Answer :
Sure, let's work through the question step-by-step:
### Part (a): Explaining why Diego's guess is incorrect
Diego guesses that each piece of paper is 0.015 inch thick.
To check if this guess is correct, we need to calculate the total height of the stack of 500 pieces of paper based on Diego's guess. Here's how you do it:
1. Multiply the thickness of each piece of paper (0.015 inch) by the number of pieces of paper (500).
[tex]\[
\text{Total height based on Diego's guess} = 0.015 \text{ inches} \times 500
\][/tex]
[tex]\[
\text{Total height based on Diego's guess} = 7.5 \text{ inches}
\][/tex]
Since the actual height of the stack of 500 pieces of paper is given as 1.875 inches, Diego's guess results in a much taller stack. Therefore, we can conclude that Diego's guess is not correct because 7.5 inches is much greater than 1.875 inches.
### Part (b): Computing the actual thickness of each piece of paper
To find the true thickness of each piece of paper, we need to divide the total height of the stack by the number of pieces of paper. Here's how you do it:
1. The total height of the stack is 1.875 inches.
2. The number of pieces of paper is 500.
So, we divide the total height by the number of pieces:
[tex]\[
\text{Actual thickness of each piece of paper} = \frac{\text{Total height of the stack}}{\text{Number of pieces of paper}}
\][/tex]
[tex]\[
\text{Actual thickness of each piece of paper} = \frac{1.875 \text{ inches}}{500}
\][/tex]
[tex]\[
\text{Actual thickness of each piece of paper} = 0.00375 \text{ inches}
\][/tex]
Therefore, the actual thickness of each piece of paper is 0.00375 inches.
### Summary
- Part (a): Diego's guess that each piece of paper is 0.015 inch thick is incorrect because this would result in a total stack height of 7.5 inches, which is much greater than the actual stack height of 1.875 inches.
- Part (b): The actual thickness of each piece of paper is 0.00375 inches.
### Part (a): Explaining why Diego's guess is incorrect
Diego guesses that each piece of paper is 0.015 inch thick.
To check if this guess is correct, we need to calculate the total height of the stack of 500 pieces of paper based on Diego's guess. Here's how you do it:
1. Multiply the thickness of each piece of paper (0.015 inch) by the number of pieces of paper (500).
[tex]\[
\text{Total height based on Diego's guess} = 0.015 \text{ inches} \times 500
\][/tex]
[tex]\[
\text{Total height based on Diego's guess} = 7.5 \text{ inches}
\][/tex]
Since the actual height of the stack of 500 pieces of paper is given as 1.875 inches, Diego's guess results in a much taller stack. Therefore, we can conclude that Diego's guess is not correct because 7.5 inches is much greater than 1.875 inches.
### Part (b): Computing the actual thickness of each piece of paper
To find the true thickness of each piece of paper, we need to divide the total height of the stack by the number of pieces of paper. Here's how you do it:
1. The total height of the stack is 1.875 inches.
2. The number of pieces of paper is 500.
So, we divide the total height by the number of pieces:
[tex]\[
\text{Actual thickness of each piece of paper} = \frac{\text{Total height of the stack}}{\text{Number of pieces of paper}}
\][/tex]
[tex]\[
\text{Actual thickness of each piece of paper} = \frac{1.875 \text{ inches}}{500}
\][/tex]
[tex]\[
\text{Actual thickness of each piece of paper} = 0.00375 \text{ inches}
\][/tex]
Therefore, the actual thickness of each piece of paper is 0.00375 inches.
### Summary
- Part (a): Diego's guess that each piece of paper is 0.015 inch thick is incorrect because this would result in a total stack height of 7.5 inches, which is much greater than the actual stack height of 1.875 inches.
- Part (b): The actual thickness of each piece of paper is 0.00375 inches.
