each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. which ordered…

Explanation:

Step1: Analyze the domain of x

The number of days late ( x ) cannot be negative or a non - integer in the context of daily fees (since the fee is charged per day at midnight, so partial days don't make sense for the number of days late in terms of fee calculation? Wait, no, actually, if we consider that the fee is $0.30 per day, and ( x ) is the number of days late, ( x ) should be a non - negative integer? Wait, no, let's check the formula. The total fee ( y = 0.30x ), where ( x\geq0 ) (number of days late can't be negative) and ( x ) should be a real number? Wait, no, in reality, the number of days late is a non - negative real number? Wait, no, the fee is charged at midnight each day. So if a book is late for 8 days, the fee is ( 0.30\times8 = 2.40 ). If it's late for 4.5 days, does that mean 4 full days and half a day? But the fee is charged at midnight, so maybe ( x ) should be a non - negative integer. Wait, but let's check the options.

First, eliminate options with negative ( x ): ((- 3,-0.90)) and ((-2.5,-0.75)) are out because the number of days late can't be negative.

Step2: Check the formula ( y = 0.30x )

For option ((4.5,1.20)): Calculate ( 0.30\times4.5=1.35\neq1.20 ), so this is incorrect.

For option ((8,2.40)): Calculate ( 0.30\times8 = 2.40 ), which matches. Also, ( x = 8) is a non - negative integer (number of days late), which makes sense in the context (8 full days late, fee charged at midnight each day, so 8 days, fee is ( 0.30\times8 = 2.40)).

Answer:

(8, 2.40)