The Transverse Tire Company produces all types of tires at its factory. Due to fixed costs associated with running the factory, the company starts with a loss of $200,000, or a profit of -$200,000, at the beginning of each month. The first major hurdle the company faces each month is to break even, or reach the point at which the profit is zero. The tires are sold in batches of 1000. The company earns $40,000 for each batch of tires they manufacture and sell 1) What are the independent and dependent quantities in this situation?

2) Write an equation to represent the profit the company will make when they manufacture and sell batches of tires.

3) What is the unit rate of change in this problem?

4) How much profit would the company make if they manufactured and sold 3 and one-half batches (3500 tires)?

5) How many batches of tires does the company have to manufacture and sell to have a profit of –$190,000?

The resumâ´es of two male applicants for a college teaching position in chemistry are placed in the same file as the resumâ´es of two female applicants. two positions become available, and the first, at the rank of assistant professor, is filled by selecting one of the four applicants at random. the second position, at the rank of instructor, is then filled by selecting at random one of the remaining three applicants. using the notation m2f1, for example, to denote the simple event that the first position is filled by the second male applicant and the second position is then filled by the first female applicant, (a) list the elements of a sample space s; (b) list the elements of s corresponding to event a that the position of assistant professor is filled by a male applicant; (c) list the elements of s corresponding to event b that exactly one of the two positions is filled by a male applicant; (d) list the elements of s corresponding to event c that neither position is filled by a male applicant; (e) list the elements of s corresponding to the event a â© b; (f) list the elements of s corresponding to the event a âş c; (g) construct a venn diagram to illustrate the intersections and unions of the events a, b, and c.