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silvia tran

silvia t.

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Suppose that in Example 9 there were three rival companies R, S, and T so that the pattern of customer retention and switching is given by the information in the matrix A where $$A = \begin{bmatrix} \frac{1}{3} & \frac{1}{2} & \frac{1}{4} \\ \frac{2}{3} & \frac{1}{4} & \frac{1}{2} \\ 0 & \frac{1}{4} & \frac{1}{4} \end{bmatrix} \begin{matrix} R \\ S \\ T \end{matrix}$$ (a) If the initial market distribution is given by $$\mathbf{x_0} = \begin{bmatrix} \frac{1}{3} \\ \frac{1}{3} \\ \frac{1}{3} \end{bmatrix}$$ then determine the market distribution after 1 year; after 2 years. (b) Show that the stable market distribution is given by $$\mathbf{x} = \begin{bmatrix} \frac{21}{53} \\ \frac{24}{53} \\ \frac{8}{53} \end{bmatrix}$$ (c) Which company R, S, or T will gain the most market share over a long period of time (assuming that the retention and switching patterns remain the same)? Approximately what percent of the market was gained by this company?

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An automobile manufacturer has given its car a 37.1 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 160 cars, they found a mean MPG of 37.0 . Assume the population standard deviation is known to be 1.5 . Is there sufficient evidence at the 0.1 level to support the testing firm's claim? Step 2 of 6 : Find the value of the test statistic. Round your answer to two decimal places.

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Find the intercepts and asymptotes of the rational function. $r(x) = \frac{3x - 18}{x - 2}$

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Evaluate the limit using the appropriate properties of limits.\\ \( \lim_{x \to \infty} \frac{8x^2 - 9}{5x^2 + x - 3} \)

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rect Question 4 The net area of the 73 7√3 5x² -7√3 (x³ + 1)4 2. √7√3 0, because the integrand is an odd function. Ⓒ2. √7√³ 5x² (x³ + 1)4 No correct answer choice is given. dx is equivalent to which of the following, and why? 5x² (x³ + 1) 4 dx, because the integrand is an even function.-da, because the integrand is an odd function. 0, because the integrand is an even function.

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The logistic equation for the population (in thousands) of a certain species is given by $\frac{dp}{dt} = 9p - 4p^2$. Complete parts (a) through (d) below.

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"In the context of the 'Paradox of Thrift', which outcome is most likely if there is a significant increase in the savings rate across an economy during a recession? A) The economy will recover more quickly due to increased capital available for investment. B) The recession will deepen, as increased savings reduce overall consumption and demand. C) There will be a significant increase in foreign investment due to the perception of economic stability. D) The increase in savings will have no impact on the economy, as consumer spending remains constant.

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Suppose that, on average, 1 in 1000 makes a numerical error in preparing his or her income tax return. If 15000 returns are selected at random and examined, find the probability that 11 ,12 ,13 of them contain an error.

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Tune an Ideal PID for servo control, using the ITAE method for the following process. $G(s) = \frac{2e^{-1s}}{4s + 1}$

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Where do we find the steepest osmotic pressure gradient between the lumen of collecting duct (i.e. the urine in it) and the surrounding renal tissue? Select one: At the border between renal cortex and medulla. In the middle region of the medulla. Deep in the medulla. Superficial in the medulla. In the renal cortex. In the adrenal glands.

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