There are 3 3-passenger taxis available so that's 3 x 3 = 9 total seats. There are 11 people needing transportation leaving 11 - 9 = 2 who will have to find other transportation.

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

\( \frac{5}{100} \) x 7 = \( \frac{5 \times 7}{100} \) = \( \frac{35}{100} \) = 0.35 errors per hour

So, in an average hour, the machine will produce 7 - 0.35 = 6.65 error free parts.

The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 6.65 = 99.8 error free parts were produced yesterday.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{4}{16}} \)
\( \frac{\sqrt{4}}{\sqrt{16}} \)
\( \frac{\sqrt{2^2}}{\sqrt{4^2}} \)
\(\frac{1}{2}\)

To multiply terms with radicals, multiply the coefficients and radicands separately:

7\( \sqrt{8} \) x 4\( \sqrt{4} \)
(7 x 4)\( \sqrt{8 \times 4} \)
28\( \sqrt{32} \)

Now we need to simplify the radical:

28\( \sqrt{32} \)
28\( \sqrt{2 \times 16} \)
28\( \sqrt{2 \times 4^2} \)
(28)(4)\( \sqrt{2} \)
112\( \sqrt{2} \)

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 16 are [16, 32, 48, 64, 80, 96]. The first few multiples they share are [16, 32, 48, 64, 80] making 16 the smallest multiple 8 and 16 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{5 x 2}{8 x 2} \) - \( \frac{3 x 1}{16 x 1} \)

\( \frac{10}{16} \) - \( \frac{3}{16} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{10 - 3}{16} \) = \( \frac{7}{16} \) = \(\frac{7}{16}\)