A water molecule is composed of 2 hydrogen atoms and 1 oxygen atom.
- Chemical formula: **H₂O**
2. **Determine the Number of Water Molecules in One Mole:**
- One mole of a... |
Llama-3.1-70B-Instruct_583 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The power $P$ in a direct current (DC) electrical circuit is given by $P=VI$, where $V$ is the voltage and $I$ is the current. Find $P$ when $V=25$ volts and $I=0.5$ amperes. | [
"Okay, so I have this problem here about finding the power in a DC electrical circuit. Hmm, power, voltage, current... I remember that power is related to voltage and current somehow. Let me think. Oh yeah, the formula is P equals V times I, right? So P = VI. That seems straightforward.",
"Alright, the problem gi... | To find the power \( P \) in a direct current (DC) electrical circuit, we use the formula \( P = VI \), where \( V \) is the voltage and \( I \) is the current. Given \( V = 25 \) volts and \( I = 0.5 \) amperes, we can calculate the power as follows:
\[
P = V \times I = 25 \, \text{volts} \times 0.5 \, \text{amperes}... |
Llama-3.1-70B-Instruct_590 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The length of a rectangular garden is 10 feet longer than its width. If the area of the garden is 375 square feet, what are the dimensions of the garden? | [
"First, I'll define the width of the garden as \\( w \\) feet. Since the length is 10 feet longer than the width, the length can be expressed as \\( w + 10 \\) feet.",
"Next, I'll use the formula for the area of a rectangle, which is length multiplied by width. Setting up the equation, I have:\n\\[\nw \\times (w ... | To determine the dimensions of the rectangular garden, let's follow these steps:
1. **Define the Variables:**
- Let \( w \) be the width of the garden in feet.
- Since the length is 10 feet longer than the width, the length can be expressed as \( w + 10 \) feet.
2. **Set Up the Equation for the Area:**
- The... |
Llama-3.1-70B-Instruct_597 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The population of a city is 350,000. If the population increases by 60,000 in 2 years, at what rate is the population increasing per year? | [
"First, I need to determine the total population increase over the two years, which is 60,000.",
"Next, I'll calculate the annual increase by dividing the total increase by the number of years: 60,000 divided by 2 equals 30,000.",
"Finally, to find the rate of increase, I'll divide the annual increase by the or... | To determine the annual rate at which the population is increasing, follow these steps:
1. **Calculate the total increase in population:**
\[
\text{Total Increase} = 60,000 \text{ people}
\]
2. **Determine the time period:**
\[
\text{Time} = 2 \text{ years}
\]
3. **Find the annual increase:... |
Llama-3.1-70B-Instruct_609 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The average height of a group of people in a room is 175 cm. If 5 people leave the room and the average height of the remaining people is 178 cm, what is the average height of the 5 people who left the room? | [
"First, I need to determine the total height of all the people in the room initially. Let’s assume there are \\( n \\) people in the room. The average height is 175 cm, so the total height is \\( 175n \\) cm.",
"When 5 people leave the room, the number of remaining people is \\( n - 5 \\). The average height of t... | To determine the average height of the 5 people who left the room, let's follow these steps:
1. **Define Variables:**
- Let \( n \) be the total number of people initially in the room.
- The average height of all \( n \) people is 175 cm.
- After 5 people leave, the average height of the remaining \( n - 5 \)... |
Llama-3.1-70B-Instruct_619 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | Dr. Patel is planning a party for her daughter's birthday. She has $120 to spend on party favors, gifts, and decorations. She wants to spend $20 on decorations and $40 on party favors. How much can she spend on gifts? | [
"First, I need to determine the total amount Dr. Patel has allocated for the party, which is $120.",
"Next, I will calculate the total amount she plans to spend on decorations and party favors. She intends to spend $20 on decorations and $40 on party favors, so the combined total is $60.",
"Finally, to find out... | **Solution:**
Dr. Patel has a total budget of \$120 for the party. She plans to spend:
- **Decorations:** \$20
- **Party Favors:** \$40
**Step 1:** Calculate the total amount allocated for decorations and party favors.
\[
\text{Total for Decorations and Party Favors} = \$20 + \$40 = \$60
\]
**Step 2:** Subtract th... |
Llama-3.1-70B-Instruct_630 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | A system of linear equations has the following coefficient matrix:
$\begin{pmatrix} 6 & 3\\ 2 & -4 \end{pmatrix}$.
