You have 9 out of the total of 100 raffle tickets sold so you have a (\( \frac{9}{100} \)) x 100 = \( \frac{9 \times 100}{100} \) = \( \frac{900}{100} \) = 9% chance to win the raffle.

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $500
i = 0.06 x $500

No payments were made so the total amount due is the original amount + the accumulated interest:

The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:

\( \frac{5}{100} \) x 5 = \( \frac{5 \times 5}{100} \) = \( \frac{25}{100} \) = 0.25 errors per hour

So, in an average hour, the machine will produce 5 - 0.25 = 4.75 error free parts.

The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 4.75 = 76 error free parts were produced yesterday.

To simplify a radical, factor out the perfect squares:

\( \sqrt{125} \)
\( \sqrt{25 \times 5} \)
\( \sqrt{5^2 \times 5} \)
5\( \sqrt{5} \)

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

6b⁵ + 2b⁵
(6 + 2)b⁵
8b⁵