Amanufacturer of metal washers needs to determine the cross-sectional area of each washer. if the outer radius of the washer is r and the radius of the hole is r, express the area of the washer as a polynomial. factor this polynomial completely.

The formula for area of any circle is :πr2.  

To find the area of the washer, subtract the area of the hole from the area of the outer circle:

A = πR2 - πr2

A = π(R2 - r2)

Now factor completely:

A = π(R + r)(R - r)

i think the correct option is the second option.

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