Find the area of the unshaded part of the figure

  unshaded area = 25(4 -π) in^2 ≈ 21.46 in^2

Each of the shaded circles has a diameter of (20 in)/4 = 5 in, which also is the width of the enclosing rectangle. Then each circle has a radius of 2.5 in, and an area of ...

  A = πr^2 = π(2.5 in)^2 = 6.25π in^2

The four circles together have an area of ...

  4A = 4·(6.25π in^2) = 25π in^2

The area of the rectangle is the product of its length and width:

  A = LW = (20 in)(5 in) = 100 in^2

Since the circles are shaded, the unshaded area is the difference between the rectangle area and the total area of the four circles:

  unshaded area = (100 in^2) - (25π in^2) = 25(4 -π) in^2 ≈ 21.46 in^2

step-by-step explanation:

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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: