Question 5) Many collectibles have values that fluctuate significantly over time. It has been found that the value of a near-mint condition 1955 Topps Roberto Clemente baseball card can be approximated by the function B (x) =-15x2 + 390x + 115 on the interval 0 x 22 where χ s in years and x = 0 corresponds to the year 1984. NOTE: Doing this problem by trial and error 5) Many collectibles have values that fluctuate significantly over time. It has been found that the value of a near-mint condition 1955 Topps Roberto Clemente baseball card can be approximated by the function B (x) =-15x2 + 390x + 115 on the interval 0 x 22 where χ s in years and x = 0 corresponds to the year 1984. NOTE: Doing this problem by trial and error or guess and check will result in a score of 0 points regardless of whether your answer is correct. When (what year) did the maximum value of this baseball card occur and what was the maximum value of this baseball card?

Solve the differential equation by variation of parameters. \[ y^{\prime \prime}+3 y^{\prime}+2 y=\cos \left(e^{x}\right) \] \[ y(x)= \] Solve the differential equation by variation of parameters. y′′+3y′+2y=cos(ex) y(x)=

The table below is from E107 simulated experiment. From the data, what is the experimental value of the heat of fusion of ice? Determining the Latent Heat of Fusion of Ice 125 g Mass of calorimeter, m. Specific Heat of calorimeter Mass of water, my 0.2174 calig 100 g 1.000 cal/gC Specific Heat of Water Ow Mass of mixture (calorimeter, water+ice), mm 2498 Mass of ice, m. 24 g Initial temperature of ice, t, 0°C Initial temperature of calorimeter, 1 50°C Initial temperature of water. 1 50°C Final temperature of mixture, 29.5°C Experimental Latent heat of fusion, L; calg Actual Latent heat of fusion, Ly 79.71 callg Percentage Error O 79.31 calg O 79.71 calg 79.13 calg O 79.8 calg The table below is from E107 simulated experiment. From the data, how much heat is lost by water in the calorimeter? Determining the Latent Heat of Fusion of Ice 125 g 0.2174 cal/gC Mass of calorimeter, m. Specific Heat of calorimeter Mass of water, m Specific Heat of Water or Mass of mixture (calorimeter, water+ice), 7. 100 g 1.000 cal/gC 2498 24 8 Mass of ice, m Initial temperature of ice. I, 0°C Initial temperature of calorimeter, 1. 50°C 50°C Initial temperature of water, I Final temperature of mixture, 29.5°C Experimental Latent heat of fusion, L calg Actual Latent heat of fusion, Ly 79.71 calg Percentage Error O 708 cal O 2050 cal O 2607 cal O 557 cal

2 The following equations were estimated using the data in BWGHT: log(bwght) = 4.66 - .0044 cigs +.0093 log(faminc) + .016 parity (.22) 0.0009) (.0059) (.006) + .027 male + .055 white 0.010) (.013) n = 1.388, R2 = .0472 and = log(bwght) = 4.65 - .0052 cigs +.0110 log(faminc) + .017 parity (.38) (.0010) 0.0085) (.006) + .034 male + .045 white - .0030 motheduc + .0032 fatheduc (.011) (.015) (0030) (.0026) n = 1,191, R2 = .0493. The variables are defined as in Example 4.9, but we have added a dummy variable for whether the child is male and a dummy variable indicating whether the child is classified as white. (i) In the first equation, interpret the coefficient on the variable cigs. In particular, what is the effect on birth weight from smoking 10 more cigarettes per day? (ii) How much more is a white child predicted to weigh than a nonwhite child, holding the other factors in the first equation fixed? Is the difference statistically significant? (iii) Comment on the estimated effect and statistical significance of motheduc. (iv) From the given information, why are you unable to compute the F statistic for joint significance of motheduc and fatheduc? What would you have to do to compute the F statistic? (v) What is the estimated effect on birth weight when smoking 20 cigarettes a day?

use nodal analysis to generate the matrix form of equations GI=I in terms of node voltages V4 3Ω V, T 2Α. 18 V 8Ω 5A 5 Ω

Suppose the interest rates on a European bond and an Australian bond are 2% and 4% per year, respectively. The exchange rate today is 0.6 Euro per Australian dollar. If the interest parity condition holds, what must be the expected exchange rate between the Euro and the dollar? (Note: round your result to 2 decimal places.) 0.61 $/€ 0.59 $/ € 1.70 $/€ 1.63 $/ € 0.82 $/ €

5 In a study relating college grade point average to time spent in various activities, you distribute a sur- vey to several students. The students are asked how many hours they spend each week in four activi- ties: studying, sleeping, working, and leisure. Any activity is put into one of the four categories, so that for each student, the sum of hours in the four activities must be 168. (1) In the model GPA = Be + B study + B sleep + B;work + B.leisure + . does it make sense to hold sleep, work, and leisure fixed, while changing study? (ii) Explain why this model violates Assumption MLR.3. 106 PART 1 Regression Analysis with Cross-Sectional Data (iii) How could you reformulate the model so that its parameters have a useful interpretation and it satisfies Assumption MLR.3? Consider the multiple regression model containing three independent variables, under Assumptions MLR.1 through MLR.4: y = Bo + B x1 + Boxe + Byty + u. You are interested in estimating the sum of the parameters on X, and Xz; call this 0,- B. + B.. 0 Show that 8, = B. + B, is an unbiased estimator of 8, (ii) Find Varê) in terms of Var(B).Var(B2), and Corr(B.B.).