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

vans = \( \frac{51}{12} \) = 4\(\frac{1}{4}\)

So, it will take 4 full vans and one partially full van to transport the entire team making a total of 5 vans.

The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 11 are [11, 22, 33, 44, 55, 66, 77, 88, 99]. The first few multiples they share are [33, 66, 99] making 33 the smallest multiple 3 and 11 have in common.

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

\( \frac{2}{8} \) x \( \frac{4}{5} \) = \( \frac{2 x 4}{8 x 5} \) = \( \frac{8}{40} \) = \(\frac{1}{5}\)

First, solve for \( \left|y - 8\right| \):

\( \left|y - 8\right| \) + 1 = 7
\( \left|y - 8\right| \) = 7 - 1
\( \left|y - 8\right| \) = 6

The value inside the absolute value brackets can be either positive or negative so (y - 8) must equal + 6 or -6 for \( \left|y - 8\right| \) to equal 6:

So, y = 2 or y = 14.

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 6 = \( \frac{7 \times 6}{100} \) = \( \frac{42}{100} \) = 0.42 errors per hour

So, in an average hour, the machine will produce 6 - 0.42 = 5.58 error free parts.

The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 5.58 = 83.7 error free parts were produced yesterday.