Find the determinant of this $2\times 2$ matrix. | [
"To find the determinant of the given 2x2 matrix, I will use the formula for the determinant of a 2x2 matrix, which is (a*d) - (b*c).",
"First, I identify the elements of the matrix:\na = 6, b = 3, c = 2, and d = -4.",
"Next, I calculate the product of the diagonal elements:\n6 * (-4) = -24.",
"Then, I calcul... | To find the determinant of the given \(2 \times 2\) matrix:
\[
\begin{pmatrix} 6 & 3 \\ 2 & -4 \end{pmatrix}
\]
we can use the formula for the determinant of a \(2 \times 2\) matrix:
\[
\text{det}(A) = ad - bc
\]
Where:
- \( a = 6 \)
- \( b = 3 \)
- \( c = 2 \)
- \( d = -4 \)
Plugging in the values:
\[
\text{det}... |
Llama-3.1-70B-Instruct_647 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The area of a rectangle is 48 square centimeters. If the length is five centimeters more than the width, what are the dimensions of the rectangle? | [
"First, I'll define the width of the rectangle as \\( w \\) centimeters. Since the length is five centimeters more than the width, the length can be expressed as \\( w + 5 \\) centimeters.",
"Next, I'll use the formula for the area of a rectangle, which is length multiplied by width. Setting up the equation \\( w... | To determine the dimensions of the rectangle, let's follow these steps:
1. **Define the Variables:**
- Let \( w \) be the width of the rectangle in centimeters.
- Since the length is five centimeters more than the width, the length can be expressed as \( w + 5 \) centimeters.
2. **Set Up the Equation for the Ar... |
Llama-3.1-70B-Instruct_650 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | In an experiment, the speed of light in a glass slab is measured to be $2 \times 10^8 \textrm{ m/s}$. Given that the speed of light in vacuum is $3 \times 10^8 \textrm{ m/s}$, find the refractive index of the glass.
The refractive index can be calculated using the formula
\[ n = \frac{\textrm{speed of light in vacuum}}... | [
"First, I identify the given values: the speed of light in a vacuum is \\(3 \\times 10^8\\) m/s, and the speed of light in the glass slab is \\(2 \\times 10^8\\) m/s.",
"Next, I apply the formula for the refractive index, which is the ratio of the speed of light in a vacuum to the speed of light in the medium. Pl... | To find the refractive index of the glass, we can use the formula:
\[
n = \frac{\textrm{speed of light in vacuum}}{\textrm{speed of light in the medium}}
\]
**Given:**
- Speed of light in vacuum, \( c = 3 \times 10^8 \) m/s
- Speed of light in glass, \( v = 2 \times 10^8 \) m/s
**Calculation:**
\[
n = \frac{c}{v} =... |
Llama-3.1-70B-Instruct_651 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The function f ( x ) = sin(4 x ) is periodic with period T . Find the value of T . | [
"To determine the period \\( T \\) of the function \\( f(x) = \\sin(4x) \\), I start by recalling the general form of the sine function, which is \\( \\sin(Bx) \\). The period of this function is given by \\( \\frac{2\\pi}{|B|} \\).",
"In this case, the coefficient \\( B \\) is 4. Applying the period formula, I s... | To find the period \( T \) of the function \( f(x) = \sin(4x) \), follow these steps:
1. **Understand the General Form:**
The general form of a sine function is:
\[
f(x) = \sin(Bx)
\]
where \( B \) affects the period of the function.
2. **Determine the Period Formula:**
The period \( T \) of... |
Llama-3.1-70B-Instruct_655 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The sum of the interior angles of a triangle is always equal to 180°. If your triangle has angles measuring 30°, 60°, and x°, what is the value of x? | [
"To determine the value of \\( x \\), I start by recalling that the sum of the interior angles in any triangle is always \\( 180^\\circ \\).",
"Given the angles \\( 30^\\circ \\), \\( 60^\\circ \\), and \\( x^\\circ \\), I can set up the equation:\n\\[\n30^\\circ + 60^\\circ + x^\\circ = 180^\\circ\n\\]",
"Comb... | To find the value of \( x \) in the triangle with angles \( 30^\circ \), \( 60^\circ \), and \( x^\circ \), follow these steps:
1. **Understand the Property:**
The sum of the interior angles of any triangle is always \( 180^\circ \).
2. **Set Up the Equation:**
\[
30^\circ + 60^\circ + x^\circ = 180^... |
Llama-3.1-70B-Instruct_660 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The probability that a randomly selected customer will place an order over the phone is 0.15. If the store receives 100 phone calls in a day from potential customers, what is the expected number of customers who will place an order over the phone? | [
"First, I recognize that this is a binomial probability problem because each phone call represents an independent trial with two possible outcomes: the customer places an order or they don't.",
"Next, I identify the parameters of the binomial distribution. The probability of success (placing an order) is 0.15, an... | To determine the expected number of customers who will place an order over the phone, we can use the concept of **expected value** in probability.
### **Step 1: Understand the Problem**
- **Probability of placing an order:** \( p = 0.15 \)
- **Number of phone calls (trials):** \( n = 100 \)
### **Step 2: Apply the Ex... |
Llama-3.1-70B-Instruct_676 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | A circle of radius 4 is inscribed in a square. What is the area of the square? | [
"Okay, so I have this problem here: \"A circle of radius 4 is inscribed in a square. What is the area of the square?\" Hmm, let me try to visualize this. An inscribed circle in a square means that the circle touches all four sides of the square, right? So, the circle is perfectly fitted inside the square, touching ... | Given a circle of radius 4 inscribed in a square, we need to find the area of the square.
