Each year, 20% of all untenured State University faculty become tenured, 5% quit, and 75% remain untenured. Each year, 90% of all tenured S. U. faculty remain tenured and 10% quit. Let U_t be the number of untenured S. U. faculty at the beginning of year t, and T_t the tenured number. Use matrix multiplication to relate the vector [U_t + 1 T_t + 1] to the vector [U_t T_t].

Step-by-step explanation:

(Ut + 1) =(Ut Tt)   (a b)

(T1 + 1)                 (c d)

a = Untenured to untenured = 0.75

c = tenured to untenured = 0

b = untenured to tenured = 0.20

d = tenured to tenured = 0.90

(Ut + 1) =(Ut Tt)   (0.75  0.20)

(T1 + 1)                 (0       0.90)

the answer is $42.96

step-by-step explanation:

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c