I'm confused on what point-of-view Ten Cents a Dance is in. What is it?
To begin, one needs to understand what the different points-of-view are in any text. There are three main points-of-view: first-person, second-person, and third-person.
In a first-person point-of-view, the narrator speaks from their own perspective. This is always denoted by the use of "I" in the text.
Second-person is denoted by the narrator's use of "you." This perspective is rarely used in texts given it tends to alienate some readers. (For example, if the narrator is talking to the reader and says "you" regarding a circumstance that the reader cannot relate to (say giving birth) male readers will fail to engage and feel alienated by the narrator and story.)
A third-person narrator tells a story from "outside" of those involved. What this means is that the narrator is not involved in the story and offers what they "see" for the reader.
Al of that being said, the main clue as to the point-of-view of the novel is found on the opening page. The last line of the first paragraph the following is found: "I didn't recognize a single person."
Given that the narrator uses the pronoun "I," the text is written in first-person.