In a household with n people, there is a common sink that is filled with dirty dishes. Only 1 member of the household has to do the dishes. Each member obtains v units of utility if someone(anyone) does the dishes. The person that does the dishes pay a personal cost of c. That is, if person i does the dishes, then he obtains the payoff v — c; if person i does not do the dishes but at least one other person does, then person i gets v; finally, if none of the n members do the dishes, then person i obtains zero. Assume v >c Find the symmetric MNE of this game (let p be the probability that the person DOES NOT do the dishes).
a) p= (v/c)ni
b) p= (c/v) n=1
c) p= (c/v)-1
d) p= (v/c)1=n

Arestaurant chef made 1 1/2 jars of pasta sauce. each serving of pasta requires 1/2 of a jar of sauce. how many servings of pasta will the chef be able to prepare using the sauce?

What makes a trapezoid an isosceles trapezoid?

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality