The problem states that a function $R(s)$ gives a "rest score" based on the number of hours of sleep, $s$, a 60-year-old gets in a day. We need to determine which of the given values could be included in the domain of this function. The domain represents the possible number of hours of sleep.

Applied MathematicsFunctionsDomainReal-world applicationModeling
2025/3/26

1. Problem Description

The problem states that a function R(s)R(s) gives a "rest score" based on the number of hours of sleep, ss, a 60-year-old gets in a day. We need to determine which of the given values could be included in the domain of this function. The domain represents the possible number of hours of sleep.

2. Solution Steps

The number of hours of sleep a person gets in a day must be a non-negative number. It is also reasonable to assume that the number of hours of sleep in a day will not exceed 24 hours.
Examine the provided values:
-9: This is a negative number. It's not possible to sleep a negative number of hours. Therefore, this value is not in the domain.
19.5: This is a non-negative number. It is possible to sleep 19.5 hours. Therefore, this value is in the domain.
6: This is a non-negative number. It is possible to sleep 6 hours. Therefore, this value is in the domain.
0: It is possible to sleep 0 hours. Therefore, this value is in the domain.
7: It is possible to sleep 7 hours. Therefore, this value is in the domain.
11: It is possible to sleep 11 hours. Therefore, this value is in the domain.
25: This is a positive number, but it exceeds the number of hours in a day. It is not reasonable to sleep 25 hours. Therefore, this value is not in the domain.
The values which could be included in the domain are those that are non-negative and less than or equal to
2
4.

3. Final Answer

19.5, 6, 0, 7, 11

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