Consider the equations describing the interactions of robinsr and worms w,dwr =ԱԼwwr,and(a) What are the (non-zero) nullclines for this system?W=(i) (w, r) = (wherethe population of worms, w isand the population of robins, r is(ii) (w, r) = (region, wherethe population of worms, w isand the population of robins, r isdr(b) Your nullclines divide the phase plane into four regions.Give a sample point in each region, and indicate for thatpoint whether each of the populations is increasing ordecreasing (by entering the word increasing or decreasingappropriate blank):(iii) (w, r) = (region, wherethe population of worms, w isand the population of robins, r isԱԼ(iv) (w, r) = (region, wherethe population of worms, w isand the population of robins, r is-r+rw.) is in one region,) is in a second) is in a third) is in the fourth

Given Data: Let us consider the given system is, dwdt=w-wrdrdt=-r+rw

Answered: dw r = u = w-wr, and dr u -r + rw. (a)…

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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lecture(12.11): Researchers were interested in the effects of co-sleeping on nightime waking and crying in infants. .They assesed the number of minutes parents reported that their infants were awake and crying for a period of three days. Five of the infants co-slept with thier mothers(Co) and four infants slept in crib(Cr).The researchers wanted to see if there was a difference in the total number of minutes of crying during the 3 nights. for the two groups. A summary of the data is given below Co-sleepers night time crying in minutes: 8, 4, 7, 7, 6 Crib-sleepers night time crying in minutes: 30, 17, 22, 25 Test the hypotheses at (aplha=.05) level of signifcance. using the 5 step hypotheses testing procedure. Clealy state the null and alternative hypotheses. Round your answer to 2 decimal places.
Calculate the correlation coefficient r, letting Row 1 represent the x-values and Row 2 the y-values. Then calculate it again, letting Row 2 represent the x-values and Row 1 the y-values. What effect does switching the variables have on r? Row 1 19 23 31 49 51 70 79 Row 2 156 155 190 141 202 191 181 Calculate the correlation coefficient r, letting Row 1 represent the x-values and Row 2 the y-values. r= 0.430 (Round to three decimal places as needed.) Calculate the correlation coefficient r, letting Row 2 represent the x-values and Row 1 the y-values. (Round to three decimal places as needed.)
High Cholesterol: A group of eight individuals with high cholesterol levels were given a new drug that was designed to lower cholesterol levels. Cholesterol levels, in milligrams per deciliter, were measured before and after treatment for each individual, with the following results: Individual Before After 1 237 208 2 239 202 3 230 185 4 245 217 5 242 180 6 282 215 7 243 182 8 286 195 Send data to Excel Part: 0 / 2 Part 1 of 2 (a) Construct a 99.9% confidence interval for the mean reduction in cholesterol level. Let d represent the cholesterol level before treatment minus the cholesterol level after. Use the TI-84 calculator and round the answers to at least one decimal place.
High Cholesterol: A group of eight individuals with high cholesterol levels were given a new drug that was designed to lower cholesterol levels. Cholesterol levels, in milligrams per deciliter, were measured before and after treatment for each individual, with the following results: Individual Before After 1 296 218 2 289 214 3 280 180 4 295 205 5 281 168 6 281 201 7 283 170 8 285 182 Send data to Excel Part: 0 / 2 0 of 2 Parts Complete Part 1 of 2 (a) Use a calculator to construct a 90% confidence interval for the mean reduction in cholesterol level. Round your answers to at least one decimal place. The confidence interval for the mean reduction in cholesterol level is , .
Question 4Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of thecompany wants to know how different variables affect the sales of his vehicles. A random sample ofyearly data was taken with the view to testing the model:SALES=?+?AGE+?MIL+?ENGWhere SALES= amount that a vehicle is sold for($000’s), AGE = age of the vehicle, MIL= the totalmileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data wasprocessed using MINITAB and the following is an extract of the output obtained: d) Hence test whether ? is significant. Give reasons for your answer. e) Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term “R-sq” and comment on its value.
Question 4 Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of the company wants to know how different variables affect the sales of his vehicles. A random sample of yearly data was taken with the view to testing the model: SALES=a+BAGE+YMIL+&ENG Where SÄLES= amount that a vehícle is sold for($000's), AGE = age of the vehicle, MIL= the total mileage of the vehicle at the point of sale and ENG= the size of the engine. The sample of data was processed using MINITAB and the following is an extract of the output obtained: The regression equation is ***** Coef StDev t-ratio p-value Predict or Constan 1.7586 0.2525 6.9648 0.0000 AGE 0.2124 0.3175 0.5042 ** MIL -0.7527 0.3586 -2.0991 7.7664 0.0000 *** ENG 4.8124 Analysis of Variance DF MS Source 3 413.1291 138.709 **** 0.00 Regressi 7 on 50 457.7607 2.2888 Error Total 53 a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values *', '**',…
QUESTION 14 CardioGood Fitness Treadmill Products Data The market research team at CardioGood Fitness retail store wants to investigate whether there are differences across the product lines of treadmills sold; TM195 (low-end model), TM498 (medium grade model) and TM798 (high-end model) with respect to customer characteristics. The team decides to collect data on individuals who purchased a treadmill at a CardioGood Fitness retail store during the past three months. One question the team is interested in is if there is a difference in the miles of intended use of the treadmill between males and Females. t-Test: Two-Sample Assuming Unequal Variances MaleMiles Female Miles Mean 112.81 89.99 Variance 2991.43 2006.76 Observations 104 76 Hypothesized Mean Difference df 176 t Stat 3.0732 P(T<=t) one-tail 0.0012 t Critical one-tail 1.6536 P(T<=t) two-tail 0.0025 t Critical two-tail 1.9735 In the essay box, clearly answer questions 1-5 below: 1. Is this conducting a one-sided test or a…
Let n=23 and consider the following information, Model One: Y = Bo + B1X, + B2X2 + B3 X3 + B4X, +e and R 90.62% Model Two: Y Bo + B1X1 + B2X2 + B4X4 + e and R2 = 82.55%, Model Three: Y = Bo+ B1X1 + B2X2 + B3X3 te and R2 Model Four: Y = Bo + B,X1 + B,X, +e and R? 86.85%, 81.19%. %3| Consider testing that Ho : B1 = B2 = B3 = 0. The value of the computed test statistic is Select one: O a. 74.45 O b. 41.83 Oc. 29.96 O d. 43.46
Calculate the correlation coefficient r, letting Row 1 represent the x-values and Row 2 the y-values. Then calculate it again, letting Row 2 represent the x-values and Row 1 the y-values. What effect does switching the variables have on r? Row 1 14 25 36 45 59 66 80 Row 2 162 166 160 106 139 143 156 Calculate the correlation coefficient r, letting Row 1 represent the x-values and Row 2 the y-values. (Round to three decimal places as needed.)

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