Questions: Which of the following does a strong mayor not have the authority to do? Appoint a commission to investigate a matter of great importance to you Direct city departments to take actions related to certain matters of importance Propose a city ordinance that meets a policy priority of your office

The answer is: Appoint a commission to investigate a matter of great importance to you.

Explanation for each option:

1. Appoint a commission to investigate a matter of great importance to you: This is the correct answer because, typically, a strong mayor does not have the unilateral authority to appoint a commission. Such actions often require approval from the city council or other governing bodies to ensure checks and balances in municipal governance.

2. Direct city departments to take actions related to certain matters of importance: In a strong mayor system, the mayor usually has significant executive powers, including the ability to direct city departments. This is part of the mayor's role in managing the day-to-day operations of the city.

3. Propose a city ordinance that meets a policy priority of your office: A strong mayor can propose ordinances as part of their legislative role. While the mayor cannot unilaterally enact ordinances (as this requires council approval), they can certainly propose them to address policy priorities.