4. During the annual conference of a professional organization, nine topics were proposed for simultaneous plenary discussions. However, some topics need to be scheduled in different time slots. The table summarizes which topic cannot be discussed in the same schedule. Topics 1 2 3 4 5 6 1 X --- 2 --- 3 X X 4 X --- X X --- --- 7. X X X --- X --- a. How many time slots should be scheduled? b. Which topic should be included in each time slot?
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- Find three positive geometric means between 2 and 8The Königsberg bridge problem asks if the seven bridges of the city of Königsberg (picture attached), over the river Preger can all be traversed in a single trip without doubling back, with the additional requirement that the trip ends in the same place it began. Trace over each bridge ONLY ONCE WITH ONE CONTINUOUS STROKE. What is the area of mathematics used to solve the problem?Suppose a company charges a premium of $150 per year for an insurance policy for storm damage to roofs. Actuarial studies show that in case of a storm, the insurance company will pay out an average of $8000 for damage to a composition shingle roof and an average of $12,000 for damage to a shake roof. They also determine that out of every 10,000 policies, there are 7 claims per year made on composition shingle roofs and 11 claims per year made on shake roofs. What is the company’s expected value (i.e., expected profit) per year of a storm insurance policy? What annual profit can the company expect if it issues 1000 such policies? Determine the probability of a composition shingle roof claim out of 10,000 = ______ Determine the probability of a shake roof claim out of 10,000 = ______ How many claims are made out of 10,000? = _______ What is the probability of no claims out of 10,000? = _______ How much does each shingle roof claim cost the company, don’t forget each person pays $150…
- John Allen Paulos has pointed out a problem with massive, untargeted wiretaps. To illustrate the problem, he sup-poses that one out of every million Americans has terrorist ties. Furthermore, he supposes that the terrorist profile is 99% accu-rate, so that if a person has terrorist ties, the profile will pick them up 99% of the time, and if the person does not have ter-rorist ties, the profile will accidentally pick them up only 1% of the time. Given that the profile has picked up a person, what is the probability that the person actually has terrorist ties? Dis-cuss how your answer affects your opinion on domestic wire-tapping. Source: Who’s Counting.1. Due to the high incidence of crime, a company is giving its employees new and secured access to the company. Instead of leaving the doors open, they are installing a card system. To open the door, employees must insert a card into a slot. If a green light comes on, it is okay to turn the handle and open the door; if a yellow light comes on it indicates the door is locked from inside and you cannot enter. Suppose that 90% of the time when the card is inserted, the door should open because it is not locked from the inside. When the door should open, the system makes errors 2% of the time. That is, the green light will appear 98% of the time. When the door should not open, the system makes errors 5% of the time (green light appears). Suppose you inserted the card and the light is green, what is the probability the door will open?Before 1918, approximately 60% of the wolves in a region were male, and 40% were female. However, cattled rachers in the area have made a determined effort to exterminate wolves. From 1918 present, approximately 65% of the wolves in the region are male, and 35% are female. Biologists suspect that male wolves are more likely than female to return to the area where the population have been greatly reduced. Round three decimals: a) Before 1918, in a ramdon sample 11 wolves spotted in the region, what is the probability that 8 or more were males? - what is the probability 8 or more were females? - what is the probability fewer than 5 were females? d) From the period 1918 to present in a ramdon sample 11wolves spotted in the region, what is the probability that 8 or more were males? -what is the probability 8 or more were females? -what is the probability fewer than 5 were females?
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