The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. 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 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{175mi}{35mph} \)
5 hours

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{74}{7} \) = 10\(\frac{4}{7}\)

So, it will take 10 full vans and one partially full van to transport the entire team making a total of 11 vans.

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:

0.0005803 in scientific notation is 5.803 x 10^-4

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 9 = \( \frac{7 \times 9}{100} \) = \( \frac{63}{100} \) = 0.63 errors per hour

So, in an average hour, the machine will produce 9 - 0.63 = 8.37 error free parts.

The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 8.37 = 150.7 error free parts were produced yesterday.