Final answer:
Derek's State income tax from his gross pay of $780.50 at a 6.5% rate is calculated by multiplying 780.50 by 0.065, resulting in $50.7325 or $50.73 when rounded to the nearest cent.
Step-by-step explanation:
To calculate Derek's State income tax, we need to apply the 6.5% income tax rate to his gross pay of $780.50. To do this, multiply 780.50 by 0.065 (6.5% expressed as a decimal).
The calculation is as follows:
780.50 × 0.065 = $50.7325
Rounding this to the nearest cent, Derek will pay $50.73 in State income tax this pay period, which is not exactly one of the options provided. The closest option is $50.78 (b), which might indicate a slight discrepancy due to the rounding of the cent value.