The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. 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 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

4a⁷ x a⁶
(4 x 1)a^{(7 + 6)}
4a¹³

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:

5,410,000 in scientific notation is 5.41 x 10⁶

If 45% of the town's 21,000 voters cast ballots the number of votes cast is:

(\( \frac{45}{100} \)) x 21,000 = \( \frac{945,000}{100} \) = 9,450

The mayor got 67% of the votes cast which is:

(\( \frac{67}{100} \)) x 9,450 = \( \frac{633,150}{100} \) = 6,332 votes.

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

vans = \( \frac{52}{14} \) = 3\(\frac{5}{7}\)

So, it will take 3 full vans and one partially full van to transport the entire team making a total of 4 vans.