!! 4. 307-Eng 02/24 Pg-644HMH-ESS Population Density (people per km) City Land Area New York 8550405 783.8 38,242 Shanghai 24 256 800 6340.5 2,059 Mumbai 12443373 603.4 20,634 T Annapolis 39,250 ANALYZE: At the population density of New York, how much land would 11 billion people need? How does it compare to the size of your state?
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- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.2. Suppose that in Example 2.27, 400 units of food A, 500 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 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1The cashier line of a canteen can facilitate up to 60 customers an hour. Frequenters of thecanteen arrive at an average of 50 an hour. Suppose that management wants toevaluate the desirability of opening a second order-processing station so that twocustomers can be served simultaneously. Assume a single waiting line with the firstcustomer in line moving to the first available server.a. What is the average arrival time in minutes of customers?b. What is the average service time in minutes of the canteen?c. What is the probability that the canteen has a customer?d. What is the probability that the canteen does not have any customer?e. How long would the line be on average (average number of customers in thesystem)?f. How many people are waiting to be served on average?g. How long in minutes would it take the customer from lining up until he leaves thewaiting line?h. How long in minutes would a customer wait to be served on average?i. Find the probability that there are 7 customers in the…
- For a certain type of salamander, the mass X of a randomly chosen adult is normally distributed. 95% of the adults in this species have a mass between 6.7 grams and 8.1 grams.AUA wants to know whether recent alumni students from MBA class earn significantly more than recent alumni from BAB class. They take a sample of several students and ask the amount of their monthly salaries in USD (Sheet 32). What can AUA conclude at alpha=0.05? Sheet 32 MBA BAB 515 300 450 420 620 380 630 450 570 420 590 490 750 510 560 470 480 530 250 570 320 480 450 620 625 190 350 280 450 350 570 250 Select one: a. t(stat)=1.92, which is greater than t(cr)=1.7, therefore, we can conclude that MBA graduates earn more BAB graduates. b. t(stat)=1.89, which is greater than t(cr)=1.75, therefore, we can conclude that MBA graduates earn more BAB graduates. c. t(stat)=2.07, which is greater than t(cr)=1.69, therefore, we cannot conclude that MBA graduates earn more BAB graduates. d. t(stat)=2.07, which is greater than t(cr)=1.69, therefore, we can conclude that MBA graduates earn more BAB graduates.Two of the mathematics professors at Enormous State University are Professor A (known for easy grading) and Professor F (known for tough grading). Last semester, roughly three-fifths of Professor F's class consisted of former students of Professor A; these students apparently felt encouraged by their (utterly undeserved) high grades. (Professor F's own former students had fled in droves to Professor A's class to try to shore up their grade point averages.) At the end of the semester, as might have been predicted, all of Professor A's former students wound up with a C− or lower. The rest of the students in the class—former students of Professor F who had decided to "stick it out"—fared better, and one-fourth of them earned higher than a C−. After discovering what had befallen them, all the students who earned C− or lower got together and decided to send a delegation to the Department Chair to complain that their grade point averages had been ruined by this callous and heartless beast!…
- 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…Company X has 10 employees, each placing an average of 20 minutes of long-distance calls per day. The average call lasts 5 minutes. It has been determined that 20% of the calls are made during busy hour. A total of 4 external phone lines are used to place the pool of calls. Calculate the traffic flow in Erlang during the busy hour.2. How can I find the distribution and density in closed form of the severity model of losses for the sum of n-losses when α = 0.5 and β = 1 (Levy)? Could someone explain to me how to calculate closed forms in general because I do not understand the concept? X_i(t) ∼ S_α(β, γ, δ; 0)
- At the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that z − u = 3(x − y) + 22 x + y = 50 + z + u and x − y + z − u = 58. How large was the audience of each of the four companies at the end of that year? Microsoft Time Warner Yahoo GoogleAt the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that z − u = 3(x − y) + 10 x + y = 50 + z + u and x − y + z − u = 46. How large was the audience of each of the four companies at the end of that year?At the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that z − u = 3(x − y) + 12 x + y = 44 + z + u and x − y + z − u = 36. How large was the audience of each of the four companies at the end of that year? Microsoft million Time Warner million Yahoo million Google million