To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 share.

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

\( \frac{6 x 5}{2 x 5} \) + \( \frac{3 x 1}{10 x 1} \)

\( \frac{30}{10} \) + \( \frac{3}{10} \)

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

\( \frac{30 + 3}{10} \) = \( \frac{33}{10} \) = 3\(\frac{3}{10}\)

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

vans = \( \frac{55}{9} \) = 6\(\frac{1}{9}\)

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

The number of students taking German or Spanish is 10 + 13 = 23. Of that group of 23, 7 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 23 - 7 = 16 who are taking at least one language. 29 - 16 = 13 students who are not taking either language.

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

2\( \sqrt{2} \) x 4\( \sqrt{2} \)
(2 x 4)\( \sqrt{2 \times 2} \)
8\( \sqrt{4} \)

Now we need to simplify the radical:

8\( \sqrt{4} \)
8\( \sqrt{2^2} \)
(8)(2)
16

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

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 25mph \times 8h \)
200 miles