Bot GPT 4-o mini To find the range of the function \( c = 30.75u + 5.75 \) for the number of uniforms \( u \) that can range from 8 to 12 (inclusive), we will calculate the cost \( c \) at the boundaries of this range.
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Calculate the cost when \( u = 8 \): \[ c = 30.75(8) + 5.75 \] \[ c = 246 + 5.75 \] \[ c = 251.75 \]
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Calculate the cost when \( u = 12 \): \[ c = 30.75(12) + 5.75 \] \[ c = 369 + 5.75 \] \[ c = 374.75 \]
Now, we can summarize the calculations:
- For \( u = 8 \), the cost \( c \) is \( 251.75 \).
- For \( u = 12 \), the cost \( c \) is \( 374.75 \).
Since \( u \) can take any integer value from 8 to 12, the function is linear and increases as \( u \) increases.
Thus, the range of the function \( c \) for \( u \) in the given interval is: \[ \text{Range of } c: [251.75, 374.75] \]
This means the total cost for purchasing uniforms for the volleyball team, given the number of players between 8 and 12, will fall within this range.
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