For what natural values of n:
is the sum (−27.1+3n)+(7.1+5n) negative?

you!

(-27.1 + 3n) + (7.1 + 5n) to be negative

(-27.1 + 3n) + (7.1 + 5n) < 0

-27.1 + 3n + 7.1 + 5n < 0

8n - 20 < 0

8n < 20

n < 20/8

n < 5/2

Since we want natural numbers we cant have fractions and since n must be less than 5/2 which is 2,5, we can only have natural numbers below 2,5 which means numbers below 2

n < 2

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