ection 3.1 Homework 1. 1+23 +... + n° = n2 (n + 1) for all natural numbers n. 1 I I - + I + и for all natural numbers n. I 2. 1(2) (2)3 3(4) n(n + 1) (n+1) 1+ud-I for any r 1 and any neN и 3. Show that k 0= - I 4. 1+2+22+ ... + 2"- = 2" -1 for all natural numbers n. 52-1 is a multiple of 8 for all natural numbers n

Q: 1+1(9)-20

A: The given expression is 1+1(9)-20 When we multiply any number by 1 the result is 1. So when we…

Q: Multiply. 3v 4v +2 6y +3 y /12

A:

Q: 4s +5 S -4

A:

Q: 3

A:

Q: n-6=5

A: Here we have to find the value of n =?  3n-6=5n

Q: 3s – 7 s- 2s + 3

A:

Q: %3D n+1 3 -2 -3

A:

Q: Find the rank of A = ( 1   -1   2   3)                                       2  6  -8   1…

A: Rank of Matrix : It is the Number of Non Zero rows in reduced row echelon form.

Q: 9 – 4x > –3

A: The given inequality is 9-4x>-3

Q: Find A for

A:

Q: 3.9b + a3 + 27 - 3a2 + 5a3 - 2a2 + 2.1b + 7

A:

Q: y X (9, –3)

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: +–3m+–9m+4+5+–10m

A: The expression is given as 1+–3m+–9m+4+5+–10m. Simplifying the given expression. 1+–3m+–9m+4+5+–10m…

Q: 5 3 + s2-8 s2+ 3.

A:

Q: 目 +8 LI +T 现 +04 +C4 |F|E|F|| ||||4 4 4 2 2

A:

Q: Evaluate 5 (²) 4. dy -2

A: ∫-2-1 (y-2)dy/y ∫-2-1 (y - 2/y)dy [ 2y3/2/3 - 4y]-2-1 -2i/3 - 4i +42i +42i -14i/3 +82i

Q: S-4 a(5-35 +16

A:

Q: Which of the following graphs represents the function g(x) = x²(x + 1)(x − 2)? 2 4 2 * 0 4 0 O 4 2 P…

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: 3 4 1 2 -2 -1 6 -3| Select one: а. 4 b. -40 C. 40 d. -4

A: Solve for the determinants

Q: (カナ) 2.

A:

Q: w + (-7), when w = - 1

A: The expression is given by w+(-7) To evaluate: The value of the expression when w=-1.

Q: 2+1+5+7

A: 2+1+5+7=3+5+7=15

Q: 1 + 2n < n° for all integers n² 2

A:

Q: 3 5 - Let C= 2 6 |. Find - 5C. - 1

A: The given matrix is                                C=-3   5  2   6  0-1 We have to find -5C.

Q: 4 1 x-1 4 | 45. +3 x-1

A:

Q: 2(3w+8)=40

A:

Q: 1+4+6+8

A:

Q: 2. S(Vw +2)Vwdx

A: Topic:- integration

Q: w+5 -dw w - 6w+10

A: A detailed solution is given below

Q: find -1 2 5+1 s(5+1)²

A:

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

A: Given that: ∫0π(4sinθ-8cosθ)dθ

Q: 75 + フチ + k「3

A:

Q: –4(–6m – 7).

A:

Q: 2. (1 + 3/2x − 1)² = 3 + √3/2x − 1

A:

Q: -7 -5 Let A = Find -2A. 2] 1.

A: Given, A=-7-512

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.