Taylor buys nail polish from a shop that cost $3.95 each. She has a maximum of $30 to spend on nail polish purchases. The total cost, with respect to polishes purchased, can be modeled by a function. Which statement correctly defines the domain of the function?

The domain is the set of all whole numbers greater than or equal to 0 and less than or equal to 8.

The domain is the set of all whole numbers greater than or equal to 0 and less than or equal to 27.65.

The domain is the set of all whole numbers greater than or equal to 0 and less than or equal to 7.

The domain is the set of all whole numbers greater than or equal to 0 and less than or equal to 30.

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Mathematics

30 March, 21:17

Taylor buys nail polish from a shop that cost $3.95 each. She has a maximum of $30 to spend on nail polish purchases. The total cost, with respect to polishes purchased, can be modeled by a function. Which statement correctly defines the domain of the function?

The domain is the set of all whole numbers greater than or equal to 0 and less than or equal to 8.

The domain is the set of all whole numbers greater than or equal to 0 and less than or equal to 27.65.

The domain is the set of all whole numbers greater than or equal to 0 and less than or equal to 7.

The domain is the set of all whole numbers greater than or equal to 0 and less than or equal to 30.

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Answers (1)

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Brenna · Answer 1

The domain is the set of all whole numbers greater than or equal to 0 and less than or equal to 7.

Step-by-step explanation:

let x be the number of nail polishes that Taylor purchases.

Therefore the amount spent by Taylor on nail polishes will be f (x) = 3.95/times x

since Taylor has only 30 dollars to spend on nail polishes.

f (x) / leq 30 dollars

therefore 3.95/times x / leq 30

x / leq 7.594

since x is an whole number x = 7

Therefore the domain is the set of all whole numbers greater than or equal to 0 and less than or equal to 7.