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

\( \frac{7}{100} \) x 9 = \( \frac{7 \times 9}{100} \) = \( \frac{63}{100} \) = 0.63 errors per hour

So, in an average hour, the machine will produce 9 - 0.63 = 8.37 error free parts.

The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 8.37 = 142.3 error free parts were produced yesterday.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{3!}{5!} \)
\( \frac{3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{5 \times 4} \)
\( \frac{1}{20} \)

There are 3 4-passenger taxis available so that's 3 x 4 = 12 total seats. There are 16 people needing transportation leaving 16 - 12 = 4 who will have to find other transportation.

If the tiger has consumed 112 pounds of food in 8 days that's \( \frac{112}{8} \) = 14 pounds of food per day. The tiger needs to consume 210 - 112 = 98 more pounds of food to reach 210 pounds total. At 14 pounds of food per day that's \( \frac{98}{14} \) = 7 more days.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-8a² + 1a²
(-8 + 1)a²
-7a²