For the Fibonacci sequence, prove the formula u²_n+1 = u_n u_n+2 + (-1)ⁿ

Q-1

# of workers   Output (flags(

0 0

1         50

2       110

3 180

4 260

5            350

The table shows the number of flags that can be made per month depending on the number of workers at Acme Flag Company. Does the Acme Flag Company experience the law of diminishing returns in the table above?

Q-2

The major characteristic of a monopoly is

Q-3

Ceteris paribus, the demand curve faced by a firm that is a monopoly will be ______the demand curve faced by a firm in perfect competition.

Q-4

As output increases, marginal cost

Q-5

   # of workers   Output (flags)

      0    0

1     50

2 110

  3    180

4 260

3    350

The table shows the number of flags that can be made per month depending on the number of workers at Acme Flag Company. The price that Acme can charge for flags is $20. What is the average product of the 4th worker?

Q-7

Long-run competitive equilibrium implies that

Q-9

Which of the following statement is true?

Q-11

A price ceiling _______ output and ________ price in a monopoly market.

Q-13

Economic theory suggests that a monopoly is the best form of business organization when

Q-15

If a local movie theater is a monopolist, price discrimination means that;

Q-16

Monopolies generally offer consumers ___ and ____ than competitive firms.

Q-16

f output changes in fixed proportion to a change in all of a firm's productive resources, the firm has

Q-17

Profits for the profit maximizing monopolist will equal

Q-18

Unlike a firm in perfect competition, a monopolist may be able to

20

he point of diminishing returns occur at the point where

Page 1 of 2 Case Study 1 A New “Garcia” on the Block Garcia Gonzalez is ready to start a new career. After spending 30 years as a market researcher and inspired by the success of Starbucks, he is ready to enter the coffee shop business. However, before opening his first shop, he realizes that a great deal of research is needed. He has some key questions in mind. ? What markets in the United States hold the most promise for a new coffee shop? ? What type of location is best for a coffee shop? ? What is it that makes a coffee shop popular? ? What coffee do Americans prefer? A quick trip to the Internet reveals more previous research on coffee, markets, and related materials than he expected. Many studies address taste. For example, he finds several studies that in one way or another compare the taste of different coffee shop coffees. Most commonly, they compare the taste of coffee from Starbucks against coffee from McDonald’s, Dunkin’ Donuts, Burger King, and sometimes a local competitor. However, it becomes difficult to draw a conclusion as the results seem to be inconsistent. ? One study had a headline that poked fun at Starbucks’ high priced coffee. The author of this study personally purchased coffee to go at four places, took them to his office, tasted them, made notes and then drew conclusions. All the coffee was tasted black with no sugar. Just cups of Garcia. He reached the conclusion that McDonald’s Premium Coffee (at about $1.50 a cup), tasted nearly as good as Starbucks House Blend (at about $1.70 a cup), both of which were much better than either Dunkin’ Donuts (at about $1.20) or Burger King (less than $1). This study argued that McDonald’s was best, all things considered. ? Another study was written up by a good critic who was simply interested in identifying the best-tasting coffee. Again, he tasted them all black with nothing added. Each cup of coffee was consumed in the urban location near the inner city center in which he lived. He reached the conclusion that Starbucks’ coffee had the best flavor although it showed room for improvement. McDonald’s premium coffee was not as good, but it was better than the other two. Dunkin’ Donuts coffee had reasonably unobjectionable taste but was very weak and watery. The Burger King coffee was simply not very good. ? Yet another study talked about Starbucks becoming a huge company and how it has lost touch with the common coffee shop coffee customer. The researchers stood outside a small organic specialty shop and interviewed 100 consumers as they exited the shop. They asked, “Which coffee do you prefer?” The results showed a preference for a local coffee, tea, and incense shop, and otherwise put Starbucks last behind McDonald’s, Burger King, and Dunkin’ Donuts. ? Still another study compared the coffee-drinking experience. A sample of 50 consumers in Edinburg, Texas, were interviewed and asked to list the coffee shop they frequented Page 2 of 2 most. Starbucks was listed by more consumers than any other place. A small percentage listed Dunkin’ Donuts but none listed McDonald’s, despite their efforts at creating a premium coffee experience. The study did not ask consumers to compare the tastes of the coffee across the different places. Garcia also wants to find data showing coffee consumption patterns and the number of coffee shops around the United States, so he spends time looking for data on the Internet. His searches don’t reveal anything satisfying. As Garcia ponders how to go about starting “A Cup of Garcia,” he wonders about the relevance of this previous research. Is it useful at all? He even questions whether he is capable of doing any primary research himself and considers hiring someone to do a feasibility study for him. Maybe doing research is easier than using research. Sources: Shiver, J., “Taste Test: The Little Joes Take on Starbucks,” USA Today (March 26, 2008), http://www.usatoday.com/money/industries/food/2006-03-26- coffee_x.htm, accessed July 20, 2008; Associated Press, “McDonald’s Coffee Beats Starbucks, Says Consumer Reports,” The Seattle Times (February 2, 2007), http:// seattletimes.nwsource.com/html/businesstechnology/2003553322_webcoffeetest02. html, accessed July 20, 2008; “Coffee Wars: Starbucks v McDonald’s,” The Economist 386 (January 10, 2008), 58. Questions 1. What are the top three key decisions faced by Garcia? 2. What are the key deliverables that an outside researcher should produce to help Joe with the key decisions? 3. How relevant are the coffee taste studies cited above? Explain. 4. What flaws in the coffee taste studies should Garcia consider in trying to weigh the merits of their results? 5. Briefly relate this situation to each of the major stages of the marketing research process. 6. Try to do a quick search to explore the question: “Are American consumer preferences the same all across the United States?” 7. Would it be better for Garcia to do the research himself or have a consultant perform the work? 8. If a consultant comes in to do the job, what are three key deliverables that would likely be important to Garcia in making a decision to launch the “A Cup of Garcia” coffee shop?

