The number of students taking German or Spanish is 14 + 12 = 26. Of that group of 26, 2 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 26 - 2 = 24 who are taking at least one language. 33 - 24 = 9 students who are not taking either language.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-5y⁵ + 6y⁵
(-5 + 6)y⁵
y⁵

The equation for this sequence is:

a_n = a_n-1 + 4(n - 1)

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 + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61

The amount of flour you need is (2\(\frac{1}{4}\) - \(\frac{3}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{18}{8} \) - \( \frac{3}{8} \)) cups
\( \frac{15}{8} \) cups
1\(\frac{7}{8}\) cups

To subtract 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:

\( \frac{4 x 3}{4 x 3} \) - \( \frac{7 x 1}{12 x 1} \)

\( \frac{12}{12} \) - \( \frac{7}{12} \)

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

\( \frac{12 - 7}{12} \) = \( \frac{5}{12} \) = \(\frac{5}{12}\)