Assessed Question 4. Suppose you roll a pair of dice until you get a double-six. What is the smallest number of times must you roll the pair of dice in order to give yourself at least a 95% chance of seeing a double six?

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Q: Given that Σ n=0 x= 1 1 to x = - X = n=0 Identify its interval of convergence. The series is…

A: Here we have to find the power series for  with centre 2 and identify its interval of convergence

Q: 5. Use Q3 to find the explicit formula for Σ₁n²x” when |x| < 1. n=1

A: (.) Given,         We have to find explicit formula  for  when .(.) Radius of convergence: Radius of…

Q: 1. Find a vector valued function that represents the curve of intersection of the semi-ellipsoid x²…

A: The equation of the semi-ellipsoid is The cylinder is

Q: 3. Consider the following matrix and answer the following questions: A = (a)-12 points Without doing…

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Q: B = {sin(t), sin(2t), sin(3t), sin(4t)} is an orthogonal set in C( [−π, π] ) with (ƒ,9) = = {…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Are the two linear transformations the same? Yes ● S: R² → R², shear such that H maps to H then…

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Q: Find an orthogonal set with the same span (and same number of elements) as 9 27 12 11 9 12 11 -9 13…

A: Here we have to find the orthogonal set of vectors with the same span.

Q: Why can we not write the following predator prey model in matrix form X'(t) = AÑ(t)? x'(t) = ax(t) —…

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Q: c) f(t) = { t², 0≤t<3 9, 3≤t a

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Q: Use the Factor Theorem to determine whether x -c is a factor of f(x). x-10 f(x)=x4-21x2-100; A) Yes…

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Q: Given that the graph of f(x) passes through the point (6, 3) and that the slope of its tangent line…

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Q: Exercise 10.4.4 Let T: R² R² be a linear transformation defined by →>> ¹([%])=[a+b] Consider the two…

A: The given linear transformation .The two bases  and .The aim is to find the matrix  of .

Q: B. Let S and T be sets of real numbers, and define S. T to be {x.y:xe Sandy e T}. Show that if S and…

A: B) Let  and   be  sets  of real numbers.    Define     Suppose that both the  sets    and   are…

Q: Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm² and whose…

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Q: A 10-foot ladder leans against the side of a wall forming an angle with the ground. Given that the…

A: Here we use the rate of pull and the angel relationship to the sides of the wall.

Q: 6 B *- {[1][*]} [6]. -- 6 [3] is an orthogonal basis of R². Find [v]®•

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Q: 2t b) L[4t +5te” +sinh(5)]=

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Q: Consider the function whose graph is the surface shown at the right. Which traces go with which…

A: To extract more information out of the graph we will try to match the traces in the following order…

Q: You cost out a New York steak dinner.    Your cost is $11.00 and you want to put this on the menu…

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Q: 4. Let S denote the surface whose equation, in cylindrical coordinates, is 2/3 +22/3 = 1 (the…

A: We have to find the volume of the region trapped inside this surface.

Q: 2 2 f(x, y) = 4x² - y² a) Sketch traces for some values of f(x, y) = k, xz-trace and yz-trace, and…

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Q: Prove by induction that Vn N 72 n(n+1)(2n - 2) Σ(i²-i) = 6 i=1

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Q: (a) Let A be a 3 x 3 matrix whose entries on the main diagonal and below the main diagonal are all…

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Q: In general, most medical practices would hope to see a no show rate that is 3% or below.  As you…

A: The objective of the question is to calculate the no show rate for the medical practice. The no show…

Q: Are the two linear transformations the same? Yes S: R² R2, shear such that √3 4 B 2 maps to OB 1 4 1…

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Q: Show that a cycle of odd length is an even permutation, and a cycle of even length is an odd…

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Q: A 36 lb weight stretches a spring 6 feet. The weight hangs vertically from the spring and a damping…

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Q: Dan's Auto Detailing business performs two major activities: exterior deanup and interior detailing.…

A: Given the time estimates for 6 cars on Monday morning asCar number1…

Q: 2. Determine the Laplace transform of the given function. a) f(t) = e³¹t4 c) f(t) = est sin(3t) e)…

A: Recall the formula of Laplace transform: For any non-negative integers L{tn}=n!sn+1 .The property of…

Q: For households in a community many different variables can be For households in a community, many…

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Q: Use the First Derivative Test to find the location of all local extrema for the function given…

A: Consider function .To illustrate the location of all extrema for given function.First derivative…

Q: (a) In cell A6, type 1. Rather than copying the numbers 2 to 25, we can fill down based on the…

A: (a)As instructed in the question, we will have the "Year" column with 1 in A6, and the next rows are…

Q: Small changes in numbers in an integrand can result in very different methods required for…

A: We evaluate the integral by using different choices for b.

Q: Consider the functional S[y] = [² dx ln(1 + x²y'), y(1) = 0, y(2) = A, where A is a constant and y…

A: The functional  S[y] is given by an integral that depends on the function y and its derivative y′…

Q: Find R 4x dA, where R is a region enclosed by 4x − y = 0, 4x − y = 2, x + y = 0 and x + y = 4. Use…

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Q: P(x)=x²-3x²-2x+4, which statement is Given true? A) (x-1) is a factor because P(-1) = 2. (x+1) is a…

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Q: Solve the linear second-order non-homogeneous differential equation with the given initial…

A: The objective of this question is to solve the given second-order non-homogeneous differential…

Q: 29. y = 1 - 8 and y = 4x²

A: We can take point of intersection y =1/x and y = 4-x2implies (1/x)=(4-x2)i.e. f(x) =…

Q: In general given two matrices A and B then: A' = B'. O None of the other answers. ○ A'B = (B' A)'.…

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Q: BIJ Compute the derivative f'cts for 5./ fcto= log (x

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Q: and Assume |A| = 16, |B|=18, |C| = 28. If , how much is given |AnB| = 7 |AnC| = 11 |BC| = 8 AUBUC…

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Q: cos - sin 0 0 where x, y, and z are distinct. sin cos 0 0 A: 0 0 cos - sin 0 0 sin 0 cos and B 1 x…

A: For a square matrix of order n×n , the greatest integer r ≤ n , such that there is at least one…

Q: Question 3.1. Use integration by parts to solve the given indefinite integral and thus evaluate…

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Q: 2. Solve for x = [0, 7] with the boundary conditions and the initial conditions Hint: cos²x = Utt-…

A: (2)We have given the partial differential equation with boundary and initial conditions.We use the…

Q: Given the graph of g(x), sketch the graph y=f(2x+2)-3.

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Q: Let (an) and (bn)1 be two sequences. Assume that the sequence (Σ1 ak)=1 is bounded, and that (bn) is…

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Q: Evaluate the line integral, where C is the given curve. Lo (x + yz) dx + 2x dy + xyz dz, C consists…

A: We have to evaluate the following line integral  Where C consists of line segments  to and from  to…

Q: Calculate the proximity to each other and the angles of each location using Law of Cosines to each…

A: To calculate the proximity (distance) between two locations and the angles formed by these locations…

Q: Given the differential equation y'' + 49y = 4e¯4t, y(0) = 0, y'(0) = 0 a) Apply the Laplace…

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