A second floor has recently been added to the local public library. There is a team of 8 workers moving crates of books from the first floor to the second floor. Each worker can move 32 crates in an hour. For each additional worker that joins the team, the output of every worker drops by 2 crates per hour, due to increased traffic on the elevators and stairways. What is the maximum possible number of crates that can be moved per hour? Use the information below. Let C = number of crates moved per hour Let w = number of workers added The total number of crates moved per hour, C, will equal the total number of workers times the output per worker. The total number of workers is the original number of workers, 8, plus the number of workers added, w. The output per worker is 32 crates per hour minus two times the number of workers added, w. C = (number of workers) × (output per worker) C = (8 + w) × (32 - 2w) C = 256 + 16w - 2w2 The graph of this function is shown to the right. A. 4 B. 256 C. 300 D. 288

step-by-step explanation:

the first 5 right here the next 5 i will upload as separate question

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)