(*100 POINTS*) BE FAIR PLSIn order to host track and field competitions, a 400-meter track needs to be created. A typical Olympic track looks like the one on the picture.

a) Show that the runner who runs in the inside lane runs 400 meters.
b) All other runners in a 400 meters race start a little further ahead since their lane is a little longer. If the radius of lane 2 (the one beside the inside lane) is 37.92 meters, find how much of a stagger (head start) the lane 2 runner should be given. Round your answer to the nearest hundredth.

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.