3 2 (x) i=1

Q: 3 max z = -X1 + 3x2 s.t. X1 - x2 4 X1, X2 2 ()

A: LINEAR programming problem graphical method

Q: 1. 2.1 y--x+ + 2x + 2x-4 3.1 4.1 y-2x-

A:

Q: ди 2. 2 ax + 3u ду = 2y - x %3D

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Q: .3 2- S(y² – 4y + 2 ) dy

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Q: 7. Differentiate a) f(x) = ev==t and b) h(x)= (5x² – 8r)e**-4". %3D

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Q: Solve x′′ +6x′ +9x=1−u(t−3), x(0)=0, x′(0)=0

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Q: 3 5) ax tây là 3y = 12 x+³y=9

A:

Q: et dt 3/2 +8 e' +

A: Given integral is, ∫ete2t+8et+732dt. It is integrated by applying u-substitution method, Substitute…

Q: 5. St V1-t dt

A: We solve this integration by substitution method by putting                         1 - t3 = u…

Q: 26. sec (- 2r) = - V2

A: Given that sec-2x=-2. We know that secx=1cosx.

Q: Max Z = 6XI  + 4X2   Subject to          7XI + 8 X2    ≤224           8XI + 12 X2 ≤192…

A:

Q: İį = 12, i2 = -x2 - T1 + x}

A:

Q: How do you solve this equation?

A: Given,

Q: 2 + 3s (s + 2)³ = (-21² + 3t) e-2i

A: Follow the procedure given below.

Q: 3 2 3 -2 -3 Oy= - (x – 3)2 – 2 Oy =- (x + 2)2 – 3 Oy = (x - 3)2 – 2 4.

A: Given : Center point ( h, k ) = ( 3 , - 2) One point through which graph passed . ( 2 , -1)

Q: 구 4- 2 -5 -4 -3 -2 -1 I 2 3 4 5 -21 -4 -7 -8- f(x) = %3D 45 3.

A:

Q: 4[8,(t-2) rect(r)dt

A: we have,  I=4∫020δ4t-2recttdt we know that  ∫t1t2xtδt-t0dt=xt0 ;   t1<t0<t20       ;…

Q: 2 3 dt. 0 1+t2

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Q: 2 has a X 2 X

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Q: Integraate :S, 22+x+! d>x 2.

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Q: 10--6A Oa) x- -6 V b) x = 6 c)x- 10 V d) x- -2 Oe) x- -8

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Q: 7. dz | zV 36z2 - 25

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Q: 16 In x xу"(х) + ху (х) - у(х) - х> 0, у(1) %3 3, у'(1) %3D 1

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Q: .1//3 7earctan(y) dy + y? 3

A:

Q: 5 А. 3f(t) dt = ·8 -4f(t) dt 2 | В. 8 С. (f(t) + 4) dt =

A: Given, The graph of function f We have to evaluate the definite integral in part A, B  and C.

Q: Зд — 3 — 0. dt

A: Use method of separation of variable. Separate the terms of t and x and then integrate.

Q: 1 B (m,n) = m-1 (1-x)"-ldx %3D

A: Concept: By definition of Beta function

Q: 6. 5<x<-1 - 2x +4, -3x +13 -15x<2 25x<6 6 SxS 10 f(x) = -3

A: Solution: The objective is to graph the given equation

Q: (4+y- sy³)ldy Vỹ 3

A: To evaluate the given integral.

Q: 24 + 16 = 0 e22-2z-3 = 0 iz = (-i)(-i)

A:

Q: solve: [x X2 X3 Б 1 0 002-20 X1 0-1/2 0 140x₂ 0 00 01 0-1] LxS) ха 0 -12 + +2] 3et+ - 1/4 0 0 with…

A: As per the instruction, we will be answering the part (b). For (b), We are given the following…

Q: 10 dS (3t2-12t-15)dt %3D

A:

Q: d/dt ŷ = [3 1] ŷ, ý(0) = [8] [-2 1] | [6]

A: Given that dy^dt=31-21y^ with initial condition y^(0)=86 Let A=31-21 and eigenvalue of A is λ. Then…

Q: 1°- 4+ 4r2 -4 dr Co T. (1²-1)(r²+2r+2)

A: Indefinite integration is the backward process of differentiation. Through integration, we find a…

Q: x3 2. J Sadx 2. 3.

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Q: 3x+ y = 3 12. priiqe X- 2y = 8 | madeve

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Q: O y'+ (oy -asin 8t y W): -1 2

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Q: (*+7X-1) the f1) - -Sz+4) If fo- is undefined

A: Here first of all we find factors of denominator which is ( X - 1) ( X - 4)

Q: 14 (3 3 1f y=/xL5x²–36 x15x²-36 X23x²+¥x-12 show that dy dx4 24

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Q: MAX Z= x,+2.x2 X+2x2 subject to X+ x224 2x, +2x0

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Q: 2 1) x² + y² + 18x - 26y+246=0 CX+972+(₂-137² = 4

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: 4 %3D X2+2x-15 is X-3 S+X

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Q: 1 y = [cosh(2x)] co* ot-1

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Q: 73.xy-z(x- y)' (19)

A: 73 Given expression is xy−zx−y2. We have to find the value of the given expression x=3, y=-2 and…

Q: 8. 5) Evaluate | x2n-1e-kx² dx

A: Definition of Gamma Function:  The function which is given by the improper integral  Γ(n)=∫0∞ xn-1…

Q: max z = x1 + x2 X1 + x2 < 4 X - x2 2 5 s.t. X1, X2 2 ()

A: We will solve this question from the graphical method . We will see that if the two inequality has…

Q: /25-22-y2 zVx² + y? + z² dz dy dr

A:

Q: (10t-24€+ /6) (1+32) dt 2. (10t-244 +16)12 +3i(10t3-24€+16) "EHE

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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.