Answer :
Sure, let's go through the solution step-by-step.
### Given:
- A stack of 500 pieces of paper is 1.875 inches tall.
### a. Why Diego's guess is not correct:
Diego guesses that each piece of paper is 0.015 inch thick. To check if Diego's guess is correct, we'll multiply his guess by the total number of pieces to see if it matches the total height of the stack.
Diego's guessed thickness per piece = 0.015 inch
Total pieces = 500
Total height based on Diego's guess = [tex]\( 0.015 \text{ inch} \times 500 \)[/tex]
= [tex]\( 7.5 \text{ inches} \)[/tex]
According to the given information, the total height of the stack is 1.875 inches, not 7.5 inches. Therefore, Diego's guess of 0.015 inch per piece is not correct.
### b. Compute the thickness of each piece of paper:
To find the actual thickness of each piece of paper, we divide the total height of the stack by the number of pieces.
Total height of the stack = 1.875 inches
Total pieces of paper = 500
Thickness per piece = [tex]\( \frac{1.875 \text{ inches}}{500} \)[/tex]
Thickness per piece = 0.00375 inch
So, the thickness of each piece of paper is 0.00375 inch.
Putting it all together, the calculations show how Diego’s guess of 0.015 inch per piece was incorrect, and the actual thickness of each piece of paper is 0.00375 inch.
### Given:
- A stack of 500 pieces of paper is 1.875 inches tall.
### a. Why Diego's guess is not correct:
Diego guesses that each piece of paper is 0.015 inch thick. To check if Diego's guess is correct, we'll multiply his guess by the total number of pieces to see if it matches the total height of the stack.
Diego's guessed thickness per piece = 0.015 inch
Total pieces = 500
Total height based on Diego's guess = [tex]\( 0.015 \text{ inch} \times 500 \)[/tex]
= [tex]\( 7.5 \text{ inches} \)[/tex]
According to the given information, the total height of the stack is 1.875 inches, not 7.5 inches. Therefore, Diego's guess of 0.015 inch per piece is not correct.
### b. Compute the thickness of each piece of paper:
To find the actual thickness of each piece of paper, we divide the total height of the stack by the number of pieces.
Total height of the stack = 1.875 inches
Total pieces of paper = 500
Thickness per piece = [tex]\( \frac{1.875 \text{ inches}}{500} \)[/tex]
Thickness per piece = 0.00375 inch
So, the thickness of each piece of paper is 0.00375 inch.
Putting it all together, the calculations show how Diego’s guess of 0.015 inch per piece was incorrect, and the actual thickness of each piece of paper is 0.00375 inch.
