Construct a polynomial function with the following properties: fifth degree, −4 is a zero of multiplicity 4, 2 is the only other zero.

is the required polynomial.

Step-by-step explanation:

Multiplicity of the polynomial = 5

⇒The highest power of the variable in the polynomial is 5.

Now, the zero of the polynomial is -4 with multiplicity 4.

⇒ is one the factor of the polynomial.

Also,  the only other zero of the polynomial is 2 with multiplicity 1.

⇒(x-2)  is the ONLY other factor of the polynomial.

Hence, the required polynomial P(x) is

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