Find the area of the shaded regions below. give your answer as a completely simplified exact value in terms of π (no approximations).

area of the shaded portion COA = 9.83 cm² = 3.128π cm²

area of the shaded portion COB = 1.442 cm² =0.459π cm²

in total= 9.83 + 1.442 = 11.27 cm² =  3.58π cm²

Step-by-step explanation:

area of sector of circle COB can be gotten by knowing the angle <COB

to calculate for the angle, we will use the three side of triangle given.

CO = 4cm, CB= 4cm and OB = 4 cm

cos θ = (OB/2)/OC =2/4 = 0.5

θ = 60 degree

since the three side are equal, that mean the triangle is equilateral

area of a sector = θ/360 * πr²

        =60/360 * π * 4 *4

       =  8.37 cm²

area of triangle COB

s = 4+4+4)/2 = 12/2 = 6cm

A =

A = 6.928 cm²

area of the shaded portion COB = area of sector - area of triangle

        = 8.37 cm² - 6.928 cm²  ==1.442 cm²

area of sector of circle COA can be gotten by knowing the angle <COA

to calculate for the angle, we will subtract 60 from 180 = 120.

θ = 120 degree

since the two side are equal, that mean the triangle is isosceles

area of a sector = θ/360 * πr²

        =120/360 * π * 4 *4

       =  16.76 cm²

area of triangle COA

    = 0.5 * 4 * 4* sine 120

    A = 6.928 cm²

area of the shaded portion COA = area of sector - area of triangle

        = 16.76 cm² - 6.928 cm²  ==9.83 cm²

area of the shaded portion COA = 9.83 cm² = 3.128π cm²

area of the shaded portion COB = 1.442 cm² =0.459π cm²

in total= 9.83 + 1.442 = 11.27 cm² =  3.58π cm²

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560