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- A Bitter Dispute With the publication of Ars Magna, a dispute intensified between Jerome Cardan and another mathematician named Niceolo Fontana, otherwise known as Tartaglia. What was the dispute, and how did it arise? In your opinion, who was at fault? Write a paragraph or two about your findings.Insurance companies can lower their risks by A) using the law of large numbers to make the number of claims more predictable. B) diversifying across insurance products. C) granting large numbers of independent risk policies. D) all of the aboveYou’re a quality control engineer working for Tinker Air Force Base. The length, width, andheight of a manufactured part used in the maintenance, repair, and overhaul of a particularaircraft type are classified as being either within or outside specified tolerance limits. In aquality inspection, 86% of the parts are found to be within the specified tolerance limits forwidth, but only 80% of parts are within specified limits for all three dimensions. Further, 2% ofthe parts are within the limits for width and length but not for height, and 3% of parts arewithin limits for width and height but not length. Also, 92% of parts are within limits for eitherwidth or height or both. If a part is within the specified tolerance limits for height, what is theprobability that it will also be within the specified limits for width?
- No. Emp. No. Prod. Wkrs. Value Added by Mfg. Cost of Materials Value of Indus. Shipmnts New Cap. Exp. End Yr. Inven. Indus. Grp. 433 370 23518 78713 4 1833 3630 1 131 83 15724 42774 4 1056 3157 1 204 169 24506 27222 4 1405 8732 1 100 70 21667 37040 4 1912 3407 1 220 137 20712 12030 4 1006 1155 1 89 69 12640 13674 3 873 3613 1 26 18 4258 19130 3 487 1946 1 143 72 35210 33521 4 2011 7199 1 171 126 20548 19612 4 1135 3135 1 21 15 23442 5557 3 605 5506 2 3 2 287 163 1 2 42 2 2 2 1508 314 1 15 155 2 6 4 624 2622 1 27 554 2 52 47 2471 4219 2 292 929 3 74 63 4307 5357 2 454 1427 3 13 12 673 1061 1 20 325 3 17 13 817 707 1 84 267 3 169 147 8986 10421 3 534 2083 3 51 41 3145 4140 2 220 697 3 55 44 4076 7125 2 176 1446 3 84 76 3806 8994 2 423 1014 3 61 47 4276 5504 2 464 1291 3 27 22 1239 716 1 22 356 4 200 178 9423 8926 3 200 2314 4 294 250 11045 11121 3 189 2727 4 38 32 1916 2283 1 29 682 4 17 14 599 364 1 21 197 4 34 28 2063 1813 1 20…Pleasantville Steel Works stamps/produces O-rings for various metal-work companies. The metal-work companies expect the O-rings to have a diameter of 30 cm. The machine that makes these O-rings does not always produce each O- ring with a diameter of exactly 30 cm (sometimes, metal shards are left behind after pressing and affect the next O-ring) and consequently, the O-rings can vary slightly. When the machine is working properly, the O-rings made on this machine have a mean diameter of exactly 30 cm. The standard deviation of the diameters of all O-rings produced on this machine is always equal to 0.5 mm. The quality control department takes a random sample of 35 such O-rings every week, calculates the mean of those diameters for these O-rings, and makes a 99% confidence interval for the population mean. If either the lower limit of this confidence interval is less than 29.9500 cm or the upper limit of this confidence interval is greater than 30.04 cm, the machine must be stopped and…1. Consumers at a ABC arrive at a rate of 45 per hr. There are three servers that can process customers at an average of 3 mins. (a) What is the average wait time? (b) What is the average number of customers waiting? (c) What is the average number of customers in the DMV? 2. A small entrepreneurial company is trying to decide between developing twodifferent products that they believe they can sell to two potential companies, one large andone small. If they develop Product A,they have a 50% chance of selling it to the largecompany with annual purchases of about 20,000 units.If the large company won't purchaseit, then they think they have an 80% chance of placing it with a smaller company, with salesof 15,000 units.On the other hand if they develop Product B, they feel they have a 40%chance of selling it to the large company, resulting in annual sales of about 17,000 units. If the large company doesn't buy it, they have a 50% chance of selling it to the small company with sales of…
- 16. In the design of an electromechanical product, 12 components are to be stacked into acylindrical casing in a manner that minimizes the impact of shocks. One end of the casingis designated as the bottom and the other end is the top. a. If all components are different, how many different designs are possible?b. If seven components are identical to one another, but the others are different, how manydifferent designs are possible?c. If three components are of one type and identical to one another and four components areof another type and identical to one another, but the others are different, how manydifferent designs are possible?1.Philippine Population 110MUrban Population 51.2% of PHMulti-unit Residential Population11.9% of Urban PopulationIf usage is 2 bottles per day and each bottle is Php12.00…What is the market size (value) per quarter for bottled water for the urban population?What is the market size (units) per quarter for those living in multi-unit residential areas?______________________________________________________________________2.UST Population 40,000 studentsCommerce Population 5,000 studentsAverage of 3 events per Schoolyear.Students are required to buy and wear separate college shirts for every event.Average price per shirt is Php350.00.What is the market size (value) for college shirts in UST? In commerce?What is the market size (units) in UST? In commerce?______________________________________________________________________3.Popo and Popi take the LRT to school on class days for School year 2019-2020.A school year is approximately 10 months.They spend Php50.00 daily fare for the LRT…A farmer would like to evaluate Miracle Grow when used on his potted daisy plants. He sets up 20 plants in a room all facing the same window, obtaining the same amount of sunlight, and waters them identically each day. For a month, he monitors how much each plant grows. Then, he adds Miracle Grow to every pot and monitors how much each plant grows during a month with Miracle Grow. At the end of two months, he discovers that 14 plants grew more with Miracle Grow. Test the hypothesis that Miracle Grow increases plant growth (using an alpha level of .01). a) Is this a one-tailed or two-tailed test? ( b) State the null hypothesis. c) State the alternative hypothesis. d) Find the critical value(s). e) Calculate the obtained statistic. f) Calculate the P-Value (significance) of the obtained statistic). g) Make a decision. h) What does your decision mean?
- A municipal solid-waste site for a city must be located at Site A or Site B. After sorting, some of the solid refuse will be transported to an electric powerplant where it will be used as fuel. Data for the hauling of refuse from each site to the power plant are shown in Table P2-4. If the power plant will pay $8.00 per cubic yard of sorted solid waste delivered to the plant, where should the solid-waste site be located? Use the city’s viewpoint and assume that 200,000 cubic yards of refuse will be hauled to the plant for one year only. One site must be selected.The Etruscans. Anthropologists are still trying to unravel the mystery of the origins of the Etruscan empire, a highly advanced Italic civilization formed around the eighth century B.C. in central Italy. Were they native to the Italian peninsula or, as many aspects of their civilization suggest, did they migrate from the East by land or sea? The maximum head breadth, in millimeters, of 70 modern Italian male skulls and 84 preserved Etruscan male skulls was analyzed to help researchers decide whether the Etruscans were native to Italy. The resulting data can be found on the WeissStats site. [SOURCE: N. Barnicot and D. Brothwell, “The Evaluation of Metrical Data in the Comparison of Ancient and Modern Bones.” In Medical Biology and Etruscan Origins, G. Wolstenholme and C. O’Connor, eds., Little, Brown&Co., 1959] a. Obtain normal probability plots, boxplots, and the standard deviations for the two samples. b. Based on your results from part (a), which would you be inclined to use to…Classic Construction Company specializes in constructing buildings with a period-correct architectural style. Three of their current projects, one in Dallas, one in St. Louis, and one in Atlanta, all require a particular reddish “scratch-faced brick,” which can only be purchased from two suppliers, one based in Newkirk, Ohio and one based in Tulsa, Oklahoma. The unit purchase costs and the availability of bricks at the two locations are given in the table below: Unit Costs (per brick) Available Supply Newkirk $0.57 95,000 (bricks) Tulsa $0.64 78,000 (bricks) The quantities (“demand”) needed by Classic Construction are given in the table below. Dallas St. Louis Atlanta 57000 44,000 68000 Suppose that shipping costs are assessed per truck. Each truck can carry up to 10,000 bricks. However, if you send a truck with only 5000 bricks from Newkirk to Atlanta, Classic Construction still pays $4000 for the half-loaded truck. The shipping costs…