You and your n-1 roommates each have five hours of free time you could spend cleaning your apartment. you all dislike cleaning, but you all like having a clean apartment: each person's payoff is the total hours spent by everyone cleaning, minus a number c times the hours spent individually cleaning. that is, assume everyone chooses simultaneously how much time to spend cleaning. find the nash equilibrium if c > 1

1. there are 25 students who started computer programming in elementary school and 25 students who started computer programming in middle school. the first group had a mean final project grade of 95% and the second group had a mean final project grade of 92%. the line plot shows the differences after 10 rerandomizations. determine whether the difference in the means of the two groups is significant based on the line plot. explain your answer.

Let f(x)=2x and g(x)=2x. graph the functions on the same coordinate plane. what are the solutions to the equation f(x)=g(x) ?me asap

Agrasshopper weighs 0.89 grams. express the grasshopper’s weight in scientific notation.