If a single cook can bake 3 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 3 x 4 = 12 large cakes during that time. 24 large cakes are needed for the party so \( \frac{24}{12} \) = 2 cooks are needed to bake the required number of large cakes.

If a single cook can bake 15 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 15 x 4 = 60 small cakes during that time. 430 small cakes are needed for the party so \( \frac{430}{60} \) = 7\(\frac{1}{6}\) 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 2 + 8 = 10 cooks.

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

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.

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{92}{12} \) = 7\(\frac{2}{3}\)

So, it will take 7 full vans and one partially full van to transport the entire team making a total of 8 vans.

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

\( \frac{6}{100} \) x 6 = \( \frac{6 \times 6}{100} \) = \( \frac{36}{100} \) = 0.36 errors per hour

So, in an average hour, the machine will produce 6 - 0.36 = 5.64 error free parts.

The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 5.64 = 112.8 error free parts were produced yesterday.