Abag contains 4 blue coins and 8 red coins. a coin is removed at random and replaced by three of the other color.

part 2 out of 3
if the first coin removed is blue, what is the probability of drawing a red coin after three red coins are put in the bag to replace the blue one?

Consider a cube that has sides of length l. now consider putting the largest sphere you can inside this cube without any point on the sphere lying outside of the cube. the volume ratio -volume of the sphere/ volume of the cube is 1. 5.2 × 10−1 2. 3.8 × 10−1 3. 1.9 4. 2.5 × 10−1 5. 3.8

Two angles are complementary. the larger angle is 36 more than the smaller angle. what is the measure of the larger angle?

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.