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

\( \frac{2}{6} \) x \( \frac{4}{9} \) = \( \frac{2 x 4}{6 x 9} \) = \( \frac{8}{54} \) = \(\frac{4}{27}\)

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

The equation for this sequence is:

a_n = a_n-1 + 4(n - 1)

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 + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-4c^6}{5c^2} \)
\( \frac{-4}{5} \) c^{(6 - 2)}
-\(\frac{4}{5}\)c⁴

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

So, in an average hour, the machine will produce 9 - 0.45 = 8.55 error free parts.

The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 8.55 = 153.9 error free parts were produced yesterday.