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- 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2Dogs are inbred for such desirable characteristics as blue eye color; but an unfortunate by-product of such inbreeding can be the emergence of characteristics such as deafness. A 1992 study of Dalmatians (by Strain and others, as reported in The Dalmatians Dilemma) found the following: (i) 31% of all Dalmatians have blue eyes. (ii) 38% of all Dalmatians are deaf. (iii) 42% of blue-eyed Dalmatians are deaf. Based on the results of this study is "having blue eyes" independent of "being deaf"? No, since .31 * .38 is not equal to .42. No, since .38 is not equal to .42. No, since .31 is not equal to .42. Yes, since .31 * .38 is not equal to .42. Yes, since .38 is not equal to .42. Submit QuestionQuestion 13A researcher conducts a research study to examine whether there is a difference between two treatments regarding depression. Which of the following is consistent conceptually with the alternative hypothesis? a. The second treatment is less effective than the first treatment regarding depression. b. There is a difference between the two treatments among the general population regarding depression. c. There is no difference between the two treatments among the general population regarding depression. d. The first treatment is less effective than the second treatment regarding depression.
- We have an initial simplex tableau given bySO what would be the L, Lq, and Wq of this problem? Assuming we are trying to develop and sovle a waiting line system that can accomodate this increased leel of passenger traffic.A three-finger Morra game is a game in which two players simultaneously show one, two, or three fingers at each round. The outcome depends on a predetermined set of rules. Here is an interesting example: If the numbers of fingers shown by A and B differ by 1, then A loses one point. If they differ by more than 1, the round is a draw. If they show the same number of fingers, A wins an amount equal to the sum of the fingers shown. Determine the optimal strategy for each player. (Enter your probabilities as fractions.) Player A should show one finger with probability _____ , two fingers with probability _____ , and three fingers with probability ______ . Player B should show one finger with probability _______ , two fingers with probability ________ , and three fingers with probability ________ . Find the expected value of the game. The expected outcome is the player A will win __________ points per round, on average.
- Three components are connected to form a system as shown in the accompanying diagram. Because the components in the 2–3 subsystem are connected in parallel, that subsystem will function if at least one of the two individual components functions. For the entire system to function, component 1 must function and so must the 2–3 subsystem. The experiment consists of determining the condition of each component [S (success) for a functioning component and F (failure) for a nonfunctioning component]. (Enter your answers in set notation. Enter EMPTY or ∅ for the empty set.) There us a graph shown in the pictures. Questions are posted on the pictures too.3. Consider a test of H0: u=55 versus Ha: u<55 performed. Make the appropriate conclusion for the given situation: z-value=-1.75, a=.05, p-value=.0401. a. reject H0 b. fail to reject H0 4. Consider a test of H0: u=40 versus Ha: u>40 performed. Make the appropriate conclusion for the given situation: z=-2.5, a=.01, p-value=.0062. a. reject H0 b. fail to reject H0A manager wants to see if geographical region (Cape Town, Durban and Gauteng) is related with ownership of a tablet (“Have a tablet” and “No tablet”). Define the null hypothesis and the alternative hypothesis. A. H1: Geographical region and ownership of a tablet are independent vs H0: No relationship exists between Geographical region and ownership of a tablet B. H0: Geographical region and ownership of a tablet are independent vs H1: A relationship exists between Geographical region and ownership of a tablet C. H1: Geographical region and ownership of a tablet are independent vs H0: Geographical region is dependent on ownership of a tablet D. H0: A relationship exists between Geographical region and ownership of a tablet vs H1: No relationship exists between Geographical region and ownership of a tablet
- The player pays a fee of $5 to play. The player then rolls a 12-sided die three times. If the player rolls a 7 on any of the three rolls, they win a prize. The prize is determined by the number of 7s rolled. If the player rolls one 7, they win $5. If the player rolls two 7s, they win a $10. If the player rolls three 7s, they win $20. Compare the theoretical results of the game to the experimental results, including a discussion of whether the results were typical or rare. Theoretical results: Roll (including all 3 rolls) Result Money earned 1 7,7,7 $15 2 2,4,5 $5 3 5,7,9 $5 4 1,9,3 $0 5 2,12,7 $5 6 3,12,3 $0 7 7,4,8 $5 8 6,7,7 $10 9 5,12,4 $0 10 7,5,7 $10 Experimental results: Roll (including all 3 rolls) Result Money earned 1 1,3,7 $5 2 3,6,4 $0 3 7,6,9 $5 4 8,7,7 $10 5 11,4,1 $0 6 6,5,7 $7 7 4,6,3 $0 8 7,1,9 $7 9…6. A smoke detector system uses two devices, an ionization sensor and a photoelectric sensor. If smoke is present, the probability that it will be detected by the ionization sensor (I) is 0.90, by the photoelectric sensor (P), 0.80, and by both devices, 0.72. a) Draw a Venn diagram to represent the problem. b) If smoke is present, determine the probability that the smoke will be detected by the system. c) if smoke is present, determine the probability that the smoke is undetected. d) are the two alarms operating independently. Justify your answer with a calculation.A diabetic patient needs at least 40 units of Vit. A, at least 30 units of Vit. C, and atleast 30 units of Vit. E each day. Each brand X multivitamin capsule contains 4 units ofVit. A, 6 units of Vit. C, and 2 units of Vit. E; each brand Y capsule contains 5 units of Vit.A, 3 units of Vit.C, and 5 units of Vit. E. If each brand X capsule costs P6.00 and eachbrand Y capsule costs P9.00, how many capsules should the patient take each day tominimize the costs? Solve using graphical method. Show complete solution.Required:1. Formulate the following:a. Decision variablesb. Objective functionc. Constraints2. Graph3. Identify feasible region.4. Solve for the value of X and Y at each point.5. Decision.
