1. What is the value of the correlation between Academic Performance and Digital Literacy? A. r=-0.6307 B. r = 0.6307 C. r=-0.3607 D. r = 0.3607 2. What is the regression equation between academic performance and digital literacy? A. y = 32.92x + 0.619 B. y = -32.92x + 0.619 C. y = 0.619x + 32.92 D.y = -0.619x - 32.92 3. What is the value of the correlation coefficient between Academic performance and Speed of internet? A. r = -0.4133 B. r=0. 4133 C. r = -0.3341 D. r = 0.3341

Q: Q1) Let D = M₂ (Z2)be a ring find the order of D and all the idempotent elements.

A:

Q: Suppose the function f: R→ R has Fourier transform 1 f(p) = e-p². 1+ 4π²p² i. What is the Fourier…

A: As per the question we are given the Fourier transform of a function f(x) as f̂(p) From that we have…

Q: Question Three Let f(x) be a function given by 0 f(x) = { sin (a) Prove whether f(x) is a Dirichlet…

A: Given: Let us consider the given function, fx=0-π≤x<0sinx0≤x≤π a) Let's show the given fx is a…

Q: Solve the initial value problem. dy +2y-4e¯X = 0, dx The solution is y(x) = y(0) = 2

A: Given differential equation is in the form of linear differential equation . So we will use…

Q: 9.) Use spherical coordinates to evaluate 3/2 (x² + y² +2²) ³¹² dydzdx. 9-1² √√9-1²-₂² √√√9-x²-2²

A: To find the given integral using spherical co-ordinate system :-

Q: Maximize z = 4x + 2y, subject to the following constraints. (See Example 8. If an answer does not…

A:

Q: 4. A composite function Function from your design Disregard desmos restrictions. Set sliders to 0 or…

A: To find: The instantaneous rate of change of a particle at x=A.

Q: Suppose G(r) is the generating function of a sequence (an), satisfying G'(r)=rG(r), G(0) = 1. iii.…

A:

Q: Find the Maclaurin series of 2 n=0 f²e-t е 0 -t9 dt. M I

A: Given         ∫0xe-t9  dt  We know that maclaurin series of  the function  ex is ,  ex =…

Q: c) Let z(x, y) containing at (1,2). = x² be a function defined on a disk D in the positive quadra:…

A: Solution : Clairaut theorem : If fxy and fyx are both defined and continuous in a region containing…

Q: 3. Consider the functions_f(x)=(x-a)(x−b), g(x)=(x−p)(x−q)_and_h(x)= g(x) If a‡b‡p‡q, then a) which…

A:

Q: a) Suppose you are given model with two explanatory variables such that: Y₁ = a + B₁x₁i + B₂x₂₁x +…

A: Given: yi=α+β1x1i+β2x2ix+ui To find: Coefficients

Q: The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. Use Lagrange…

A: Note that here we have to extremize x2+y2+z2 , whch is eqivalently ,to extrimize x2+y2+z2.

Q: The mean weight of 800 college students is 56 kg and the standard deviation is 5 kg. Assuming that…

A: given , mean weight of 800 college students is 56 kg and the standard deviation is 5 kg. determine…

Q: Power series p₁(z) and p2(x) are given below. P₁(z) = 1 + 7x +49x² + 343x³ +2401x¹ +... P2(x) = 1 +…

A:

Q: 1. Explain why there are no tangents to the curve y = with negative slope. (Explain by 2x+1 4x+3…

A: Given: y=2x+14x+3 To explain: Why there is no tangents to the given curve.

Q: LP Model Minimize: subject to: z = x-y 4x-3y ≤0 x+y ≤ 10 x.y 20

A: We have given a LP model ,  min z = x - ysubject to,         4x - 3y ≤ 0         x + y ≤ 10…

Q: Consider the Recurrence relation an+10an-1+25an-2=0 a1 =17 1) What is the order of the above…

A:

Q: 4. Prove that a permutation matrix is orthogonal.

A: Permutation matrix: Each column of a permutation matrix has only entry equal to 1 and all other…

Q: Problem: A farmer is planning to raise wheat and barley. Each acre of wheat yields a profit of $50,…

A: We have to find the number of acres of wheat and barley to maximize the farmer's profit.

Q: Evaluate the following integral by reversing the order of intgeration: √ 2π [²² 1²² cos(7x²) dxdy…

A:

Q: Find the volume of the region cut from the solid sphere

A: Given the region cut from the solid sphere x2+y2+z2≤4a2by the cylinder x2+y2=a2.

