Example 1 Compute the Fourier sine and cosine transforms of f(x) = e¯c.

/ Solve the equation Laplac transfoms:- wt = wxx WCX10) = 0 w (o,t) = f(t) lim w(x,t) = 0 X∞

Q/Find the Fourier sine and cosine transforms of f(x) = Xe-X

Q/solve the equation Laplac transforms:- x>0, to 43 1 иху u cx,α) = f(x) и a Cort ) = • lim u(x,t) = 0 8700 و X>0 , to

Please conduct a step by step of these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points.  The data for the following questions is provided in Microsoft Excel file on 4 separate sheets. Please conduct these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points.   1. One Sample T-Test: Determine whether the average satisfaction rating of customers for a product is significantly different from a hypothetical mean of 75.  (Hints: The null can be about maintaining status-quo or no difference; If your alternative hypothesis is non-directional (e.g., μ≠75), you should use the two-tailed p-value from excel file to…

Explain how the answer could be 2 or 1.8 WITHOUT changing the question

+21 Rsts = R₁ (R+R) Calculate the total system relibility using the given formula including an explantion of how this formula was discvered.

3. Use Laplace transforms to solve the semi-infinite wave problem a) utt = c²urr, x>0,t> 0, u(x, 0) = u(x, 0) = 0, u(0,t) = f(t), lim u(x,t) = 0. PIX

a/ Solved by de Alembert utt = c²uxx u(x, 0) = f(x) ut (x, 0) = g(x) f and y are given by where CI C = 1 f(x) = 3 e-x² ,д (x)=0 2 C=3 و f(x)=0 9 9CX = Xe-X