A mathematics professor lost a test paper belonging to one of her students. She remembered that the mean score for the class of 20 was 81 and that the sum of the 19 other scores was 1530. What was the grade on the paper she lost?

Q: Problem 6. Use the snake argument to prove that Z × Z is countable.

A: We know that the set Z of all integers is a countable set.  Now, consider the product Z×Z.

Q: Problem 1. Draw the following relation and write down the properties it has (among reflexive,…

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Q: 5. Stanley Bank offers a money market account that earns 1.85% compounded continuously: a) If…

A: (a). The formula for continuous compounding is A=Pert, Where, A is the final amount,P is the…

Q: Evaluate the definite integral. Show all work. You may check your answer by using your So x² dx…

A: The given integral is ∫01x2x3+2dx. We have to solve this integral.

Q: {5t sin²t}=

A: We have to find the L{5tsin2(t)} We know that sin2t=(1-cos2t)/2

Q: Is this using a comparison test or monotone convergence theorm or some other method? If so how do…

A: The convergence of first sequence was done by the usual definition of a convergent sequence. i.e.,…

Q: Factor completely. (x² − 3)²+7(x²− 3) − 18 Simplify your answer as much as possible.

A:

Q: Let G be any group and A (G) the set of all 1-1 mappings of G, as a set, onto itself. Define La: G→…

A: "As part b is marked, we will solve that part only" Let G be any group and A(G) the set of all 1-1…

Q: A linear programming model is represented by the following: Maximize: P = 6x + 4y subject to: 4x +…

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Q: Suppose the daily supply equation for noise cancelling wireless headphones is given by p = S(x) = 30…

A: The daily supply equation for noise-cancelling wireless headphones is given by p=Sx=30+30e0.09x,…

Q: Determine £¹{F}. F(s) = 3 6s³ - 3s² - 9s+27 3 s (s-3)

A: Introduction: To find the inverse Laplace transform , first find the partial fraction of the given…

Q: 2. Solve for x: 63x+1 = 22x-3 Leave your answer in exact form

A: 63x+1=22x-3

Q: 2 iel D = {(x, y² = x² + y² ≤ 1, y>0} and F:DIR² by avector field given by FCx, y) = 1 Evaluate the…

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Q: Directions: Use the blank number line to make a line plot and represent the data below. Write a…

A: The given table is, .

Q: (b) Let K be the set of integers with the operation o defined by xoy=x+y + 1. Prove that K with the…

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Q: Find the area of the surface S defined by z = xy and x² + y² ≤ 3. (Use syntax like 2*pi/3)

A: (.)  Given ,  Area of the surface S defined by z=xy and x2+y2≤3 .   If  z=f(x,y) ∀ (x,y)∈R  the…

Q: Fast pls solve this question correctly in 5 min pls I will give u like for sure Nidi Consider the…

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Q: Find the first four nonzero terms in a power series expansion about x = 0 for a general solution to…

A: We have to find the value of y(x) using frobenius method . The procedure is given below

Q: 7. y'-y (t-3)H(t-3), y(0) = 1.

A: The given problem is to find the solution for the given initial value problem with given initial…

Q: Direction: Write T if the statement is true and if it is false, underline the word/s that made the…

A: The statements defining and describing the mathematical concepts or definitions or terms used.

Q: (3) What does the Alternating Series Test say about whether (-0.5) converges or diverges? n n=1

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Q: Write each of the following numerals in base 10. For base twelve, T and E represent the face values…

A: To Write: following numerals in base 10: (a) 4325 (b) 110102 (c) 59E12.

