State governments have several responsibilities regarding public education. The applicable responsibilities from your list include:
- Running school boards: State governments often have oversight or a role in the governance of school boards.
- Providing funding: State governments are typically a primary source of funding for public education.
- Setting standards: States are responsible for establishing educational standards for K-12 education.
- Hiring teachers: While the actual hiring process may be conducted by local school districts, states often set certification and licensing requirements for teachers.
Therefore, all options listed are responsibilities that state governments have with respect to public education.