To find the function that describes the average expense for a player per game played, in terms of [tex]\( x \)[/tex], let's break down the given information:
1. Entry Fee: \[tex]$11. This is a one-time cost you have to pay regardless of the number of games played.
2. Cost per Game: \$[/tex]1.
If a player plays [tex]\( x \)[/tex] games, the total cost [tex]\( T(x) \)[/tex] for playing [tex]\( x \)[/tex] games would be:
[tex]\[ T(x) = \text{Entry Fee} + (\text{Cost per Game} \times x) \][/tex]
[tex]\[ T(x) = 11 + 1x \][/tex]
[tex]\[ T(x) = 11 + x \][/tex]
The average expense per game [tex]\( C(x) \)[/tex] is then calculated by dividing the total cost [tex]\( T(x) \)[/tex] by the number of games played [tex]\( x \)[/tex]. So, we have:
[tex]\[ C(x) = \frac{T(x)}{x} \][/tex]
[tex]\[ C(x) = \frac{11 + x}{x} \][/tex]
We can simplify this expression:
[tex]\[ C(x) = \frac{11}{x} + \frac{x}{x} \][/tex]
[tex]\[ C(x) = \frac{11}{x} + 1 \][/tex]
We need to match this function to one of the given options:
A. [tex]\( C(z)=\frac{511+118}{14} \)[/tex] - This option does not match the form we derived and has different variables and constants.
B. [tex]\( C(x)=\frac{112}{z} \)[/tex] - This option appears to have a different variable, but let's consider a possible typo in the problem statement. If it meant [tex]\( C(x) = \frac{11}{x} + 1 \)[/tex], it matches our derived formula.
C. [tex]\( C(x)=\frac{3 \| x+31}{x} \)[/tex] - This is not a valid mathematical expression for the situation.
D. [tex]\( C(x)=\frac{511+11}{z} \)[/tex] - The constants and variables here do not match our derived form.
Correcting for any potential typographical errors, the correct choice is:
B. [tex]\( C(x) = \frac{11}{x} + 1 \)[/tex]
Thus, the correct option that best describes the average expense for a player per game played is Option B, assuming there's an error and the intent was to have the form [tex]\( C(x) = \frac{11}{x} + 1 \)[/tex].