1. The radius of the circle is 4, so the diameter is twice the radius, which is \(2 \times 4 = 8\).
2. The diameter of the circle is equal to the side length of the square because the circle is inscribed in the square.
3. Therefo... |
Llama-3.1-70B-Instruct_693 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The surface area of a cube can be calculated using the formula 6s^2, where s is the length of one side of the cube. If a cube has a surface area of 384, what is the length of one side of the cube? | [
"First, I recognize that the surface area of a cube is given by the formula 6s², where s is the length of one side.",
"Given that the surface area is 384, I can set up the equation 6s² = 384.",
"To solve for s², I divide both sides of the equation by 6, which gives s² = 64.",
"Taking the square root of both s... | To find the length of one side of a cube when its surface area is given, follow these steps:
**Given:**
- Surface area of the cube = 384
**Formula:**
The surface area \( A \) of a cube is calculated using the formula:
\[
A = 6s^2
\]
where \( s \) is the length of one side of the cube.
**Step 1:** Set up the equation... |
Llama-3.1-70B-Instruct_696 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | A new skate shop, "The Board Room", is opening and the owner, Alex, wants to order boards that will appeal to local skaters. After researching local skate parks and talking to experienced skaters, Alex decides on a mix of 110 standard (S) and 90 specialty (T) skateboards to stock the shop. The S boards cost $25 each an... | [
"First, I need to determine how many standard (S) and specialty (T) skateboards Alex can order within the $5,000 budget.",
"I'll start by defining variables for the number of S and T boards. Let’s say Alex orders \\( x \\) S boards and \\( y \\) T boards.",
"The cost for the S boards is $25 each, and the cost f... | To determine how many standard (S) and specialty (T) skateboards Alex can order within the \$5,000 budget, let's break down the problem step by step.
### **Given:**
- **Cost of one S skateboard (S):** \$25
- **Cost of one T skateboard (T):** \$30
- **Total Budget:** \$5,000
- **Desired Mix:** 110 S and 90 T boards
##... |
Llama-3.1-70B-Instruct_708 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The document consists of 20 pages. If 8 pages are removed, what percentage of the document remains? | [
"First, I need to determine how many pages remain after removing 8 pages from the original 20 pages.",
"Subtracting the removed pages from the total gives 12 pages remaining.",
"Next, to find the percentage of the document that remains, I divide the remaining pages by the original total and multiply by 100.",
... | To determine the percentage of the document that remains after removing 8 pages, follow these steps:
1. **Calculate the number of remaining pages:**
\[
\text{Remaining pages} = \text{Total pages} - \text{Pages removed} = 20 - 8 = 12
\]
2. **Determine the percentage of the document that remains:**
... |
Llama-3.1-70B-Instruct_710 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The manager of a company has $100,000 to spend on bonuses. A total of 15 employees are eligible, and each employee will get a bonus of (8000 + 100r) dollars, where r is the employee's rating on a scale of 1 to 5. What is the total bonus paid to all employees if the rating distribution is 5 employees with a rating of 1,... | [
"First, I need to determine the bonus for each employee based on their rating. The bonus formula is \\$8,000 plus \\$100 multiplied by the rating (r).",
"Next, I'll calculate the total bonus for each group of employees with the same rating. For example, employees with a rating of 1 will each receive \\$8,000 + \\... | To determine the total bonus paid to all employees, we'll calculate the bonus for each rating group and then sum them up.
**Bonus Formula:**
\[
\text{Bonus per employee} = \$8,\!000 + \$100 \times r
\]
where \( r \) is the employee's rating.
**Rating Distribution:**
- **Rating 1:** 5 employees
- **Rating 2:** 4 emplo... |
Llama-3.1-70B-Instruct_725 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The area of a triangle with vertices \((x_1,y_1)\), \((x_2,y_2)\), and \((x_3,y_3)\) can be calculated using the formula:
\[
\text{Area} = \frac{1}{2} \lvert x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \rvert
\]
Given the vertices \((0,5)\), \((-2,-3)\), and \((4,1)\), find the area of the triangle formed by the... | [
"First, I identify the coordinates of the three vertices: (0,5), (-2,-3), and (4,1).",
"Next, I apply the area formula by substituting these coordinates into the formula. This involves calculating each term step by step to ensure accuracy.",
"After performing the calculations, I sum the terms and take the absol... | To find the area of the triangle with vertices \((0,5)\), \((-2,-3)\), and \((4,1)\), we can use the formula:
\[
\text{Area} = \frac{1}{2} \lvert x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \rvert
\]
**Step 1:** Assign the coordinates to the variables.
\[
\begin{align*}
(x_1, y_1) &= (0, 5) \\
(x_2, y_2) &= (-2... |
Llama-3.1-70B-Instruct_737 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | In a particular week, the total rainfall in Woodville was 15 inches. During the first 5 days of the week, some days had no rain, and the total rainfall for those days was 3 inches. The rainfall on the last 2 days of the week was 4 times the rainfall in the first 5 days. How much rain feel on each of the last two days o... | [
"First, I need to determine the total rainfall for the entire week, which is given as 15 inches.",
"Next, I know that the rainfall during the first 5 days was 3 inches. This means that the remaining rainfall, which occurred on the last 2 days, is the total rainfall minus the rainfall from the first 5 days. So, 15... | Let's break down the problem step by step to find out how much rain fell on each of the last two days of the week in Woodville.