Q: In a 24-hour period, a human's body temperature will vary ab When at rest (usually at night), the…

A: The derivative of a function of a real variable measures the sensitivity to change of the function…

Q: (2) y" (t) - cy'(t) + gy(t) = 6t²²t where: you) = Y(u) =

A:

Q: Find the orthogonal compliment of the subspace W of 2x2 upper triangular matrices in the vector…

A: Using standard inner product in the space of matrices.

Q: A mark of at least 50 is required to pass a course. The marks this year run from a low of 45 to a…

A: Solution:   Required marks to pass = 50. Marks this year goes from 45 to 83. Let X1, X2, X3,...Xn be…

Q: Assume that f(x) is a function defined by x²-3x+1 f(x) = 2x - 1 for 2 ≤ x ≤ 3. Prove that f(x) is…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Apply Frobenius theorem on the following differential equation: ..2..!!

A: Given the differential equation                        x2y''-3x(x-1)y'-8(x+1)y=0

Q: ) = x² + y² - 8x - 6y subject to the

A: Given that fx,y=x2+y2-8x-6y. First we have to find the extreme point on the domain given in the…

Q: Suppose F(2) = 1, F(8) = − 1, and F'(x) = f(x). - 10 [ f(x) dz = 10

A:

Q: 2. Find the LU factorization of the following matrices without pivoting 1 2 3 a) A = 2 5 4 354 1 -1…

A:

Q: (c) Let z(x, y) = xr be a function defined on a disk D in the positive quadrant containing the point…

A: Follow the steps.

Q: 3. A student had 93% in Chemistry which had a class average of 85% and standard deviation of 8%. The…

A: Solution

Q: y = -x^2 + 4x + 3, y = -x^3 + 7x^2 - 10x + 5, x = 1, x=2* 4.083 sq. units ○ 4.183 sq. units O 4.283…

A: We know that the area between the curves can be evaluated by double integration method. We will find…

Q: Find the general solution to the differential equation y" - 2y + y = ex 1+x² (where y' = dy)

A:

Q: If the Laplace transform of a function f is defined and denoted by F(p), find an expression for the…

A: The solution is given as

Q: The zeros in the given matrix make its characteristic polynomial easy to calculate. Find the general…

A:

Q: If u = (1,0), then Düfz(-3, 4) = ƒxy(−3, 4). True False

A:

Q: Determine the 2nd degree Taylor polynomials Q(x, y) for f(x, y) = ln(x² + y² + 1) for (x, y) near…

A: Given function is fx,y=lnx2+y2+1. We have to find the 2nd degree Taylor polynomials Qx,y for the…

Q: 1. Given: y = (3)¹²-9: a. Determine the y-intercept algebraically b. State the asymptote c. State…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: The function f:P (₂)→Xº for X is a two-element set (0,1) is?. a) Bijective b) Surjective c)…

A: Bijective

Q: Obtain the general solution to the equation. (x² +19) dy dx + xy - 2x = 0 The general solution is…

A: Using integrating factor method

Q: z² (3+j5)z + j8-5=0

A: We have z2-3+j5z+j8-5=0' The solution of the quadratic equation az2+bz+c=0 is z=-b±b2-4ac2a Now, we…

Q: (b) Show that the function defined by IN if (x, y) (0,0), √√√z²+y² f(x, y) = 0 if (x, y) = (0,0) is…

A:

Q: Which of the following is NOT a circuit in the graph? B E F D CC OABFEA OBFDCB O None of the Above

A:

Q: The heat capacity of a gas is tabulated at series of temperatures: TCO 20 50 80 110 Cp J/mol.C 28.95…

A: We have to calculate the values of heat capacity corresponding to 28 C° and 93 C° using the newton…

Q: 1. Based on the data, what is the mean nominal wage? A. 123.26 B. 291.81 C. 350.00 D. 358.88 2.…

A: Part (1) The nominal wages are: 537, 350, 340, 360, 400, 400, 320, 310, 395, 386, 315, 316, 365,…

Q: 9. For some set A to be considered countably infinite, we know that... (Select all the choices that…

A: Countably infinite: A set which has one to one correspondence with the set of integers, is called a…

Q: √zez dz

A:

Q: Question 8* Problem III Let f(x, y, z)= -2xy - x² + 3yz + x² + y² + 2². Question 1 The set of…

A: