If 41% of the town's 45,000 voters cast ballots the number of votes cast is:

(\( \frac{41}{100} \)) x 45,000 = \( \frac{1,845,000}{100} \) = 18,450

The mayor got 65% of the votes cast which is:

(\( \frac{65}{100} \)) x 18,450 = \( \frac{1,199,250}{100} \) = 11,993 votes.

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

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 25mph \times 4h \)
100 miles

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-9y³ - 2y³
(-9 - 2)y³
-11y³

The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. 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 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.