At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.15 and the probability that the flight will be delayed is 0.16. The probability that it will not rain and the flight will leave on time is 0.81. What is the probability that it is raining if the flight leaves on time? Round your answer to the nearest thousandth.

0.853

Step-by-step explanation:

Use conditional probability.  The probability of event A, given that event B has occurred, is:

P(A|B) = P(A and B) / P(B)

The probability that it is not raining, given that the flight leaves on time, is:

P(not raining | on time) = P(not raining AND on time) / P(on time)

P(not raining | on time) = 0.81 / (1 − 0.05)

P(not raining | on time) = 0.853

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240