R. Statements Reasons 1)Wen 2) SVen 1) 2OMP ZRPM 2) MP bisects 2OMR 3) 3) 2OMP E ZRMP 4) given 4) PM bisects ZOPR 5) 5) 2OPM 3ZRPM 6) 6) 2OMP+ ZRMP = LOMR 7) 7) 2OPM + ZRPM =ZOPR 8) 8) 2OMR EZOPR
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- Suppose in a small town there are three places to eat, a Chineserestaurant, a Mexican restaurant, and a pizza place. Everyone in town eats dinnerin one of these places or has dinner at home. Assume that 20% of those who eat inthe Chinese restaurant go to Mexican next time, 20% eat home and 30% go to thepizza place. From those who eat in the Mexican restaurant, 10% go to the pizzaplace, 25% go to the Chinese restaurant, and 25% eats at home next time. Fromthose who eat at the pizza place, 30% eat at home, 30% eat at the Chineserestaurant, and 10% eat at the Mexican restaurant next time. Those who eat athome, 20% go to the Chinese restaurant, 25% go to Mexican restaurant, and 30% tothe pizza place. a. Set us the matrix of transition probabilities and show the transition b. Find the steady state probabilities c. In the long run, which restaurant will have the most customerSuppose in a small town there are three places to eat, a Chineserestaurant, a Mexican restaurant, and a pizza place. Everyone in town eats dinnerin one of these places or has dinner at home. Assume that 20% of those who eat inthe Chinese restaurant go to Mexican next time, 20% eat home and 30% go to thepizza place. From those who eat in the Mexican restaurant, 10% go to the pizzaplace, 25% go to the Chinese restaurant, and 25% eats at home next time. Fromthose who eat at the pizza place, 30% eat at home, 30% eat at the Chineserestaurant, and 10% eat at the Mexican restaurant next time. Those who eat athome, 20% go to the Chinese restaurant, 25% go to Mexican restaurant, and 30% tothe pizza place. a. Set us the matrix of transition probabilities and show the transition diagram b. Find the steady state probabilities c. In the long run, which restaurant will have the most customerGive a contrapositive proof: For every 2D table of blue and gray pebbles, if the total number of gray pebbles is at most the number of columns, then at least half of the columns are almost-blue. (Note: almost-blue is to mean the column has at most one gray pebble.) Be sure to clearly explain.
- Construct a Venn Diagram for the scenario. Suppose that a total of 208 students are enrolled in a Math course which offers three classes under Instructor X, Instructor Y, and Instructor Z. 4 students are enrolled under all three instructors. 48 students are enrolled under Instructor. Y. Twice as many students are enrolled under Instructor Y and Z (but not Instructor X) as those who are enrolled under both Instructor Y and X (but not Instructor Z), and 4 times as many as those enrolled under all three instructors. 124 students are enrolled in Instructor Z. 27 students are not enrolled in any class. Students enrolled under both Instructor Y and Z (but not Instructor X) is exactly the same size as the students enrolled under both Instructor X and Z.Either deposit should be required on beer and soft drink containers, or these containers will be discarded along highways and the countryside will look like a dump. If these containers will be discarded either in parks or along highways, then deposits should be required on soft drink containers. Therefore, deposits should be required for soft drink containers. (B, S, H, C, P)Among 100 students attending VMS, 45 students took “Math”, 50 students took“English” and “Programming”, and 35 students took “Business” and “IT” of the curriculumfor the first semester. Ten students did not take any of these subjects. 15 students took“English”, “Programming”, “Business” and “IT”. 10 students took “Math”, “English”, and“Programming”. 10 students took “Math”, “Business” and “IT”.Draw a Venn diagram for this problem. Is there any students who tool all these 5 subjects?
- In a class of 130 SHS students, 41 offers agricultural science, 62 offers business and 31 offers visual art. 16 of those students offers both agricultural science and business only and 14 offers both business and visual arts. Assuming none of the students offers all the three subjects 1. Illustrate the information on a ven diagram 2. Find the number of students who offer I. Only two subjectsEULER DIAGRAM. Determine if the following arguments are valid or invalid. 1. Some skaters drink Surge. Some skaters drink Citra. Therefore, some Surge drinkers are Citra drinkers. 2. All horses have hooves. Some horses eat oats. Therefore, some oat-eaters have hooves. 3. Some fish are tasty. All fish can swim. Therefore, some tasty things can swim 4. Some scavengers eat road-kill. All crows eat road-kill. Therefore, all crows are scavengers 5. All burglars are criminals. Some thieves are criminals. Therefore, some burglars are thieves. 6. All whales are huge marine creatures. Some huge marine creatures have gills. Therefore, some whales have gills. 7. Some mammals are bats. All bats can fly. Thus, some mammals can fly. 8. Some squirrels fly. Some squirrels gather acorns. Therefore, some acorn-gatherers fly 9. All primates are curious. Some primates are carnivores. Thus, some carnivores are curious. 10. All tattoo painter are body-artists. Some tattoo painter drive Harleys.…Suppose in a small town there are three places to eat, a Chinese restaurant, a Mexican restaurant, and a pizza place. Everyone in town eats dinner in one of these places or has dinner at home. Assume that 20% of those who eat in the Chinese restaurant go to Mexican next time, 20% eat home and 30% go to the pizza place. From those who eat in the Mexican restaurant, 10% go to the pizza place, 25% go to the Chinese restaurant, and 25% eats at home next time. From those who eat at the pizza place, 30% eat at home, 30% eat at the Chinese restaurant, and 10% eat at the Mexican restaurant next time. Those who eat at home, 20% go to the Chinese restaurant, 25% go to Mexican restaurant, and 30% to the pizza place. FIND THE STEADY STATE PROBABILITIES
- Suppose in a small town named Oshiland there are three places to eat, a Chinese restaurant, a Mexican restaurant, and a pizza place. Everyone in town eats dinner in one of these places or has dinner at home. Assume that 20% of those who eat in the Chinese restaurant go to Mexican next time, 20% eat home and 30% go to the pizza place. From those who eat in the Mexican restaurant, 10% go to the pizza place, 25% go to the Chinese restaurant, and 25% eats at home next time. From those who eat at the pizza place, 30% eat at home, 30% eat at the Chinese restaurant, and 10% eat at the Mexican restaurant next time. Those who eat at home, 20% go to the Chinese restaurant, 25% go to Mexican restaurant, and 30% to the pizza place. a. Set us the matrix of transition probabilities. b. Find the steady state probabilities. c. In the long run, which restaurant will have the most customers?There are two kinds of inhabitants in an island, one is knights, who always tell the truth, and the other, their opposites, knaves, who always lie. If you encounter three people P, Q, and R. What are P, Q, and R, if P says “Q and R are the same types”, Q says “R is knave”, and R says “P and R is the opposite types”? Show your work in detail and validate your answer in a mathematical way using truth table or proposition.Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer Methods. Each section of Finite Math holds 40 students and earns the college $1,300 in revenue per student. Each section of Applied Calculus holds 45 students and earns the college $1,600 per student, and each section of Computer Methods holds 15 students and earns the college $1,900 per student. Assuming that the college can offer a total of seven sections, wishes to accommodate 240 students, and wishes to bring in $357,000 in revenues, how many sections of each course should it offer?