What is the product of [x-(4+13i)][x-(4+13i)]

x^2 - (4+13i)^2

Step-by-step explanation:

This product has the form (a-b)(a+b), which is a 'special product' equal to a^2 - b^2.  Following this pattern, [x-(4+13i)][x-(4+13i)] = x^2 - (4+13i)^2.  The 2nd term could be expanded if desired, but the above result is the most compact one possible.

4096 bacteria

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