Question 1165966: Jenny gets paid $9 per hour working as a waiter at a local restaurant. Her boss also pays her $10 per hours to design graphics for their weekly specials menu. She works a total of 30 hours each week. The following functions can be used to define this situation. Let x represent the hours that Jenny works each week as a waiter. Let s represent the number of hours that Jenny works designing menu graphics each week.
b(x) = 9x
h(x) = 30 - x
g(s) = 10s
Select the equation for g(h(x)) and what does it represent in context.
Group of answer choices
10(9x)
10(30-x)
30 - 10s
30 - 9x
The amount of money Jenny earns waiting tables each week
The number of hours Jenny waits tables each week
The amount of money Jenny earns designing menu graphics each week
The number of hours Jenny designs graphics for the menu each week
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! b(x) = 9x tells you how much she makes each week by waiting on tables.
h(x) = 30 - x tells you how many hours she works on designing graphics for their weekly specials menu.
g(s) = 10s tells you how much she makes each week designing menu graphics.
g(h(x)) replaces s in the equation of g(s) with 30 - x from the equation of h(x)
start with g(s) = 10 * s
replace s with 30 - x to get g(h(x)) = 10 * (30 - x)
g(h(x)) = 10 * (30 - x) tells you how much she makes by designing menu graphics each week.
consider:
she works a total of 30 hours each week.
she works x hours as a waitress and s hours as a special menu graphics designer.
assume she worked 10 hours as a waitress.
b(x) = 9 * x becomes b(10) = 9 * 10 = 90 dollars each week that she makes as a waitress.
g(s) = s tells you how many hours she works as a designer.
h(x) = 30 - x also tells you how many hours she works as a designer.
assuming you don't know the value of s but only know the value of x, the you would use g(h(x)) to find out how much she made as a designer.
g(h(x)) replaces s in g(s) with 30 - x from h(x).
you get:
g(h(x)) = 10 * (30 - x)
since you know that h(x) = 10, then the formula becomes:
g(10)) = 10 * 20 = 200
this says she makes 90 dollars as a waitress and 200 dollars as a designer for a total weekly salary of 290 dollars.
x = 10, so b(x) = 9 * 10 = 90
s = (30 - 10) = 20, so g(s) = 10 * 200
your answers to the questions are shown below:
Select the equation for g(h(x)) and what does it represent in context.
Group of answer choices
10(9x)
10(30-x) ***** select this one
30 - 10s
30 - 9x
The amount of money Jenny earns waiting tables each week = 90
The number of hours Jenny waits tables each week = 10
The amount of money Jenny earns designing menu graphics each week = 200
The number of hours Jenny designs graphics for the menu each week = 20
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