8. Working over R, suppose that M = PDP ' where P 1 Then, for any positive integer k, we have that Mk is 7* 5k – 7k (a) | (b)| - (- 7k – 5k 5k 5k 7k

Q: In the expansion of (x+y)35

A: We use the Binomial Theorem to find the required coefficient in the given question.

Q: Let A = {1,{2,3}}. Find P(A), n(A) and n (P(A)).

A: The power set of a set is the set of its subsets. The expression nA represents the number of…

Q: Find Im(z) if z(8 + i) = 7+ (384 + 448i)

A:

Q: Find the Cholesky factorization A-[-+-+4] -1 20) A =

A:

Q: Expand (-3x + 11)(-4x – 9)

A: We have to expand the given expression.

Q: 0 Find m/RTS R 7x+1 19x + 11 T 6x - 4 S

A: Given query is to find indicated angle.

Q: Show that Sn is solvable when n ≤ 4.

A: Given: Sn. We have to show that Sn is solvable when n≤4.

Q: What is the least common multiple of 1/6x + 1/5y + 1/10z

A: given

Q: 5) Evaluate the expressions below if K(s) = 3s² - s+6. a) K(s+2) b) K(s) +2

A:

Q: 11. Find MZJHI. K (3x + 2) (12r - 17)°

A:

Q: Differentiate f (x) = 71n(x²-6x+3) A. (2x – 6) 7ln(x²-6x+3) f' (x) = x2 – 6x + 3 - В. In(7) (2x – 6)…

A: Given query is to find the derivative of the expression.

Q: 10. Use the binomial theorem to evaluate (2r³ - y) 5.

A:

Q: Expand and simplify    (i) (2k − 3)(k − 2)

A:

Q: Find the coefficient of x3y2z3w in the expansion of(2x + 3y − 4z + w)9.

A: The given expansion is 2x+3y-4z+w9. We have to find the coefficient of x3y2z3w.

Q: Jack has a large baseball card collection of 2640 cards. He has them organized alphabetically from…

A: We have to find

Q: 2 – |- 2(x + 1) – –s-+ 3x X-3 5х-3

A:

Q: 22. Evaluate |(x – a) (x – b) (x – c) . . . (x – y) (x – z) where the second term of each factor…

A:

Q: [a + 9   5z+1   9m]       [10a    9z    6m]        [20     -55    135]…

A: Given that: a+95z+19m9k35+10a9z6m8k35=20−5513568610 To find the value of a, z, m, and k.

Q: In the expansion of (x + y)16 which term has the same coefficient as x14y2? O a. x12,4 Oc x3y14 O d.…

A:

Q: In the expansion of (4x + y) ^ 9, the coefficient of x3y4 is

A:

Q: 36 6 10. Find the coefficient of x³6 in (x + x² + x³ + x² + x³ + x² + x² + x³) ³

A: To find the coefficient of the term x36 in the expansion of x+x2+x3+x4+x5+x6+x7+x85.

Q: * Let z1 = 2 + i and z2 = 5 + 2 i. Find 3 z1/ ( z1 - z2) - (12/ 10 ) - (3/10)i O (1/10 ) + ( 3/10) i…

A:

Q: How many terms are there in the expansion of (4.x + 7y)0.+ (4x- 7y)10 ?

A:

Q: 3 Check the box under the output column for the scenario where input is not equal to output for any…

A:

Q: Find the product of (2x+ 3)(3x- 2) A 6x + 9x – 5 B 6x + 9x - 6 C6x +5x- 6 D 622 6x + 5x-5

A: (2x+3)*(3x-2)=?

Q: 12. Find m/R. (&x - 12) (3x + 5)

A:

Q: Consider the function f (same as in the previous problem) defined on the interval [0, 10] as…

A: Given Data: fx=35xx∈0,53x∈5, 10-y''=λy, y0=0, y'10=0To find: cn

Q: ndicate the least integer n for which (3x5 + x2)4 is O(xn).

A: Solved using the binomial theorem

Q: What is the 5th term in the expansion of (2x²y³ – ¹y)° O 14.25x7 y 20 15.75x10 y 19 15.05x¹0y17…

A: Given: 2x2y3-14y9=2x2y3-y49

Q: Find a and b if a + (5 – 3b) i = ai + 2 (b + 5)

A: See the attachment.

Q: If p = 4x³ + x² + 2x + 5 and          q = 6x³ + 3x² + x + 2  Find ||p||  and ||q||

A:

Q: If / (7-4) (x + 8) 12 O 4 dx Adx - A+B 4 Bdx x+8' , then A+B =

A:

Q: 20 41. Find ²k²(k − 3). (Use Table 2.)

A:

Q: Show that c12 2 dx = ln (7 + 4v/3). 8, Va2 – 8x -

A:

Q: Make this nonlinear problem to a BINARY INTEGER PROBLEM.   Max z = x2y + 3x3yw     subject to…

A: As per the question we are given a nonlinear optimization problem which we have to convert into a…

Q: Z4×Z6 has an element of order 24. true or false ?

A:

Q: Find the coefficient of x8 y18  in the expansion of (1x2  -4y6)7

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.