The Mayor shall appoint the various department executives, subject to the approvals provided in this Charter, namely that of the Director of Law, Director of Finance, Director of Public Safety, Director of Parks, Recreation and Public Lands, and Director of Public Service, all within thirty (30) days after assuming office.  He shall make such other appointments as provided by this Charter.  In the case of resignation, death, or removal of any appointed official, the power of appointing a replacement shall remain with the Mayor providing such appointment is made within thirty (30) days.  These appointments of the Mayor, except as otherwise provided in this Charter, shall become official only when the Council has approved of the appointments by a two thirds (2/3) vote of all the members elected to Council.  If the Mayor submits the name of any person or persons for the above named offices or appointments, and the Council fails to act within thirty (30) days on approving or rejecting the name or names for appointment, the name or names of the Mayor's appointments shall become effective as though they had received the approved vote of the Council.  If the Council rejects any person or persons named as an appointee of the Mayor within the thirty (30) day period, it shall then become the duty of the Mayor to immediately make another appointment or appointments before or at the next regular Council meeting.  The Mayor shall be the chief conservator of the peace within the City, and shall see that all ordinances, resolutions and laws are faithfully obeyed and enforced.  The Council shall receive from the Mayor and the Director of Finance, on or before the thirtieth (30th) day of November of each year an annual estimate of revenues and expenditures for the succeeding year and he shall advise the Council as to the financial condition and needs of the Municipality including necessary  appropriation measures.  The Mayor, along with the Director of Finance, shall execute on behalf of the City, all contracts, conveyances, evidences of indebtedness, and other instruments to which the City is a party and shall at the first regular meeting in January report to Council concerning the affairs of the City.  (Amended November 8, 2005)