Alaboratory animal may eat any one of three foods each day. laboratory records show that if the animal chooses one food on one trial, it will choose the same food on the next trial with a probability of 50%, and it will choose the other foods on the next trial with equal probabilities of 25%. what is the stochastic matrix for this situation?

Step-by-step explanation:

let a, b and c be the type of foods used in trail.

Example matrix combination for (1,1) is (a,a) is 0.5. Another Example for (1,2) is (a,b) is 0.25.

The diagonals are (a,a), (b,b) and (c,c) which means same food in two trails and its probability is 0.5. the rest would be 0.25

Therefore, stochastic matrix would have 3 by 3 matrix such as (a,a), (a,b) .... (c,c)

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.

113.1

step-by-step explanation:

v=4

3πr3=4

3·π·33≈113.09734