1)A force of 2 N stretches a spring 0.5 meters. The mass of 1 kg is attached to the spring and set into motion in a medium that offers a damped force equal 4 times the velocity. If the mass is at stating from 0.5 m above the equilibrium position with a downward initial velocity of sec/2.0m a) Find the equation for the position if the system is exerted by an external force of f(t)=4cos(t) b)Estimate the position of the mass at t = π/8 and t = π/4 sec c)Describe the motion after a long period of time

1. In light of the university admission scandal, discuss Type 1 and 2 errors with costs and consequences (which are many) if the null H0 is that the student is qualified.

2. In light of the recent flooding around Tampa, one subdivision has approached the county to do something about the flooding for years. The Ha is that there is not flooding potential. Again identify Type 1 and 2 errors with costs and consequences, which are again many.

Question 1

A) Show that the functions y1(t) = 1 + t 2 ; y2(t) = 1 − t 2 are linearly independent directly from the definition of linear independence.

B)Find three functions y1(t), y2(t), y3(t) such that any two of them are linearly independent but three of them are not linearly independent.

1.) Choose all of the following pairs that would share 1/2 of their genome (assuming no crossing over and non sex chromosome inheritance).

-Father and child

-mother and child

-Full siblings

-uncle and niece

-grandparent and grandchild

2.) A man who is an achondroplastic dwarf with normal vision marries a color-blind woman of normal height. The man's father was 6 feet tall, and both the woman's parents were of average height. Achondroplastic dwarfism is autosomal dominant, and red-green color blindness is X-linked recessive.

What proportion of their sons would be color-blind and of normal height?

Fibonacci numbers are defined by F0 = 0, F1 = 1 and Fn+2 = Fn+1 + Fn for all n ∈ N ∪ {0}.

(1) Make and prove an (if and only if) conjecture about which Fibonacci numbers are multiples of 3.
(2) Make a conjecture about which Fibonacci numbers are multiples of 2020. (You do not need to prove your

conjecture.) How many base cases would a proof by induction of your conjecture require?