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Jenny and Henry are sitting down to play a friendly game. Each time they play Jenny might win or Henry might win. They agree to repeatedly play the game until one of the following happens: Jenny wins 4 games in a row, Henry wins 2 games in a row, or 5 games have been played. How many different sequences of game results are possible? 19 20 21 22 23

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1. Demand and supply functions of two firms are following \[ \begin{array}{ll} \mathrm{Q}_{\mathrm{d} 1}=45-(15 / 2) \mathrm{P}_{1}+(5 / 2) \mathrm{P}_{2}, & \mathrm{Q}_{\mathrm{d} 2}=30+\mathrm{P}_{1}-5 \mathrm{P}_{2} \\ \mathrm{Q}_{\mathrm{s} 1}=-5+10 \mathrm{P}_{1} & \mathrm{Q}_{\mathrm{s} 2}=-5 \quad+(15 / 2) \mathrm{P}_{2} \end{array} \] In which, $ \mathrm{Q}_{\mathrm{d} 1}, \mathrm{Q}_{\mathrm{d} 2}, \mathrm{Q}_{\mathrm{s} 1}, \mathrm{Q}_{\mathrm{s} 2} $ are quantities of demand and supply of firm 1 và 2. $ P_{1} $, and $ P_{2} $ are price of firm 1 và 2 . a. Explain the coefficients of $ \mathrm{P}_{1} $ and $ \mathrm{P}_{2} $ in supply and demand functions. b. Are two firms complement or competition? What is your answer if the signs of these coefficients are changed? c. Find the market balance (price, quantity) of two firms. 2. Suppose demand and supply functions of three goods as following: \[ \begin{array}{l} \mathrm{Q}_{\mathrm{s} 1}=-5+3 \mathrm{P}_{1}-\mathrm{P}_{2}-\mathrm{P}_{3} \\ \mathrm{Q}_{\mathrm{d} 1}=8-2 \mathrm{P}_{1}+\mathrm{P}_{2}+\mathrm{P}_{3} \end{array} \] \[ \begin{array}{l} \mathrm{Q}_{\mathrm{s} 2}=-2-\mathrm{P}_{1}+3 \mathrm{P}_{2}-\mathrm{P}_{3} \\ \mathrm{Q}_{\mathrm{d} 2}=11+\mathrm{P}_{1}-2 \mathrm{P}_{2}+\mathrm{P}_{3} \end{array} \] \[ \begin{array}{l} \mathrm{Q}_{\mathrm{s} 3}=-1-\mathrm{P}_{1}-\mathrm{P}_{2}+3 \mathrm{P}_{3} \\ \mathrm{Q}_{\mathrm{d} 3}=12+\mathrm{P}_{1}+\mathrm{P}_{2}-2 \mathrm{P}_{3} \end{array} \] a. Construct a system of linear equations in case of market balance. b. Is it a Crame system? Explain c. Find a solution for the market balance. 3. We have a matrix of technical coefficients $ \mathrm{A}: A=\left(\begin{array}{ccc}0.1 & 0.3 & 0.2 \\ 0.4 & 0.2 & 0.3 \\ 0.2 & 0.3 & 0.1\end{array}\right) $ And final demand of these sectors [118; 52; 36]. Find total demand of each sector. 4. We have inter-industry demand and final demand of four sectors \begin{tabular}{|l|l|l|l|l|l|} \hline I/O & S1 & S2 & S3 & S4 & D \\ \hline S1 & 10 & 30 & 50 & 40 & 20 \\ \hline S2 & 20 & 50 & 80 & 30 & 10 \\ \hline S3 & 60 & 20 & 30 & 10 & 40 \\ \hline S4 & 70 & 40 & 10 & 80 & 20 \\ \hline \end{tabular} a. Find the matrix of technical coefficients A b. For S3, to make $ \$ 1 $ of its output, how much does it pay S1? c. Find percentage of added value of each sector

