If a single cook can bake 5 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 5 x 2 = 10 large cakes during that time. 38 large cakes are needed for the party so \( \frac{38}{10} \) = 3\(\frac{4}{5}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 12 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 12 x 2 = 24 small cakes during that time. 310 small cakes are needed for the party so \( \frac{310}{24} \) = 12\(\frac{11}{12}\) 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 + 13 = 17 cooks.

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

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

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

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

So, in an average hour, the machine will produce 8 - 0.72 = 7.28 error free parts.

The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 7.28 = 138.3 error free parts were produced yesterday.

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