The number of students taking German or Spanish is 12 + 15 = 27. Of that group of 27, 9 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 27 - 9 = 18 who are taking at least one language. 33 - 18 = 15 students who are not taking either language.

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

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

6\( \sqrt{63} \) - 5\( \sqrt{7} \)
6\( \sqrt{9 \times 7} \) - 5\( \sqrt{7} \)
6\( \sqrt{3^2 \times 7} \) - 5\( \sqrt{7} \)
(6)(3)\( \sqrt{7} \) - 5\( \sqrt{7} \)
18\( \sqrt{7} \) - 5\( \sqrt{7} \)

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 prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.