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.

There are 3 5-passenger taxis available so that's 3 x 5 = 15 total seats. There are 20 people needing transportation leaving 20 - 15 = 5 who will have to find other transportation.

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:

0.0003334 in scientific notation is 3.334 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:

\( \frac{4}{100} \) x 5 = \( \frac{4 \times 5}{100} \) = \( \frac{20}{100} \) = 0.2 errors per hour

So, in an average hour, the machine will produce 5 - 0.2 = 4.8 error free parts.

The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 4.8 = 76.8 error free parts were produced yesterday.

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 30% the radius (and, consequently, the total area) increases by \( \frac{30\text{%}}{2} \) = 15%