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Q1: 4. To test Ho: = 60 versus H: µ<60, a random sample of size n= 23 is obtained from a population that is known to benormally distributed. Complete parts (a) through (d) below. (a) If x = 57.8 and s = 11:1, compute the test statistic.to =.(Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a = 0.1 level of significance, determine the critical value(s).Although technology or a t-distribution table can be used to find the critical value, in this problem use the t-distribution tablegiven. Critical Value: (c) Draw a t-distribution that depicts the critical region. Choose the correct answer below. OA.O B.С. (d) Will the researcher reject the null hypothesis? A. No, because the test statistic falls in the critical region.B. Yes, because the test statistic falls in the critical region.C. No, because the test statistic does not fall in the critical region.D. Yes, because the test statistic does not fall in the critical region.See Answer
Q2: Find the correct form of the particular solution to the following DE. Do not go on to find the specific numerical values of the undetermined coefficients! y^{\prime \prime}+4 y^{\prime}+3 y=5 e^{-3 t}+\sin (t)+\cos (2 t)-7 t^{2}See Answer
Q3: 3. Determine the t-value in each of the caşes, (a) Find the t-value such that the area in the right tail is 0.20 with 24 degrees of freedom.(Round to three decimal places as needed.) (b) Find the t-value such that the area in the right tail is 0.025 with 24 degrees of freedom.(Round to three decimal places as needed.) (c) Find the t-value such that the area left of the t-value is 0.05 with 14 degrees of freedom. [Hint: Use symmetry.](Round to three decimal places as needed.) (d) Find the critical t-value that corresponds to an area of 0.01 to the left. Assume 19 degrees of freedom. [Hint: Usesymmetry.](Round to three decimal places as needed.)See Answer
Q4: 14.25 In water-resources engineering, the sizing of reservoirs depends on accurate estimates of water flow in the river that is being impounded. For some rivers, long-term historical records of such flow data are difficult to obtain .In contrast, meteorological data on precipitation are often available for many years past. Therefore, it is often useful to determine a relationship between flow and precipitation .This relationship can then be used to estimate flows for years when only precipitation measurements were made. The following data are available for a river that is to be dammed: Plot the data. Fit a straight line to the data with linear regression . Superimpose this line on your plot. Use the best-fit line to predict the annual water flow if the precipitation is 120 cm. If the drainage area is 1100 km(2) estimate what fraction of the precipitation is lost via processes such as evaporation, deep groundwater infiltration, and consumptive use. See Answer
Q5: Fit a cubic polynomial to the following data: Along with the coefficients, determine r^{2} \text { and } s_{y / x^{*}}See Answer
Q6: 14.7 The following data were gathered to determine therelationship between pressure and temperature of a fixedvolume of 1 kg of nitrogen. The volume is 10 m. Employ the ideal gas law pV = nRT to determine R on the basis of these data. Note that for the law, T must be expressed in kelvins.See Answer
Q7: 15.5 For the data from Table P15.5, use polynomial regression to derive a predictive equation for dissolved oxy-gen concentration as a function of temperature for the case where the chloride concentration is equal to zero. Employ a polynomial that is of sufficiently high order that the predictions match the number of significant digits displayed in the table.See Answer
Q8: Problem 3:Consider the following 2nd order ODE: \frac{d^{2} y}{d t^{2}}-\left(1-y^{2}\right) \frac{d y}{d t}+y=0 with the initial conditions given by y(t=0)=1, \quad \frac{d y}{d t}(t=0)=1 (a) Convert this into a system of two 1 st order ODES. (b) Solve this system of ODES for t = 0 to 10 in Matlab by writing a script that uses the M-file function rk4sys.m, which is based on the classical fourth order Runge-Kutta method,posted in Canvas under Lecture 25 with two different time steps h= 0.25 and 0.125. Plotthe results of the two dependent variables as a function of time. (c) Solve this system of ODES for t = 0 to 10 in Matlab by writing a script that invokes the Matlab built-in function ode45, which uses adaptive time steps, i.e., determines the time step needed automatically. Plot the results of the two dependent variables as a function of time.Note: The syntax for this built-in function is [t, y] = ode45(odefun, tspan, y0), where odefun is the name of the function that contains the right side of the system of differential equations and tspan contains the initial and final values of the independent variables.See Answer
Q9: In the thermos shown in figure 4, the innermost compartment is separated from the middle container by a vacuum. There is a final shell around the thermos. This final shell is separated from the middle layer by a thin layer of air. The outside of the final shell comes in contact with room air. Heat transfer from the inner compartment to the next layer q, is by radiation only (assume the space is evacuated). Heat transfer between the middle layer and outside shell q2 is by convection in a small space. Heat transfer from outside shell to the air g3 is by natural convection. The heat flux from each region of the thermos must be equal at steady state (that is q1 = q2 = 93).Find the temperatures T1 and T2 at steady state. To = 500°C and T3 = 25°C. \begin{array}{l} q_{1}=10^{-9}\left[\left(T_{0}+273\right)^{4}-\left(T_{1}+273\right)^{4}\right] \\ q_{2}=4\left(T_{1}-T_{2}\right) \\ q_{3}=1.3\left(T_{2}-T_{3}\right)^{4 / 3} \end{array} See Answer
Q10: Q-1: Modify If.. Structure as used in exercise 3.3.1 by input and disp function. Test the code by changing the variable grade'See Answer
