Numerade

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QUESTION 1 1.1 Compare the processes of decomposing and transforming a time series. 1.2 What distinguishes the multiplicative decomposition model from the additive decomposition model in time series analysis? QUESTION 2 The data in the following table give quarterly sales $y_t$ ($t = 1,2, ..., 12$) of the Ultimate cartoon character costumes for kids at the V-Mart variety store for the last three years. Assume that the Multiplicative decomposition method is used to forecast sales for year 4. In the following parts of the question, it is recommended to do calculations by hand, but the use of an Excel spreadsheet is also acceptable. Year Quarter Time (t) Sales ($y_t$) 1 1 1 21 2 2 26 3 3 36 4 4 45 2 1 5 29 2 6 35 3 7 44 4 8 49 3 1 9 33 2 10 38 3 11 47 4 12 52 2.1 Write down the general expression (before fitting to data) of the multiplicative decomposition model of a time series and indicate the meaning of each component. STA2604/016/0 2.2 Compute appropriate four-point moving averages and centered moving averages for these data. 2.3 Use the data to compute estimates of the components indicated in part (2.1). Show all calculations steps and summarize them into tables. Round your answers to two decimal places. 2.4 Does the model exhibit any well-defined cycle? Briefly explain your answer.

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Use technology to solve this equation: $$\frac{7x+4}{6} = \frac{5x+13}{3}$$ $$x = \boxed{\phantom{}}$$

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10 4 points The demand for good X is given by Qxd=6,000-(1/2)Px - Py+9Pz+ (1/10)M Research shows that the prices of related goods are given by Py = $6,500 and P? = $100, while the average income of individuals consuming this product is M = $70,000. a. Indicate whether goods Yand Z are substitutes or complements for good X. Good Y is: a complement Good Z is: a substitute b. Is X an inferior or a normal good? Good X is: a normal good c. How many units of good X will be purchased when Px = $5,230? 4785 d. Determine the demand function and inverse demand function for good X. Graph the demand curve for good X. Instruction: Enter all values as integers, or if needed, a decimal rounded to one decimal place. Demand function: 7400 - 5 Px Inverse demand function: Px = 14800 - 2 Qxd Instruction: Use the tool provided 'D' to graph the inverse demand curve from Qx = 0 to Qx = 6,000 (two points total). Your Graph Score: 0% 16000 14000 12000 10000 Price of X 8000 6000 4000 Inverse Demand Function 2000 0 2000 4000 6000 8000 Quantity of X D

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1 Suppose that $k$ is a field of characteristic $\neq$ 2. Decompose into irreducible components the closed set $X \subset \mathbb{A}^3$ defined by $x^2 + y^2 + z^2 = 0$, $x^2 - y^2 - z^2 + 1 = 0$. 2 Prove that if $X$ is the closed set of Exercise 4 of Section 2.4 then the elements of

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2-20 A beam is supported and loaded as shown in Figure P2-11b. For the data given in the assigned row(a) in Table P2-2, find the static safety factor: (a) If the beam is a ductile material with S_(v)=300MPa, (b) If the beam is a cast-brittle material with S_(ut)=150MPa,S_(uc)=570MPa. please give me free body diagram and solve this problem *2-20 A beam is supported and loaded as shown in Figure P2-llb. For the data given in the assigned row() in Table P2-2, find the static safety factor: (a) If the beam is a ductile material with S,=300MPa bIf the beam is a cast-brittle material with Su=150 MPa,Suc=570MPa Table P2-2 Data for Problems2-22 through 2-25 Use only data relevant to the particular problem. Lengths in m, forces in N, I in m4 Row 1 a b w* F 1 c E Va 1.00 0.40 0.60 200 500 2.85E08 2.00E02 steel b 0.70 0.20 0.40 80 850 1.70E-08 1.00E02 steel 0.30 0.10 0.20 500 450 4.70E09 1.25E-02 steel d 0.80 0.50 0.60 65 250 4.90E-09 1.10E02 steel e 0.85 0.35 0.50 96 750 1.80E08 9.00E03 steel f 0.50 0.18 0.40 450 950 1.17E-08 1.00E02 steel g 0.60 0.28 0.50 250 250 3.20E09 7.50E03 steel h 0.20 0.10 0.13 400 500 4.00E09 5.00E03 alum i 0.40 0.15 030 50 200 2.75E09 5.00E03 alum x * 0.20 0.10 0.15 150 80 6.50E10 5.50E03 alum k 0.40 0.16 030 70 880 4.30E08 1.45E02 alum 0.90 0.25 0.80 90 600 4.20E08 7.50E03 alum m 0.70 0.10 0.60 80 500 2.10E08 6.50E03 alum 0.85 0.15 0.70 60 120 7.90E09 1.00E02 alum * Note that w is a unit force of N/m Mi R1 (b)

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Part A The electric and magnetic field vectors at a specific point in space and time of an electromagnetic wave are illustrated in (Figure 1). Based on this information, in what direction do the waves propagate?

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4.27 An aircraft window is approximated as a simply supported circular plate of radius a. The window is subject to a uniform cabin pressure $p_o$. Determine its maximum deflection, assuming that a diametrical section of the bent plate is parabolic. Employ the Ritz method. Take $\nu = 0.3$.

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13. Your friend offers you a coin-toss gamble. If heads, you get $150. If tails, you lose $20. Your utility function for income Y is U(Y ) = (100+Y ) 1/3 . Should you take the gamble? If another friend offers you $5 to let him take gamble, should you take the certain $5 instead of the gamble? E(Ugamble)= 0.5(100 + 150)1/3 + 0.5(100 − 20)1/3 = 6.3 + 4.3 = 10.6 E(U no gamble)= (100)1/3 = 4.6 You should take the gamble Certainty equivalent = (105)1/3 = 4.7 You should not let your friend take the gamble. 14. Show using budget constraints and indifference curves why an increase in the interest rate increases saving in the current period.

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Consider a European call option on an asset with current price S, expiration time in one year, and the strike price S. You are told that a year from now the price of the asset will have either risen by a factor of u (u > 1) or will have decreased by a factor of 1 u . If the risk-free interest rate on one-year deposits is r > 0, show that the price of the European call option is an increasing function of the variable u

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(b) Convert to radian measure using exact values. rad (c) Name the reference angle in both degrees and radians. rad

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pedro c.