State governments have several responsibilities with respect to public education. The correct selections from your list are:
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Hiring teachers - State governments play a role in setting certification requirements and hiring at the state level, though local school districts handle most hiring.
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Running school boards - While school boards are typically local entities, state governments provide oversight and support, sometimes influencing their operations.
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Providing funding - State governments are responsible for allocating funds to education, including direct funding to school districts.
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Setting standards - State governments establish educational standards that schools must meet for curriculum and assessments.
Thus, all of the options presented are related to the responsibilities of state governments in public education.