The scores on a test are normally distributed, with a mean of 82 and standard deviation of 8. What percent of scores are less than 90? Explain your answer.

Q: Exercise 5 (a) Find a complete solution of Clairaut's equation: 1/3 1/3 z=xp+yq +3pq (b) Show that…

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Q: C. Determine the radius and the interval of convergence for the given power series: a. (x-2)3(x-2)5…

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Q: 3. Sketch the domain of the following functions: a) f(x,y)= 1-x-2y et² + y² - e b) f(x, y, z)= xyz…

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Q: 22. Let d = gcd(a, b). Prove that ged(a/d, b/d) = 1. Fl of th om of congruences

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Q: Find the eigenvalues and eigenvectors of the given matrix. 18 3 6-1 The eigenvalue(s) is/are…

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Q: Find Ix, ly and I。 for the first-quadrant area outside the circle r = 2a and inside the circle r =…

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Q: Solve y" + 2y + 2y = e cos(x) with y(0) = y'(0) = 1.

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Q: 3. Give an explicit real value general solution following equations. 2 x 6x² + 8x = 2e-97 b) y"-y-2y…

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Q: Let f(t) be a function on [0, ∞). The Laplace transform of f is the function F defined by the…

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Q: Find the radius of convergence, R, of the series. (x - 10)" n R = 10 ∞ n = 1 I = Find the interval,…

A: Given series is ∑n=1∞x-10nnn

Q: 7. Count the dots of each hexagonal shape and fill in the table. Terms a2 A3 Dots 6 16 8. What is…

A: Total poitnts in outer =24 in scond inner shelf =11 third shelf =7 fourth =3

Q: Construct the formal proof of validity for each of the following arguments.

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Q: Use the method of Lagrange multipliers to find the absolute minimum and the absolute maximum of the…

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Q: Find a vector in 3- dimensional space whose magnitude is 4 and whose components have the largest p

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Q: x= x³ = x Find the equilibrium points and their stability in the system

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Q: Which of the following subsets of P2 are subspaces of P2? □Ā. {p(t) | √√√p(t)dt = 0} B. {p(t) | p'…

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Q: Describe the steps in words that you would use to show that (x - a) is a factor of xn - an. Your…

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Q: Write a in the form a=a+T+aNN at the given value of t without finding T and N. r(t) = (2 e¹ sin t)i…

A: INTRODUCTION: The formula of the Tangential component of the vector r(t) is given by, aT=v·av The…

Q: How much monthly deposit into a sinking fund at 8.5% compounded monthly will be needed to accumulate…

A: Please check step 2 for solution.

Q: Find a general solution for the given differential equation with x as the independent variable.…

A: Given differential equation is y''' + y'' - 6y' = 0

Q: Find the derivative where w=5xyz, x=2t, y=4t, and z=3t-³. dw 1 dt dw dx (Type an expression using x,…

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Q: You flipped a loaded coin four times. The coin is loaded such that a head is twice like to appear as…

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Q: 2. The region R is bounded by y = x², y = 1, y = 2 and the Y-axis. (a) Pick a method (Disk/Washer…

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Q: Let G and L be relations on A = {1, 2, 3, 4} with G = {(1, 2), (2, 3), (4, 3)} and L = {(2, 2), (1,…

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Q: Pool construction. Refer to the rectangular swimming pool shown below. a. Find the perimeter of the…

A: The pool is rectangular in shape. a. The perimeter of the rectangle is =2(length+width) =2(150+75) =…

Q: 3x + y + z = 0; z(0) = −1

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Q: Find the exact value of the following double integrals: a. S² S/² √ysin(y) dydx Ꮭ Hint: Switch order…

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Q: Use the method of Lagrange

A: Given the function                  f(x, y, z)=x2+y2+z2 with the two constraints…

Q: Find the radius of convergence, R, of the series. x4n n (In(n))² R = 8 Σn n = 2 Find the interval,…

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Q: Consider the solid in the first octant which lies between the cones 2= and the spheres √3 3 √x² + y²…

A: We have to SET UP an integral in spherical coordinates for the Mass of the solid bounded by the…

Q: Theorem: If P is the transition matrix from a basis B' to a basis B, then P is invertible and the…

A: By the given theorem we have, B'| B→In | P-1. Given B=1,0,1,-1 and B'=1,1, 1,-1. So B' |…

Q: Find the equation of the tangent line to the common curve of the two surfaces with equations z = x²…

A: Please check step 2 for solution.

Q: method

A: We use Cauchy's Residue theorem.

Q: Find the solution of the given initial value problem: y"+y' = sec(t), y(0) = 11, y'(0) = 5, y'(0) =…

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Q: Find a fundamental matrix for the system x'(t) = Ax(t) for the given matrix A. A= 12 27 -1 Choose…

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Q: The function f(x, y, z) = x² − y² − z ² increases in the direction 〈六〉 (1, 1, 1). at the point

A: Please check step 2 for solution.

Q: The integral of the right hand member of the first order LDE A B C с D -2sin³0 3 COS 2 2sin³0 3 sin…

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Q: Find the solution of the given initial value problem: y"" + y' = sec(t), y(0) = 11, y′(0) = 5, y'(0)…

A: To Solve: The differential equation given with initial conditionsy'''+y'=sec(t) , y(0)=11, y'(0)=5,…

Q: Theorem: If P is the transition matrix from a basis B' to a basis B, then P is invertible and the…

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Q: Solution:- Given H(jw) -(4+jw) 6+5jw-w² It Can rewrite as:- (jw+4) 6+ (jw)² + 5jc (jas+ 4) -1 (jw+3)…

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Q: Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies.…

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Q: Let n, meN and let f: R²R given by f(x, y) Task 1 T-ym-1, Calculate f(x, y)d(x, y), 1 [ f(x, y)d(x,…

A: Given : n, m∈ℕ and f :ℝ2→ℝ2 is given by               fx, y=xn-1ym-1 To find : ∫0, 1×0, 1fx, ydx, y…

Q: 10. f sin x dx 25+cos²x

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Q: The general solution of (y-1)dx −2(x+y+1)dy=0 by CL2V is

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Q: Which of the following statements is TRUE about a smooth function fat (a, b), if f(a, b) = c, fxx…

A: Given two questions as follows  1. 2.

Q: dw Find the derivative where w=5xyz, x=2t, y=4t, and z=3t-³ 1 dt dw dx (Type an expression using x,…

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Q: 4.8. Show that Dirichlet's function 1, if x is a rational number, { otherwise f(x) = 0, is not of a…

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Q: 5. Solve (t³ +7t³x²)dt + xe* dx=0 with x(0) = 0. Leave in implicit form

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Q: 4.3. Show that the function f(x) = Ja² sin, if x 0, 0, if x = 0 is not of a bounded variation over…

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Q: ® + 9[

A: solution is given below: