Mathematics

Question

Bill earns $12 per hour and works at most 40 hours per week. Identify the independent and dependent quantity in the situation, and find reasonable domain and range values.

A.amount of money earned; hours worked; 0 to 40; $0 to $480

B.hours worked; amount of money earned; $0 to $480; 0 to 40

C.hours worked; amount of money earned; 0 to 40; $0 to $480

D.amount of money earned; hours worked; $0 to $480; 0 to 40

2 Answer

  • The answer is D for sure

  • The amount of money earned is dependent quantity.

    The number of hours Bill worked is independent quantity.

    The domain values are 0 to 40.

    The range values are 0 to $480.

    What is independent quantity?

    An independent quantity is a variable that does not depend on any other variable for its value.

    What is dependent quantity?

    A dependent quantity represents a quantity whose value depends on how the independent quantity is manipulated.

    What is range?

    The definition of range is the set of all possible values that the function will give when we give in the domain as input.

    What is the domain?

    The domain of a function is the set of values that we are allowed to plug into our function.

    According to the given question.

    Amount of money Bill earn in one hour is $12.

    Maximum hours Bill works is 40 hours.

    Since, it Bill choice that how many hours he want to work.

    So, Number of hours Bill worked is independent quantity.

    But, the amount of money he earned totally depends on how many hours he worked.

    For example, if he worked x hours.

    Then the amount of money he earned = [tex]x \times 12 = 12x[/tex].

    ⇒ Amount of money he earned is dependent quantity.

    The minimum number of hours Bill can work is 0 hours.

    And, the maximum number of hours Bill can work is 40 hours.

    So, the domain values are 0 to 40.

    And,

    The maximum amount of money Bill can earn

    = [tex]12 \times maximum \ number \ of\ hours[/tex]

    [tex]= 12 \times 40[/tex]

    = $480

    The minimum amount of money Bill can earn

    [tex]= 12 \times minimum\ number\ of\ hour[/tex]

    [tex]= 12 \times 0[/tex]

    = $0

    Therefore, the range values are $0 to $480.

    Hence,

    The amount of money earned is dependent quantity.

    The number of hours Bill worked is independent quantity.

    The domain values are 0 to 40.

    The range values are 0 to $480.

    Find out more information about domain, range, dependent and independent quantities here:

    https://brainly.com/question/1400056

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