Latoya scored 86% on the test meaning she earned 86% of the possible points on the test. There were 150 possible points on the test so she earned 150 x 0.86 = 129 points. Each question is worth 3 points so she got \( \frac{129}{3} \) = 43 questions right.

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:

43,000 fans x \( \frac{5}{6} \) = \( \frac{215000}{6} \) = 35,833 fans.

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:

2,019,000 in scientific notation is 2.019 x 10⁶

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 5 = \( \frac{9 \times 5}{100} \) = \( \frac{45}{100} \) = 0.45 errors per hour

So, in an average hour, the machine will produce 5 - 0.45 = 4.55 error free parts.

The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 4.55 = 68.3 error free parts were produced yesterday.

By buying two shirts, Roger will save $48 x \( \frac{20}{100} \) = \( \frac{$48 x 20}{100} \) = \( \frac{$960}{100} \) = $9.60 on the second shirt.