Paddling with the current in a river, jake traveled 16 miles. Even though he paddled upstream for an hour longer than the amount of the time he paddled downstream jake could only travel 6 miles against the current. I'm still waterJake paddles at a rate of 5 mph. What is the speed of the current I the river

the rate of the current is 3 mph.

Step-by-step explanation:

Let x represent the rate of the current.

In still water, Jake paddles at a rate of 5 mph. Paddling with the current in a river, Jake traveled 16 miles. It means that the speed with which she travelled downstream (with the current) is (5 + x) mph

Time = distance/speed

Time spent in paddling downstream is

16/(5 + x)

While paddling upstream, it took an hour longer. The speed with which he paddled upstream is (5 - x) mph.

Jake could only travel 6 miles against the current. It means that the time spent in travelling upstream us

6/(5 - x)

Since it took 1 hour longer, then

6/(5 - x) = 16/(5 + x) + 1

Cross multiplying by (5 - x)(5 + x), it becomes

6(5 + x) = 16(5 - x) + 1(5 + x)(5 - x)

30 + 6x = 80 - 16x + 25 - 5x + 5x - x²

30 + 6x = - x² - 16x + 5x - 5x + 25 + 80

30 + 6x = - x² - 16x + 105

x² + 16x + 6x + 30 - 105 = 0

x² + 22x - 75 = 0

x² + 25x - 3x - 75 = 0

x(x + 25) - 3(x + 25) = 0

x - 3 = 0 or x + 25 = 0

x = 3 or x = - 25

Since x cannot be negative, then x = 3 mph

d

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