Q: The gradient of f(x, y) = x sin (y²) is the vector field F (x, y) = at (2,√π/6) and ending at…

A: Here we are given that the gradient of f(x,y)=xsin(y2) is the vector field F(x,y)=sin(y2)2xycos(y2)

Q: In Problems 4-7, use the Laplace transform to solve the IVP. You can use the following dictio- nary:…

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Q: Evaluate the surface integral. ²2² ds, s is the part of the cone y = √ x² + z² given by 0 ≤ y ≤ 4

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Q: ou must use sine and cosine as part of the parameterizations. (a) Parameterize the curve of…

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Q: a. A rectangular solar panel is made up of small squares. A particular solar panel is 1 square by 24…

A: (a) We are given that           A solar panel consists of 1 square by 24 squares.       So, there…

Q: Evaluate •1 1₁ 2² x²zdS, where S is the part of the plane z = 1+ 2x + 3y above the rectangle [0, 4]…

A: We have to find

Q: Use the method of Frobenius and the larger indicial root to find the first four nonzero terms in the…

A: We have to find the value of y(x) using frobenius method  The procedure is given below

Q: Find the flux of F= ²7 + x³z³7 + 3xzk out of the closed region bounded by the planes z = 0, y = 0, x…

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Q: Find the second order Taylor approximation of the function f(x,y)=3e* sin y + 5x-2y near the point…

A: We are given that      f(x, y) = 3ex sin y + 5x - 2y   => f(0, 0) = 3e0 sin0 + 5×0 - 2×0 = 0…

Q: •11• F(x, y, z) = xyzi + xyj + x²yzk, S consists of the top and four sides (but not the bottom) of…

A: We have to find the ∫∫curlF ds

Q: Prob 2. Let TEL(V). Show that (v, u)r: (Tv, u) is an inner product on V if and only if T is positive…

A: Introduction: An invertible positive operator is a linear operator on a vector space that is both…

Q: Which of the following degree sequences are possible for a graph? A. (9, 8, 8, 7, 6, 5, 4, 2, 1, 1)…

A: The degree sequences are: A. (9, 8, 8, 7, 6, 5, 4, 2, 1, 1) B. (6, 5, 5, 3, 3, 2) C. (7, 7, 6, 6, 6,…

Q: Quation-1) Investigate the convergence of T Provide reasons! dx -1 + Inx

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Q: 2. Prove that the complement of a simple planar graph with at least 11 vertices is nonplanar.…

A: we know a graph is said to be non planar if it cannot be drawn in a plane so that no edge cross.…

Q: Question-2)[ dx (tanx + secx)5 cos²x -dx =?

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Q: Which one of the following functions grows most rapidly when x → ∞? J In z x² Tln(z) ○ (In x)²

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Q: Question 2 (a) Explain the concepts of present value and annuity. (b) Compute the future values of…

A: Present value: Given a certain rate of return, present value (PV) is the current value of a future…

Q: Find all subgroups S3 and S4

A: A subgroup is a subset of a group that has the same algebraic structure as the larger…

Q: 6. Let F = (4e" cos(4x), e sin(4x) + 2y) be a vector field and let C be a curve in the first…

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Q: Let S be the unit sphere centered at the origin. What is ſſ (3+z) dS? (Use syntax like 2*pi/3 .)

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Q: Show that there is exactly one positive number u such that In(u² + 1) + Tu = 2021.

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Q: Letter C is 59E, not 53E

A: We need to write (59E)twelve in base 10. (It is given that face value of E is 11)

Q: 4. Let the torus T be the image of the map T(u, v) = (x(u, v), y(u, v), z(u, v)) = ((R+r cos v) cos…

A: Let the torus T be the image of the map. Therefore,…

Q: A6. Let 1 an be a series. (a) State precisely what is meant by the phrase "-1 an converges". (b)…

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Q: xy² (0) (Use syntax like [3,-4,5] for vectors.) Let F (x, y, z) = xz5 What is the value of curl F at…

A: The vector F(x, y, z) is given. We have to find the value of curl F at (3, 2,1) .

Q: [ 0 1. Answer the following for matrix M = -2 2 and vector b = 3 4 2 3 a. Use the Gram-Schmidt…

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Q: Find parametric equations for the path of a particle that moves along the circle x2 + (y - 1)2 = 9…

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Q: f(2)= 1 N² (1-2) Separate laurent expansion of the function Z(1-2) according to the powers of z and…

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