(c) Consider the subgroups H = (−1) and K = (5) of G. Show that GHxKZ₂ x Z2m-2. (d) As an application to number theory, find the number of positive integers x less than 128 such that x¹000 - 1 is divisible by 128. (Hint: Show that this is the same as the number of elements (a, b) € Z₂ × Z25 such that (1000 ā, 1000 6) = (0,0).)

Q: P(A)=0.45, P(B)=0.58, and P(B|A)= 0.05. What is P(A and B)?

A: Given that  P(A)=0.45, P(B)=0.58, and P(B|A)= 0.05

Q: Suppose P(C) = 0.3 and P(D|C) = 0.8. Find P(C&D).

A: Given that,P (C) =0.3P (D/C) =0.8P (C&D) =?

Q: 3K².4K•K³

A: Given: 3k2·4k·k23

Q: 29(P − 34) = 464

A:

Q: こ= (t)} () て= () %3D - (^),J %3D てんn ZトXC

A: →∫eax+bdx = eax+ba + C, where 'C' is the constant of integration.→∫xndx = xn+1n+1 + C

Q: If P(A or B) = 0.7 and P(A) = 0.44, and P(A and B) = 0.22, determine P(B)

A:

Q: proot p(cn ANB) - ecen B)-p(ANB) P(B) PCB).

A:

Q: If P(A or B)= 0.8, P(A)= 0.5 and P(A and B) = 0.25, find P(B)

A:

Q: Let P(A) = 0.6 P(B)= 0.2 and P(AUB)= 0.7 Find P(AB) 4

A:

Q: (g) P(A)– P (B) (h) P(AnB) (f) P(A)n P(B) (i) P(A)× P(B)

A:

Q: According to information released by the U.S. Census Bureau in July 2009, the population of…

A: The answer is found in step-2

Q: IfP(A =0.3,P(B)=0.4andP(A and B)=0.7areAandBME?

A: The probabilities of the events are given as follows:

Q: nd the value of o(1999), p(101), p(243), 9(1998).

A: Phi function

Q: If P(B) = 0.3, P(A or B)= .06, and P(A and B)= .2, find P(A)

A: From the properties of probability, for any two events A and B we have

Q: 3. For each problem, find the general solution to x' = Ax, where A is the given matrix. (a) A = -4…

A:

Q: Suppose P(A) = 0.18, P(B)= 0.38, P(A | B) = 0.51 What is P(A and B)?

A: Answer: From the given data, P(A) = 0.18 P(B) = 0.38 P(A|B) = 0.51

Q: If P(A) = 0.5 and P(B) = 0.80, then P(A or B) must be 0.95.   TRUE or FALSE

A: From the provided information, P (A) = 0.5 and P (B) = 0.80

Q: L(P-5)0

A: Explanation of the answer is as follows

Q: Suppose P(A) = 0.6 and P(B| A) = 0.4. Find P(A&B).

A:

Q: Find 5 [(7x³ + 3x³) dz

A: use the algebraic property of integrals.

Q: t(r) dr

A:

Q: If P(A)=0.32, P(B)=0.16, and P(A | B)=0.625, find P(A and B), P(A or B) and P(B|A).

A: This question is based on Probability formula.

Q: 36z dr = O ez +C O 2 e +C O 2 e +C O e +C O 2 e5z' +C

A: We do integration of the following question

Q: 3) S dz z3-z2-6z

A: In the question it is asked to calculate the integral of the following function given:

Q: 7

A:

Q: If n(A U B) = 96 and n(A) = n(B) = 69, find n(A n B).

A: Let A, B be sets and n(A), n(B), n(A∪B) be the cardinality of the sets A, B and A∪B respectively. It…

Q: Suppose P(A) = 0.76, P(B) = 0.12 and P(A or B) = 0.54. Determine P(A and B).

A: The information provided in the question are as follows :- P(A) = 0.76 P(B) = 0.12 And P(A or B) =…

Q: 12. Find a normal vector n and an equation for the planes in Figures & (A)-(C).

A:

Q: Suppose P(A) = .17, P(B) = .18, and P(C) = .65. Assume that P(D | A) = 3 P(D | B) = 8 P(D | C). Find…

A: Given,P(A) = 0.17P(B) = 0.18P(C) = 0.65P(D | A) = 3P(D | B) = 8P(D | C)

Q: Suppose G = and Ja] = 144. %3D Then | %3= (A) 48 (B) 72 (C) 24 (D) 144 (Ef 10

A:

Q: Use the following matrices and find an elementary matrix E that satisfies the stated equation. =( A…

A: The given matrices are:

Q: P(A) = 0.4 and P(B) = 0.6. If A and B are independent, what is P(A given B)

A: Given that A and B are independent. P(A) = 0.4 P(B) = 0.6

Q: Let F(x, y) = -o (a) + F. dr + j. Find the value of the line integral.

A: The general form of a vector-valued function in two dimensions is given by F=F1i+F2j, where F1 and…