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jonathan nguyen

jonathan n.

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Basic Math Skills Listen When multiplying 4.73 by 2.1 , how many decimal places will the p 0 3

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Which of the following is true about the sequence with general term $a_n = (-2)^n$? The sequence diverges. The sequence converges to -2. The sequence converges to 2. None of these

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Company X wants to maximize its profits for shareholders. It decides to sell one of its poorly performing factories to a competitor. Will this be a good example of financial management? Yes, because the employees want to sell the factory. No, because the increase of capital will increase the tax liability of the company. No, because the factory performs poorly. It w be worth much. Yes, because the sale will provide capital and reduce expenses.

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An inferior product with a large advertising budget sells well when it is introduced, but sales fall as people discontinue use of the product. Suppose that the weekly sales S are given by

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Which of the following is true? a. money was invented in the 12th century BC by Sir John Money b. money is the result of complex social evolution c. money's origins are to be found the government safeguards of legal tender d. a and c of the above

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Question 1 (1 point) Which one of the following substances is classified as an element? C$_6$H$_{12}$O$_6$ KCl NO P$_4$

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(1 point) Consider the initial value problem $\vec{y}' = \begin{bmatrix} -6 & 1\\ 0 & -6 \end{bmatrix} \vec{y}$, $\vec{y}(0) = \begin{bmatrix} -1\\ 4 \end{bmatrix}$. a. Find the eigenvalue $\lambda$, an eigenvector $\vec{v}_1$, and a generalized eigenvector $\vec{v}_2$ for the coefficient matrix of this linear system. $\lambda = -6$, $\vec{v}_1 = \begin{bmatrix} 1\\ 0 \end{bmatrix}$, $\vec{v}_2 = \begin{bmatrix} 0\\ 1 \end{bmatrix}$ b. Find the most general real-valued solution to the linear system of differential equations. Use $t$ as the independent variable in your answers. $\vec{y}(t) = c_1$ c. Solve the original initial value problem. $y_1(t) = $ $y_2(t) = $

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2. The Compaq Corporation has $500,000 of debt outstanding, and it pays an annual interest rate of 10%. Compaq's annual sales are $2 million, average tax rate is 30%, and its net profit after-tax is $1,00,000. If the company does not maintain a minimum operating income level of $250,000, its bank will refuse to renew the loan and bankruptcy will result. Calculate Compaq Corporation's current operating income and comment on its eligibility of this loan renewal. [5 Marks]

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Consider the function $f$ that is defined over $]0;+\infty[$ by: $f(x) = f \quad x = -\frac{1}{2}x + 1 + \frac{\ln x}{2x}$, and designate by $(C)$ its representative curve in an orthonormal system $(0, \vec{i}, \vec{j})$. 1. Calculate $\lim_{x \to 0^+} f(x)$, $\lim_{x \to +\infty} f(x)$. Deduce an asymptote to $(C)$. 2. Prove that the straight line $(d)$ of equation $y = -\frac{1}{2}x + 1$ is an asymptote to $(C)$. 3. Study the relative position between $(C)$ and $(d)$. 4. Prove that : $f'(x) = \frac{-2g(x)}{4x^2}$. 5. Deduce the sign of $f'(x)$ and set up the table of variations of $f$. 6. Prove that the equation $f(x) = 0$ admits two solutions $\alpha$ and $\beta$ such that: $\frac{1}{3} < \alpha < \frac{1}{2}$ and $2 < \beta < \frac{5}{2}$. 7. Draw $(C)$ and $(d)$. (graphic unit: 2cm).

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Carbon Tax: The U.S. government is considering the implementation of a carbon tax to fight climate change and raise much-needed government revenue. They have asked you to help them determine how much gasoline demand will drop and how much revenue will be raised following the implementation of a $150 carbon tax. After some rigorous statistical work, you come up with the following table of values, prices, and quantities for gas demand in the short and long run: Short Run: PS QS $0.00 1200 $1.00 1100 $2.00 1000 $3.00 900 $4.00 800 $5.00 700 $6.00 600 $7.00 500 $8.00 400 $9.00 300 $10.00 200 $11.00 100 Long Run: PL QL $0.00 1200 $0.50 1100 $1.00 1000 $1.50 900 $2.00 800 $2.50 700 $3.00 600 $3.50 500 $4.00 400 $4.50 300 $5.00 200 $5.50 100 Inelastic: QIN 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 Note: PS and QS are short-run values; PL and QL are long-run values; and QIN stands for inelastic where there is no demand response to change in price. The quantities in the table represent yearly consumption in gallons for each household in the US. You will use this table to answer the questions below. In addition to the information in the table, please make the following assumptions: (1) the average price of gas in the U.S. is $2.00 per gallon; each gallon of gas contains 5.5 lbs. of carbon with 2,000 lbs. in a ton; and there are 115 million households in the U.S. Use the data in the table above to derive and plot curves for inelastic, short-run, and long-run demand for gas in the U.S. Assume that in the very short run there is no demand response by households. How much will the carbon tax cost each household? How much revenue will be raised? Now, using your short-run demand curve estimates, redo part b to determine how much the carbon tax costs each household and how much revenue it raises. Finally, redo part b using the values from your long-run demand curve. How does your answer change in comparison to part b and why?

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