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

You have 5 out of the total of 250 raffle tickets sold so you have a (\( \frac{5}{250} \)) x 100 = \( \frac{5 \times 100}{250} \) = \( \frac{500}{250} \) = 2% chance to win the raffle.

First, solve for \( \left|a - 1\right| \):

\( \left|a - 1\right| \) - 7 = 9
\( \left|a - 1\right| \) = 9 + 7
\( \left|a - 1\right| \) = 16

The value inside the absolute value brackets can be either positive or negative so (a - 1) must equal + 16 or -16 for \( \left|a - 1\right| \) to equal 16:

So, a = -15 or a = 17.

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

vans = \( \frac{65}{12} \) = 5\(\frac{5}{12}\)

So, it will take 5 full vans and one partially full van to transport the entire team making a total of 6 vans.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 12 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{2 x 3}{4 x 3} \) + \( \frac{2 x 1}{12 x 1} \)

\( \frac{6}{12} \) + \( \frac{2}{12} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{6 + 2}{12} \) = \( \frac{8}{12} \) = \(\frac{2}{3}\)