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 6 = \( \frac{7 \times 6}{100} \) = \( \frac{42}{100} \) = 0.42 errors per hour

So, in an average hour, the machine will produce 6 - 0.42 = 5.58 error free parts.

The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 5.58 = 100.4 error free parts were produced yesterday.

To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 300 meters to kilometers, divide the distance by 1000 to get 0.3km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.3km + 20.9km + 11.4km
total distance = 32.6km

A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:

41,000 fans x \( \frac{5}{6} \) = \( \frac{205000}{6} \) = 34,167 fans.

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:

-6x⁵ - 1x⁵
(-6 - 1)x⁵
-7x⁵

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).