4. Suppose a study indicates that the distribution of income for plumbers is given by the Lorenz curve .        (a) Find the Gini Index for plumbers.         (b) Suppose the Gini index for roofers is 0.32. Which profession has more equal income distribution?

1. Calculate each integral. You do not need to simplify your answer. Show all work.     (a) 

6. For the following problem we refer to the graph of below. All curved lines in the graph are parts of circles.     (a) Calculate

(e) i: True or False.

Evaluate the following improper integral or show that it is divergent. If the integral converges, compute the value, but you do not need to simplify your numerical answer. Show all work. 

(c) Consider the graph of the demand function and the supply function below. Which area represents the producers’ surplus at demand level A?

What is the difference between an origin and an insertion? Describe one muscle and how it uses its origin and insertion to produce a specific movement. Bullet your answer please. No long lines

What is depolarization? Which ion is associated with depolarization? How and where does this ion move during depolarization? Bullet your answer please. No long lines.

Describe the processes of depolarization and repolarization. In each process, show which ions moves during the process and in which to direction does it move? How does the membrane’s voltage change in each of the depolarization and repolarization? Please bullet your answers. No long lines!

What is the primary function of the Circle of Willis?