1. Which of the following is an integral representation of the gamma function? dx r(x) = x - 1)1 dx rx) - eta

Q: Example 1. Evaluate the following: b) A" + (4B)"; c) (A + 2B)" 0 3 4 [-3 2 4 A =-1 and B =-1 8. -5 a…

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Q: Find the inverse of laplace, f(t) if: 10s? + 12 13. F(s) = (s + 2)³(s² + 2s + 5)

A: We have to find the inverse Laplace transformation of F(s).

Q: We use Moore-Penrose pseudo-inverse to determine the solution of Ax b which also corresponds to the…

A: We have to check whether given statement is true or not.

Q: 1. Find the canonical prime factorization using Fermat's Method a) 40425 b) 491 2. Find the sum of…

A: 1. To find the canonical prime factorization using Fermat's Method: a. 40425 b. 491 2. To find the…

Q: Derive the following Laplace Transform using the definition: Assuming that IfCt)]= FG), find LFf4)]…

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Q: Determine whether S is a basis for the indicated vector space. S = {(0, 0, 0), (3, 6, 5), (5, 1, 3)}…

A: Given S = {(0, 0, 0), (3, 6, 5), (5, 1, 3)}

Q: 1 (a) The remainder when the expression x - 11x2 + kx – 30 is divided by x – 1 is 4 times the…

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Q: confirm that the intergal test is applicable and use in to determine whether the series converges…

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Q: Evaluate the volume of the solid generated by revolving the plane region about an axis. Show your…

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Q: 3) Consider the following statement: Statement A: V integers m and n, if 2m + n is odd then m and n…

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Q: use Euler me thod to solve y's 3x²+J h=0.25

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Q: Solve the given initial-value problem. The DE is homogeneous. (x + yeY/x) dx – xe'lx dy = 0, y(1) =…

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Q: > Activity 5: Step by Step! Work in pairs. Transform the given quadratic functions into the formy=…

A: A quadratic function is a polynomial function with one or more variables in which the highest…

Q: Find the Fourier series of f(x) as given over one period and sketch f(x) and partial sums: Sx + 1…

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Q: What are the possible rational roots of the equation x+ 6x2 11x +6 = 0 A.-6, -3, -2, -1 C.+6, +3,…

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Q: A. Solve the following problems. Perlita owns a shop which sells bags. During her inventory, she…

A: To solve this problem, we have to take one of the three items in the shop as a variable and develop…

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Let A = {a, b, c, d} and define a relation R on A. The directed graph of the relation is shown here.…

A: We have: The relation is: R=a,c,b,a,c,d,d,b

Q: Let E be the solid parallekepiped with vertices Co,0,o).(LLO).co,l,3),(1,0,). C1,2,3),Cし,4).(2,1,1)…

A: Here, vertices are given in 3D. So, for taking limits of X and Y, we'll look for the projection of…

Q: 1) Construct truth table for given statement (a) (P^ ~q) → [~(P^9)] (b) [rn(~pVq)] ->

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Q: 2, i, Find out the roots of the following by completing the square. 5x^2-2х-4-0

A: To Find: the roots of the following by completing the square: 5x2-2x-4=0.

Q: iii. Identify coefficient of correlation and interpret its meaning. iv. Find the coefficient of…

A: (3) Using Desmos, the coefficient of correlation is 0.4377

Q: State whether the following numbers are rational or irrational. a) V4+7/2 b) 36 c) V11²510716 State…

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Q: The indicated function y, (x) is a solution of the given differential equation. Use reduction of…

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Q: Find the distance from y to the plane R3 spanned by uj and u2. (* -3 3 y = -9 Uj = -5 U2 = 1 1

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Q: Use Rung Kalä uethad y'= X+2y Fo Solve yco)so h: 02 An:hf (Xnggn)

A: Ruge kutta forth order

Q: Find 1341 (mod 713). Your answer should be an integer of the form a, where 0<r<712. Make sure to…

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Q: Evaluate (z – i) dz where C:y(t) = VE² +1 + it³, 0<t < 1

A: We have to find ∫Cz-idz where C: γt=t2+1+it3, 0≤t≤1

Q: 2, i, Find out the roots of the following by completing the square. 5x^2-2х-4-0

A: We have to find the roots of the equation 5x2-2x-4=0

Q: Find the inverse of laplace, f(t) if: 8s2 + 12 12. F(s) = (s – 2)²(s² – 6s + 10) -

A: The given problem is to find the inverse Laplace transform of the given function F(s). Given…

Q: An indicator function of the set A is the function on N given by if w E A lo if w € A so that 1,…

A: an indicator function or a characteristic function of a subset of a set is a function that maps…

Q: 3. у %3D ах + bx2

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Q: (1) Show that planes perpendicular to the x-axis have equations of the form r = a sec 0 in…

A: Given (1) r=asecθ (2) r=bcosecθ (3) The plane ax+by=c

Q: Let f(t) = 6+ 5t, 0 <t< 2 and let the half-range cosine series representation of its even periodic…

A: Let us considre the function y=f(x) 0&lt;x&lt;L Thus, the half range cosine series of the function…

Q: Find the radius of convergence, R, of the series. (x – 9)" n-1 Find the interval, 1, of convergence…

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Q: Given the plane f = (-2,1,5) + s(3, -2,0) + t(1,1,5), s,t e R. The plane cuts the x, y and z-axes to…

A: Given, Plane,r→=-2,1,5+s(3,-2,0)+t(1,1,5),s,t∈RTo find: Volume of a pyramid

Q: Solve for the disk of convergence of >G)( :) (z +2 – i)?". - 3 n=0

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Q: 2. The seats in a theater are arranged in thirty-one rows. Forty seats in the first row, forty-two…

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Q: 4) In how many ways you express 10$ as a sum of dimes (10c) and quarters (0.25$)? 5) Solve 50000a +…

A: To solve this problem we use the concept of diophantine   equation .  Diophantine equation : An…

Q: SYSTEMS OF ODES Using the Laplace transform and showing the details of your work, solve the IVP: 2.…

A: Solution of system of differential equations, using Laplace transferoms

Q: 3 If A = and B = find A + B, B- A, and 2A + 3B. (If an answer does not exist, enter DNE into any…

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Q: 12. (Strang 4.3.1, 5) Consider the four points (t;, b;): (0,0), (1,8), (3, 8), and (4, 20). (a) Set…

A: Given the four points ti, bi:  0, 0, 1, 8, 3, 8 &amp; 4, 20 (a) we have to set up and solve the…

Q: Using Euler's Method, Solve for K in Y(4) = K Given the following: Y' = 2x -2y +3 h = 0.2 Y(3)…

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Q: e roots of ur w2n n

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Q: Let f(z) = u(x, y)+iv(x,y) be entire such that u(x, y) 4v(x, y). Show that f is constant. %3D

A: Here we use CRE equation to prove this

Q: solve the differenhal equa hon by varianon of parameters y" + 3y't 2y 7 te* y (x)

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Q: The Laplace transform of f(t) = is 1

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Q: Match the two matrices A, B with their product AB. i Instructions 1 0 2 6 7 4 3 4 5 -3 9 0 6 1 [1 -2…

A: Match the two matrices A, B with their product AB.

Q: Express the sum of integrals as an iterated integral in polar coordinates: •2/3 r4+v16–x² x dx dy +…

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Q: есх Find the derivative of y = Arccot (tan(esec*)) in its simplest form secr

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.