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Select the correct answer.

The student council is hosting a homecoming event for past graduates and current students. The treasurer determines that the event's revenue from the event can be represented by [tex]$R(x) = 0.05x^3 - 75$[/tex], where [tex]$x$[/tex] is the number of tickets sold. The cost to put on the event is represented by the function [tex]$C(x) = 30x + 12,500$[/tex].

Which function describes the funds raised, [tex][tex]$F(x)$[/tex][/tex], as a function of the number of tickets sold?

A. [tex]$F(x) = 0.05x^3 + 30x - 12,425$[/tex]

B. [tex]$F(x) = 0.05x^3 - 30x - 12,575$[/tex]

C. [tex][tex]$F(x) = 0.05x^3 - 30x - 12,425$[/tex][/tex]

D. [tex]$F(x) = 0.05x^3 + 30x - 12,575$[/tex]

Sagot :

GinnyAnsweridn
To determine the function [tex]\(F(x)\)[/tex] that describes the funds raised as a function of the number of tickets sold, we need to calculate the difference between the revenue function [tex]\(R(x)\)[/tex] and the cost function [tex]\(C(x)\)[/tex].

Given:
[tex]\[ R(x) = 0.05x^3 - 75 \][/tex]
[tex]\[ C(x) = 30x + 12,500 \][/tex]

The funds raised, [tex]\(F(x)\)[/tex], can be represented as:
[tex]\[ F(x) = R(x) - C(x) \][/tex]

Substituting the given functions [tex]\(R(x)\)[/tex] and [tex]\(C(x)\)[/tex] into the equation:
[tex]\[ F(x) = (0.05x^3 - 75) - (30x + 12,500) \][/tex]

Now, we will distribute the negative sign and combine like terms:
[tex]\[ F(x) = 0.05x^3 - 75 - 30x - 12,500 \][/tex]
[tex]\[ F(x) = 0.05x^3 - 30x - 75 - 12,500 \][/tex]
[tex]\[ F(x) = 0.05x^3 - 30x - 12,575 \][/tex]

Therefore, the function describing the funds raised, [tex]\(F(x)\)[/tex], is:
[tex]\[ F(x) = 0.05x^3 - 30x - 12,575 \][/tex]

So the correct answer is:
[tex]\[ \boxed{F(x)=0.05 x^3-30 x-12,575} \][/tex]
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