What is the difference between a direct democracy and a republic?

I suck at social studies

Which were accomplishments of jane addams? check all that apply. she established hull house. she founded the sierra club. she served on chicago’s board of education. she published a book of photographs showing the urban poor. she won the nobel peace prize in 1931.

1. the responsibilities of the u.s. federal reserve system include overseeing the banking system and regulating the quantity of money in the economy setting the level of real interest rates working with congress to devise a financial plan for the country and execute the president's orders calculating and reporting the unemployment rate 2. to increase the supply of money when the economy is weak, the fed closes banks reduces inflation sells bonds buys bonds 3. the federal funds rate is the short-term interest rate that banks charge their best customers when borrowing banks earn on savings accounts with the fed banks charge each other when borrowing or lending to each other the fed charges banks when borrowing 4. when the fed increases the money supply and consequently lowers interest rates, the value of the dollar will rise by more in the market for foreign exchange, all else equal will fall, all else equal is not impacted by fed policy will rise, all else equal

What is the rule relating the ratio of marginal utility to prices of two goods at the optimal choice? explain why, if this rule does not hold, the choice cannot be utility-maximizing.