Final answer:
In New York City, the Mayor is responsible for appointing members of the Panel for Educational Policy, which functions as the city's education board.
Step-by-step explanation:
The members of the New York Board of Education, like similar education boards, are typically appointed by local authorities. In the context of New York City, the Mayor of New York appoints the schools chancellor and the members of the New York City Panel for Educational Policy, which replaces the traditional notion of a board of education. Therefore, for New York City, the answer is B. The Mayor of New York. This reflects the general principle that the governance of public education at the city level is often vested in municipal authorities and not at the state or federal level.