I find the answers here to all be highly confusing, and completely off the mark. The real question is how many Amps does the CPAP draw, and how many Watts. This page says typical 53W and 104W peak for the Airsense 10:
https://www.easybreathe.com/AirSense-10-AutoSet-CPAP-Machine-with-HumidAir-p4381.html
I'm not sure how peak factors into normal use, but 53W at 12V is **ONLY** 4.4A, and nothing like 45A.
53W/12V = 4.4A
Then, if you're running off a 12V-to-120VAC inverter, factor in a bit of inefficiency, and then the typical draw will be maybe 5A, or 60W from the 12V batteries.
You don't need 2 gauge wire, and a common 300W inverter should be fine. Use the wires that come with it to connect to your batteries. I'd say best get a "pure sinewave" inverter to be safe, rather than the cheaper "modified" sinewave type.
So, now once you know the amperage draw, you can compute the AH in use, or
5A * 8Hr = 40AH draw from your 12V batteries over night.
That is consistent with your numbers, but the Amps are wrong. W=V*A, A=W/V, and AH=A*Hr.
EDIT: the other thing is Watts relate to power draw, and are "consistent" across different voltages. So, 60W=12V*5A is roughly 120V*(1/2 A). There is a fudge factor in relating AC to DC, but this gives you a usable estimate.