There shall be appointed by a majority of the City Council, on the nomination of the Mayor or any member of the City Council, a City Manager, a City Secretary, a Municipal Judge or Judges, a City Health Officer, a City Attorney, and other officers as may be required by State Constitution or state law, any of whom may be removed by a majority vote of the City Council. These appointive officers shall serve at the will of the City Council and may be removed, with or without cause, by a majority vote of the City Council, but not less than four (4) affirmative votes for removal. These appointive officers shall be responsible to the City Manager for the administration of his or her department and for carrying out and enforcement of the resolutions and ordinances of the City Council. The duties of such officers shall be as prescribed by state law, or ordinance or direction of the City Council. The compensation of such officers shall be set by the City Council.