To subtract 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 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.

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

\( \frac{7 x 3}{2 x 3} \) - \( \frac{3 x 1}{6 x 1} \)

\( \frac{21}{6} \) - \( \frac{3}{6} \)

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

\( \frac{21 - 3}{6} \) = \( \frac{18}{6} \) = 3

The equation for this sequence is:

a_n = a_n-1 + 7

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 7
a₆ = 29 + 7
a₆ = 36

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

0.0005543 in scientific notation is 5.543 x 10^-4

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

vans = \( \frac{41}{12} \) = 3\(\frac{5}{12}\)

So, it will take 3 full vans and one partially full van to transport the entire team making a total of 4 vans.

The number of students taking German or Spanish is 11 + 13 = 24. Of that group of 24, 8 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 24 - 8 = 16 who are taking at least one language. 25 - 16 = 9 students who are not taking either language.