Ms. Donaldson earns $19.20 per hour for the first 40 hours she works in a week. She earns 1 1/2 times that amount per hour for each hour she works beyond 40 hours in a week. Last week Ms. Donaldson worked 45.5 hours. a) How much money did she earn last week? b) A health insurance payment of $34.75 was deducted from Ms. Donaldson's earnings for the week. After the insurance deduction, payroll taxes equal to 32% of the balance were deducted. What was the amount that Ms. Donaldson received?

a) $926.40

b) $606.32

Step-by-step explanation:

a)

If she worked a total of 45.5 hours, she will receive $19.20 per hour in the first 40 hours and 1.5 * $19.20 for the exceeding 5.5 hours, so her earnings is:

19.2 * 40 + 1.5 * 5.5 * 19.2 = $926.40

b)

The deduction is $34.75, so the remaining will be:

926.40 - 34.75 = $891.65

Then, after this deduction, the taxes is 32% of the remaining, so:

891.65 - 0.32 * 891.65 = $606.32

She received $606.32

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: