incorrect,7.3.13 Twelve different video games showing substance use were observed and the duration of times of game play​ (in seconds) are listed below. The design of the study justifies the assumption that the sample can be treated as a simple random sample. Use the sample data to construct an 80​% confidence interval estimate of sigma​, the standard deviation of the duration times of game play. Assume that this sample was obtained from a population with a normal distribution. 4 .607 3 . 970 3 . 926 4 . 652 3 . 915    4 . 400 4 . 065 4 .264 4 . 237 4 . 102 4 . 687 3 . 804 LOADING... Click the icon to view the table of​ Chi-Square critical values. The confidence interval estimate is nothing secless thansigmaless than nothing sec. ​(Round to one decimal place as​ needed.)

What is the benefit of using Fourier transforms in complex formulation.

1. Implement the Explicit Euler Scheme for Initial Value Problems of the form:
        y'(t) = F(t, y(t)) ,  t0 ≤ t ≤ tend
        y(t0) = y0

   The function F(t,y) should be coded in a function subprogram FCN(...).
   Input data: t0, y0, tend, Nsteps.  Thus the time-step will be h=(tend-t0)/Nsteps.
   Your code should print out the input data and then the pairs:
                tn          Yn
   At the end, it should print out the final n, tn, Yn
   (appropriately labelled, of cource).

2. Solve, on paper, the simple (integration) problem:
                y' = 2t ,   0 ≤ t ≤ 1
                y(0) = −1

3. To debug your code, run it on the problem above. 
   Compare the numerical solution Yn with the exact solution yEXACT(tn),
   i.e. modify your output to print out:
        tn      Yn      yEXACTn         ERRn
   where ERRn = |Yn - yEXACT(tn)|, and keep track of the maximum error.
   At the end of the run, print out the above values (at time tend) 
   and the maximum overall error ERRmax.  Test with N=10 and N=100.
   Turn off printing of tn  Yn ... and test with N = 1000, 10000 and larger.

   Once the code is debugged, only FCN(...) and input data need to be changed 
   to solve other IVPs.

4. Now solve the IVP:
        y' = −t/y ,   0 ≤ t ≤ 1
        y(0) = 1

   Find the exact solution at t = 1 (by hand),
   and compare the numerical and exact values at t = 1.  
   Try small (N=10) and larger (N=100, 1000, 10000, ... ) number of time-steps.
   At which time does the worst error occur in this problem ?
   Plot the exact solution.  Do you see why it occurs there?

Solve each of the following systems by the eigenvalue method. If ICs are given, find the particular solution to the system. If no ICs are given, find the general solution. Write all solutions in vector form.

x'₁ = -2x₁ + 5x₂, x'₂ = -6x₁ + 9x₂; x₁(0) = 1; x₂(0) = 3

An object of 4 kg (assuming the acceleration of gravity g = 10 m / s2 ) suspended from a spring causes the spring to stretch 2 cm downwards. The object is moved 3 cm down from from its equilibrium position in the positive direction of movement, then it is released with speed zero initial. Assuming that there is no damping and that the object is under external force equal to:

20cos4(t) (N)

a) Formulate the initial value problem that describes the movement of the object.

b) Draw the graph of the solution

c) If the given external force is replaced by a force of 40sinw(t) (N) of frequency w find the value of w for which a resonance occurs.

Consider the following first-order ODE dy/dx=x^2/y from x = 0 to x = 2.4 with y(0) = 2. (a) solving with Euler’s explicit method using h = 0.6 (b) solving with midpoint method using h = 0.6 (c) solving with classical fourth-order Runge-Kutta method using h = 0.6. Plot the x-y curve according to your solution for both (a) and (b).

Make a distinction between simple linear and multiple linear regression. Can you think of examples in your business world where these techniques are or should be applied? Share the details, where possible.

Solve the following equations in non-negative integers.

1. x² - y² = 221

2. a + b = ab

3. gcd(a,b)lcm(a,b) = b + 9

4. x⁴ + 2x³ - y²(1+2x) + x²(1-y²) = 2299

Consider the following second-order ODE: (d^2 y)/(dx^2 )+2 dy/dx+2y=0 from x = 0 to x = 1.6 with y(0) = -1 and dy/dx(0) = 0.2. Solve with Euler’s explicit method using h = 0.4. Plot the x-y curve according to your solution.

Solve the following differential equations using method of undetermined coefficients:

a) y''-5y'+6y=2t-3e^(-4t)

b)y''+4y=5cos(2x)

c)y''''-y''=3x+yxe^(-x)

d)y''-3y'-4y=3+e^(4t)

Find the order and the inverse of the element in the indicated group. (a) (17, 4) ∈ Z-18 × Z-18 (b) (10,(1 4 5),(1 2)(3 4 5)) ∈ Z-12 × A-5 × S-5 (c) (35, 18, 30, 4) ∈ Z-45 × Z-26 × Z-35 × Z-38

A painter wants to know the amount of paint needed to paint only the walls and the interior side of the door in a room. The chosen paint covers 100 square feet per gallon. There are two windows in the room. Create the criteria / constraint chart for this problem Create the PAC for this problem What are the data that you would need to know to solve this problem? How would not painting the interior side of the door alter your problem definition? Create the IPO for this problem. Assuming the task list contains a task for input of data, a task for the calculations, and a task for output show the flowchart and pseudocode for the calculation module in this problem.

Find the exact solution : y''+9y'=cosπt, y(0)=0,y'(0）=1