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 9 = \( \frac{8 \times 9}{100} \) = \( \frac{72}{100} \) = 0.72 errors per hour

So, in an average hour, the machine will produce 9 - 0.72 = 8.28 error free parts.

The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 8.28 = 132.5 error free parts were produced yesterday.

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

2\( \sqrt{9} \) x 4\( \sqrt{9} \)
(2 x 4)\( \sqrt{9 \times 9} \)
8\( \sqrt{81} \)

Now we need to simplify the radical:

8\( \sqrt{81} \)
8\( \sqrt{9 \times 9} \)
8\( \sqrt{9 \times 3^2} \)
(8)(3)\( \sqrt{9} \)
24\( \sqrt{9} \)

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

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

\( \frac{4\sqrt{21}}{2\sqrt{3}} \)
\( \frac{4}{2} \) \( \sqrt{\frac{21}{3}} \)
2 \( \sqrt{7} \)

To raise a term with an exponent to another exponent, retain the base and multiply the exponents: