Consider the equations describing the interactions of robins r and worms w,drdtr = 1(a) What are the (non-zero) nullclines for this system?W= 1dwdt(i) (w, r) = ( 12the population of worms, w isand the population of robins, r is decreasing12increasing(b) Your nullclines divide the phase plane into four regions. Give a sample point in each region, and indicate for that pointwhether each of the populations is increasing or decreasing (by entering the word increasing or decreasing appropriate blank):) is in one region, where"(ii) (w, r) = ( 32the population of worms, w isand the population of robins, r is increasing12increasing(iv) (w, r) = (the population of worms, w isand the population of robins, r is= w ― wr,-"(iii) (w, r) = ( 0.5the population of worms, w isand the population of robins, r is decreasing0.5increasingand-r + rw.) is in a second region, where) is in a third region, where) is in the fourth region, where

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

Answered: (b) Your nullclines divide the phase…

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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Q.2. Below are the commodity data. In the row for one of the commodity named "Toothpaste", their "Quantity" the cell “X" replace with your last two digits of your ID card number. (a) Determine Laspeyers' price index and Laspeyer's quantity index. (b) Determine the Paasche price index. (c) Determine Fisher's ideal index January 2020 Price ($) January 2020 Quantity 99 January 2021 Price ($) January 2021 Quantity X Commodity Toothpaste Shampoo Cough tablets Antiperspirant 4.29 5.49 4.45 4.29 6.29 3.79 4 5.67 4 4.89 6.
15) The intercept is 0, the autoregressive coefficient is 0.2 and the moving average coefficient is 0.5 in an ARIMA(1,1,1) model. What is the one-step ahead forecast if the shock for the current period is -2 and the current and one-period lagged values of the forecast variable are 110 and 105?
Q4: The following data reflect the number of defects produced on an assembly line at the Dearfield Electronics Company for the past 8 days. 3 0 2 0 1 3 5 2 5 1 3 0 0 1 3 3 4 3 1 8 4 2 4 0 a. Determine if there is a mode number of defects and, if so, indicate the mode value.
Table 1 gives data on GDP (Y - in billions), foreign direct investment (X₂ - in billions), and corruption index (X3) 31. Y 45 50 54 58 63 69 74 78 X₂ 75 78 83 86 90 93 98 100 X3 15 12 9 6 3 -2 -5 -8 What is the value of Σx and Σx3, given that x₁ = X; - X? A. 579 and 475 B. 959 and 737 C. 675.2500 and -518.2500 D. - 567.1456and 255.3750
Answer this question correctly, selecting the correct answer choice for this question.
2.) Explain why the relative frequency column of a frequency table might not sum to 1.0.
A random sample of 42 earthquakes that have occurred between January 2015 and September 2017 was selected and for each earthquake the magnitude of the earthquake and the number of people killed was recorded. The data appear in the scatterplot below. 400 350 300 250 200 150 100 50 0 3 -50 4 5 6 7 8 9 10 -100 -150 Magnitude of Earthquake 8 Consider the scatterplot above question 2. Use this scatterplot to describe completely the relationship between the magnitude of the earthquake and the number of people killed. Positive and linear Negative, moderate, linear O Negative, strong, linear Positive, moderate, linear Number of People Killed ---
4.) A person's muscle mass is expected to decrease with age. To explore this relationship, a researcher randomly selected 10 persons from ages 40 to 79 years old and measured their muscle mass (unit). The result is as follows: X (age) Y (muscle mass) 71 64 43 67 56 73 68 56 76 65 82 91 100 68 87 73 78 80 65 84 Based on the given data, do the following: a) Plot the scatter diagram of the given data. [3pts] b) Obtain the regression line equation. [4pts] c) Estimate the muscle mass when age of the person is 60 years old. [3pts] 5.) Recognize how each shape has transformed. [2pts each] a.) b.) c.)
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 *', '**',…
This dataset of size n - 51 is for the 50 states and the District of Columbia in the United States. The variables are - year 2002 birth rate per 1000 females 15 to 17 years old and z- poverty rate (the percent of the state's population living in households with in- comes below the federally defined poverty level) i- 13.1 - 22.3 R- 51, Su - E(-2) - 914.7 S, - E( -2)( - 6) - 1, 256.2 Su - E(m - M) - 3, 249 SSE - E(w - - 1, 509.6 1. Find A. A and r. 2. Write the fitted linear regression model for ý, in terms of z, A, and A- For A and , use the values you obtained in problem 1. 3. Interpret the slope of the least squares line based on the context. 4. Find SST, SE and SSR. 5. Find R* and . 6. Complete a chart for ANOVA df MS pvalue Source Regression Error Total 7. Complete a chart for Parameter Estimates. t-value pvalue Parameter Intercept Slope Estimate S.e. 8. What is the residual e, for the observation (.) - (20.1,31.5)? 9. What is the conclusion for the test Ha : -0 vs Ho : +0 with a -…
22 of 47 > Five strains of the Staphylococcus aureus bacteria were grown for 24 hours either at 35 degrees Celsius or at 43 degrees Celsius. The table gives the resulting bacterial counts for each condition: 24 hours at 35 degrees Celsius 24 hours at 43 degrees Celsius 66 98 71 67 93 42 102 31 62 77 Suppose we had plotted bacterial count at 35 degrees Celsius on the y axis instead of the x axis. How would this change affect the value of the correlation coefficient? The correlation would be the inverse of, or I over, the original value. The correlation coefficient would have the opposite sign. The correlation coefficient would be exactly the same. The correlation coefficient would have an entirely different magnitude.

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