The number of students taking German or Spanish is 15 + 7 = 22. Of that group of 22, 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 22 - 2 = 20 who are taking at least one language. 28 - 20 = 8 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:

-3z² + 5z²
(-3 + 5)z²
2z²

First, solve for \( \left|a - 4\right| \):

\( \left|a - 4\right| \) - 6 = 7
\( \left|a - 4\right| \) = 7 + 6
\( \left|a - 4\right| \) = 13

The value inside the absolute value brackets can be either positive or negative so (a - 4) must equal + 13 or -13 for \( \left|a - 4\right| \) to equal 13:

So, a = -9 or a = 17.

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 50% the radius (and, consequently, the total area) increases by \( \frac{50\text{%}}{2} \) = 25%

To divide fractions, invert the second fraction and then multiply:

\( \frac{3}{5} \) ÷ \( \frac{2}{8} \) = \( \frac{3}{5} \) x \( \frac{8}{2} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{5} \) x \( \frac{8}{2} \) = \( \frac{3 x 8}{5 x 2} \) = \( \frac{24}{10} \) = 2\(\frac{2}{5}\)