A plane can fly 360 mph in still air. If it can fly 210 miles downwind in the same amount of time it can fly 150 miles upwind, find the velocity of the wind. mph

55 mph

Step-by-step explanation:

Assuming that

v = velocity of the plane in still air,

w = velocity of the wind.

We are given that v = 360 mi/hr.

Using the equation

x = vt

where

x is the distance an object travels

v is the speed of the object

t is the time taken

While the plane is flying downwind, the velocity becomes v + w. On the other hand, if it is flying upwind, the velocity becomes v - w.

For a particular time t = T, distance traveled x = 210 mi at downwind, and x = 150 mi at upwind.

Creating an equation from the two, we have

210 mi = (360 + w)T

150 mi = (360 - w)T

Solving for T, we have

T = 210/(360 + w)

T = 150/(360 - w)

And since T is the same in both cases, we say that

So, 210/(360 + w) = 150/(360 - w)

Or on rearranging,

(360 + w)/210 = (360 - w)/150

(360)(150) + 150w = (210)(360) - 210w

55800 + 150w = 75600 - 210w

360w = 19800

Therefore, the speed of the wind is 55 mile per hour

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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