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?

Students at a high school were asked about their favorite outdoor activity. the results are shown in the two-way frequency table below. fishing camping canoeing skiing total boys 36 44 13 25 118 girls 34 37 22 20 113 total 70 81 35 45 231 select all the statements that are true based on the given table. more girls chose camping as their favorite outdoor activity than boys. more girls chose canoeing as their favorite outdoor activity than those who chose skiing. more boys chose skiing as their favorite outdoor activity than girls. there were more boys surveyed than girls. twice as many students chose canoeing as their favorite outdoor activity than those who chose fishing. more students chose camping as their favorite outdoor activity than the combined number of students who chose canoeing or skiing.