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Re: AFCI Circuit Breakers
Edited to fix the colors of the test buttons
I think QO and Homeline breakers have more or less the same innards just in a different package. I have 2 QO AFCI breakers that I installed about 20 years ago and I don't think I have ever had them nuisance trip. They are on the 2 circuits that run most of the lighting and general purpose receptacles on the main floor of my house so they are the bedroom, living room, and the 2nd bedroom that has my ham shack in it. When I had an issue with an antenna that wasn't balanced that put a lot of RF in the shack that tripped a couple GFCIs, caused the CO detector to save a reding of like 486 ppm, caused the thermostat to reboot and caused the garage door operator to lock up, they didn't trip. They are whatever type has the light blue test button.
I did have an AFCI receptacle trip a few times with a dehumidifier plugged in to it but it isn't clear that there wasn't a problem with that dehumidifier, it ultimately had its refrigerant escape and it has never tripped on the Aprilaire dehumidifier.
In the last 5 years or so I added a circuit for a bidet seat in my bathroom that is on a afci/gfci breaker and that has nuisance tripped but only when there is a power outage, either something about the power going out or coming back on causes it to see something it doesn't like. The last time it tripped there was nothing connected to the circuit, it was just romex to a single receptacle but it was when the power went out and came back on. It has a purple test button.

Re: AFCI Circuit Breakers
I use Square D QO breakers. Only the one issue noted previously with one breaker not liking one particular vacuum cleaner.

Re: AFCI Circuit Breakers
Back to the OP. I think Eaton has some odball designs of AFCI breakers. They I think have a breaker that has a neutral connection for the breaker but not for the load. I didn't look in to this too far, maybe i will now, but they may be for use for the rule in the code about a certain type of breaker in the panel allows you to use an AFCI receptacle to meet the requirement in combination or they may have just been trying to get away with not having a neutral load connection. Of course everyone has a bad batch of product sometime too. I don't know that I would take accounts of people having problems with specific models of AFCI breaker as an inherent problem with the technology.
Also, refrigerant and oil are nonpolar. There should be no leakage current in a properly designed compressor. I more suspect that issues with refrigerators and GFCI trips have to do with wiring and terminals that aren't adequately protected from condensate and ice.

Re: Need Help Sizing Boiler for Complex (for me) Situation in Minnesota
Yes, though outdoor temp is largely irrelevant for a basement wit heated space above. The surface area of all the concrete/CMU walls and slab in a typical fully buried basement would average maybe 50* if unheated, so the actual makeup is much less than the upper level which may be exposed to -30* outdoor temps if left unheated. The differential required to be overcome by the heat loss for your upper level is approaching 100* while the differential for the basement is only maybe 20*- theoretically only needing 20% of the amount of BTU to keep the same indoor temp. Even if the basement needed 10 BTU/SF at design, that would dictate the upper level(s) would need maybe 50, which is all but unheard of unless you can feel the wind blow through the house.

Re: Surprise gas line behind wall sconce
This definitely looks like an old gas line. My house was built in 1899. When we redid the electricity, behind each wall sconce, there was an old gas line. I traced all the gas line back down to the basement and all the way up to the attic.
Re: Surprise gas line behind wall sconce
I have a house in North Eastern NJ 30 mins outside of NYC built in 1927 and I found one of those cast iron mounts behind a flush mount in a bedroom. I have the same cloth buffered rubber BX in my house where it hadn’t been replaced during renovations by the previous owner.
I wound up removing the cast iron mount (mine had no connected gas) and replacing it with an old work fan box and romex back to the switch. I know this isn’t to code but did check for ground and I have it (yes I’ve read the story’s of high resistance grounding on BX causing it to glow like a toaster coil when there’s a fault) and I also replaced the breaker with an AFCI. I didn’t like the idea of having the BX leads in their condition living in the canopy of the fixture attached to a mount that wasn’t designed to carry the fixture. I was laminating my ceiling so I wasn’t concerned about damage, I appreciate that your case is likely different than mine in terms of total work.
What I found interesting is I removed a portion of the BX from that circuit and once you got 6 inches or more from the fixture end of the circuit, the leads were in really good condition below the sheathing. The rubber was very pliable and didn’t crack when you bent it. There was also was what appeared to be a very light gauge bonding strip inside the sheathing so I’m not sure if this wiring was circa 1927 or newer
I would say if yours isn’t connected to gas, I’d remove it and see if you couldn’t get the wiring into a metal old work box, use a anti short bushing, and check for ground continuity.
Re: Math Problem
Divide it up into person/days, i.e. 1 person 12 days = 12 PDs, 2 people 4 days = 8 PDs. Divide the total cost ($3,572) by the total number of PDs, then assign individual cost by the PDs used.

Re: Math Problem
Ratio is correct.
To put it into algebra. For each person staying (a-g) replace the letter with the number of nights they are staying so:
(a+b+c+d+e+f+g) * x = $3,572
where x is the cost per person-night.
x = $3,572 / (a+b+c+d+e+f+g)
Then the actual cost per person is
a*x = Cost for a
b*x = Cost for b
etc

Re: OT Electric: Hedgetrimmer & Other Ext Cord Choices
My refrigerators are wired with 18 gauge wire and plugged into a 20A circuit.
Many modern refrigerators, lamps etc are still wired with 18 gauge wire, 16 if you're lucky.
A 16 gauge ungrounded cord is perfectly acceptable.
If you draw 15 amps on that 16 gauge cord over 50 feet all that's going to happen is excessive voltage drop and the cord will feel warm.

Re: OT Electric: Hedgetrimmer & Other Ext Cord Choices
16 gauge cord is fine on a 15 amp circuit especially with the small load you have. Using a larger cord with a short piece of 16 gauge is a good idea as it will limit voltage drop although probably not necessary with the small load.
Plug into a GFCI receptacle if you can.
The trimmer is not internally grounded it is considered double insulated.