The responsibilities and duties of the Mayor are to:
(a) Serve as the legal and ceremonial head and chief executive officer of the City. The Mayor, by right, shall be permitted to speak on and vote on all proceedings of the Council, but shall have no veto power. The Mayor shall be the presiding officer of the Council.
(b) Authenticate by signing such instruments as the Council, this Charter, or the laws of the State and the United States require.
(c) Exercise only such powers as State law, this Charter, or the Council shall specifically confer upon or require of the office.
(d) Be a member ex-officio of such other boards as the Council requires or permits by ordinance or laws of this State.
(e) The Mayor shall nominate persons to fill vacancies on boards and councils in not more than 45 days after the date a vacancy first occurs. The Mayor shall notify the Council of each nomination at least 15 days prior to the meeting at which the Council is to consider a nomination. Any such nomination shall become effective only upon approval of the Council. If the Council does not approve or reject the nomination at its first meeting following the 15-day notification period, the nominee shall be considered as having been approved. By majority vote the Council may waive the 15-day notification requirement of this subsection.