"She demonstrates that she knows some recipes."
Translation:Elle démontre qu'elle connaît des recettes.
I thought "connait" was for knowing people. But it works here, it seems. Is there a particular reason?
Connaître is always used for knowing people, but sometimes used for other things.
Generally, connaître is to know something in the sense of to be familiar with it, while savoir is used to know something in the sense of knowing a fact. That's why you always use connaître when you know a person or place (you don't know the person/place as a fact, you know them in the sense that you're familiar with them.)
In this case, she knows (as in, she's familiar with) some recipes, so connaître is used. If it was a factual statement about the recipe such "she knows that there's some sugar in the recipe", then it's a fact that she knows, and you would use savoir instead. ("Elle sait qu'il y a du sucre dans le recette.")
It seems both work in this case. I always thought that connait was for something that cannot ever be fully known. It seems that most proper nouns are placed with connait, such as people and places. It is because you can only be familiar with a person or place, and never know someone/some place completely.