**Given:**
- **Total rainfall for the week:** 15 inches
- **Rainfall during the first 5 days:** 3 inches
- **Rainfall on the last 2 days:** 4 times the rainfall of the first 5 days
**Step 1:... |
Llama-3.1-70B-Instruct_755 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | What is the coefficient of $x^{2}$ in $(5 + x)^{4}$? | [
"To find the coefficient of \\( x^{2} \\) in \\( (5 + x)^{4} \\), I can use the Binomial Theorem. The theorem states that \\( (a + b)^{n} = \\sum_{k=0}^{n} \\binom{n}{k} a^{n - k} b^{k} \\).",
"Here, \\( a = 5 \\), \\( b = x \\), and \\( n = 4 \\). I need the term where the power of \\( x \\) is 2, which correspo... | To find the coefficient of \( x^{2} \) in the expansion of \( (5 + x)^{4} \), we can use the **Binomial Theorem**. The Binomial Theorem states that:
\[
(a + b)^{n} = \sum_{k=0}^{n} \binom{n}{k} a^{n - k} b^{k}
\]
In this case:
- \( a = 5 \)
- \( b = x \)
- \( n = 4 \)
We are interested in the term where the power of... |
Llama-3.1-70B-Instruct_758 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | On an arithmetic sequence, the 8th term is 112 and the 10th term is 118. Find the common difference and the first term of the arithmetic sequence. | [
"First, I recognize that in an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. This constant is called the common difference, denoted as \\( d \\).",
"Given that the 8th term (\\( a_8 \\)) is 112 and the 10th term (\\( a_{10} \\)) is 118, I can set up the following... | To find the common difference (\( d \)) and the first term (\( a_1 \)) of the arithmetic sequence, we can use the given information:
1. **Given:**
- The 8th term (\( a_8 \)) is 112.
- The 10th term (\( a_{10} \)) is 118.
2. **Recall the formula for the \( n \)-th term of an arithmetic sequence:**
\[
a_n =... |
Llama-3.1-70B-Instruct_768 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | A bakery sells a total of 405 bread loaves per day. The bakery sells two types of bread loaves, namely, whole wheat and white bread. For every 3 whole wheat bread loaves sold, 5 white bread loaves are sold. What is the number of whole wheat bread loaves sold per day? | [
"First, I need to determine the number of whole wheat bread loaves sold per day at the bakery. The total number of bread loaves sold daily is 405, and the ratio of whole wheat to white bread loaves is 3:5.",
"I'll start by letting the number of whole wheat loaves be represented by 3x and the number of white loave... | To determine the number of whole wheat bread loaves sold per day, let's follow these steps:
1. **Define Variables:**
- Let the number of whole wheat loaves sold be \( 3x \).
- Let the number of white bread loaves sold be \( 5x \).
2. **Set Up the Equation:**
The total number of bread loaves sold per day is t... |
Llama-3.1-70B-Instruct_789 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | In a town, there are 9000 people. A survey was conducted to find the number of people who like to read books and watch movies. The survey showed that 60% of the people like to read books, 70% like to watch movies, and 30% like to do both. How many people like to read books or watch movies? | [
"First, I need to determine the number of people who like to read books, watch movies, or both.",
"There are 9,000 people in total.",
"60% of 9,000 people like to read books, which is 5,400 people.",
"70% of 9,000 people like to watch movies, which is 6,300 people.",
"30% of 9,000 people like both reading b... | To determine the number of people who like to read books or watch movies, we'll use the principle of **inclusion-exclusion**. Here's a step-by-step solution:
1. **Total Population:**
\[
\text{Total people} = 9000
\]
2. **People Who Like to Read Books:**
\[
60\% \text{ of } 9000 = 0.60 \times 9000 = 540... |
Llama-3.1-70B-Instruct_791 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | After 5 years of service, an employee is eligible for a 2-week paid vacation. Furthermore, for every year of service after the initial 5 years, the employee earns an additional day of paid vacation. If an employee has 12 years of service, how many days of paid vacation is the employee eligible for? | [
"First, I recognize that after 5 years of service, the employee is entitled to a 2-week paid vacation, which is equivalent to 10 working days.",
"Next, for each additional year of service beyond the initial 5 years, the employee earns one extra day of paid vacation. Since the employee has 12 years of service, the... | To determine the total number of paid vacation days an employee with 12 years of service is eligible for, follow these steps:
1. **Initial Eligibility:**
- After **5 years** of service, the employee is eligible for a **2-week paid vacation**.
- Assuming a 5-day workweek, 2 weeks amount to:
\[
2 \text{ ... |
Llama-3.1-70B-Instruct_797 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | What is the value of the sum of the digits of the number 123456? | [
"To determine the sum of the digits of the number 123456, I will first identify each individual digit. The number 123456 consists of the digits 1, 2, 3, 4, 5, and 6.",
"Next, I will add these digits together: 1 + 2 + 3 + 4 + 5 + 6.",
"Calculating the sum step by step:\n1 + 2 equals 3,\n3 + 3 equals 6,\n6 + 4 eq... | To find the sum of the digits of the number **123456**, follow these steps:
1. **Identify each digit in the number:**
\[
1,\ 2,\ 3,\ 4,\ 5,\ 6
\]
2. **Add the digits together:**
\[
1 + 2 + 3 + 4 + 5 + 6
\]
3. **Calculate the sum step by step:**
\[
1 + 2 = 3
\]
\[
3 + ... |
Llama-3.1-70B-Instruct_810 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | This problem involves independent random variables. Let \(X\) and \(Y\) be independent and identically distributed (i.i.d.) random variables. Let \(f_{X}(x)\) be the probability mass function (pmf) of \(X\) and \(Y\), and let \(f_{X|Y}(x|y)\) be the conditional probability mass function of \(X\) given \(Y=y\). Since \(... | [
"Okay, so I have this problem about independent random variables. Let me try to understand it step by step. The problem says that X and Y are independent and identically distributed, which means they have the same probability distribution and they don't affect each other. The pmf, or probability mass function, of X... | Given that \(X\) and \(Y\) are independent and identically distributed (i.i.d.) random variables, we know that their joint probability mass function (pmf) is the product of their individual pmfs. Since they are identically distributed, the pmf of \(Y\) is the same as the pmf of \(X\). Therefore, the joint pmf is given ... |
Llama-3.1-70B-Instruct_812 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The sum of the first n natural numbers is given by the formula Sn = n(n+1)/2. Find the value of n for which the sum of the first n natural numbers is 253. | [
"First, I recognize that the sum of the first \\( n \\) natural numbers is given by the formula \\( S_n = \\frac{n(n + 1)}{2} \\).",
"Given that \\( S_n = 253 \\), I can set up the equation \\( \\frac{n(n + 1)}{2} = 253 \\).",
"To solve for \\( n \\), I'll multiply both sides of the equation by 2 to eliminate t... | To find the value of \( n \) for which the sum of the first \( n \) natural numbers is 253, we can use the formula for the sum of the first \( n \) natural numbers:
\[
S_n = \frac{n(n + 1)}{2}
\]
Given that \( S_n = 253 \), we set up the equation:
\[
\frac{n(n + 1)}{2} = 253
\]
**Step 1:** Multiply both sides of th... |
Llama-3.1-70B-Instruct_827 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The weights of 80% of the students in a class are above 50 kg and 70% are above 60 kg. If the total number of students in the class is 25, then what percentage of students weigh more than 50 kg but less than 60 kg? | [
"First, I need to determine the number of students who weigh more than 50 kg. Since 80% of the 25 students weigh above 50 kg, I calculate 80% of 25, which is 20 students.",
"Next, I calculate the number of students who weigh more than 60 kg. 70% of 25 students weigh above 60 kg, so that's 17.5 students. Since the... | To determine the percentage of students who weigh more than 50 kg but less than 60 kg, follow these steps:
1. **Calculate the number of students above 50 kg:**
\[
80\% \text{ of } 25 = 0.80 \times 25 = 20 \text{ students}
\]
2. **Calculate the number of students above 60 kg:**
\[
70\% \text{ of... |
Llama-3.1-70B-Instruct_829 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The functions $f$ and $g$ are defined for all real numbers and satisfy
$$f(x) + f(-x) = 5$$
$$g(x) + g(-x) = 3$$
If $a$ and $b$ are real numbers such that $f(a) = b$, what is $f(-a)$? | [
"To determine \\( f(-a) \\), I start with the given equation \\( f(x) + f(-x) = 5 \\).",
"Since \\( a \\) is a real number, I can substitute \\( x = a \\) into the equation, which gives me \\( f(a) + f(-a) = 5 \\).",
"I know that \\( f(a) = b \\), so I substitute \\( b \\) into the equation: \\( b + f(-a) = 5 \... | To find \( f(-a) \), we can use the given property of the function \( f \):
\[
f(x) + f(-x) = 5 \quad \text{for all real numbers } x.
\]
**Step 1:** Substitute \( x = a \) into the equation:
\[
f(a) + f(-a) = 5.
\]
**Step 2:** We are given that \( f(a) = b \). Substitute \( b \) into the equation:
\[
b + f(-a) = 5... |
Llama-3.1-70B-Instruct_831 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The mean of four numbers is 71. If one of the numbers is 50, what is the mean of the remaining three numbers? | [
"Okay, so I have this problem here: The mean of four numbers is 71. If one of the numbers is 50, what is the mean of the remaining three numbers? Hmm, let me try to figure this out step by step.",
"First, I remember that the mean of a set of numbers is calculated by adding all the numbers together and then dividi... | The mean of four numbers is 71, so the total sum of these four numbers is calculated as follows:
\[
4 \times 71 = 284
\]
One of the numbers is 50, so the sum of the remaining three numbers is:
\[
284 - 50 = 234
\]
To find the mean of the remaining three numbers, we divide the sum by 3:
\[
\frac{234}{3} = 78
\]
Th... |
Llama-3.1-70B-Instruct_849 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The figure shows a triangle with angle measures 30°, 60°, and 90°.
What is the area of the triangle? | [
"First, I need to identify the sides of the 30-60-90 triangle. In such a triangle, the sides are in the ratio 1 : √3 : 2, where 1 corresponds to the side opposite the 30° angle, √3 corresponds to the side opposite the 60° angle, and 2 is the hypotenuse.",
"Next, I'll assign the given side length to its correspond... | To find the area of a 30-60-90 triangle, follow these steps:
### Step 1: Understand the Side Ratios
In a 30-60-90 triangle, the sides are in the ratio:
- **1** (short leg opposite the 30° angle)
- **√3** (long leg opposite the 60° angle)
- **2** (hypotenuse)
### Step 2: Assign the Given Side
Assume the side opposite ... |
Llama-3.1-70B-Instruct_872 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The city of Boomville has decided to install speed cameras at regular intervals along the Boomville Boulevard. The goal is to ensure that the average speed of vehicles on this road is limited to 60 km/h. The cameras will be installed at a distance of every 5 km. Given that a vehicle travels 60 km in 1 hour, calculate t... | [
"First, I need to determine the time it takes for a vehicle to travel between two consecutive speed cameras, given that the cameras are installed every 5 km and the speed limit is 60 km/h.",
"I know that time is equal to distance divided by speed. The distance between two cameras is 5 km, and the vehicle's speed ... | To determine the time it takes for a vehicle to travel between two consecutive speed cameras in Boomville, follow these steps:
1. **Understand the Given Information:**
- **Distance between cameras:** 5 km
- **Speed limit:** 60 km/h
2. **Use the Formula:**
The basic formula to calculate time when distance... |
Llama-3.1-70B-Instruct_873 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | What is the area of the trapezoid with bases 4 and 6 and height 2? | [
"Okay, so I need to find the area of a trapezoid. Hmm, I remember that a trapezoid is a four-sided shape with at least one pair of parallel sides. Those parallel sides are called the bases, right? And the distance between these two bases is the height.",
"The problem says the bases are 4 and 6, and the height is ... | To find the area of the trapezoid with bases 4 and 6 and height 2, we use the formula for the area of a trapezoid, which is the average of the two bases multiplied by the height.
First, we add the lengths of the two bases:
\[ 4 + 6 = 10 \]
Next, we find the average of the two bases by dividing the sum by 2:
\[ \frac... |
Llama-3.1-70B-Instruct_883 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | This problem is about combinatorics, and it's a bit tricky because it asks for two different things.
**Problem Statement**
Anne lives in a village of 10 people. There are 3 people, {A,B,C}, that she particularly dislikes. If Anne is to form a group of 3 people from the remaining 7 people, in how many ways can she do ... | [
"First, I need to determine the total number of people Anne can choose from. Since there are 10 people in total and she dislikes 3 of them, there are 7 people she is willing to form a group with.",
"Next, I need to calculate the number of ways to choose 3 people out of these 7. This is a combination problem becau... | **Solution**
Anne wants to form a group of 3 people from her village, but she dislikes 3 specific individuals ({A, B, C}). To find out how many ways she can form this group, follow these steps:
1. **Determine the Total Number of People Available:**
- **Total villagers:** 10
- **People Anne dislikes:** 3 ({A... |
Llama-3.1-70B-Instruct_911 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | In the previous problem, the mean of the data set is 7.4. Given that the data set includes exactly five values, what is the sum of the data values? | [
"Okay, so I have this problem here where the mean of a data set is 7.4, and there are exactly five values in the data set. I need to find the sum of these data values. Hmm, let me think about how to approach this.",
"First, I remember that the mean of a data set is calculated by adding up all the values and then ... | The mean of a data set is given as 7.4, and the data set includes exactly five values. To find the sum of the data values, we use the formula for the mean:
\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}
\]
Rearranging the formula to solve for the sum, we get:
\[
\text{Sum of all values} = ... |
Llama-3.1-70B-Instruct_922 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The seven days of the week, starting with Sunday, are assigned the numbers 1 to 7, respectively. An integer \( n \) is randomly chosen from 1 to 7 (inclusive), and a six-sided die is rolled. If the sum of the integer and the die roll is 8, then the result is considered a "win." What is the probability of winning? | [
"First, I need to determine the total number of possible outcomes. There are 7 possible integers (1 through 7) and 6 possible die rolls (1 through 6), resulting in a total of 7 multiplied by 6, which equals 42 possible outcomes.",
"Next, I'll identify the winning combinations where the sum of the integer and the ... | To determine the probability of winning, let's break down the problem step by step.
### **Step 1: Understand the Possible Outcomes**
- **Integer Selection:** An integer \( n \) is chosen from 1 to 7. So, there are **7 possible integers**.
- **Die Roll:** A standard six-sided die is rolled, resulting in **6 possible o... |
Llama-3.1-70B-Instruct_946 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The product of two natural numbers is 63. How many ordered pairs (x, y) exist such that x is the smaller number and y is the larger number? | [
"First, I need to find all pairs of natural numbers whose product is 63. To do this, I'll list the factors of 63.",
"Next, I'll pair these factors in such a way that the product of each pair equals 63. This will give me all possible ordered pairs (x, y).",
"Since the problem specifies that x should be the small... | To determine the number of ordered pairs \((x, y)\) where \(x\) and \(y\) are natural numbers, \(x\) is the smaller number, \(y\) is the larger number, and their product is 63, follow these steps:
1. **List the factors of 63:**
The natural number 63 can be factored into:
\[
63 = 1 \times 63,\quad 3 \times... |
Llama-3.1-70B-Instruct_950 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The number 72,735 has a remainder of 12 when divided by 27. What is the smallest positive integer n, such that 72,735 + n is divisible by 27? | [
"First, I need to determine the remainder when 72,735 is divided by 27. I'll perform the division of 72,735 by 27 to find this remainder.",
"Once I have the remainder, I'll subtract it from 27 to find the smallest positive integer \\( n \\) that needs to be added to 72,735 to make the sum divisible by 27.",
"Fi... | To find the smallest positive integer \( n \) such that \( 72,\!735 + n \) is divisible by \( 27 \), follow these steps:
1. **Find the remainder when \( 72,\!735 \) is divided by \( 27 \):**
\[
72,\!735 \div 27 = 2,\!699 \text{ with a remainder of } 12
\]
This means:
\[
72,\!735 = 27 \times ... |
Llama-3.1-70B-Instruct_959 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The length of a rectangle is 5 cm more than its width. The area of the rectangle is 56 square cm. What are the width and length of the rectangle? | [
"First, I'll define the width of the rectangle as \\( w \\) cm. Since the length is 5 cm more than the width, the length can be expressed as \\( w + 5 \\) cm.",
"Next, I'll use the formula for the area of a rectangle, which is length multiplied by width. Setting up the equation: \\( w \\times (w + 5) = 56 \\).",
... | Let's solve the problem step by step.
**Given:**
- The length of the rectangle is 5 cm more than its width.
- The area of the rectangle is 56 square cm.
**Let’s denote:**
- Let the width of the rectangle be \( w \) cm.
- Then, the length of the rectangle will be \( w + 5 \) cm.
**Area of the rectangle is given by:**... |
Llama-3.1-70B-Instruct_967 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The base of a right triangle is 14 inches and the height is 48 inches. What is the area of this triangle? | [
"Okay, so I have this problem here: the base of a right triangle is 14 inches and the height is 48 inches. I need to find the area of this triangle. Hmm, let me think about how to approach this.",
"First, I remember that the area of a triangle is generally calculated using the formula: Area = (base × height) / 2.... | The base of a right triangle is 14 inches and the height is 48 inches. To find the area, we use the formula for the area of a triangle, which is:
\[
\text{Area} = \frac{\text{base} \times \text{height}}{2}
\]
Substituting the given values:
\[
\text{Area} = \frac{14 \times 48}{2}
\]
First, calculate the product of t... |
Llama-3.1-70B-Instruct_990 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The difference between the melting points of two alloys is 70 degrees Celsius. If the melting point of the first alloy is 630 degrees Celsius what is the melting point of the second alloy? | [
"First, I recognize that the problem involves finding the melting point of the second alloy when the difference between the two alloys is given.",
"I know that the melting point of the first alloy is 630 degrees Celsius, and the difference between the two alloys is 70 degrees Celsius.",
"To find the melting poi... | To determine the melting point of the second alloy, follow these steps:
1. **Given:**
- Melting point of the first alloy (\( A_1 \)) = 630°C
- Difference in melting points (\( \Delta A \)) = 70°C
2. **Relationship:**
\[
A_2 = A_1 - \Delta A
\]
3. **Substitute the known values:**
\[
A_2 = 630°... |
Llama-3.1-70B-Instruct_992 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | The town of Eden has 5 buses and each bus has 50 seats. The manager of the buses wants to find out the average number of passengers for each bus so he can plan for the rush hour. He decided to find the average by dividing the total number of passengers by the total number of seats. The total number of passengers in the... | [
"First, I need to determine the total number of seats available in all the buses. There are 5 buses, each with 50 seats, so the total number of seats is 5 multiplied by 50, which equals 250 seats.",
