Question IV. It can be shown that for any three events A, B, and C. the probability that at least one of them will occur is given by P(AUBUC)-P(A) PB)P(C) Verify that this formula holds for the probabilities of the Venn Diagram below 0.24 0.06 0.19 0.0 0.160.11 0.09 0.11

Given the program below, fill in all necessary blanks: // This programs demonstrates a recursive function // that calculates Fibonacci numbers. #include int fib(int); int main() { cout << "The first 10 Fibonacci numbers are: \n"; for (int x = 0; x< ; x++) cout << fib )«< ""; << endl; } int (int n) { if <=0) return else if (n == 1) return ; fib(n - 1) + fib(n - ); }

For the following exercises, find the surface area of the volume generated when the following curves revolve around the y-axis. If you cannot evaluate the integral exactly, use your calculator to approximate it. 199. y = x2 from x = 0 to x = 2

For the following exercises, find the lengths of the functions of y over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. 181. y = 5 - 3x from y = 0 to y = 4 – 4

C. Which of the following organisms are most closely related? Are any two the same species? On what did you base your answer? 2.0 A B D C Rod Rod Coccus Rod + + Fermentative Oxidative Fermentative Fermentative Characteristics Morphology Gram Reaction Glucose utilization Cytochrome oxidase GC moles % Present Present Absent Absent 48-52 23-40 50-54 49-53

For this week's discussion, you are asked to generate a continuous and differentiable function f (2) with the following properties: • f(x) is decreasing at x = -6 • f(x) has a local minimum at x = -3 • f (x) has a local maximum at x = 3 Hints: • Use calculus! • Before specifying a function f (2), first determine requirements for its derivative f' (2). For example, one of the requirements is that f' (-3) = 0. • If you want to find a function g(x) such that g(-9) = 0 and g(8) = 0, then you could try g(x) = (x + 9) (x – 8). • If you have a possible function for f' (2), then use the techniques in Indefinite Integrals this Module to try a possible f (x). You can generate a plot of your function by clicking the plotting option (the page option with a "P" next to your function input). You may want to do this before clicking "How Did I Do?". Notice that the label "f(2) =" is already provided for you. Once you are ready to check your function, click "How Did I Do?" below (unlimited attempts). Please note that the bounds on the x-axis go from -6 to 6. f(x) = How Did I Do? Try Another

. Explain which types of market inefficiencies derive from monopolies. Use examples from the textbook to support your claims. • Describe the types of inefficiencies that derive from monopolistic competition. Use examples from the textbook to support your claims. How are monopolies and monopolistic competitive firms profitable? Use examples from the textbook . Explain which types of market inefficiencies derive from monopolies. Use examples from the textbook to support your claims. • Describe the types of inefficiencies that derive from monopolistic competition. Use examples from the textbook to support your claims. How are monopolies and monopolistic competitive firms profitable? Use examples from the textbook to support your analysis.