You have 15 out of the total of 300 raffle tickets sold so you have a (\( \frac{15}{300} \)) x 100 = \( \frac{15 \times 100}{300} \) = \( \frac{1500}{300} \) = 5% chance to win the raffle.

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{49}{8} \) = 6\(\frac{1}{8}\)

So, it will take 6 full vans and one partially full van to transport the entire team making a total of 7 vans.

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

To multiply terms with radicals, multiply the coefficients and radicands separately:

2\( \sqrt{4} \) x 8\( \sqrt{6} \)
(2 x 8)\( \sqrt{4 \times 6} \)
16\( \sqrt{24} \)

Now we need to simplify the radical:

16\( \sqrt{24} \)
16\( \sqrt{6 \times 4} \)
16\( \sqrt{6 \times 2^2} \)
(16)(2)\( \sqrt{6} \)
32\( \sqrt{6} \)

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 24 meters so the equation becomes: 2w + 2h = 24.

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

2w + 2h = 24
w + h = \( \frac{24}{2} \)
w + h = 12
w = 12 - h

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

w = 12 - 2w
3w = 12
w = \( \frac{12}{3} \)
w = 4

Since h = 2w that makes h = (2 x 4) = 8 and the area = h x w = 4 x 8 = 32 m²