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

\( \frac{8}{100} \) x 6 = \( \frac{8 \times 6}{100} \) = \( \frac{48}{100} \) = 0.48 errors per hour

So, in an average hour, the machine will produce 6 - 0.48 = 5.52 error free parts.

The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 5.52 = 110.4 error free parts were produced yesterday.

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{14\sqrt{25}}{7\sqrt{5}} \)
\( \frac{14}{7} \) \( \sqrt{\frac{25}{5}} \)
2 \( \sqrt{5} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{8} \) x \( \frac{2}{5} \) = \( \frac{3 x 2}{8 x 5} \) = \( \frac{6}{40} \) = \(\frac{3}{20}\)

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

First, solve for \( \left|b + 8\right| \):

\( \left|b + 8\right| \) + 6 = -7
\( \left|b + 8\right| \) = -7 - 6
\( \left|b + 8\right| \) = -13

The value inside the absolute value brackets can be either positive or negative so (b + 8) must equal - 13 or --13 for \( \left|b + 8\right| \) to equal -13:

So, b = 5 or b = -21.