In making a fruit punch for a party, you mixed 1/2 gallon of grape juice with 1/5 gallon of orange juice. how many gallons of punch did you make?

Acertain population of bacteria demonstrates exponential growth doubles in size every 4 days. how long will it take the population to triple in size?

Acircus act has 3 times as many elephants as acrobats. jorge noticed that all together there were 56 legs in the circus ring. how many elephants were in the show?

Exercise: counting committees 0.0/2.0 puntos (calificable) we start with a pool of n people. a chaired committee consists of k≥1 members, out of whom one member is designated as the chairperson. the expression k(nk) can be interpreted as the number of possible chaired committees with k members. this is because we have (nk) choices for the k members, and once the members are chosen, there are then k choices for the chairperson. thus, c=∑k=1nk(nk) is the total number of possible chaired committees of any size. find the value of c (as a function of n ) by thinking about a different way of forming a chaired committee: first choose the chairperson, then choose the other members of the committee. the answer is of the form c=(α+nβ)2γn+δ. what are the values of α , β , γ , and δ ?