]give a proof by contradiction: let g be any directed graph in which every pair of nodes u and v has exactly one edge (either uv or u v but not both), and let w be a node with highest out-degree. then every node is reachable from w by a path of length 3 2.

When early motion pictures played in movie theaters, they were often accompanied by live organ or piano music. which of the following are the most likely reasons that this happened? (select all that apply). the music was provided to distract audience members from the loud sounds made when filmstrips were changed. the music accompanied the movies because the movies were silent and audiences were used to hearing music during plays in theaters. the music usually was played before, and sometimes after the movie, as an alternative form of entertainment. the music viewers to interpret the dramatic action in the films.