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7. A stack of 500 pieces of paper is 1.875 inches tall.

a. Diego guesses that each piece of paper is 0.015 inch thick. Explain how you know that Diego's answer is not correct.

b. Compute the thickness of each piece of paper. Show your reasoning.

Answer :

Sure, let's solve the problem step-by-step.

### Part (a)

Diego guesses that each piece of paper is 0.015 inch thick. To check if Diego's guess is correct, we need to see if the total height of the stack according to Diego's guess matches the actual height of the stack.

1. Diego's guess for the thickness of each piece of paper:
[tex]\[
0.015 \text{ inches}
\][/tex]

2. Number of pieces of paper:
[tex]\[
500
\][/tex]

3. Calculate the total height of the stack based on Diego's guess by multiplying the guessed thickness by the number of pieces:
[tex]\[
\text{Total height} = 0.015 \times 500 = 7.5 \text{ inches}
\][/tex]

According to Diego's guess, the stack would be 7.5 inches tall. However, we know that the actual height of the stack is only 1.875 inches. Since 7.5 inches is much taller than 1.875 inches, Diego's guess is clearly incorrect.

### Part (b)

Now, let's compute the actual thickness of each piece of paper.

1. The actual height of the stack is:
[tex]\[
1.875 \text{ inches}
\][/tex]

2. Number of pieces of paper:
[tex]\[
500
\][/tex]

3. To find the thickness of one piece of paper, we divide the total height of the stack by the number of pieces:
[tex]\[
\text{Thickness per paper} = \frac{1.875}{500} = 0.00375 \text{ inches}
\][/tex]

So, the thickness of each piece of paper is
[tex]\[
0.00375 \text{ inches}.
\][/tex]

Thus, we can conclude:
- Diego's guess of 0.015 inch per paper was incorrect because it would make the stack much taller than the actual height.
- The correct thickness of each piece of paper is 0.00375 inches.

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