The action of the Board of Aldermen shall require the approval of the Mayor, except as herein otherwise provided, for the enacting of all ordinances and bylaws and the awarding of any contracts, the appointment of any officers or committees, or the passing of any resolution. If the Mayor shall approve any ordinance, by-law, resolution, appointment, or contract made or voted by the City Council, the same shall be reduced to writing and the Mayor shall sign the same. If he or she does not sign the same he or she shall return it with his or her objections in writing to the Board of Aldermen at their next regular meeting, provided he or she shall have not less than one week to consider such ordinance, by-law, resolution, appointment, or contract. The Board of Aldermen shall then proceed to consider such ordinance, by-law, resolution, contract, or appointment, and if, upon such reconsideration, three-fourths of the whole number of aldermen shall vote in favor of the same it shall be valid and take effect, notwithstanding the objection of the Mayor. If any such ordinance, by-law, resolution, appointment, or contract shall not be returned by the Mayor to the Board of Aldermen at their next regular meeting after the period of one week has elapsed after he or she shall have received it, the same shall be valid and take effect without his or her approval. The fiscal year for all departments of said City shall begin on July 1st and end on the following June 30th.