Ajay is going to invest his money into 222 different stocks. Both stocks are independent, and each stock has a 50\%50%50, percent chance of being successful and a 50\%50%50, percent chance of failing. Each stock will make Ajay \$500$500dollar sign, 500 if it succeeds or lose him \$500$500dollar sign, 500 if it fails

Jonathan can type 20 documents in 40 minutes ,and susan can type it in 30 minutes and jack can type it in 24 minutes working together ,how much time will it is take them type the same document

Solve the following pair of equations for x and y: ax/b_ by /a= a +b; ax - by = 2ab

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.