For the funcations f(x) =2x-6 and g(x) =5x+1 which composition produces the greatest output

C. f(g(x)) produces the greater output.  

Step-by-step explanation:

ƒ(x) = 2x - 6

g(x) = 5x + 1

f(g(x)} = 2(5x + 1) - 6 = 10x + 2 - 6 =10x - 4

g(f(x)) = 5(2x- 6) + 1 = 10x - 30 + 1 = 10x - 29

f(g(x)) - g(f(x)) = 10x - 4 - (10x -29) = 10x - 4 - 10x + 29 = 25

f(g(x)) is always 25 units greater than g(f(x)), no matter the value of x.

Thus f(g(x)) produces the greater output.

Cost = $86.67

Step-by-step explanation:

Given

Yards = 4⅓ (missing part of the question)

Cost per yard = $2.00

Required

Determine cost of chains produced in 10 minutes

If 4⅓ yards is made in a minute, then

4⅓ * 10 yards are made in 10 minutes

Total = 4⅓ * 10

Total = 13/3 * 10

Total = 130/3 yards

Cost of a yard of chain is $2.00.

Cost of 130/3 yards would be:

Cost = $2.00 * 130/3

Cost = $260.00/3

Cost = $86.67 (approximated)

Hence, the required cost is approximately $86.67