The marks scored by 10 students out of 75 are given as 3, 30, 10, 13.9, 41, 56, 30, 71, 30, 13.9, then the mode is 30 71 О 56 00000 0 41

Q: 1. Fix R € (0,1). Prove that oth converges pointwise to f(t) = ₁¹t on S = [-R, R]. Hint: Fix R € (0,…

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Q: I. Select the best answer for each item. I.A) Antisymmetric Relation * A relation R on a set A is…

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Q: Define T:R2 R2 by T(x) = Ax. Find a basis B for R2 with the property that [T] is diagonal. A = 51 15…

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Q: Determine the natural boundary conditions at x = 0 and x = 1 for the func- tional I[u] = ¹ [(u')² -…

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Q: Solve the D.E. using Bernoulli Differential Equation (3siny - 5x) dx + 2x²cotydy = 0

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Q: Problem 5. the Ratio Test. (a) 8 n=1 πn n! State whether each of the following series converges or…

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Q: What is the left Riemann sum with 4 intervals for the function tan on [0, 4] equal to ?

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Q: Let f (x) be a polynomial function with a zero of multiplicity of 1 at 3 and a zero of multiplicity…

A: The polynomial f(x) has a zero at 3 of multiplicity 1,and a zero at 1 of multiplicity 2. Let g(x) be…

Q: ) Write a proof of the following statement: If λ is an eigenvalue of a real square matrix A, it lso…

A: We can prove the given statement.

Q: 5 Points] S1~ S₂ S3 Find the first five terms of the sequence of partial sums. (Round your answers…

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Q: a 24 r(²7) r(5)r(7.25) b. Set t'dt C. dx √-In(x) SOJ . Evaluate using Gamma Function:

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Q: 1) If A = Find:- a) B2 5 -1-2 4 (2) -1 -2 and B = 3 b) determinant A c) Adjoint B d) A-¹

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Q: Consider the following data x -4,-3,-2,-1,0 P(X=x) 0.3,0.1,0.2,0.1,0.3 Find the variance. Round your…

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Q: Example

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Q: Find the inverse Laplace transform f(t) = L¯¹{F(s)} of the function F(s) = = You may use h(t) for…

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Q: Let f(x)=(x−1)^5 on the interval [0,4]   . a) Calculate: f′′(x)= b) What is the maximum value of…

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Q: π 1. (separation of variables) Solve: sin x cos² y dx + cos² x dy = 0, y(0) = 4

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Q: Laplace's First Finite Integral for P(x) P, (x) = − √5 [ x ± √ √(x² − 1) cose] de, ne N

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Q: Find the length of the parametric curve x = 1+ 15t², y = 4+10t³, 0≤t≤ 1.

A: We have to find the length of the given parametric curves

Q: So F(x, y, z) = xi+yj + 6(x² + y²)k and C is the boundary of the part of the paraboloid where z = 81…

A: Using Stokes’ Theorem to evaluate ∫CF. dr where Fx, y, z=xi+yj+6x2+y2k and C is the boundary of the…

Q: Apply Bisection method to find the root (only one root) of the function: f(x) = (8) sin(x)…

A: we here see that the given function is     f(x) = 8sinx+8cosx -x   Assuming the  trigonometric…

Q: The unit step function IR→ R is defined as if x 0. I(x) = 0 1 (i) Let s € (a, b), and suppose f :…

A: Note: We will be solving part (i) as mentioned. Given that s∈a,b, and suppose f:a,b→ℝ is bounded on…

Q: Simplify the sums given below. (1) + ¹ (1) + ¹² (2²) 4n ™ ¹″ (3) − 4¹ -¹ (1²) + 4²¹²¹² ( 2 ) + . . .…

A: Here we have to simplify the given sums by using the Binomial theorem. The Binomial theorem is given…

Q: Define T: R² → R² by T(x) = Ax. Find a basis B for R² with the property that [T] is diagonal. -=[₁…

A: Given, A=2-7-54   We have to find basis B.

Q: Find the upper and lower sums for the region bounded by the graph of the function and the x-axis on…

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Q: Use Newton’s method to find the root of f(x) = (z)x 3 – (y)x 2 + 5 = 0 between a = 0 to b = 2. Use 4…

A: Given: The given function is f(x) =x3-x2+5 with initial value x0=-0.2. To Find: One needs to find…

Q: The solution to the recurrence relation a = 10a_ n n-1 (2+n)5" B 2-3"-(-5)" C (-2)" + 2.3" D 2-3" +…

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Q: (1) Let A={1,{2},{1,{2}}} (a)True or false: 2 € A, {2} € A, {{2}}CA, {1,2}CA, 3x(x € A^xA)

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Q: Evaluate the circulation of G = xyi + zj + 4yk around a square of side 4, centered at the origin,…

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Q: 16.3 Q8

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Q: 60. Show that for motion in a straight line with constant accelera- tion a, initial velocity vo, and…

A: Solution (60):-    Acceleration = avelocity =  a dt = at +cwhen t = 0, v = v0 so c = v0

Q: Which rule of inference is used in the following argument, "If it snows today, then we will go…

A: Given a argument, "if  it snows today, then we will go skiing." "If it snowing today; therefore, we…

Q: Prove that H is a subring with unity of M2x2(ℤ), under the usual matrix addition and matrix…

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Q: Why is answer A+B=1 and 2A-3B=-2 ?

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Q: Suppose g (0) = –8 and g'(x) is given by the following graph. y 1.0 0.5 -0.5 -1.0 -1.5 -2.0 1 2 3 4…

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Q: Prove that Σ k=1 log k kp p> 1 converges.

A: The integral test says if ∫1∞fxdx converges then ∑k=1∞ak converges, where fx=ax. Now, given ∑k=1∞log…

Q: Elsa, Milan, and Chau have a total of $132 in their wallets. Milan has $6 less than Elsa. Chau has 4…

A: Question can be solved using method of algebraic equations.  Find the required equation and then…

Q: The data in the table shows the number of mother-to-child HIV infections diagnosed in the United…

A: Let x be the number of years after 1985 and y be the number of cases. 1. Create a scatter plot of…

Q: Find the sum of the convergent series. 1+1/1/2+. 4+2 +1+

A: Given series 4+2+1+12+.....

Q: In an optimization problem, how many variables should eventually occur in the function we are trying…

A: We have find the how many variables eventually occur in the function in an optimization problem.

Q: Determine whether given boundary value problems have a unique solution, no solution or infinitely…

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Q: CURRENT OBJECTIVE Use divergence to understand the flow of a fluid Question Suppose the vector field…

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Q: 10.Let V=P(1), the vector space of real polynomials. Determine whether or not W is a subspace of V,…

A: Given: V=Pt, the vector space of real polynomials. To Determine whether or not W is a subspace of V,…

Q: Express the answers in simplest form. If a die is rolled one time, find the probability of Part 1 of…

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Q: Let {an} be a sequence defined by ao = 2, a₁ = 3 and There is a solution is of the form: for…

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Q: This is my word problem. Thank you.  The accounting department at Factory Shoe has determined that…

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Q: Compute the instantaneous rate of change of the function at at x = a. f(x)=23-6x, a = -6 OA. -6 OB.…

A: Instantaneous rate if change at a point us equal to derivative of the function at that point.

Q: Use the Laplace transform table and the linearity of the Laplace transform to determine the…

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Q: Find the mean for the data items in the given frequency distribution. 2 3 5 1 8 Score, x Frequency,…

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Q: Problem 7.7: Use LT to find the PS of x"" +x" + x² + x = et (x(0) = x'(0) = x'(0) = 0

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