3. (10 points) A particle moves on a circle through points which been marked 0,1,2,3,4 (in a clockwise order). At each step it has a probability p of moving to the right (clockwise) and 1- p to the left (counterclockwise). Let X denote its location on the circle after nth step. The process { Xn, n>= 0} is a Markov Chain a. Find the transition probability matrix. b. Calculate the limiting probabilities.

Write an introductory paragraph for this corrie ten boom and her family were faced with some difficult choices after hitler came to power. some family members paid the ultimate price. write a carefully thought-out paper of at least 200 words dealing with the following concepts: --how should a christian act when evil is in power? --what do you think it would be like to live in an occupied country? remember to proofread anything you write thoroughly.

Clarence wants to buy a new car. he finds an ad for a car that costs 27,200 dollars. suppose his local sales tax is 7%. -how much would he have to pay? -what is the cost of the car including tax? -if clarence has 29,864 saved, can he pay cash to buy the car?

X= 3y - 6 2x - 4y = 8 solve the system of equations using substitution. a) (-12,-2) b) (15,7) c) (21,9) d) (24,10)