Answer :
Sure! Let's tackle the question step-by-step:
### Part a: Explanation
Diego guessed that each piece of paper is 0.015 inches thick. To verify if this is a reasonable estimate, we can consider a typical ream of paper, which contains 500 sheets.
If each sheet were 0.015 inches thick, a ream of paper would be:
[tex]\[ \text{Total thickness} = 0.015 \, \text{inches/sheet} \times 500 \, \text{sheets} = 7.5 \, \text{inches} \][/tex]
This total of 7.5 inches is unrealistic because a ream of paper is typically around 2 inches thick. Therefore, Diego's estimate of 0.015 inches per sheet is much too high.
### Part b: Calculate the Thickness of Each Piece of Paper
Let's determine the actual thickness per sheet, given that we know a typical ream is about 2 inches thick and contains 500 sheets.
Given:
- Total thickness of the ream = 2 inches
- Number of sheets in the ream = 500
To find the thickness of each sheet, we divide the total thickness by the number of sheets:
[tex]\[ \text{Thickness per sheet} = \frac{\text{Total thickness of the ream}}{\text{Number of sheets}} \][/tex]
[tex]\[ \text{Thickness per sheet} = \frac{2 \, \text{inches}}{500} \][/tex]
[tex]\[ \text{Thickness per sheet} = 0.004 \, \text{inches} \][/tex]
Therefore, each piece of paper is approximately 0.004 inches thick.
### Part a: Explanation
Diego guessed that each piece of paper is 0.015 inches thick. To verify if this is a reasonable estimate, we can consider a typical ream of paper, which contains 500 sheets.
If each sheet were 0.015 inches thick, a ream of paper would be:
[tex]\[ \text{Total thickness} = 0.015 \, \text{inches/sheet} \times 500 \, \text{sheets} = 7.5 \, \text{inches} \][/tex]
This total of 7.5 inches is unrealistic because a ream of paper is typically around 2 inches thick. Therefore, Diego's estimate of 0.015 inches per sheet is much too high.
### Part b: Calculate the Thickness of Each Piece of Paper
Let's determine the actual thickness per sheet, given that we know a typical ream is about 2 inches thick and contains 500 sheets.
Given:
- Total thickness of the ream = 2 inches
- Number of sheets in the ream = 500
To find the thickness of each sheet, we divide the total thickness by the number of sheets:
[tex]\[ \text{Thickness per sheet} = \frac{\text{Total thickness of the ream}}{\text{Number of sheets}} \][/tex]
[tex]\[ \text{Thickness per sheet} = \frac{2 \, \text{inches}}{500} \][/tex]
[tex]\[ \text{Thickness per sheet} = 0.004 \, \text{inches} \][/tex]
Therefore, each piece of paper is approximately 0.004 inches thick.
