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 \( \sqrt{7} \)

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 8 = \( \frac{8 \times 8}{100} \) = \( \frac{64}{100} \) = 0.64 errors per hour

So, in an average hour, the machine will produce 8 - 0.64 = 7.36 error free parts.

The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 7.36 = 117.8 error free parts were produced yesterday.

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

-1z³ - 7z³
(-1 - 7)z³
-8z³

If a single cook can bake 2 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 2 x 3 = 6 large cakes during that time. 22 large cakes are needed for the party so \( \frac{22}{6} \) = 3\(\frac{2}{3}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 10 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 10 x 3 = 30 small cakes during that time. 280 small cakes are needed for the party so \( \frac{280}{30} \) = 9\(\frac{1}{3}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 4 + 10 = 14 cooks.

By buying two shirts, Bob will save $44 x \( \frac{35}{100} \) = \( \frac{$44 x 35}{100} \) = \( \frac{$1540}{100} \) = $15.40 on the second shirt.