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

\( \frac{2}{100} \) x 8 = \( \frac{2 \times 8}{100} \) = \( \frac{16}{100} \) = 0.16 errors per hour

So, in an average hour, the machine will produce 8 - 0.16 = 7.84 error free parts.

The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 7.84 = 172.5 error free parts were produced yesterday.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [21, 42, 63, 84] making 21 the smallest multiple 3 and 7 share.

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

\( \frac{7 x 7}{3 x 7} \) + \( \frac{6 x 3}{7 x 3} \)

\( \frac{49}{21} \) + \( \frac{18}{21} \)

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

\( \frac{49 + 18}{21} \) = \( \frac{67}{21} \) = 3\(\frac{4}{21}\)

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

The equation for this sequence is:

a_n = a_n-1 + 5

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 + 5
a₆ = 21 + 5
a₆ = 26

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).