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 - 9 = 15 hours yesterday so you would expect that 15 x 9.6 = 144 error free parts were produced yesterday.

The equation for this sequence is:

a_n = a_n-1 + 2(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 + 2(6 - 1)
a₆ = 21 + 2(5)
a₆ = 31

If the tiger has consumed 18 pounds of food in 3 days that's \( \frac{18}{3} \) = 6 pounds of food per day. The tiger needs to consume 60 - 18 = 42 more pounds of food to reach 60 pounds total. At 6 pounds of food per day that's \( \frac{42}{6} \) = 7 more days.

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

\( \frac{2}{9} \) x \( \frac{2}{5} \) = \( \frac{2 x 2}{9 x 5} \) = \( \frac{4}{45} \) = \(\frac{4}{45}\)

To divide fractions, invert the second fraction and then multiply:

\( \frac{2}{8} \) ÷ \( \frac{2}{7} \) = \( \frac{2}{8} \) x \( \frac{7}{2} \)

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

\( \frac{2}{8} \) x \( \frac{7}{2} \) = \( \frac{2 x 7}{8 x 2} \) = \( \frac{14}{16} \) = \(\frac{7}{8}\)