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If a single cook can bake 3 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 3 x 2 = 6 large cakes during that time. 25 large cakes are needed for the party so \( \frac{25}{6} \) = 4\(\frac{1}{6}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 14 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 14 x 2 = 28 small cakes during that time. 290 small cakes are needed for the party so \( \frac{290}{28} \) = 10\(\frac{5}{14}\) 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 + 11 = 16 cooks.

A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:

38,000 fans x \( \frac{5}{6} \) = \( \frac{190000}{6} \) = 31,667 fans.

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

\( \frac{7}{100} \) x 10 = \( \frac{7 \times 10}{100} \) = \( \frac{70}{100} \) = 0.7 errors per hour

So, in an average hour, the machine will produce 10 - 0.7 = 9.3 error free parts.

The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 9.3 = 139.5 error free parts were produced yesterday.

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

c⁶ x c⁵
(1 x 1)c^{(6 + 5)}
c¹¹