1. Using the following map showing the temperature of certain cities on April 25 2018, • Seattle 51 Portland 54 • Minneapolis 44 •Chicae Detroitu New York City • San Francisco • Salt Lake City 39 •Denver 49 Baltimore 53 Washington, D.C. 52 Los Angeles 53 Phoenix 67 San Diego 57 Dallas 63 Austin 69 Houston 69 Miami 74 Bob argues that the average temperature of the United States is (51+54+49 +53+67+57+39+49+63+69+69+44+47+41+74+52 +53+56)/18 = 54.8°F. Alice, who is from the state of Rhode Island (a very small state) disagrees. She proposes that it would be better to take one city from each state, and take the average of those temperatures. Charlotte, who is from Texas (a large state) doesn't like this idea. She feels it is unfair. (a) Why could Charlotte feel this way? (No essays or formulas! Just 1-2 common sense sentences will suffice.) (b) If given the temperature from a city in each state, what is the formula that will most accurately give the average temperature of the United States? You'll probably want to use geographical areas of states. Say, for a state s, we can denote its area by A(s). (Hint: when taking Riemann sums, you don't necessarily need to subdivide into squares.) (c) If you are given the temperature in a town from each county in the U.S., what would be a similar to (1.b) formula for the average temperature in the U.S.? Generally speaking, comparing the estimates you obtain in (1.b) and here, which one do you expect to be closer to the true value of the average temperature?