The length of a rectangle is five feet less than
its width. If the area of the rectangle is 84
square feet, find its dimensions.

Length is w-5

Area  = length x width

84 = (w-5)w

84 = w^2 - 5w

0 = w^2 - 5w - 84

0 = (  w     -    12 )( w   +     7    )

w + 7 = 0 leads to negative measures.

w-12=0 ---> w = 12

width is 12, length is 5 less, or 7

more detail

step-by-step explanation:

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