Two cards are drawn at random, in succession and without replacement, from a deck of 52 cards. (a) Find the number of ways in which the ace of spades and a queen can be selected, in that order.     (b) What is the probability of drawing the ace of spades and a queen in that order? (Enter your probability as a fraction.)

Q: John Thacker Spiral Review Solve this system of linear equations. 4x + 4y = 12 6x - 4y = -32 Enter…

A: Given that :-           4x + 4y = 12 ................... ( 1 )               6x - 4y = -32…

Q: What rule of inference is used in this argument? "No man is an island. Manhattan is an island.…

A: Argument : "No man is an island. Manhattan is an island. Therefore, Manhattan is not a man."

Q: Using u = x the ODE dy dx = y²ex/y x²-2xy becomes

A:

Q: [37] Find the Laplace transform of f(t) = 2226 2t - 8 te 21 t 6.

A:

Q: Consider a set of vectors S = {V₁, V2, V3} following statements is true? = {··]} Which one of the

A:

Q: Find a basis of the following subspace of R³: W linear independence. {(a+b,b+c, c-a)}. Hint:…

A: Given Subspace is, W={(a+b,b+c,c-a):a,b,c∈ℝ}   Now, (a+b,b+c,c-a) =a(1,0,-1)+b(1,1,0)+c(0,1,1)   So,…

Q: f-1 کج (2 - 4)

A: We have to find L-1(s2s2-a4 )

Q: Graph the function, considering the domain, critical points, symmetry, relative extrema, regions…

A:

Q: Find the bases of Null, Col, and Row space of the following matrices and determine their rank -3 -3…

A: Introduction: To find the bases for the Null space, column space and row space of the matrix we have…

Q: In GF(2^8), find the multiplicative inverse of (x^7+x) modulo (x^8 + x^6 + x^5 + x + 1). Use table…

A: The extended Euclidean algorithm is a method for finding the greatest common divisor (GCD) of two…

Q: ercise 108. Determine all maximizers and minimizers of the function f(11, 12, 1₂): ect to = 1…

A:

Q: 5. A 3 x 3 matrix is given by A = 0 20 -i 01 (a) Verify that A is hermitian. (b) Calculate Tr (A)…

A: A 3×3 matrix is given by: A=10i020-i01

Q: Sketch the function below, express it in terms of window and step functions, and compu its Laplace…

A: A function gt=t0<t<22cost-22<t<4π+210t-2t>4π+2 To Find : Sketch the given function…

Q: 14. The inside temperature of a building is modelled by T(t) = 3cos(15t) + 22, where T' is the…

A: we have given, T(t)=3cos(15t)+22 standard notation is, T(t)=Acos(ωt)+B From the graph, Period is 24…

Q: dy dx 2− + 1,_y(1) = 0 X

A:

Q: Based on the vectors AB=b and AC=C that coincide with the sides of the triangle ABC, determine the…

A: Given that AB¯=b→, AC¯=c→, that coincide with the sides of the triangle ABC. The aim is to determine…

Q: Prove that a set E ⊂ ℝ is measurable iff l(I) = m∗(I ∩ E) + m∗(I ∩ E′) for any open interval I = (a,…

A: A set E ⊂ ℝ is measurable if and only if l(I) = m∗(I ∩ E) + m∗(I ∩ E′) for any open interval I =…

Q: 0 Solve in Series the equation; 2x²y" + (2x²__x) y² +y=o. 11

A:

Q: Use a computer or calculator with Euler's method to approximate the flow line through (1, 2) for the…

A: v→=y2i→+1.3x2j→ Initial point 1,2 ∆t=0.1

Q: 37 Use the properties of logarithms to expand log√x'z'y. Each logarithm in your answer should…

A: The logarithmic function is: logx3z7y. We have to expand the given logarithmic function.

Q: al shown below gives the circumference of an ellipse. 5√5√1-(sin(0)²00 Use Simpson's Rule with n-8…

A: The circumference is given by, 53∫0π21-23sinθ2dθ. We have to approximate the circumference using…

Q: 12. Fj; S is the part of the cylinder lying above the curve in the xy plane expressed in polar…

A: Surface S is the part of cylinder. Bounded below by the xy-plane and above by the cone z2=x2+y2.

