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thomas brady

thomas b.

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Calculate the 20th percentile of the data set shown x 3.6 4.7 8.3 9.1 11.6 12.2 13.1 16.6 16.9 27

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During the Whiskey Act, who does the tax incidenxe falls on, the producer or the consumer, when the supply is inelastic and the demand is elastic. Cosider, if the demand falls as proce rises, are consumers carrying burden of that tax?

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Find the domain of the expression.\\ $\frac{\sqrt{3x}}{x+2}$\\ $x \leq -2$\ $x \geq 0$\ $x \neq -2$\ all real numbers\ $x \leq 0$

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How does the human eye and brain detect the different energies of light? 1: colour 2: temperature 3: odour 4: intensity of the burn 5: pain A. 1 & 2 B. 1, 2, & 5 C. 1, 2, 3, 4, & 5 D. 3, 4, & 5 E. 4 & 5

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Texts: Prove Proposition 1 - 4 Then u is the weak derivative of Du and we write u = D(Du). By definition, Du = -uVEC0e. Since E C0E C0, and hence (Du = -u). The result is that = VEC0 (11.6) Definition: Du = D(Dw) is called the second order weak derivative of u. Proposition 1: The function D2u is uniquely defined by (11.6). Proof: Exercise. Denote the subset of functions in (20,) with weak derivative up to order 2 by H0. Proposition 2: Suppose the functions u and v are in H20, and c is any real number. Then u+v and cu are in H20, and Du+v = Du + D(Dv); D2cw) = cD2u. Proof: Exercise. Definition: uv2 = uv + DwDv + DrDv Proposition 3 is an inner product for H20. Proof: Exercise. Notation: Norm for the vector space H0: |u|2 = /uw Remark 1: |u|3 = 1|u|2 + ||Du|2 + ||D2u||2 Proposition 4: The space H20 is complete. Proof: Exercise.

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2. (2 points) Let $A = \begin{bmatrix} 1 & 2 & 1 \\ 1 & 1 & 1 \end{bmatrix}$. Does the pseudoinverse of A exists? If yes, find it; if no, explain why.

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Problem #5 (20 points) Solve the initial-value problem $x^2y''(x) + 6xy'(x) + 6y(x) = 20x^2$, $y(\frac{1}{2}) = 1$, $y'(\frac{1}{2}) = 2$ where $x$ is an independent variable; $y$ depends on $x$, and $x \ge 1/2$. Then calculate the maximum of $y''(x)$ for $x \ge 1/2$. Round-off your numerical result for the maximum to FOUR significant figures and provide it below (20 points): (your numerical answer must be written here)

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Consider the following system with variable gain K: R(s) \rightarrow + \rightarrow K \rightarrow \frac{10}{(s+1)(s^2 + 4s + 5)} \rightarrow C(s) 1) Sketch this system's root locus by following all the steps specified in the lecture. 2) Based on the root locus sketch, determine the range(s) of K for which the system is stable.

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Exercise: The joint distribution is given by: Y X 0 1 2 0 0.11 0.03 0.06 1 0.07 0.20 0.05 2 0.08 0.11 0.29 0.16 0.34 0.4 (a) Compute Var(2X+3) (b) Give the relationships between Var(2X-Y) and Var(X) and Var(Y)

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Question # 3 (4 points) A wholesaler will start his new business of importing sugar and selling it in Saudi market starting from April 1, 2022. The following information are given to you: Fixed Costs: a. Warehouses Annual Rent = SR200,000 b. Annual Insurance Fees = SR10,000 c. Salaries of Administrative Staff = SR150,00 Variable Costs (per unit sold) a. Labor Cost = SR5 b. Transportation Cost = SR2 c. Raw material = SR10 Price Per Unit: P = SR60 Target Profit Level in March 31, 2023 = SR480,000 Average Monthly Sales = 3,600 units Based on the above information, answer the following questions: 1. Find out the number of unite need to be sold to breakeven? 2. How many units need to be sold to achieve the target profit level? 3. How many months will it takes to achieve the target profit level? 4. If the wholesaler achieves the target profit level, find out the margin of safety?

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