There are 5 boys and 4 girls in my class. all of them are distinguishable. in how many ways can they be seated in a row of 9 chairs such that at least 3 girls are all next to each other?

Simplify (a/b - b/a) times (a - a^2/a+b) a - a^2/a=b is a mixed number

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.

Find the volume of the solid bounded by the plane z=0 and the paraboloid z=1-x^2 –y^2