You got this you can do it I don’t know the answer but I hope you find someone who does(:
Answer: 2^14
Step-by-step explanation:
Answer 384
Explanation
In total 632 and there were either adult or students so
632/2=316
So because it said 68 tickets were sold less for the students I added it to 316
316+68=384
Adults=384
I hope this helps if I’m wrong someone please correct me
Answer:
(a)0.16
(b)0.588
(c)![[s_1$ s_2]=[0.75,$ 0.25]](https://tex.z-dn.net/?f=%5Bs_1%24%20s_2%5D%3D%5B0.75%2C%24%20%200.25%5D)
Step-by-step explanation:
The matrix below shows the transition probabilities of the state of the system.

(a)To determine the probability of the system being down or running after any k hours, we determine the kth state matrix
.
(a)


If the system is initially running, the probability of the system being down in the next hour of operation is the 
The probability of the system being down in the next hour of operation = 0.16
(b)After two(periods) hours, the transition matrix is:

Therefore, the probability that a system initially in the down-state is running
is 0.588.
(c)The steady-state probability of a Markov Chain is a matrix S such that SP=S.
Since we have two states, ![S=[s_1$ s_2]](https://tex.z-dn.net/?f=S%3D%5Bs_1%24%20%20s_2%5D)
![[s_1$ s_2]\left(\begin{array}{ccc}0.90&0.10\\0.30&0.70\end{array}\right)=[s_1$ s_2]](https://tex.z-dn.net/?f=%5Bs_1%24%20%20s_2%5D%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7D0.90%260.10%5C%5C0.30%260.70%5Cend%7Barray%7D%5Cright%29%3D%5Bs_1%24%20%20s_2%5D)
Using a calculator to raise matrix P to large numbers, we find that the value of
approaches [0.75 0.25]:
Furthermore,
![[0.75$ 0.25]\left(\begin{array}{ccc}0.90&0.10\\0.30&0.70\end{array}\right)=[0.75$ 0.25]](https://tex.z-dn.net/?f=%5B0.75%24%20%200.25%5D%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7D0.90%260.10%5C%5C0.30%260.70%5Cend%7Barray%7D%5Cright%29%3D%5B0.75%24%20%200.25%5D)
The steady-state probabilities of the system being in the running state and in the down-state is therefore:
![[s_1$ s_2]=[0.75$ 0.25]](https://tex.z-dn.net/?f=%5Bs_1%24%20s_2%5D%3D%5B0.75%24%20%200.25%5D)
(B) - Yes, because the amount owed changes by 2.25 every time the miles change by 1.
Starting at 1 mile the price is 2.5 dollars.
Mile 2 is 4.75 dollars. What is the difference between 4.75 and 2.5? 2.25
Mile 3 is 7 dollars. What is the difference between 7 and 4.75? 2.25
Mile 4 is 9.25 dollars. What is the difference between 9.25 and 7? 2.25
Mule 5 is 11.5 dollars. What is the difference between 11.5 and 9.25? 2.25
The change is always 2.25 dollars.
The change is 2.25 dollars per mile.
One way to solve for this is (11.5 - 2.5)/(5-1)=2.25
This is (y2-y1)/(x2-x1). By picking 2 points, (x1,y1) and (x2,y2) you can solve for the slope (rate of change) between them.