I have 7.5 quarts of fluid that needs changed; however, the fluid can only be removed and replaced 2.5 quarts at a time. How many 2.5 quart changes do I need to make to have 80% or more new fluid?

Number of times to change fluid = 3

Step-by-step explanation:

The amount of fluid that needs to be changed is 7.5 quarts.

The fluid can only be removed and replaced 2.5 quarts at a time.

How many 2.5 quart changes do we need to have 80% or more new fluid?

Lets first find out the 80% amount of the fluid that needs to be changed.

80% amount of fluid = 0.80*7.5

80% amount of fluid = 6 quarts

Now let us find out the number of times required to change the fluid.

Number of times = 6 quarts/2.5 quarts

Number of times = 2.4

We cannot have number of times in fraction so we can either go with 2 times or 3 times, since 2 times is not enough to make 80% or more new fluid, we must change the fluid 3 times, therefore the required number of times to change the fluid is

Number of times to change fluid = 3

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: