o Prove that for each real number x, (x + v2) is irrational or is irrational.

Q: 1/3+2/9

A: Given 1/3 + 2/9

Q: Evaluate x²+3x+5

A:

Q: Prove that X Pn dx %3D

A: Recurrence relation.  Partial fraction.

Q: 48y3 - 27y

A:

Q: 4x e 3x

A: I = ∫4x e−3x dx

Q: b2 over b-a + a2 over a-b

A:

Q: 1.25a +3> 0.5a-6 and 2.5a 129-1.5a

A:

Q: 60 27 2. + $6

A:

Q: 12 R 10 5

A:

Q: Find d dx (45x+6)

A:

Q: 5 1 1 + 2r dr

A:

Q: こ (0) of

A:

Q: 196. 2(n+1)

A:

Q: 1b+1b

A: Applying  addition operation since terms with same variable  binomial addition

Q: х3 — 2х dx х — 1 -3 10. 2

A: Given: I=∫23x3-2xx-1dx For evaluating given integral, we substitute x-1=t…

Q: A 2/15 B 30 V35 5 20

A: Given,  A circle with secant and tangent  We have to find the value of x

Q: 1805

A:

Q: Find the LU factorization of A = A = 1 1 -3 0 9 3 -17 5 2

A:

Q: 2070 = (16a + 10)15

A: 2070 = (16a+10)15 And (16e+11)17 =3723 To find  the values of a and e

Q: 40 (3x +10)°

A: Using concept of opposite Angles.

Q: 8√Z S sec³(s) ds 3/7/2

A: let  A=782∫sec3(s)dswe know  1+tan2s=sec2sA=782∫sec(s)sec2(s)

Q: d. 1 3a+18 = 1 - 8 a+6

A:

Q: 36-9z

A: Given that:36-9z

Q: dw V5-e-2w

A: Given,           ∫dw5-e-2w

Q: Multiplt. 3i(4-i)

A:

Q: (402-25)

A: Given: I=4θ2-25dθ We know that ∫x2-a2dx=x2x2-a2-a22logx+x2-a2+c…

Q: ext dx 8X-X

A: We have to evaluate the ∫dx8x-x2

Q: Evalvate S (4sin co) -8cos co) )do

A: Given that: ∫0π(4sinθ-8cosθ)dθ

Q: (1– 3csc(

A:

Q: 8y3 + 216

A:

Q: –4(–6m – 7).

A:

Q: いーx)dx

A:

Q: 12 2х A = 2x

A: (6(a):- Given matrix Q is                              6(b) Singular Matrix:- A matrix is called…

Q: (1 +i)(13 – 4i)(1 - i)

A: We have to simplify the given expression: 1+i13-4i1-i We know that a+ba-b=a2-b2i=-1i2=-1 Where, i is…

Q: 5х -44 j 2х+ 7 k

A: We have been given that j || k

Q: 2. (1 + 3/2x − 1)² = 3 + √3/2x − 1

A:

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.