Let's analyze each option systematically in relation to the percentage change.
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Option A:
- Claim: The number of visitors at the zoo increased by 113%.
- Expression: \( z + 1.13z \)
- Evaluation: An increase of 113% means the new visitors would be the original plus an additional 113% of the original, which is \( z + 1.13z = 2.13z \). This indicates a total of 213% of the original number of visitors, which is not a typical increase and doesn't align with the percentage described. This statement is false.
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Option B:
- Claim: The number of visitors at the zoo increased by 13%.
- Expression: \( z + 0.13z \)
- Evaluation: An increase of 13% means the new visitors would be the original plus an additional 13% of the original: \( z + 0.13z = 1.13z \), representing a total of 113% of the original number of visitors, which correctly reflects a 13% increase. This statement is true.
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Option C:
- Claim: The number of visitors at the zoo decreased by 113%.
- Expression: \( z - 1.13z \)
- Evaluation: A decrease of 113% is nonsensical, as it implies a reduction beyond the total number of visitors. The expression would result in a negative number of visitors (specifically, \(-0.13z\)), which does not apply here. This statement is false.
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Option D:
- Claim: The number of visitors at the zoo decreased by 13%.
- Expression: \( z - 0.13z \)
- Evaluation: A decrease of 13% means that the new visitors would be \( z - 0.13z = 0.87z \). This indicates that the number of visitors was 87% of the original, which accurately reflects a 13% decrease. This statement is true.
Conclusion:
The true statements are:
- B: The number of visitors at the zoo increased by 13%. An equivalent expression that represents this situation is \( z + 0.13z \).
- D: The number of visitors at the zoo decreased by 13%. An equivalent expression that represents this situation is \( z - 0.13z \).
These two statements are true, while A and C are false.
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