Functions 1. The following table shows the most medals won by any country in the given year of the Olympic Winter Games: Year Most medals won by a country Country 1988 29 Soviet Union 1992 26 Germany 1994 26 Norway 1998 29 Germany 2002 36 Germany 2006 29 Germany 2010 37 United States 2014 29 Russia (a) Identify the independent and the dependent variables, and describe the domain and range. (b) Describe the function in words.
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- Including an interaction term between two independent variables, X1 and X2, allows for the following: a. the interaction term lets the effect on Y of a change in X1 depend on the value of X2. b. the effect of a unit increase in X1, keeping X2 constant, is transmitted through the coefficient on X1 and the interaction term coefficient. c. the interaction term lets the effect on Y of a change in X2 depend on the value of X1. d. the effect of a unit increase in X2, keeping X1 constant, is transmitted through the coefficient on X2 and the interaction term coefficient. e. All of the above. f. None of the above.. Nutrition The following table gives the calories,fat, and carbohydrates per ounce for three brands ofcereal, as well as the total amount of calories, fat, andcarbohydrates required for a special diet. To find the number of ounces of each brand thatshould be combined to give the required totals ofcalories, fat, and carbohydrates, let x represent thenumber of ounces of All Bran, y represent thenumber of ounces of Sugar Frosted Flakes, and z represent the number of ounces of Natural Mixed Grain.a. Use the information in the table to write a systemof three equations.b. Solve the system to find the amount of each brandof cereal that will give the necessary nutrition.Orange production The table below shows that as thenumber of oranges on a tree increases, the fruit tends toget smaller. Create a model for this relationship, andexpress any concerns you may have. Number ofOranges/Tree Average Weight/Fruit (lb)50 0.60100 0.58150 0.56200 0.55250 0.53300 0.52350 0.50400 0.49450 0.48500 0.46600 0.44700 0.42800 0.40900 0.38
- When money is spent on goods and services, those who receive the money also spend some of it. The people receiving some of the twice-spent money will spend some of that, and so on. Economists call this chain reaction the multiplier effect. In a hypothetical isolated community, the local government begins the process by spending $D$ dollars. Suppose that each recipient of spent money spends $100 c \%$ and saves $100 s \%$ of the money that he or she receives. The values $c$ and $s$ are called the marginal propensity to consume and the marginal propensity to save and, of course, $c+s=1$(a) Let $S_{n}$ be the total spending that has been generated after $n$ transactions. Find an equation for $S_{n}$(b) Show that $\lim _{n \rightarrow \infty} S_{n}=k D,$ where $k=1 / s$. The number $k$ is called the multiplier. What is the multiplier if the marginal propensity to consume is $80 \% ?$ Note: The federal government uses this principle to justify deficit spending. Banks use this principle to…6 - It is desired to compare the average age of 35 people working in the production department and 30 people working in the management department in an enterprise. What is the dependency structure between the groups to be compared? a) Dependant B) discrete NS) Independent D) Qualitative TO) Quantitative2.62 For the period 2001–2008, the Bristol-Myers Squibb Company, Inc. reported the following amounts (in billions of dollars) for (1) net sales and (2) advertising and product promotion. The data are also in the file XR02062. Source: Bristol-Myers Squibb Company, Annual Reports, 2005, 2008. Year Net Sales Advertising/Promotion 2001 $16.612 $1.201 2002 16.208 1.143 2003 18.653 1.416 2004 19.380 1.411 2005 19.207 1.476 2006 16.208 1.304 2007 18.193 1.415 2008 20.597 1.550 For these data, construct a line graph that shows both net sales and expenditures for advertising/product promotion over time. Some would suggest that increases in advertising should be accompanied by increases in sales. Does your line graph support this?
- (a) Suppose education and experience are important determinants of wage and you decide to add them in the regression. Propose a regression equation to examine the return to college education. Name variables as you wish. Be careful with notation in your answer; that is, be clear with whether you use the population regession function or the sample regression function (or fitted line) (b) Suppose you want to test whether graduates from top 10 universities fare better in the labor market. Propose a regression equation that allows a wage gap between top-10 University graduates (Group 1) and non-top-10 University graduates (Group 2). Define relevant variable(s). Write down the null and alternative hypotheses to test whether the mean log wages differ between the two groups. (c) Propose a regression equation that allows the return to college education to vary with experience. Write down the null and alternative hypotheses to test whether the return to college education vary with experience.…A stable population of 35,000 birds lives on three islands. Each year 10% of the population on island A migrates to island B, 20% of the population on island B migrates to island C, and 5% of the population on island C migrates to island A. Find the number of birds on each island if the population count on each island does not vary from year to year.iven group data: Gp l1 l2 . f . 1 20 30 7 2 30 40 9 . Find: Midquartile 3 40 50 12 4 50 60 15 5 60 70 5 6 . 70 80 4
- IKEA has a contract to deliver 100, 250, 190, 140, 220, and 110 home windows over the next 6 months. Production cost (labor, material, and utilities) per window varies by period and is estimated to be $50, $45, $55, $48, $52, and $50 over the next 6 months. To take advantage of the fluctuations in manufacturing cost, IKEA can produce more windows than needed in a given month and hold the extra units for delivery in later months. This will incur a storage cost at the rate of $8 per window per month, assessed on the end-of season inventory. Now IKEA wants to minimize their respective cost. Based on this data answer the following questions Qus.1)Write down the objective function of the linear programming consistent with the objective of IKEA.4. The data below represent the number of fatal commercial airline incidents in the United States foreach year from 1998–2011. Find the mode.1 2 3 6 0 2 2 3 2 1 2 1 0 0 5. The table shows the list of average high temperatures in degrees Farenheit for each of the month ofthe year on an island country. Find the mode. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 81 82 82 83 85 86 87 87 87 86 84 82 6. Five hundred college graduates were asked how much they donate to their alma mater on an annualbasis. Find the mode of the responses. Responses Frequency$500 or more 45Between 0 to $500 150Nothing 275Refused to answer 30 7. The data shows the number of losses by the team that won the NCAA men’s basketball championshipfor the year…4. For each of the following situations, state the independent variable and the dependent variable. a. A study is done to determine if elderly drivers are involved in more motor vehicle fatalities than other drivers. The number of fatalities per 100,000 drivers is compared to the age of drivers. b. A study is done to determine if the weekly grocery bill changes based on the number of family members. c. Insurance companies base life insurance premiums partially on the age of the applicant. d. Utility bills vary according to power consumption. e. A study is done to determine if a higher education reduces the crime rate in a population