I need urgent help please !!

2^(8p) =2^(5p+15)

Step-by-step explanation:

16 ^ 2p  = 32 ^ (p+3)

Rewrite each number as a power of 2

16 = 2^4

32 = 2^5

2^4 ^ 2p =2^5 ^ (p+3)

We know a^b^c = a^(b*c)

2^(4 * 2p) =2^(5 * (p+3))

2^(8p) =2^(5p+15)

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