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Question 3 1 pts For a certain physical system you have determined that the appropriate relationships describing it are: $F_c = ma_c$ and $a_c = \frac{v^2}{r}$ The known quantities for the system are $F_c$, $m$, and $v$ and the unknown quantities for the system are $a_c$ and $r$. Solve for $r$ in terms of just the knowns. $O r = \frac{v^2}{a_c}$ $O r = F_c m v^2$ $O r = \pm \sqrt{\frac{F_c v}{m}}$ $O r = \frac{m v^2}{F_c}$

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Clinical psychology rose in response to which event? The U.S. Civil War

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Reagan-era tax cuts disproportionately benefitted the wealthy. ? True ? False

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[OPTIONAL] 2.3 #3: $z^\circ$ $a^\circ$ $b^\circ$ $c^\circ$ $d^\circ$ $e^\circ$ $l^\circ$

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In an interdisciplinary team, members maintain professional roles; however, they interact with each other using a problem-solving focus for patient care. True False In an interdisciplinary team, members maintain professional roles; however, they interact with each other using a problem-solving focus for patient care. True False

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When no output gap exists actual output ______ potential output and the rate of inflation will tend to ______. Select one: a. exceeds; increase b. equals; remain the same c. is less than; decrease d. exceeds; decrease

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In oceans near the equator, the surface temperature gradient with respect to deep sea temperatures is very high. It goes from 500 to 1,000 meters. A relatively constant temperature difference of 15-25°C is observed depending on the position in relation to the depth. So, between electricity. When large, cold water can be used as a heat sink and hot water can be used as a heat source. This technology is known as Ocean Thermal Energy Conversion (OTEC). a) Consider the temperature of the water surface at 27°C and the temperature at 750m deep at 6°C. These temperature levels are. What is the efficiency of a Carnot engine operating between? b) Part of the power cycle output draws cold water to the surface on which the cycle is located. It should be used to. The intrinsic efficiency of the actual cycle is 0.6 of the Carnot value and 1/3 of the difference in generated power. What is the actual efficiency of the cycle when used to transfer gowns to surfaces?

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ty in (b) when n = 1 million, 4 million, and 10 million. 17. A Time article (13 March 1989, Medicine section) sounded warning bells about the fast- growing in vitro fertilization industry, which caters to infertile couples who are desperate to have children. At the time, U.S. in vitro programs charged in the vicinity of $7,000 per attempt. There is a lot of variability in the success rates both between clinics and within a clinic over time, but we will use an average rate of 1 success in every 10 attempts. Suppose that 4 attempts ($28,000) is the maximum a couple feels they are prepared to pay and that they will try until they are successful up to that maximum. (See Case Study 5.2.1.) (a) Write a probability function for the number of attempts made. (b) Compute the expected number of attempts made. Also compute the standard deviation of the number of attempts made. (c) What is the expected cost when embarking on this program? (d) What is the probability of still being childless after paying $28,000? The calculations you have made assume that the probability of success is always the same at 10% for every attempt. This will not be true. Quoted success rates will be averaged over both couples and attempts. Suppose the population of people attending the clinics is made up of three groups. Imagine that 30% is composed of those who will get pregnant compar- atively easily, say pr(success) = 0.2 per attempt; 30% are average with pr(success) = 0.1 per attempt; and the third group of 40% have real difficulty and have pr(success) = 0.01.13 After a couple are successful, they drop out of the program. Now start with a large number, say 100,000 people and perform the following calculations. ?(e) Calculate the number in each group you expect to conceive on the first attempt and hence the number in each group who make a second attempt. Note: It is possible to find the probabilities of conceiving on the first try, on the second given failure at the first try, and so on, using the methods of Chapter 4. You might even like to try it. The method you were led through here is much simpler, though informal. ?(f) Find the number in each group getting pregnant on the second attempt and hence the number in each group who make a third attempt. Repeat for the third and fourth attempts.

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donald h.