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365 days/year
5/7 of these days are work days, or 260.7
We'll round up to 261 since we ignored leap years
261 days/year * 8 hours/day is 2088 hours/year
2088 hours/year divided by 12 months/year = 174 hours/month
Obviously, some months have one more work day than others, so that's still approximate.