Q11: Q-8 Determine the roots of f(x) = -13 +18x? by using Part (a) Built-in Matlab function fzero Part (b) Using graphical method (fplot).See Answer
Q12: Q-4: Calculate value of k2-50 for all integers in [-10, 10] domain but only until k2-50 becomes negative. Use while----break structure and fprintf for displaying results.See Answer
Q13: 5. A college entrance exam company determined that a score of 22 on the mathematics portion of the exam suggests that astudent is ready for college-level mathematics. To achieve this goal, the company recommends that students take a corecurriculum of math courses in high school. Suppose a random sample of 150 students wha completed this core set ofcourses results in a mean math score of 22.3 on the college entrance exam with a standard deviation of 3.8. Do theseresults suggest that students who complete the córe curriculum are ready for college-level mathematics? That is, are theyscoring above 22 on the math portion of the exam? Complete parts a) through d) below.-el 4 lu en a) State the appropriate null and alternative hypotheses. Fill in the correct answers below. The appropriate null and alternative hypotheses areHо: (1)(2)versusH;: (3) b) Verify that the requirements to perform the test using the t-distribution are satisfied. Check all that apply. A. The students were randomly sampled.B. The students' test scores were independent of one another.C. The sample size is larger than 30.D. None of the requirements are satisfied. c) Use the classical approach at the a=0.10 level of significance to find the critical value and test the hypotheses. Identifythe test statistic. to =(Round to two decimal places as needed.) Identify the critical value. Select the correct choice below and fill in the answer box within your choice.(Round to two decimal places as needed.) A. ta/2=%3D O B. ta = d) Write a conclusion based on the results. Choose the correct answer below. sufficient evidence to conclude that the(5).the null hypothesis and claim that there (6)than 22.population mean is (7).See Answer
Q14: Digitalis is a technology company that makes high-end computer processors. Their newest processor, the luteA, is going to be sold directly to the public. The processor is to be sold for $5100, making Digitalis a profit of $502. Unfortunately there was a manufacturing flaw, and some of these luteA processors are defective and cannot be repaired. On these defective processors, Digitalis is going to give the customer a full refund. Suppose that for each luteA there is a 12%chance that it is defective and an 88% chance that it is not defective. If Digitalis knows it will sell many of these processors, should it expect to make or lose money from selling them? How much?See Answer
Q15: Avicenna, a major insurance company, offers five-year life insurance policies to 65-year-olds. If the holder of one of these policies dies before the age of 70, the company must pay out $22,700 to the beneficiary of the policy. Executives at Avicenna are considering offering these policies for $454 each. Suppose that for each holder of a policy there is a 2% chance that they will die before the age of 70 and a 98% chance they will live to the age of 70. If the executives at Avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? How much?See Answer
Q16: Consider the primal linear programming problem below. \begin{aligned} &\text { Maximise } 8 x_{1}+10 x_{2}+8 x_{3}\\ &\text { subject to }\\ &8 x_{1}+6 x_{2}+3 x_{3} \leq 12\\ &6 x_{1}+12 x_{2}+16 x_{3} \leq 20\\ &x_{1}, x_{2}, x_{3} \geq 0 \end{aligned} a) Construct the dual problem and solve it graphically. b) Determine a solution to the primal problem, stating clearly any results that youuse (do not use the simplex algorithm).See Answer
Q17: Three car showrooms A, B and C are supplied by cars from three ports, 1, 2 and 3.The table below gives the cost, in pounds, of transporting a car from each port toeach showroom. Ports 1, 2 and 3 have stocks of 600, 400 and 800 cars respectively.A, B and C require 400, 500 abd 700 cars respectively.The aim is to minimise the total cost of transporting the cars. a) Formulate, but do not solve, the problem in the form of a linear program. b) Now write the problem in the form of a transportation array, explaining how you deal with the fact that the total demand and the total supply are not equal. c) Find the optimal transportation solution.See Answer
Q18: A catenary cable is one that is hung between two points not in the same vertical line. As depicted in figure 3, it is subject to no loads other than its own weight. Thus, its weight (N/m) acts as a uniform load per unit length along the cable. A free-body diagram of a section AB is depicted in figure 3, where TĄ and TR are the tension forces at the end. Based on horizontal and vertical force balances, the following differential equation model of the cable can be derived asdx²1+ТА%3D Calculus can be employed to solve this equation for the height y of the cable as a function of distance x, y=\frac{T_{A}}{w} \cosh \left(\frac{w}{T_{A}} x\right)+y_{0}-\frac{T_{A}}{w} \text { where } \cosh x=\frac{1}{2}\left(e^{x}+e^{-x}\right) Determine the value of TA given the values for the parameters w = 12 and yo = 5, such that the cable height has a height of y = 15 at x = 40. See Answer
Q19: Use Euler's method with At = .2 and then At = .1 to estimate the solution of the initial value problem x^{\prime \prime}+3 x^{\prime}+10 x=0 x(0) = 9, x'(0) = 0, for 0 <t< 10. Give a plot of both approximate solutions you obtain. Make sure to label axes,provide a legend, and give a name to your plot.See Answer
Q20: 14.12 On average, the surface area A of human beings is related to weight W and height H. Measurements on a number of individuals of height 180 cm and different weights(kg) give values of A (m2) in the following table: Show that a power law A = aW(b) fits these data reasonably well. Evaluate the constants a and b, and predict what the surface area is for a 95-kg person.See Answer

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