As others have mentioned, you don't calculate the resistances - because you don't (and can't) use resistances for doing this.
You first need to decide exactly what you're wanting to do, what the current requirements are for the different parts, and what battery life you expect to get.
Assuming you're talking about 4 x 9V PP3 size batteries, then those are far too small for feeding motors (and probably the pump?), but one should be fine for feeding a micro-controller - although why do you think it's 10V?, or is it a board (such as an Arduino?).