There are no state laws regarding this. Generally, however, around the age of 12 is considered to be old enough; again that's in general. Much depends on the circumstances - how long are they going to babysit for, how many children, what are their ages, is it in a safe environment, how often, etc.
Basically, it is up to the adult in charge to make the decision as to whether or not the child is not only old enough but mature enough to handle all of this.
If in doubt, then you should probably not allow it.
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