What is the area of F?

area of circle F = 9 pi

Step-by-step explanation:

An interesting problem, combining geometry and algebra.

It has not been indicated, but it will be assumed that GH is a tangent to the circle F, hence the tangent-secant theorem from point H applies.

Produce HF to point E on the circumference such that EJ forms a diameter of circle F.

By the tangent-secant theorem,

HG^2 = HJ*HE

Substitute given values,

(x+2)^2 = 2*(2*(2x-1)+2)

Expand algebraically

x^2+4x+4 = 2(4x-2+2)

x^2+4x+4 = 8x

x^2-4x+4 = 0

Factor

(x-2)^2 = 0

=>

x=2

Substitute x=2 into radius FG = 2(x)-1 = 3

Therefore area of circle F

= pi r^2

= pi (3)^2

= 9 pi

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

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so

step-by-step explanation:

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