In a bag there are pink buttons, yellow buttons and blue buttons. There are five times as many pink buttons as yellow buttons.
number of yellow buttons : number of blue buttons = 4 : 7

One button is selected at random.
Work out the probability that the button is either pink or blue.
Give your answer as a fraction in its simplest form.

Through non-collinear points there is exactly one plane.

You are designing a rectangular pet pen for your new baby puppy. you have 30 feet of fencing you would like the fencing to be 6 1/3 feet longer than the width

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.