You have 12 out of the total of 150 raffle tickets sold so you have a (\( \frac{12}{150} \)) x 100 = \( \frac{12 \times 100}{150} \) = \( \frac{1200}{150} \) = 8% chance to win the raffle.

The number of students taking German or Spanish is 10 + 8 = 18. Of that group of 18, 3 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 18 - 3 = 15 who are taking at least one language. 22 - 15 = 7 students who are not taking either language.

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 30 meters so the equation becomes: 2w + 2h = 30.

Putting these two equations together and solving for width (w):

2w + 2h = 30
w + h = \( \frac{30}{2} \)
w + h = 15
w = 15 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 15 - 2w
3w = 15
w = \( \frac{15}{3} \)
w = 5

Since h = 2w that makes h = (2 x 5) = 10 and the area = h x w = 5 x 10 = 50 m²

The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 3 factors [1, 2, 4] making 4 the greatest factor 32 and 60 have in common.

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

8\( \sqrt{48} \) - 8\( \sqrt{3} \)
8\( \sqrt{16 \times 3} \) - 8\( \sqrt{3} \)
8\( \sqrt{4^2 \times 3} \) - 8\( \sqrt{3} \)
(8)(4)\( \sqrt{3} \) - 8\( \sqrt{3} \)
32\( \sqrt{3} \) - 8\( \sqrt{3} \)

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