For which values of c is the topological space xc : = {(x, y) € c^2 e: x^2 - y^2 = c} a riemann surface? you do not need to explicitly construct charts, but you do need to prove your answer is correct. (warning: use the implicit function theorem to produce a complex structure. the hardest part is proving that x. is not a manifold for certain values of c. if you get stuck, try drawing a picture.)

At the olympic games, many events have several rounds of competition. one of these events is the men's 100-meter backstroke. the upper dot plot shows the times (in seconds) of the top 8 finishers in the final round of the 2012 olympics. the lower dot plot shows the times of the same 8 swimmers, but in the semifinal round. which pieces of information can be gathered from these dot plots? (remember that lower swim times are faster.) choose all answers that apply: a: the swimmers had faster times on average in the final round. b: the times in the final round vary noticeably more than the times in the semifinal round. c: none of the above.

In 2000, for a certain region, 27.1% of incoming college freshman characterized their political views as liberal, 23.1% as moderate, and 49.8% as conservative. for this year, a random sample of 400 incoming college freshman yielded the frequency distribution for political views shown below. a. determine the mode of the data. b. decide whether it would be appropriate to use either the mean or the median as a measure of center. explain your answer. political view frequency liberal 118 moderate 98 conservative 184 a. choose the correct answer below. select all that apply. a. the mode is moderate. b. the mode is liberal. c. the mode is conservative. d. there is no mode.

The hockey team has been great! in 2008, they won 20% more games than in 2007 in 2009 they won 50% more games than in 2008 what was their overall percentage increase from 2007 through2008?