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Answer :
Let's find the percent change for each scenario by following these steps:
1. Identify the initial and final values: This will help us determine the amount of change.
2. Calculate the change: Subtract the initial value from the final value to get the change in value.
3. Use the percent change formula:
[tex]\[
\text{Percent Change} = \left( \frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \right) \times 100
\][/tex]
4. Round to the nearest percent.
Let's apply these steps to each part:
19. From 16 m to [tex]\(11 \frac{1}{4}\)[/tex] m:
- Initial value: 16 m
- Final value: [tex]\(11 \frac{1}{4}\)[/tex] m, which is 11.25 m in decimal form.
Calculate the percent change:
[tex]\[
\text{Percent Change} = \left( \frac{11.25 - 16}{16} \right) \times 100 = \left( \frac{-4.75}{16} \right) \times 100 \approx -30\%
\][/tex]
So, the percent change is approximately [tex]\(-30\%\)[/tex].
20. From 76 ft to [tex]\(58 \frac{1}{2}\)[/tex] ft:
- Initial value: 76 ft
- Final value: [tex]\(58 \frac{1}{2}\)[/tex] ft, which is 58.5 ft in decimal form.
Calculate the percent change:
[tex]\[
\text{Percent Change} = \left( \frac{58.5 - 76}{76} \right) \times 100 = \left( \frac{-17.5}{76} \right) \times 100 \approx -23\%
\][/tex]
So, the percent change is approximately [tex]\(-23\%\)[/tex].
21. From [tex]\(215 \frac{1}{2}\)[/tex] lb to [tex]\(133 \frac{1}{4}\)[/tex] lb:
- Initial value: [tex]\(215 \frac{1}{2}\)[/tex] lb, which is 215.5 lb in decimal form.
- Final value: [tex]\(133 \frac{1}{4}\)[/tex] lb, which is 133.25 lb in decimal form.
Calculate the percent change:
[tex]\[
\text{Percent Change} = \left( \frac{133.25 - 215.5}{215.5} \right) \times 100 = \left( \frac{-82.25}{215.5} \right) \times 100 \approx -38\%
\][/tex]
So, the percent change is approximately [tex]\(-38\%\)[/tex].
These are the step-by-step solutions for finding the percent changes in each case.
1. Identify the initial and final values: This will help us determine the amount of change.
2. Calculate the change: Subtract the initial value from the final value to get the change in value.
3. Use the percent change formula:
[tex]\[
\text{Percent Change} = \left( \frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \right) \times 100
\][/tex]
4. Round to the nearest percent.
Let's apply these steps to each part:
19. From 16 m to [tex]\(11 \frac{1}{4}\)[/tex] m:
- Initial value: 16 m
- Final value: [tex]\(11 \frac{1}{4}\)[/tex] m, which is 11.25 m in decimal form.
Calculate the percent change:
[tex]\[
\text{Percent Change} = \left( \frac{11.25 - 16}{16} \right) \times 100 = \left( \frac{-4.75}{16} \right) \times 100 \approx -30\%
\][/tex]
So, the percent change is approximately [tex]\(-30\%\)[/tex].
20. From 76 ft to [tex]\(58 \frac{1}{2}\)[/tex] ft:
- Initial value: 76 ft
- Final value: [tex]\(58 \frac{1}{2}\)[/tex] ft, which is 58.5 ft in decimal form.
Calculate the percent change:
[tex]\[
\text{Percent Change} = \left( \frac{58.5 - 76}{76} \right) \times 100 = \left( \frac{-17.5}{76} \right) \times 100 \approx -23\%
\][/tex]
So, the percent change is approximately [tex]\(-23\%\)[/tex].
21. From [tex]\(215 \frac{1}{2}\)[/tex] lb to [tex]\(133 \frac{1}{4}\)[/tex] lb:
- Initial value: [tex]\(215 \frac{1}{2}\)[/tex] lb, which is 215.5 lb in decimal form.
- Final value: [tex]\(133 \frac{1}{4}\)[/tex] lb, which is 133.25 lb in decimal form.
Calculate the percent change:
[tex]\[
\text{Percent Change} = \left( \frac{133.25 - 215.5}{215.5} \right) \times 100 = \left( \frac{-82.25}{215.5} \right) \times 100 \approx -38\%
\][/tex]
So, the percent change is approximately [tex]\(-38\%\)[/tex].
These are the step-by-step solutions for finding the percent changes in each case.
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