Two circles with radii of 7 and 12 are drawn with the same center. The smaller inner circle is painted purple, and the part outside the smaller circle and inside the larger circle is painted yellow. What is the ratio of the areas painted yellow to the area painted purple?

From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 5 cm, 7 cm and 3 cm. Find the area of the triangle.

Mark measures the heights of 9 of his friends as follows (in centimetres) 123 , 141 , 149 , 120 , 123 , 143.7 , 119 , 140 , 150 What is the average of their heights?

n is a positive integer. Let's say that {n} denotes the sum of all the positive divisors of n except for n itself. For example, {4} = 1 + 2 = 3 and <8> = 1+2+4 = 7. What is {{{6}}}?