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 7 = \( \frac{7 \times 7}{100} \) = \( \frac{49}{100} \) = 0.49 errors per hour

So, in an average hour, the machine will produce 7 - 0.49 = 6.51 error free parts.

The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 6.51 = 123.7 error free parts were produced yesterday.

The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.

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:

5,980,000 in scientific notation is 5.98 x 10⁶

If 47% of the town's 46,000 voters cast ballots the number of votes cast is:

(\( \frac{47}{100} \)) x 46,000 = \( \frac{2,162,000}{100} \) = 21,620

The mayor got 60% of the votes cast which is:

(\( \frac{60}{100} \)) x 21,620 = \( \frac{1,297,200}{100} \) = 12,972 votes.

Diane scored 83% on the test meaning she earned 83% of the possible points on the test. There were 120 possible points on the test so she earned 120 x 0.83 = 100 points. Each question is worth 4 points so she got \( \frac{100}{4} \) = 25 questions right.