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 = \( \frac{100mi}{25mph} \)
4 hours

To subtract these radicals together their radicands must be the same:

8\( \sqrt{50} \) - 5\( \sqrt{2} \)
8\( \sqrt{25 \times 2} \) - 5\( \sqrt{2} \)
8\( \sqrt{5^2 \times 2} \) - 5\( \sqrt{2} \)
(8)(5)\( \sqrt{2} \) - 5\( \sqrt{2} \)
40\( \sqrt{2} \) - 5\( \sqrt{2} \)

Now that the radicands are identical, you can subtract them:

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{3!}{6!} \)
\( \frac{3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4} \)
\( \frac{1}{120} \)

A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:

49,000 fans x \( \frac{4}{5} \) = \( \frac{196000}{5} \) = 39,200 fans.