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 8 = \( \frac{8 \times 8}{100} \) = \( \frac{64}{100} \) = 0.64 errors per hour

So, in an average hour, the machine will produce 8 - 0.64 = 7.36 error free parts.

The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 7.36 = 110.4 error free parts were produced yesterday.

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

0.0008403 in scientific notation is 8.403 x 10^-4

First, solve for \( \left|x + 9\right| \):

\( \left|x + 9\right| \) + 7 = 5
\( \left|x + 9\right| \) = 5 - 7
\( \left|x + 9\right| \) = -2

The value inside the absolute value brackets can be either positive or negative so (x + 9) must equal - 2 or --2 for \( \left|x + 9\right| \) to equal -2:

So, x = -7 or x = -11.

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

\( \frac{4}{7} \) ÷ \( \frac{3}{7} \) = \( \frac{4}{7} \) x \( \frac{7}{3} \)

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

\( \frac{4}{7} \) x \( \frac{7}{3} \) = \( \frac{4 x 7}{7 x 3} \) = \( \frac{28}{21} \) = 1\(\frac{1}{3}\)

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

4b⁷ - 6b⁷
(4 - 6)b⁷
-2b⁷