Based on where the appalachian mountains are located which is the only river that runs through the range?

The Hudson river. C I hope this helps

C b/c The colorado river is in the west, whereas the Appalachian Mts, are in the East so not a. Ohio River doesn't cut through any mountain ranges and is essentially the border of Ohio. 

And the Hudson cuts through the Poconos, Adirondacks, and Appalachians, so C.

The sun's parallax would be 180 degrees, greater than which you can't get.  so a. would be your anwser