In which of the following forms of government does the city council hire someone to run the day-to-day operations of the city?

None of them.

The form of government where the city council hires someone to run the day-to-day operations of the city is known as a "Council-Manager" system. To determine if a particular form of government follows this model, we need to understand the different types of local government structures and identify the key characteristics of each.

1. Mayor-Council System: In this system, the city council is elected by the public, and the mayor is either elected separately or selected from among the council members. The mayor serves as both the political leader and the chief executive, responsible for managing the city's operations.

2. Council-Manager System: In this system, the city council is elected by the public, and a professional city manager is hired to oversee the day-to-day administrative tasks. The city manager is appointed by the council, and they work closely with elected officials to implement policies and manage city operations.

3. Commission System: This system involves a commission or board of elected officials who collectively manage various aspects of the city's responsibilities. Each commissioner is responsible for a specific area, such as finance, public works, or public safety.

Based on the descriptions above, the form of government where the city council hires someone to run the day-to-day operations is the Council-Manager System.

To determine if a specific city follows the Council-Manager system, you can research the local government structure and review the city's charter, bylaws, or official website. These sources usually contain information on the roles and responsibilities of city officials and provide insights into the decision-making processes of the local government. Additionally, contacting the city council or reaching out to local government agencies can provide accurate information regarding their governance structure.