Slaves did not just capitulate to their situation. what were some ways slaves
resisted? how did they demonstrate a sense of semi-independence or self- worth?
why did masters allow some of this behavior?

Some ways that slaves resisted slavery was by rebelling, being less productive at work, stealing from their owners, and sometimes actually harming their owners (or just other white people).  The slaves demonstrated a sense of semi-independence or self- worth through having their own subculture with their own unique music, having a religion and their own churches to tie them together, as well as celebrating their African roots and traditions. Slave masters allowed some of these behaviors so as to avoid their slaves becoming really aggressive towards them, as well as giving the slaves some "freedoms" encouraged and motivated slaves so they didn't get too hostile. 

Im pretty sure the answer is d.) is more densely populated.