MATH SOLVE

5 months ago

Q:
# A point in the figure selected at random. find the probability that the point will be in the part that is NOT shaded.

Accepted Solution

A:

Answer:The probability that the point will be in the part that is NOT shaded is about 20% ⇒ 4th answerStep-by-step explanation:* Lets look to the figure- There are four circles inscribed in a square- The four circles touched each other and touched the four sides of the square∴ The side of the square = twice the diameter of a circle- If the side of the square is l and the diameter of the circle is d∴ l = 2d ⇒ divide the two sides by 2∴ d = (1/2) l∵ The radius of the circle = (1/2) the diameter∴ r = (1/2) d∵ d = (1/2) l ∴ r = (1/2)(1/2) l = (1/4) l* Now lets find the area that NOT shaded∵ The area of the square = side × side∴ The area of the square = l × l = l²∵ The area of the circle = πr²∵ r = (1/4) l∴ r² = [(1/4) l]² = (1/4)² × l² = (1/16) l²∴ The area of one circle = (1/16)πl²- The shaded part is the four circles∴ The shaded area = 4 × (1/16)πl² = (1/4)πl²- The part is not shaded = Area of the square - Area of the shaded part∴ The area of not shaded = l² - (1/4)πl² ⇒ take l² as a common factor∴ The area of not shaded = l²(1 -1/4 π)- The probability that the point will be in the part that not shaded is area of the part not shaded/area of the square∴ P = l²(1 - 1/4 π)/l² ⇒ cancel l² from up and down∴ P = (1 - 1/4 π )/1 = 0.2146 ≅ 0.2- Chang it to percent number∴ P = 0.2 × 100% = 20%* The probability that the point will be in the part that is NOT shaded is about 20%∴ r = (1/2) d∴