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Math  /  Algebra

QuestionUnit test Google Classroom Microsoft Teams
Carter plays on a football team. He modeled a few relationships. \begin{tabular}{|l|l|l|} \hline Function & Input & Output \\ \hline N\boldsymbol{N} & Winning percentage, w\boldsymbol{w} & Average number of fans per game, N(w)N(w) \\ \hline P\boldsymbol{P} & Average daily practice time, x\boldsymbol{x} & Winning percentage, W(x)\boldsymbol{W}(\boldsymbol{x}) \\ \hline P\boldsymbol{P} & Number of rainy days, r\boldsymbol{r} & Average daily practice time, P(r)\boldsymbol{P}(\boldsymbol{r}) \\ \hline \end{tabular}
The expression N(W(x))N(W(x)) represents which of the following? Choose 1 answer:
A The team's winning percentage as a function of the average daily practice time (B) The average number of fans per game as a function of the number of rainy days in a season (C) The average number of fans per game as a function of the team's average daily practice time

Studdy Solution

STEP 1

1. We are given three functions: N(w) N(w) , W(x) W(x) , and P(r) P(r) .
2. N(w) N(w) gives the average number of fans per game based on the winning percentage.
3. W(x) W(x) gives the winning percentage based on the average daily practice time.
4. P(r) P(r) gives the average daily practice time based on the number of rainy days.
5. We need to interpret the expression N(W(x)) N(W(x)) .

STEP 2

1. Understand the composition of functions.
2. Analyze the expression N(W(x)) N(W(x)) .
3. Determine what N(W(x)) N(W(x)) represents.

STEP 3

The composition of functions involves applying one function to the result of another function. In this case, N(W(x)) N(W(x)) means we first apply W(x) W(x) and then apply N N to the result.

STEP 4

First, W(x) W(x) takes the average daily practice time x x and outputs the winning percentage. Then, N(W(x)) N(W(x)) takes this winning percentage and outputs the average number of fans per game.

STEP 5

The expression N(W(x)) N(W(x)) represents the average number of fans per game as a function of the team's average daily practice time.
The correct answer is:
(C) The average number of fans per game as a function of the team's average daily practice time

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