Suppose a Markov chain has three states, A, B, and C. It changes to a different state each step (no loops). The probability it will change from A to B is 0.8, the probability it will change from B to A is 0.2, and the probability it will change from C to A is 0.2. Find the long-term distribution for this Markov chain. What proportion of the time will it spend at state A

1. there are 25 students who started computer programming in elementary school and 25 students who started computer programming in middle school. the first group had a mean final project grade of 95% and the second group had a mean final project grade of 92%. the line plot shows the differences after 10 rerandomizations. determine whether the difference in the means of the two groups is significant based on the line plot. explain your answer.

Which points are solutions to the linear inequality y < 0.5x + 2? check all that apply. (–3, –2) (–2, 1) (–1, –2) (–1, 2) (1, –2) (1, 2)

Valentina is subtracting from . she finds the lcd to be 15y2. what is valentina's next step?