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

\( \frac{4}{100} \) x 10 = \( \frac{4 \times 10}{100} \) = \( \frac{40}{100} \) = 0.4 errors per hour

So, in an average hour, the machine will produce 10 - 0.4 = 9.6 error free parts.

The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 9.6 = 172.8 error free parts were produced yesterday.

The equation for this sequence is:

a_n = a_n-1 + 6

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 6
a₆ = 25 + 6
a₆ = 31

To simplify a radical, factor out the perfect squares:

\( \sqrt{48} \)
\( \sqrt{16 \times 3} \)
\( \sqrt{4^2 \times 3} \)
4\( \sqrt{3} \)

To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 500 meters to kilometers, divide the distance by 1000 to get 0.5km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.5km + 30.3km + 12.1km
total distance = 42.9km

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.

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

\( \frac{6 x 3}{2 x 3} \) + \( \frac{5 x 1}{6 x 1} \)

\( \frac{18}{6} \) + \( \frac{5}{6} \)

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

\( \frac{18 + 5}{6} \) = \( \frac{23}{6} \) = 3\(\frac{5}{6}\)