ballcock nut

I was looking at under my bathroom sinks to start replacing the faucets and the water supply is hooked up with the hoses that are used for toilets. They have the 7/8" ballcock nuts on the end. Another problem is the union that the hose is attached to the shutoff valve is all one piece. The hose...

This one should be an easy answer, but I can't seem to find it (I'm probably not using the right search terms...), so any help/redirection would be appreciated! I'm putting in a shower-over-bath in an alcove, and, lo and behold, after the tiler put in the tile, when I came back to put the final...