Let P = 0.5 0.9 0.5 0.1 be the transition matrix for a Markov chain with two states. Let x0 = 0.5 0.5 be the initial state vector for the population. Find the steady state vector x. (Give the steady state vector as a probability vector.) x =

1. if we have 3 babies what is the probability they’re going to be all boys? 2. if we roll 2 die at the same time what is the probability of getting less than 10 on the first roll and a 5 on the second roll 3. if we have 3 babies what is the probability their is going to be 2 girls? 4. if we have 3 babies what is the probability of having no more than 1 girl? 5. it we have 3 babies and then have another 3 babies what is the probability of us having at least 1 boy and then having all girls?

Alicia puts $400 in a bank account. each year the account earns 5% simple interest. how much money will be in her bank account in six months?

Apool measures 12.3 feet by 16.6 feet. if the longer wall of the pool has a diagonal of 17.8 feet, what is the volume of the pool? (round to nearest tenth)