Question
The total cost in dollars to buy uniforms for the players on a volleyball team can be found using the function c = 34.95u + 6.25, where u is the number of uniforms bought. If there are at least 8 players but not more than 12 players on the volleyball team, what is the domain of the function for this situation?
F.
0 < u ≤ 12
G.
0 < c ≤ 425.65
H.
{ 8, 9, 10, 11, 12 }
J.
{ 285.85, 320.80, 355.75, 390.70, 425.65 }
F.
0 < u ≤ 12
G.
0 < c ≤ 425.65
H.
{ 8, 9, 10, 11, 12 }
J.
{ 285.85, 320.80, 355.75, 390.70, 425.65 }
Answers
GPT-4o mini
To determine the correct domain of the function \( c = 34.95u + 6.25 \) given the conditions, we need to look at the number of uniforms \( u \) that can be bought based on the number of players on the volleyball team.
The problem states that there are at least 8 players but not more than 12 players. Therefore, the possible values for \( u \), which represents the number of uniforms, must range from 8 to 12 inclusive.
This means the domain of the function \( c \) in this context is:
\[
u \in \{ 8, 9, 10, 11, 12 \}
\]
From the given options:
F. \( 0 < u \leq 12 \) — This domain is broader than the range of players specified.
G. \( 0 < c \leq 425.65 \) — This is related to the total cost, not the domain of \( u \).
H. \( \{ 8, 9, 10, 11, 12 \} \) — This correctly captures the possible number of uniforms based on the number of players.
J. \( \{ 285.85, 320.80, 355.75, 390.70, 425.65 \} \) — This is related to the costs rather than the number of uniforms.
Therefore, the correct answer is:
**H. \{ 8, 9, 10, 11, 12 \}**
The problem states that there are at least 8 players but not more than 12 players. Therefore, the possible values for \( u \), which represents the number of uniforms, must range from 8 to 12 inclusive.
This means the domain of the function \( c \) in this context is:
\[
u \in \{ 8, 9, 10, 11, 12 \}
\]
From the given options:
F. \( 0 < u \leq 12 \) — This domain is broader than the range of players specified.
G. \( 0 < c \leq 425.65 \) — This is related to the total cost, not the domain of \( u \).
H. \( \{ 8, 9, 10, 11, 12 \} \) — This correctly captures the possible number of uniforms based on the number of players.
J. \( \{ 285.85, 320.80, 355.75, 390.70, 425.65 \} \) — This is related to the costs rather than the number of uniforms.
Therefore, the correct answer is:
**H. \{ 8, 9, 10, 11, 12 \}**