four friends share a chocolate cake: Theresa eats 1/2 while Linnea eats 1/3 of the cake. Felix and john share the rest of the cake how much of the chocolate cake john gets

During a bike challenge riders have to collect various colored ribbons each 1/2 mile they collect a red ribbon each eighth mile they collect a green ribbon and each quarter mile they collect a blue ribbion wich colors of ribion will be collected at the 3/4 markrer

If the ratio of sum of the first m and n terms of an ap is m2 : n2 , show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1).

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.