There are 60 students in the speech contest. Yesterday, 2/3 of them gave their speeches. Today, 1/4 of the remaining students gave their speeches. How many students still haven’t given their speeches?

15

Step-by-step explanation:

60 x 2/3 = 120/3 which is 40 students that gave their speech the first day

Second day there are 20 students left to speak.

20 x 1/4 = 20/4 which is 5 students that gave their speech.

Now there are 15 students left to give their speech

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.