Some carpet cleaning costs are 1 room for $125, 2 rooms for $175, 3 rooms for $225. and 4 rooms for $275.00.find and interpret the rate of change and the initial value for this situation.

First calculate the hourly rate, which is the difference of cleaning 2 and 1 rooms:
175-125=50

then calculate the initial value by subtracting the hourly rate from the "1 room" cost:
125-50=75

The initial cost might be something like driving to the place (which is only necessary once), while the rate covers work time or cleaning utensils used.

The answer above ^ just gave you the right explanation.

You first change the mixed number into an improper fraction
5 2/3 = 17/3.

Then do the reciprocal. This means that you just have to turn the fraction upside down.

= 3/17.