Q: Decrypt the message CFEJFE which was encrypted using the affine cipher: Alphabet: A = 0, B = 1,...,…

A:

Q: Using Euler Theorem, determine degree of homogeneity to: f(x,y) = (x5 + y5)1/2

A:

Q: Let Fg elements be represented with the binary polynomials where p(x)=x²+x+1=0 mod 2 and x-x=0 mod…

A: The idea of the problem is to look reduce higher polynomial powers of x by using the equation x^3 +…

Q: 3. If f(x) = 2√√x+1-5, determine ƒ (8).

A: Given that, If f(x)=2x+1-5, determine f(8).

Q: Let R be a commutative ring with unity and let a, b E R. Show that (a, b), the smallest ideal of R…

A: Here, R be a commutative ring with unity and let a,b∈R. It has to be proved that <a,b>, the…

Q: Let f: [0, ∞0)→ [0, ∞) be the square-root function, that is, f(x)=√x for every nonnegative real…

A: The given function is f(x)=x. A proof that this function is not differentiable at x=0, is given in…

Q: A metropolitan area consisting of a city and its suburbs has a constant total population. Suppose…

A:

Q: Use implicit differentiation to find the derivative dy/dx of the following: x5 + 4x*y-y² = 8 (3 m

A: I have explained everything with in the solution. Please go through that.

Q: Which of the following statements is true about the series A B D The series converges conditionally.…

A:

Q: Q7. The solution of the initial value problem: is y" - 3y' - 4y = 0, y(0) = 0, y'(0) = 5, A) y(x)…

A:

Q: Find the extremals, = √₁² x F(y) = if any, where m > 1 is a constant. y(y)² dx, y(0) = m, y(1) = 4m.

A: Solution:  Given  that  F(y)=∫01 yy'2dx ………(1)                                    where  y(0)=m,…

Q: Find all local constrained extrema of f(x, y) = x² + 2y - z² + z under cionstraints 2x - y = 0, x +…

A:

Q: b) Determine all real values of x for which ✓log2x log₂ (4x) + 1+ log2x log2 V . (₁) +9=4 64.

A:

Q: ve the following differential equations, using the given initia constants. Indicate which part of…

A: Introduction: The solution of non-homogeneous differential equation is divided into two parts one is…

Q: Use the Laplace transform to solve the following initial value problem, _y" — 4y′ − 45y = 5(t−3),…

A:

Q: Let f(z) = u(x,y) + iv(x,y). If u (x,y) = 2x-x^3+3xy^2, determine v(x,y) such that f(z) is analytic.…

A:

Q: 4. Find the order of each of the following permutations. b.(147) c. (14762) d. (a₁a2...ak) a. (14)

A: The order of a permutation of a finite set  is the least common multiple of the lengths of the…

Q: Exercise 114. Find the maximizers and the minimizers of the function subject to the given con-…

A: a) To find the maximizers and minimizers of the function ye^(x-z) subject to the constraints 9x^2 +…

Q: Solve the initial value problem below using the method of Laplace transforms y" + 36y=144t² - 36t+…

A:

Q: The answer "6" for the last input is incorrect here, please recalculate.

A:

Q: Does the vector t belong to the Span(u,v,w)? Support your answer with calculation. (a) u = (1,3,2),…

A:

Q: 10. You will be scheduled to work 40 hours during the March Break. You can choose the method of…

A: Given that: Total hours is 40. Choice 1: Paid $22 per hour. Choice 2:For the first hour paid $1, the…

Q: = (an−1+ an−2+ an-3), N = 30 20. [T] a₁ = 1, a2 = 2, a3 = 3 and for n ≥ 4, an =

A:

Q: 8) Identify which of the following trig functions represents that of a sin, cos, tan, cot, csc, and…

A:

Q: Let (x, e) and (y, d) be metric space with e(x, y) = { 1 and let fr→y be a function. Is f…

A:

Q: Let F = (x^2 + y^2, x^2 + y^2) be a vector field and C be the simple closed curve given by circles…

A:

Q: Solve the system: ý₁ || -Y1 2 = —32 + 22 ܐ=ܐ

A: The given information in the question is a system of three first-order ordinary differential…

Q: 46. Σ(-1)*ke-k2 k=1

A: