If n(A) = 105, n (A ⋃ B) = 142, and n (A ⋂ B) = 46, find n(B)

Q: Given the matrix A 3 2 -3 -4 9 -3 -1 -2 5 (a) Find the eigenvalues and eigenvectors of A, and list…

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Q: To complete the sale of a house, the you accept a 210-day note for $9,000 at 8% simple interest.…

A: Principal, P=$9000Rate of interest, r=8%=0.08Time, t=30 days

Q: Solve the given initial value problem using the method of Laplace transforms: y" − 3y' +2y=e4;…

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Q: Q4. Solve numerically by using Runge-Kutta method y' =√xy+1 with y(0) = 1 to find y(0.05 and h =…

A: 4. Given,                  y'=xy+1;    y(0)=1.  To find the value of y(0.05) and h=0.025.

Q: 6 7 Let A = -14 -15 Find S, D, and S-¹ such that A = S = 188 SDS-¹. D = [881-1881 0 0

A: A=67-14-15

Q: you have the English sentence “Something is missing” (M, missing), then the paraphrase is ∃xMx. (i)…

A: As per the guideline I’m supposed to solve first three sub-parts of the given problem.Given that…

Q: The sum of two irrational numbers is irrational.

A: The given statement is, the sum of two irrational numbers is irrational. To illustrate whether given…

Q: Diagonalize a matrix to find all functions f (x)and g(x) solving the differential equation: f′(x) =…

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Q: Solve the initial value problem below using the method of Laplace transforms. y" -y=4t-4e-¹, y(0) =…

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Q: 6.(2) Please I really need help with this!!     Determine the slope of the tangent to the curve…

A: The given problem is to find the slope of tangent to curve at point whose abscissa is -1. Given…

Q: 8. Evaluate •S.F.d F-dr where F(x, y, z) = (-7 sin(7x)-yz, π cos(ny)-xz, -xy) and C is any path that…

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Q: Question: Which of the following sets of matrices is a subspace of R³ ? |---] (e) (a) a a -⠀] (b) 0…

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Q: Determine where the following function is differentiable? Where is it holomorphic? Determine the…

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Q: Please make sure to show your work & calculations step by step. I really need help with this.…

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Q: Linear algebra Let D1 and D2 be two concurrent lines of R2. (c) What is the distance between the…

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Q: Form a polynomial whose real zeros and degree are given. Zeros: 4, 0, 5; degree: 3 Type a polynomial…

A: We know that  : An expression of the form P(x) = anxn + an-1xn-1 +an-2xn-2 + ………………. + a1x + a0…

Q: 28. Using the method of reduction of order, show that if 7₁ is a repeated root of r(r-1) +ar+ 3 = 0,…

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Q: Question7: a) Show that (x² + 1)/(x + 1) is 0(x+1).

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Q: Use the given transformation to evaluate the integral. J. (9x +9y) dA. where R is the parallelogram…

A: Using the given transformation to evaluate the integral of (9x+9y) dA, where R is the parallelogram…

Q: Find the complex zeros of the following polynomial function. Write f in factored form. f(x)=x³-6x²…

A: Find the complex zeros of f(x) =x^3 -6x^2 +37x -58

Q: For the function defined by y = f(x) , the expression (shown in the picture) represents: i) the…

A: For the function defined by y = f(x) , the expression  limx→afx-fax-a.

Q: Can the following problems be solved using precalculus, or do you need calculus? Explain your…

A: a) We have to find distance travelled in sixteen seconds using given data b)We have to find  rate of…

Q: Question 2. (a) Prove that [65] 186 has a multiplicative inverse in the ring Z186. (b) Compute this…

A: (a) To Prove: 65 has a multiplicative inverse in ℤ186. (b) To Find: Inverse of 65 in ℤ186.

Q: Consider the vector field F = (xªy³, x³y¹). O The vector field is not conservative O The vector…

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Q: Sketch the curve with the given polar equation by first sketching the graph of r as a function of in…

A: The given curve is r2θ=49. To Sketch: the curve in cartesian plane and then whole polar curve.

Q: Suppose T is the transformation from R2 to R² that results from a y-shear of 3 followed by a…

A: Let T : R2→R2 be a linear transformation given by rotating vectors through an angle or θ , then the…

Q: 1) A $20, two $10 bills, three $5 bills and four $1 bills are placed in a bag. If a bill is chosen…

A: Let us define the random variable       X = chosen amount Then, from the given information, we see…

Q: Find a particular solution of the indicated linear system that satisfies the initial conditions x₁…

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Q: 2) In a game you flip a coin twice and record the number of heads that occur. You get 10 points for…

A: We have to find the what is the expected value for the number of points you will win per turn.

Q: Find the parametric and symmetric equations of the line that passes through the point P(3, 0, -2)…

A: We know, the general equation for a line that passes through the point located at point P and which…

Q: Consider the graph given above. Add an edge so the resulting graph has an Euler path (without…

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Q: 3) There is an equally likely chance that a falling dart will land anywhere on the rug below. The…

A: Total number of squares on the rug are 15. The black squares are 6. The probaility that the dart…

Q: QUESTION I Consider the operator R³ → R³ given by left-multiplication by the matrix: -6 -8 A = 2 -1…

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Q: 11. Construct a 95% confidence interval for 31 for the following: 31 =31, s-3, SSxx=32, n= 12

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Q: Given the matrix 3 -2 A = 0 0 8 1 find a diagonalization of A. Show all of your work. 0 1

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Q: The Inverse Laplace Transform for the function F(s): = 5s²+8s-1 (s+3)(s²+1) is

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Q: Use the variation of parameters formula to find a general solution of the system x'(t) = Ax(t) +…

A: According to the data, find the general solution of the given system.

Q: 9. High school students in one school chose their favorite leisure activity. Find each probability.…

A: We have to find e)P(hiking|female)  f)P(hiking|male)  g)P(male|shopping)  h)P(Female|shopping)…

Q: Consider the following matrix A = 0 1 0 Compute the 1 1 0 rank of A. What is the dimension of space…

A: One has to find the rank of the matrix.

Q: Given compound statement is, (qVr) → [(p^q) v (q^r)] We have to find out corresponding truth table.…

A: Here in the truth table the working formulae are  or formulae    T v T = T v F = F v T = T    F v F…

Q: Suyin has 56 pennies and 196 nickels. She wants to place them all in stacks so that each stack has…

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Q: A: Find the solution of the following differential equation by Laplace transform with initial…

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Q: A certain college had 80,410 students enrolled as of Fall 2022. Each student enrolled must be…

A: The problem requires finding the minimum number of digits necessary to assign unique ID numbers to…

Q: Let u be the solution to the initial boundary value problem for the Heat Equation, with Mixed…

A: The given problem is to find the solution for the given heat equation partial differential equation…

Q: 1(e) Answer with "true or false". In addition, if the answer is false, correct the statement.…

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Q: Are the statements true or false? Prove or give a counter example. (i) (3x)(Vy)(Vz)(x+y = z).…

A: The given statement, ∃x∀y∀zx+y=z. We have to prove this statement or give a counter-example if the…

Q: 4. Use Green's Theorem to evaluate x²y dx - y²x dy ,where C is the boundary of the region in the…

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Q: 4. x. 5. y"+y sin² x.

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Q: 1. Prove the identity sin x secx = COS X cot x + COS X-

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Q: Suppose f is a continuous function, and we know the following data: t f(t) 7.5 8 8.5 9 9.5 10 10.5…

A: The given data is, To Find: Left endpoint, Right endpoint, and Midpoint sum over the interval…