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To calculate the contestant's balance of prize money, we need to determine the total amount lost due to the wrong answers.
The contestant loses $12.50 for each wrong answer. Since the contestant answered 6 questions wrong, the total loss is:
\[
\text{Total loss} = \text{Loss per wrong answer} \times \text{Number of wrong answers} = 12.50 \times 6 = 75.00
\]
Since the contestant answered no questions correctly, their balance of prize money is equal to the total loss, which would be negative:
\[
\text{Balance} = -75.00
\]
Thus, the contestant's balance of prize money is \(-75.00\) (negative $75.00).
The correct response is:
**−$75.00 (negative $75.00)**