$(1)$ If the assets of a business are $$400,000$ and the liabilities are $$150,000,$ how much is the equity?

$(2)$ If the equity in a business is $$100,000$ and the liabilities are $$190,000,$ how much are the assets?

$(3)$ A company reported monthly revenues of $$340,000$ and monthly expenses of $$75,000.$ What is the result of operations for the month?

$(4)$ If the beginning balance of retained earnings is $$170,000,$ revenue is $$65,000,$ expenses total $$20,000,$ and the company declares and pays a $$10,000$ dividend, what is the ending balance of retained earnings?