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

Related problems in "Applied Mathematics"

The problem describes a population of cottontail rabbits that doubles every 12 years. We are given t...

Exponential GrowthPopulation ModelingLogarithms
2025/4/7

The problem provides an equation to calculate the accrued value $A$ of an investment made by Jolene:...

Compound InterestExponential GrowthFinancial MathematicsLogarithms
2025/4/7

We are given that 53 white-tail deer were introduced into a state park. The population quadruples ev...

Exponential GrowthPopulation ModelingLogarithms
2025/4/7

The problem describes a population of cottontail rabbits that starts at 66 and quadruples every 16 y...

Exponential GrowthModelingLogarithmsPopulation Dynamics
2025/4/7

(a) The population of a city increased from 23,400 to 27,800 between 2008 and 2012. We need to find ...

Linear FunctionsPopulation GrowthStatisticsChi-SquareCombinatoricsPermutations
2025/4/6

(a) Find the constant change in population per year of a city from 2008 to 2012, given an increase f...

Linear FunctionsStatisticsCombinatoricsPopulation Growth
2025/4/6

The problem provides the cost function $C(x) = -2350 + 80x - 0.04x^2$ and the price function $P(x) =...

OptimizationCalculusProfit MaximizationMarginal AnalysisCost FunctionRevenue FunctionProfit FunctionDerivatives
2025/4/6

A company makes square and triangular boxes. Square boxes take 2 minutes and yield a profit of K4 ea...

OptimizationLinear ProgrammingConstraintsInteger Programming
2025/4/6

The problem states that the number of cups in a stack is a function of the height of the stack in ce...

ModelingFunctionsGraphingLinear FunctionsReal-world Application
2025/4/4

Problem 4 describes a function $C$ that gives the cost in dollars of buying $n$ apples. We need to i...

FunctionsModelingCost AnalysisLinear FunctionsReal-world application
2025/4/4