To find the average of these 4 numbers add them together then divide by 4:

\( \frac{18 + 12 + 16 + 14}{4} \) = \( \frac{60}{4} \) = 15

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. 21 large cakes are needed for the party so \( \frac{21}{6} \) = 3\(\frac{1}{2}\) 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 2 hours, a single cook can bake 15 x 2 = 30 small cakes during that time. 140 small cakes are needed for the party so \( \frac{140}{30} \) = 4\(\frac{2}{3}\) 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 + 5 = 9 cooks.

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

-3z⁵ + 4z⁵
(-3 + 4)z⁵
z⁵

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

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 6 = \( \frac{9 \times 6}{100} \) = \( \frac{54}{100} \) = 0.54 errors per hour

So, in an average hour, the machine will produce 6 - 0.54 = 5.46 error free parts.

The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 5.46 = 103.7 error free parts were produced yesterday.