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FUNDRAISING The Pep Club rented a shaved ice machine to sell shaved ice as a fundraiser. They paid an initial fee and then an hourly
charge. The table shows the cost per hour. Find and interpret the rate of change and initial fee. Assume the relationship between the two
quantities is linear
Number of
3
14
s
Hours, x
Cost (S).
30 35 140 145
Oa 5,50; The rate of change is $5 per hour. The initial value is $50.
Ob. 20,5; The rate of change is $20 per hour. The initial value is $5.
Oc 5,25; The rate of change is $5 per hour. The initial value is $25.
Od 5, 20; The rate of change is $5 per hour. The initial value is $20.

Solve FUNDRAISING The Pep Club Rented A Shaved Ice Machine To Sell Shaved Ice As A Fundraiser They Paid An Initial Fee And Then An Hourly Charge The Table Shows class=

Sagot :

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Answer:

Sorry it's late but it was C

MrRoyal

The true option is (d) 5, 20; The rate of change is $5 per hour. The initial value is $20.

(a) The rate of change

Write out any two points from the table

(x,y) = (2,30) (4,40)

So, the rate is calculated using the following slope formula

[tex]Rate = \frac{y_2-y_1}{x_2 -x_1}[/tex]

This gives

[tex]Rate = \frac{40-30}{4-2}[/tex]

Simplify

[tex]Rate = \frac{10}{2}[/tex]

Divide the fraction

[tex]Rate = 5[/tex]

So, the rate is $5

(b) The initial value

This is the y value, when x = 0.

Represent this point with (0,y).

Calculate the slope (m) of the table using points (0,y) and (2,30).

So, we have:

[tex]m = \frac{30 - y}{2-0}[/tex]

This gives

[tex]m = \frac{30 - y}{2}[/tex]

Substitute 5 for m

[tex]\frac{30 - y}{2} = 5[/tex]

Multiply both sides by 2

[tex]30 - y = 10[/tex]

Collect like terms

[tex]y = 30 -10[/tex]

[tex]y = 20[/tex]

Hence, the initial value is $20

Read more about linear functions at:

https://brainly.com/question/15602982

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