A motorboat sets out in the direction Upper N 70 degrees 48 prime Upper E. The speed of the boat in still water is 34.4 mph. If the current is flowing directly south, and the actual direction of the motorboat is due east, find the speed of the current and the actual speed of the motorboat.

11.31 mph

Step-by-step explanation:

60' = 1°

48'=x°

X = 48/60

X = 0.8°

Hence 70°48' = 70.8°

θ = 90°-70.8°

θ = 19.2°

Sin 19.2 = bc/34.4

Bc = sin 19.2 × 34.4

Bc = 0.32866×34.4

BC = 11.31 mph

1,645,493,059.35

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