Rap music feeds from Alternative

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Hey there! I was just listening to some music on my Zune on shuffle a little while ago. One of my favorite songs, 'Float On' by Modest Mouse, came on; followed by 'The Show Goes On' by Lupe Fiasco. I realized that these two songs were mearly identical in sense of musicality, but were in two completely differet genres. My question is how often do rap artists alter the songs from the Alternative genre and why is there such a nice connection between the two opposite genres?