The answer is simple in concept but can get complex in details. The inverter takes 12 volts DC IN and "inverts" it to 120 volts AC OUT.
The key formula is simple: Watts = Volts X Amps
Therefore, Volts = Watts / Amps, and Amps = Watts / Volts
Ignoring a bit of inefficiency (lost watts) in the inverter, and rounding the probably 117VAC to 120VAC and the probably 13VDC to 12VDC to make it simple, if you need to run a 600 watt coffee maker...
On 120VAC, 600 watts / 120 volts = 5 amps
On 12VDC, 600 watts / 12 volts = 50 amps
In round numbers the AMPS of current draw on the 12VDC battery is about 10 times the AMPS of current draw on the 120VAC power.
What makes the question complex is deciding how much current the battery can handle before it poops out.
Batteries are commonly rated in ampere-hours. If a battery is rated 250 ampere-hours and it is providing 50 amps, it can do so for 5 hours -- IN THEORY.
I'm using a coffee pot as a simple example, and 600 watts for simple math, but real coffee makers might draw more or less (mine draws about 350 watts because it doesn't have a warmer, it has a thermos carafe. This saves power making the coffee, and uses no power to keep it warm after it is made.
TV power varies depending on type, but might be 100 watts.
Coach batteries vary in power too, so my numbers are just for example.
And of course everything else that is sucking from the battery counts too, such as lights and an external TV amplifier or DVD or VCR or satellite, etc.
The devil is always in the details.
Final note: If an inverter is mounted in the coach, wired into the AC system, it might not run ALL the AC devices -- coach makers do odd things in this area, such as assuming you want to watch TV but not make coffee, or vice versa. Some people use external inverters at each device, matched to what the device needs.
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