Q.3. Table shows the age in years and the retail value in thousands of dollars of a randor sample of ten automobiles of the same make and model. a) Compute the linear correlatio coefficient. Interpret its value in the context of the problem. b) Compute the least square regression line Data on Age and Value of Used Automobiles of a Specific Make and Model 2 3 3 4 4 5 5 28.7 24.8 26.0 23.8 24.6 23.8 20.4 X y 3 30.5 5 21.6 6 22.1

Q: Use Definition 7.1.1, to find (f(t)). (Write your answer as a fun £{f(t)} = (s > 0) on of

A: This is a problem of Laplace transformation.

Q: S In واں U₁₂ U₂ are two TRY. U₁ = one U₂ = 3 2 3 (0000) 2 2 base surfaces 2 3 1000 3 Determine U₁₂…

A: Given : U1= 3221 , 3321 , 2121 , 2121 U2=1040 , 2323 , 1202  To find : basis and dimension of U1 ,…

Q: Determine the volume V and total surface area A of the solid generated by revolving the area shown…

A: Cross section area (A) = π2(R)2 + μ*2R A = π2(53)2 + 38*2*53A = 4410.13 + 4028A = 8438.13 mm2

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Q: QUESTION 5 Given the matrix A = -1 (10) 3 -3 a) Find all the eigenvalues of the matrix A. b) Find…

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Q: Find the exact sum of each series.

A: We have to find the exact sum of given series.

Q: Questions 24. The graphs of f(x) and g(x) are shown below. The value of (fg) (-1) is: f(x) g(x) 5x…

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Q: 4 6. Given two functions f : A → B and g: B → C, if gof: A → C is bijective, then g is onto and f is…

A: Given : f: A→B and g: B→C be the functions such that g o f : A→C is bijective. To show :  g is onto…

Q: How many terms of the series > a = 2 2n (Inn) to within 0.004? On e ام 1.000 1.000 n<e ¹ would you…

A: option b is correct

Q: Answer true or false.. The function f(t) = (e) 10 is of exponential order. True False

A: We need to determine if the function: f(t)=et10 is of exponential order or not.

Q: (1)=1 1/21 )=3/14, f(1)=17/28 ]=2/7, f(1)=13/21,

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: 8. Consider the IVP y"" = t+y², y(0) = 1, y'(0) = 1, y"(0) = -1. Use Euler's method with step size h…

A: Given that :  IVPy"'=t+y2 ,y(0)=1,y"'(0)=1, y"(0)=1 h=.5  To Find : estimate the value of y(2)

Q: 6. Use the following information to answer the next question Two functions are shown. y = f(z) is…

A: Transformation of functions means that the curve representing the graph either moves to…

Q: Exercise 6.44. Let E be a subset of Rn. (i) Prove that E is closed if and only if it contains all…

A: This is a question of Topology.

Q: Find the angle between the vectors. (Round your answer to two decimal places.) u = (4, 5), v = (3,…

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Q: Find a set of parametric equations for the curve of intersection of the cylinder (x − 1)² +: 4 the…

A: We will use trigonometric identity  sin2t+cos2t=1 and parametric form of standard ellipse to find…

Q: 7. DETAILS ZILLDIFFEQMODAP11 7.R.005. Answer true or false. F(s) = s²/(s² + 4) is not the Laplace…

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Q: 5x−y=12 Step 2 of 2 :   Determine the missing coordinate in the ordered pair (?,1/2) so that it…

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Q: Find the singular sol" of the differential eqh (P+1)² (y-px) = 1 -

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Q: (16x²16 x + 4)D²y = 4x² - 4x + 4

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Q: Find the coordinate vector [x] of x relative to the given basis B = - 1 2 -⠀⠀⠀ b₂ 2 b3 -2 , X = - 3…

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Q: 278. Suppose that sin(ln x) = 3, and that sin(ln y) = }. If 0 < ln x < and 0 < ln y < , use the…

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Q: Given the equation F=95C+32F=95C+32 where C is the temperature in degrees Celsius and F is the…

A: given F=95C+32 where C is the temperature in degree and F is the temperature is Fahrenheit. Given…

Q: Question 28 Which of the following statements is (are) true if all vectors are in R"? d) If W is a…

A:

Q: Show that R[x]/ is a field.

A: In this question, we have to show that ℝxx2+1 is a field.

Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

A: As per company guidelines we can solve one question at a time so i am solving first one please…

Q: How many shortest lattice paths start at (5,5) and a. end at (10, 10)? b. end at (10, 10) and pass…

A: Solution :-

Q: Use the Laplace transform to solve the given initial-value problem. y(t) = 2y+3y" - 3y - 2y = et,…

A: The initial value problem is :                                              2y'''+3y''-3y'-2y =e-t,…

Q: 5) Consider the vector function r = (9- 2t, 4+2t, √2t²) a. Find the length of the path on 0 ≤ t ≤1.…

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Q: Calculate the volume for each of the following figures b) d) DO o a) Diameter of base = 4cm Height =…

A: As per the policy of bartleby the provisions is to solve only 3 subparts of questions

Q: 15. If f(x)=2x2-3, x ≥ 0, then a function that will have the same domain but a different range than…

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Q: Suppose f: N→ N satisfies the recurrence f(n+1) = f(n) +7. Note that this is not enough information…

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Q: Determine the class average if the standard deviation was 8% and Henry’s mark of 85% is equivalent…

A: Given that,  The standard deviation =8%, Marks of Henry's =85%, and z-score =1.30.

Q: Let the sequence g., be recursively defined by 90 = 0, 91 = 1, 9n = 9n-1 +29-2 for n 22. Show that…

A: Given : gn be the sequence defined by ;  g0 = 0,  g1 = 1  and  gn = gn-1+2gn-2 ∀  n≥2 To show :…

Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 12 inches above the…

A:

Q: 46. y' - 2xy

A: Given differential equation is y' - 2xy = x

Q: Solve the initial value problem below using the method of Laplace transforms. y"+y' - 2y = 0, y(0) =…

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Q: Find the surface area of the torus with parametric equations: r(u, v) = ((4+ cos v) cosu, (4+cos…

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Q: 3. Let A be mxnand B be nxm. a) Show that the matrices C = 0 -(BBA) b) Conclude that the nonzero…

A: detC=0 and detD=0Given A be m×n matrix and B be the n×m matrix. a We have to show that matrix…

Q: Determine solutions for the equation 5sin2x + 2sinx = 0 in the interval x £[-2π, 2π] algebraically.…

A: Given equation is 5sin2x+2sinx=0        (1) Since  sin2x=2sinxcosx

Q: (a) Find the general solutions of the differential equations x² ² dy + (1+x)y² = 2x³y². dx (b) Show…

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Q: Use the Integral Test to determine whether the series is convergent or divergent. Make sure you show…

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Q: 2x 17y + 11z = 0 6) -x+11y-7z = 8 3y2z = -2 -

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Q: Find regular expression over [0,1] that defines the following language: Any string that starts with…

A: Regular expressions are patterns used to match character  combinations in strings.

Q: Which of the following statements is (are) false, assuming that all vectors are in R"? O Statements…

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Q: Determine whether these matrices are invertible and find the inverse if it exists.  (5     -10)…

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Q: (a) The Rodrigues formula says that H₂ (§) = (-1)"¹ es ² * (₁) * (1) Use it to derive H3 and H₁. (b)…

A: Since you have added many problem in one question, here I am answering first two parts (a) and (b).

Q: Questions 2. If the function y = f(z) is transformed to the function y=f(-12 horizontal translation…

A: