X = x 1 + ( x 2 − x 1 ) t , y = y 1 + ( y 2 − y 1 ) t where 0 ≤ t ≤ 1 describe the line segment that joins the points P 1 ( x 1 , y 1 ) and P 2 ( x 2 , y 2 ) . Use a graphing device to draw the triangle with vertices A ( 1 , 1 ) , B ( 4 , 4 ) , C ( 1 , 6 ) . Find the parametrization, including endpoints, and sketch to check. (Let x and y be in terms of t .)

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 ?