7. The function () = ( − 2) 2 + 10 is not one-to-one. Identify a restricted domain that makes the function one-to-one, and find the inverse function.

The function () = ( − 2) 2 + 10 is not one-to-one. Identify a

1/15

Step-by-step explanation:

Given

1 out of every 5 national flight is followed by an international flight.

p = 1/5

q = 1 - p

q = 1 - 1/5

q = 4/5

π0 = 0.25

We want to determine

p:the fraction of international flights that are followed by a national flight.

Let X = 0

If the nth flight is national

Let X = 1

if the flight is international

This gives rise to a two state Markov chain with transition probability as follows

P = (4/5. 1/5. p. 1-p)

The long run proportion are the below solution gotten from the Markov chain above

π0 = 4/5π0 + pπ1 1

π1 = 1/5π0 + (1 - p)π1 2

π0 + π1 = 1 . 3

Solving the above equations,

We have

Substitute 0.25 for π0 in (3)

0.25 + π1 = 1

π1 = 1 - 0.25

π1 = 0.75

Solving 1 and 3

Substitute 0.75 for π1 and 0.25 for π0 in (1)

0.25 = 4/5 * 0.25 + 0.75p

0.25 = 0.2 + 0.75p

0.75p = 0.25 - 0.2

0.75p = 0.05

p = 0.05/0.75

P = 1/15 or 0.0667(6.67%)

So, one out of every 15 international flights is followed by a national flight (or 6.66 percent)