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

What is the process of obtaining a Fourier series solution for the heat equation with Dirichlet boundary conditions and an arbitrary initial condition.

We define a relation ∼ on R^2 by (x1,y1)∼(x2,y2) if and only if (y2−y1) ∈ 2Z. Show that the relation∼is an equivalence relation and describe the equivalence class of the point (0,1).

Sunshine Juices sold $16.6 million in the U.S. pomegranate juice drink market last year, but the 11.4 million customers who bought from Sunshine Juices spent a total of $39.2 million in this market. Across the whole marketplace, 75.6 million buyers contributed to total industry sales of $178.3 million of pomegranate juice drinks. Calculate usage index for Sunshine Juices' customers in the U.S. pomegranate juice drink market. Report your answer as a percent, and round your answer to the nearest tenth of a percent. Report 27.5%, for example, as "27.5".

Answer: 145.8. Please show the steps on how to get to 145.8.

Apply the Gram-Schmidt orthonormalization process to transform the given basis for Rⁿ into an orthonormal basis. Use the vectors in the order in which they are given.

B = {(−5, 0, 12), (1, 0, 5), (0, 2, 0)}

Use Newton's method to find the absolute maximum value of the function f(x) = 3x cos(x), 0 ≤ x ≤ π; correct to six decimal places.

Graph a sample space for the experiments:
In drawing 2 screws from a lot of right handed and left handed screws. let A,B,C,D mean at a least 1 right
handed, at least 1 left handed, 2 right handed, 2 left handed, respectively. Are A and B mutually exclusive?C and D?

Let A be a bounded linear operator on Hilbert space. Show that if R(A) is closed, so is R(A*)