A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:

49,000 fans x \( \frac{5}{6} \) = \( \frac{245000}{6} \) = 40,833 fans.

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:

8z⁵ - 1z⁵
(8 - 1)z⁵
7z⁵

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:

2,483,000 in scientific notation is 2.483 x 10⁶

49% of the water consumption is industrial use and 28% is personal use so (49% - 28%) = 21% more water is used for industrial purposes. 20,000 gallons are consumed daily so industry consumes \( \frac{21}{100} \) x 20,000 gallons = 4,200 gallons.

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 = \( 15mph \times 5h \)
75 miles