30) 30) At a liberal arts college, students are classified as humanities or science majors. There is a probability of 0.9 that a humanities major will change to science and of 0.2 that a science major will change to humanities. What are the long-term predictions for each major

hence the long-term prediction for each major ; [ 1 , 1 ]

Step-by-step explanation:

Probability of A humanities major changes to Science = 0.9

P( science major changes to humanities ) = 0.2

Determine the long term predictions for each Major

The Transition matrix can be written as

Find the equilibrium matrix p' of the Transition matrix above by finding the values of p, p^2 , p^3 ......... until any row of the resultant matrix

The eigen ( equilibrium ) vectors of the matrix

hence the long-term prediction for each major ; [ 1 , 1 ]

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.

since no one answered yet i will give it a shot, not completely sure tho.

i think it should be y=cos(x+2pi), (third answer, answer c)

good luck.