A point in the figure is selected at random. Find the probability that the point will be in the shaded region.

A.) about 90%
B.) about 70%
C.) about 60%
D.) about 80%

Option D - about 80% is the answer

Step-by-step explanation:

Step 1 :

Let L be the length of the square

Since the 2 semi circles are drawn with side of the square as diameter , the diameter of the 2 shaded semicircles is L

Hence the radius =  

Step 2 :

The total outcome  = the point is inside the square =  area of the square = L²

The favorable outcome is that the point is inside the shaded area  = Area of  2 shaded semi circles of radius L/2 = × =   ×

The probability that the point is inside the shaded area = favorable outcome ÷ the total outcome

  = ( × ) ÷  L² =  = = 0.785

Converting this into percentage it give 78.5% which is about 80%

Step 3 :

Answer :

Option D - about 80% is the answer

yes

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240