"Next, I have the total number of passengers, which is 1350. To find the average number of passengers per seat, I d... | To determine the average number of passengers per seat in the town of Eden, follow these steps:
1. **Calculate the Total Number of Seats:**
\[
\text{Total Seats} = \text{Number of Buses} \times \text{Seats per Bus} = 5 \times 50 = 250
\]
2. **Determine the Total Number of Passengers:**
\[
\text... |
Llama-3.1-70B-Instruct_1031 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | In this problem, we have three positive numbers $a,b,c$ and $2b=a+c$. We have to find $b$ in terms of $a$ and $c$. | [
"First, I recognize that the equation provided is \\(2b = a + c\\). To solve for \\(b\\), I need to isolate it on one side of the equation.",
"I can achieve this by dividing both sides of the equation by 2. This will eliminate the coefficient 2 that is currently multiplying \\(b\\).",
"After performing the divi... | To find \( b \) in terms of \( a \) and \( c \) given the equation \( 2b = a + c \), follow these steps:
1. **Start with the given equation:**
\[
2b = a + c
\]
2. **Solve for \( b \) by dividing both sides of the equation by 2:**
\[
b = \frac{a + c}{2}
\]
3. **Final expression for \( b \):**
\[
... |
Llama-3.1-70B-Instruct_1032 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | In the universe with four dimensions, each of the four dimensions can be either positive or negative. How many different combinations of dimensions are possible? | [
"To determine the number of different combinations of dimensions in a four-dimensional universe where each dimension can be either positive or negative, I start by recognizing that each dimension has two possible states: positive or negative.",
"Since there are four independent dimensions, and each dimension's st... | To determine the number of different combinations of dimensions in a four-dimensional universe where each dimension can be either positive or negative, we can follow these steps:
1. **Understand the Problem:**
- We have **4 dimensions**.
- Each dimension can independently be either **positive (+)** or **negative... |
Llama-3.1-70B-Instruct_1044 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | In the United States, there are 10 hotels with 100 beds each. Every night, 6 guests stay in each hotel. On average, how many beds are there per guest? | [
"First, I need to determine the total number of beds available in all the hotels. There are 10 hotels, each with 100 beds, so the total number of beds is 10 multiplied by 100, which equals 1000 beds.",
"Next, I calculate the total number of guests staying each night. Each of the 10 hotels accommodates 6 guests pe... | To determine the average number of beds per guest in the hotels, follow these steps:
1. **Calculate the total number of beds:**
\[
\text{Total beds} = \text{Number of hotels} \times \text{Beds per hotel} = 10 \times 100 = 1000 \text{ beds}
\]
2. **Calculate the total number of guests per night:**
... |
Llama-3.1-70B-Instruct_1047 | Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | In a survey, 100 people were asked how many books they had read last year. The results are as follows:
| Number of Books | Frequency |
| --- | --- |
| 0 | 15 |
| 1 | 20 |
| 2 | 30 |
| 3 | 20 |
| 4 | 15 |
Find the mean number of books read last year.
Mean = $\frac{\sum(f \times x)}{\sum f}$
Where 'f' is the frequency... | [
"First, I need to calculate the total number of books read by multiplying each number of books by its corresponding frequency and then summing these products.",
"Next, I'll calculate the total number of participants by summing all the frequencies.",
"Finally, I'll determine the mean by dividing the total number... | To find the **mean** number of books read last year, we'll use the formula:
\[
\text{Mean} = \frac{\sum (f \times x)}{\sum f}
\]
Where:
- \( f \) is the **frequency** (number of people),
- \( x \) is the **number of books**.
Let's apply the formula step by step.
### Step 1: Calculate the Total Number of Books Read
... |
End of preview. Expand in Data Studio
Magpie Reasoning V2 Mini
A compact reasoning dataset derived from Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B. Each row contains id, source, question, steps, and answer; steps is a nonempty list of reasoning-step strings. Instances with fewer than 3 or more than 50 reasoning steps are excluded, and every step is whitespace-stripped. Usage remains subject to the source dataset's licensing terms.
Dataset statistics
| Metric | Value |
|---|---|
| Final records | 75,279 |
| File size | 142,007,754 bytes |
| Retention from original source population | 30.121% |
| Sources represented | 1 |
| Total reasoning steps | 404,590 |
| Mean steps per record | 5.37 |
| Median steps per record | 4 |
| Steps per record | 3–45 |
| Mean individual step length | 144.51 characters |
| Median individual step length | 128 characters |
| Individual step-length range | 1–937 characters |
| Median total reasoning length | 592 characters |
| Total reasoning-length range | 133–3583 characters |
| Answer-length range | 3–2734 characters |
| Question-length range | 13–3123 characters |
Source composition
| Source | Records |
|---|---|
| Magpie-Align/Magpie-Reasoning-V2-250K-CoT-Deepseek-R1-Llama-70B | 75,279 |
| Total | 75,279 |
- Downloads last month
- 111