To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{81}{16}} \)
\( \frac{\sqrt{81}}{\sqrt{16}} \)
\( \frac{\sqrt{9^2}}{\sqrt{4^2}} \)
\( \frac{9}{4} \)
2\(\frac{1}{4}\)

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

\( \frac{4}{100} \) x 10 = \( \frac{4 \times 10}{100} \) = \( \frac{40}{100} \) = 0.4 errors per hour

So, in an average hour, the machine will produce 10 - 0.4 = 9.6 error free parts.

The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 9.6 = 172.8 error free parts were produced yesterday.

If a single cook can bake 4 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 4 x 2 = 8 large cakes during that time. 40 large cakes are needed for the party so \( \frac{40}{8} \) = 5 cooks are needed to bake the required number of large cakes.

If a single cook can bake 19 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 19 x 2 = 38 small cakes during that time. 280 small cakes are needed for the party so \( \frac{280}{38} \) = 7\(\frac{7}{19}\) 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 5 + 8 = 13 cooks.

The factors of a number are all positive integers that divide evenly into the number. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

By buying two shirts, Ezra will save $38 x \( \frac{10}{100} \) = \( \frac{$38 x 10}{100} \) = \( \frac{$380}{100} \) = $3.80 on the second shirt.