Consider a population of voters uniformly distributed along the ideological spectrum from left (x = 0) to right (x = 1). each of the candidates for a single office simultaneously chooses a campaign platform (i. e., a point on the line between x = 0 and x = 1). the voters observe the candidates choices, and each voter votes for the candidate whose platform is closest to the voters position on the spectrum. if there are two candidates and they choose platforms x1 = 0.3 and x2 = 0.6, for example, then all voters to the left of x = 0.45 vote for candidate 1, all those to the right vote for candidate 2, and candidate 2 wins the election with 55% of vote. suppose that the candidates care only about being elected. if there are two candidates, what is the pure strategy nash equilibrium?

Miss henderson wants to build a fence around a rectangular garden in her backyard in the scale drawing the perimeter of the garden is 14 in of the actual length of a b is 20 ft how many feet of fencing what you need

The biologist has a second culture to examine. she knows that the population of the culture doubles every 15 minutes. after 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. a) what was the size of the initial population? b) predict the size of the culture at t=3 hours. what was the size of the population at 40 minutes? explain and justify your answers. c) create a graph of the population as a function of time. find an equation that can be used to predict the size of the population at any time t. d) examine the rate at which the bacteria culture is growing. how fast is the culture growing after 1 hour? after 1.5 hours? after 2 hours? use a time interval of h = 0.01 hours to estimate these rates. interpret these rates in terms of the context of the problem situation. how do these three rates compare?

Acollection of nickels and quarters is worth $2.85. there are 3 more nickels than quarters.how many nickels and quarters are there?