A plane has a cruising speed of 250 mph when there is no wind. At this speed, the plane flew 300 miles with the wind in the same amount of time it flew 200 miles against the wind. Find the speed of the wind.

the speed of the wind is 50 mph.

Step-by-step explanation:

Let x represent the speed of the wind.

The plane has a cruising speed of 250 mph when there is no wind. At this speed, the plane flew 300 miles with the wind. This means that the total speed at which the plane flew was (250 + x) mph

Time = distance/speed

The time spent by the plane in flying 300 miles is

300/(250 + x)

In the same amount of time, it flew 200 miles against the wind. This means that the total speed at which the plane flew was (250 - x) mph

Time = distance/speed

The time spent by the plane in flying 200 miles is

200/(250 - x)

Since the time is the same, then

300/(250 + x) = 200/(250 - x)

Cross multiplying, it becomes

200(250 + x) = 300(250 - x)

50000 + 200x = 75000 - 300x

200x + 300x = 75000 - 50000

500x = 25000

x = 25000/500

x = 50

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )

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