In a certain city only two newspapers $$A$$ and $$B$$ are published, it is known that $$25$$% of the city population reads $$A$$ and $$20$$% reads $$B$$ while $$8$$% reads both $$A$$ and $$B$$. It is also known that $$30$$% of those who read $$A$$ but not $$B$$ look into advertisements and $$40$$% of those who read $$B$$ but not $$A$$ look into advertisements while $$50$$% of those who read both $$A$$ and $$B$$ look into advertisements. What is the percentage of the population that reads an advertisement?

$$A, B, C$$ and $$D,$$ are four points in a plane with position vectors $$a, b, c$$ and $$d$$ respectively such that $$$\left( {\overrightarrow a - \overrightarrow d } \right)\left( {\overrightarrow b - \overrightarrow c } \right) = \left( {\overrightarrow b - \overrightarrow d } \right)\left( {\overrightarrow c - \overrightarrow a } \right) = 0$$$

The point $$D,$$ then, is the ................ of the triangle $$ABC.$$

The points with position vectors $$a+b,$$ $$a-b,$$ and $$a+kb$$ are collinear for all real values of $$k.$$

If the complex numbers, $${Z_1},{Z_2}$$ and $${Z_3}$$ represent the vertics of an equilateral triangle such that
$$\left| {{Z_1}} \right| = \left| {{Z_2}} \right| = \left| {{Z_3}} \right|$$ then $${Z_1} + {Z_2} + {Z_3} = 0.$$