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.

First, solve for \( \left|a - 1\right| \):

\( \left|a - 1\right| \) + 4 = 3
\( \left|a - 1\right| \) = 3 - 4
\( \left|a - 1\right| \) = -1

The value inside the absolute value brackets can be either positive or negative so (a - 1) must equal - 1 or --1 for \( \left|a - 1\right| \) to equal -1:

So, a = 2 or a = 0.

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

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

\( \frac{9}{100} \) x 6 = \( \frac{9 \times 6}{100} \) = \( \frac{54}{100} \) = 0.54 errors per hour

So, in an average hour, the machine will produce 6 - 0.54 = 5.46 error free parts.

The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 5.46 = 87.4 error free parts were produced yesterday.

To add these radicals together their radicands must be the same:

5\( \sqrt{50} \) + 2\( \sqrt{2} \)
5\( \sqrt{25 \times 2} \) + 2\( \sqrt{2} \)
5\( \sqrt{5^2 \times 2} \) + 2\( \sqrt{2} \)
(5)(5)\( \sqrt{2} \) + 2\( \sqrt{2} \)
25\( \sqrt{2} \) + 2\( \sqrt{2} \)

Now that the radicands are identical, you can add them together: