Answer :
Certainly! Let's go through the problem step by step:
### Part a:
Diego guesses that each piece of paper is 0.015 inches thick. To determine if his guess is correct, we need to consider the total height of the stack and compare it with his guess.
1. Reasoning:
- If each piece of paper were 0.015 inches thick, the total height of 500 pieces would be calculated as:
[tex]\[
\text{Total height} = 500 \times 0.015 = 7.5 \text{ inches}
\][/tex]
- However, the given height of the stack of 500 papers is only 1.875 inches. This is much smaller than the 7.5 inches calculated using Diego's guess.
Therefore, Diego's guess of 0.015 inches per sheet is not correct.
### Part b:
Now, we'll find the actual thickness of each piece of paper.
1. Given Information:
- The total height of the stack of paper is 1.875 inches.
- There are 500 pieces of paper in the stack.
2. Calculation:
- To find the thickness of one sheet of paper, divide the total height by the number of sheets:
[tex]\[
\text{Thickness per sheet} = \frac{1.875 \text{ inches}}{500}
\][/tex]
- Solving this gives:
[tex]\[
\text{Thickness per sheet} = 0.00375 \text{ inches}
\][/tex]
Therefore, the actual thickness of each piece of paper is 0.00375 inches.
### Part a:
Diego guesses that each piece of paper is 0.015 inches thick. To determine if his guess is correct, we need to consider the total height of the stack and compare it with his guess.
1. Reasoning:
- If each piece of paper were 0.015 inches thick, the total height of 500 pieces would be calculated as:
[tex]\[
\text{Total height} = 500 \times 0.015 = 7.5 \text{ inches}
\][/tex]
- However, the given height of the stack of 500 papers is only 1.875 inches. This is much smaller than the 7.5 inches calculated using Diego's guess.
Therefore, Diego's guess of 0.015 inches per sheet is not correct.
### Part b:
Now, we'll find the actual thickness of each piece of paper.
1. Given Information:
- The total height of the stack of paper is 1.875 inches.
- There are 500 pieces of paper in the stack.
2. Calculation:
- To find the thickness of one sheet of paper, divide the total height by the number of sheets:
[tex]\[
\text{Thickness per sheet} = \frac{1.875 \text{ inches}}{500}
\][/tex]
- Solving this gives:
[tex]\[
\text{Thickness per sheet} = 0.00375 \text{ inches}
\][/tex]
Therefore, the actual thickness of each piece of paper is 0.00375 inches.
