Which sentence uses capital letters correctly?
a. her ancestors immigrated to the united states from ireland four generations ago.
b. her ancestors immigrated to the united states from ireland four generations ago.
c. her ancestors immigrated to the united states from ireland four generations ago.

b. Her ancestors immigrated to the United States from Ireland four generations ago.

hey my good buddy lemme ask are u male or female? ?

the sentence that avoid faulty coordination is:

culture, which is well represented in philadelphia, plays a major role including theatre, music, and the visual arts.  

faulty coordination occurs when the writer gives equal importance two different ideas (clauses) which in fact are not equivalent. in order to correct a misplaced clause or idea, the writer can place less important or emphatic ideas in a relative clause as in the previous sentence.