Simplify.

a. 128

b. 4,096

c. 32

d. 162

4096 is the simplified form of

Option: B

Step-by-step explanation:

Given that

represents 2 to the power 3 that means the number appears three times in multiplying.

represents  2³ to the power 4 means the number 4 appears four times in multiplying.

Hence the simplified form of is 4096.

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