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

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions