The number of students taking German or Spanish is 7 + 8 = 15. Of that group of 15, 5 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 15 - 5 = 10 who are taking at least one language. 22 - 10 = 12 students who are not taking either language.

Latoya scored 78% on the test meaning she earned 78% of the possible points on the test. There were 100 possible points on the test so she earned 100 x 0.78 = 78 points. Each question is worth 2 points so she got \( \frac{78}{2} \) = 39 questions right.

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

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

2 + (2 + 2) ÷ 2 x 5 - 3²
P: 2 + (4) ÷ 2 x 5 - 3²
E: 2 + 4 ÷ 2 x 5 - 9
MD: 2 + \( \frac{4}{2} \) x 5 - 9
MD: 2 + \( \frac{20}{2} \) - 9
AS: \( \frac{4}{2} \) + \( \frac{20}{2} \) - 9
AS: \( \frac{24}{2} \) - 9
AS: \( \frac{24 - 18}{2} \)
\( \frac{6}{2} \)
3

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.

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

\( \frac{6 x 5}{9 x 5} \) - \( \frac{2 x 3}{15 x 3} \)

\( \frac{30}{45} \) - \( \frac{6}{45} \)

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

\( \frac{30 - 6}{45} \) = \( \frac{24}{45} \) = \(\frac{8}{15}\)