If a single cook can bake 3 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 3 x 3 = 9 large cakes during that time. 39 large cakes are needed for the party so \( \frac{39}{9} \) = 4\(\frac{1}{3}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 11 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 11 x 3 = 33 small cakes during that time. 370 small cakes are needed for the party so \( \frac{370}{33} \) = 11\(\frac{7}{33}\) 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 + 12 = 17 cooks.

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 5 = \( \frac{9 \times 5}{100} \) = \( \frac{45}{100} \) = 0.45 errors per hour

So, in an average hour, the machine will produce 5 - 0.45 = 4.55 error free parts.

The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 4.55 = 72.8 error free parts were produced yesterday.

The factors of a number are all positive integers that divide evenly into the number. The factors of 64 are 1, 2, 4, 8, 16, 32, 64.

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{9} \) x \( \frac{2}{6} \) = \( \frac{3 x 2}{9 x 6} \) = \( \frac{6}{54} \) = \(\frac{1}{9}\)

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

8,143,000 in scientific notation is 8.143 x 10⁶