(3 pts) Forf(x) =x3+ 2x2-x-4, use the Intermediate Value Theorem to determine

which interval must contain a zero off. A. Between-1 and 0 B. Between 0 and 1 C. Between 1 and 2 D. Between 2 and 3

(7 pts) Solve | 6-5x| > 1

(5 pts) Forz= 7-2iandw= 4 + 3i, findzw. That is, determine (7-2i)(4 + 3i) and

simplify as much as possible, writing the result in the forma+bi, whereaandbare real numbers.Show some work.

9. (10 pts) Consider the equation 5x2+ 5 = 6x. Find the complex solutions (real and non-real) of the equation and simplify as much as possible.Show algebraic work.

10. (12 pts) The line of best fit, the regression line, isy= 0.0433x-9.205, wherex= year andy= average Boston temperature in degrees. (a) Use the regression line to estimate the average Boston temperature in 1890, to the nearest tenth of a degree. Show some work. (b) Use the regression line to predict the average Boston temperature in 2018, to the nearest tenth of a degree. Show some work. (c) What is theslopeof the regression line? In a sentence, interpret what the slope is telling us, in the context of this real-world application. (d) In what year (to the nearest year) does the regression line predict an average Boston temperature of 60.0 degrees? Show work, solving an appropriate equation.

11. (20 pts) The cost, in dollars, for a company to producexwidgets is given byC(x) = 4000 + 4.00xforx0, and the price-demand function, in dollars per widget, isp(x) = 300.02xfor 0x1500. In Quiz 1, problem #7(d), we saw that the profit function for this scenario is P(x) =-4000 + 26x-0.02x2

(a) The profit function is a quadratic function and so its graph is a parabola. Does the parabola open up or down? __________

(b) Find the vertex of the profit functionP(x) using algebra.Show algebraic work.

(c) State the maximum profit and the number of widgets which yield that maximum profit:

The maximum profit is _______________ when ____________ widgets are produced and sold. (d) Determine the price to charge per widget in order to maximize profit. (e) Find and interpret the break-even points.