The population of predators and prey in a closed ecological system tends to vary periodically over time. In a certain system, the population of owls O can be represented by where t is the time in years since January 1, 2001. In that same system, the population of mice M can be represented by . What is the maximum number of owls and how many years does it take to reach this population for the first time? A. 120 owls, 15 years B. 120 owls, 7.5 years C. 135 owls, 15 years D. 135 owls, 7.5 years

Description of the data set is provided in page 161 (problem 12 in chapter 8). Dataset “EX0812.txt” is posted. (Note: If you use infile and input statement to read in data, put “$” after the variable sex to indicate that the values are characters. E.g. input id x1 x2 y clrzne sex $ ;) Fit the regression model of Y (change in refraction error) on X1, sex and X1*sex. Write down the fitted regression model.Based on the fitted model in (a), write down the regression models of Y on X1 for males and females separately. What is the difference of intercepts in these two models? What is the difference of slopes in these two models? Which do they correspond to the estimated coefficient in model (a), respectively?Test whether the straight lines for males and females coincide (i.e., are the same) with alpha=0.1. State your null hypothesis in terms of the coefficients. Provide you SAS code and output for conducting the analysis. Figure out your F value and p value based on output, and then draw a conclusion.Test whether the straight lines for males and females are parallel with alpha=0.1. State your null hypothesis in terms of the coefficients. Provide you SAS code and output for conducting the analysis. Figure out your F value and p value based on output, and then draw a conclusion.Based on your answers to questions (c) and (d), comment on differences and similarities in the change in refraction-baseline refractive error relationship for males and females.

Week Three - Application AssignmentAnswer the following questions in a Word document and upload the document to the appropriate drop box.1) A museum borrows $2,000,000 at simple annual interest to purchase new exhibits. Let x represent the amount borrowed at 7%, y represent the amount borrowed at 8.5%, and z represent the amount borrowed at 9.5%. Set up a system of linear equations to determine how much is borrowed at each rate given that the total annual interest is $169,750 and the amount borrowed at 8.5% is four times the amount borrowed at 9.5%. You do not have to solve the system.2) At a local store, the numbers of gallons of skim milk, 2% milk, and whole milk sold over the weekend are represented by a matrix A. Skim 2% Whole Friday 40 64 52 Saturday 60 82 76 Sunday 76 96 84The selling prices per gallon and the profits per gallon for the three types of milk are represented by B. Selling price Profit Skim $3.45 $1.20 2% $3.65 $1.30 Whole $3.85 $1.45 a) Compute AB and interpret the result. b) Find the store’s total profit from milk sales for the weekend3) A florist is creating 10 centerpieces. Roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each. A customer plans on spending $300 on 10 centerpieces with each centerpiece containing 12 flowers, with twice as many roses as the number of irises and lilies combined.a) Write a system of linear equations that represents the situation. Then write a matrix equation that corresponds to your system.b) Find the number of flowers of each type that the florist can use to create the 10 centerpieces.4) One hundred liters of a 50% solution of a chemical mixture is obtained by mixing a 60% solution with a 20% solution. Using a system of linear equations determine how many liters of each solution are required to obtain the 50% mixture. Solve the system using matrices.