Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Patty is going to hire a makeup artist for a fashion show and is comparing prices. Vincent charges $23 as a booking fee and an additional $69 per hour. Reagan charges $38 per hour, plus a booking fee of $85. Depending on the length of the show, the cost could end up being the same for either artist. How long would the show be? What would the cost be?

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 ?