Consider a species of elk that can be split into 4 age groupings: those aged 0-1 years, those aged 1-2 years, and those aged 2-3 years, andthose aged 3-4 years. The population is observed once a year. Given that the Leslie matrix is equal to01.11.70.80 01.3]0L=00.6 000 00.20and the initial population distribution is 40 of the first age group, 17 of the second age group, 10 of the third group, and 5 of the oldest age group,answer the following questions.The initial population vector is x0 =How many elk aged 1-2 years are there expected to be after 10 years?How many elk aged 0-1 years are there expected to be after 20 years?How many elk are there expected to be after 30 years?Calculate the dominant eigenvalue of the Leslie matrix good to 3 decimal places. λ1=What is the long-term growth rate of this population of elk as a percent? growth rate =over/under 100%.)Are the elk thriving, static, or going extinct? ?(The growth rate is the percentage of growth

1. the initial population vector is x0=⎣⎢⎢⎢⎡4017105⎦⎥⎥⎥⎤ 2. After ten years, there are expected…

Answered: Consider a species of elk that can be…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A chi-square test for goodness of fit is used to examine the distribution of individuals across five categories, and a chi-square test for independence is used to examine the distribution of individuals across six categories in a 2 X 4 matrix of categories. Which test has the larger value for df? Select one: a. The test for independence has the larger value. b. The goodness of fit has the larger value. c. The df value depends on the sizes of the samples that are used. d. Both tests have the same df value.
Suppose you are a production manager for a small firm that manufactures designer phone cases. Your production facility utilizes three machines. Quality is binary — each phone case is either defective or it is not defective. Each hour, Machines 1, 2, and 3 produce 10, 10 and 20 phone cases, respectively. But because the machines differ slightly in their technology, data on past production has shown that they differ in terms of their rates of defective output — specifically, Machines 1, 2, and 3 have rates of defective production of 2%, 4%, and 5%, respectively. If one phone case is selected randomly from one hour’s total output, and that phone case is found to be defective, what is the probability that it was produced by Machine 1? Machine 2? Machine 3?
A simplified version of input-output analysis of a national economy has the following input-output matrix: Agriculture Manufacturing Households 0.245 0.051 0.099 0.279 0.433 0.011 A. Agriculture Manufacturing Households 0.102 0.291 0.372 units of Manufacturing are need to produce one unit of Households B. Given Demand (in billions of dollars) for the three sectors are as follows 32.6 = Manufacturing, 3.5-Agriculture 31.8-Households Find the amount of each commodity that should be produced (nearest 0.1 billion) = Agriculture - Manufacturing Households C. If the external demand of Households raises by $1 billion then manufacturing production needs to increase by $ billion (nearest 0.01) in order to meet that increase in household external demand
Question No. 4: According to the All Pakistan Software Developer Association (APSDA), developers generally spend more than 40 hours each week working on software and web development. The Table 4.1 shows the number of hours worked per week for a sample of 15 Software developers and a sample of 10 Web developers. Table 4.1 Software Developers 56 54 54 49 61 48 58 60 59 53 50 58 55 57 52 Web Developers 47 50 46 47 48 49 46 55 44 42 ---- a) What is the third quartile of spending working hours for Software developers? b) Create a box plot for the number of hours worked for Software developers. c) Create a box plot for the number of hours worked for Web developers. d) Comment on the differences between the box plots for Software & Web developers.
Given the Leslie matrix below, what is the population size after 2 timesteps given the starting population size of J= 10, T=10, A=100? Round to nearest whole number. J T A J 0.5 0.5 3.0 T 0.2 0 A O 0.2 0 O a. J=162; T=62; A=1 O b. J=10; T=10; A=100 O c. J=200; T=25; A=5 O d. J=310; T=2; A=3
Question 1 The following data matrix includes 8 data points each having 2 dimensions X(1) and X(2) X(1) X(2) 1 5 3 2 4 1 4 st C 3 Lo | 2 T 0 O 1.42 The correlation coeffecient between X(1) and X(2) is: O 1.25 F O 130 3 2 4 1 4 3 2 Question 2 The following data matrix includes 8 data points each having 2 dimensions X(1) and X(2) X(1) X(2) 1 5 7 6 00 8 8 5 6 7 Show Transcribed Text O 1.00 ת O 1.42 O Infinity The correlation coeffecient between X(1) and X(1) is: 7 6 8 8 5 6 7
11:14 Question 1. WHO keeps track leprosy cases in the world using the regions and the World Banks income groups. Data on leprosy cases in different countries collected in the year 2011 is summarized in the table below. High WHO Region Income Americas Eastern Mediterranean Europe Western Pacific Africa World Bank Income Group South-East Asia 174 54 10 26 0 0 Upper Lower Middle Middle Income Income 36,028 615 6 0 0 1,883 39 0 LTE 85% Row Low Total Income 0 0 36,817 604 2,547 216 3,689 1,155 5,086 10 1,986 15,928 17,953 149,896 10,236 160,132 Column Total 264 36,289 158,069 27,923 222,545 Required Is there evidence to show that income level and WHO region are independent when dealing with the disease of leprosy? Test at the 5% level. (Also calculate the Chi-Square) 1. State the null and alternative hypotheses and the level of significance 2. Find the test statistic and p-value 3. Give the conclusion on Hypothesis and further give an explanation.
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A car rental service in a certain town has a fleet of about 600 cars, at three locations. A car rented at one location may be returned to any of the three locations. The various fractions of cars returned to the three locations are shown in the matrix to the right. Suppose that on Monday there are 295 cars at the airport (or rented from there), 65 cars at the east side office, and 240 cars at the west side office. What will be the approximate distribution of cars on Wednesday? Cars Rented From: Airport East West 0.95 0.03 0.12 0.00 0.94 0.06 0.05 0.03 0.82 Returned To: Airport East West On Wednesday, 274 cars will be at the airport, 52 cars will be at the East location, and 274 cars will be at the West location. (Round to the nearest integer as needed.)
A population with three age classes has a Leslie matrix L = compute x₁, x₂, and x3. X1 = x3 = 600 90 80 1010 H 540 72 1838 909 57.6 1 0.9 0 14 0 0 0.8 0 If the initial population vector is xo = 100 100 100
A car rental agency in a major city has a total of 4600 cars that it rents from three locations: Metropolis Airport, downtown, and the smaller City Airport. Some weekly rental and return patterns are shown in the table (note that Airport means Metropolis Airport). Returned to AP DT CA 90% 10% 10% Airport (AP) Downtown (DT) 5% 80% 5% Rented from At the beginning of a week, how many cars should be at each location so that the same number of cars will be there at the end of the week (and hence at the start of the next week)? AP DT CA Need Help? cars cars cars Read It Watch t Talk to a Tutor

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