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

\( \frac{8}{100} \) x 10 = \( \frac{8 \times 10}{100} \) = \( \frac{80}{100} \) = 0.8 errors per hour

So, in an average hour, the machine will produce 10 - 0.8 = 9.2 error free parts.

The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 9.2 = 193.2 error free parts were produced yesterday.

1

Betty scored 84% on the test meaning she earned 84% of the possible points on the test. There were 200 possible points on the test so she earned 200 x 0.84 = 168 points. Each question is worth 4 points so she got \( \frac{168}{4} \) = 42 questions right.

First, solve for \( \left|c + 6\right| \):

\( \left|c + 6\right| \) + 7 = -4
\( \left|c + 6\right| \) = -4 - 7
\( \left|c + 6\right| \) = -11

The value inside the absolute value brackets can be either positive or negative so (c + 6) must equal - 11 or --11 for \( \left|c + 6\right| \) to equal -11:

So, c = 5 or c = -17.

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.