Let p and q be distinct prime numbers and let n = p²q². Determine all the subgroups of Zn and draw the lattice diagram for subgroups. Justify your work.

Q: Find the area bounded by the curves an arch of y= (4)sin (xA)

A: Given:        y=14sinx4 The area under the curve is the area between a curve f(x) and x-axis on the…

Q: Prove that (23-1a,b)* = {2}-1/a})(27-1) j=1 for all real numbers a₁,..., an and b₁,..., bn. i=1

A: The detailed process is described in step 2.

Q: 21.1 Evaluate the following integral: * 7/2 (6 + 3 cos x) dx (a) analytically; (b) single…

A: Solution :-

Q: 1. Factoring by Grouping la. xy + 2x + y +2 2a. uv + 3u +2v+6 3a. x³ + 2x²+x+2. b. 8rs + 4r + 2s + 1…

A: Since you have posted multiple questions i can do first question as per our company guidelines.…

Q: Parabolas with axis parallel to the x-axis with focal distance "a" fixed.

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Activity 3: Find Me! To further strengthen the foundations in solving permutations, you may search…

A: 1) the covered walk of a school is to be lined with flags. how many different arrangements are there…

Q: Show that the function f defined by (x, y) = (1, –1) f(x, y) = { x2 + y (x, y) # (1, –1) x + y is…

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Q: * 32. Find the probability of throwing 7 with two dice in a single throw.

A: Answer:

Q: Show detailed solution

A: Langrage's  Formula for unequal interval Newtons divided difference interpolation formula

Q: Problem: A machine produces cylindrical metal pieces. A sample of pieces is taken, and the diameter…

A: Given that  Observation: XX X^2X2 1 1.01 1.0201 2 0.97 0.9409 3 1.03 1.0609 4 1.04 1.0816…

Q: Z Let ƒ (z) = 1+|z|* (a) Prove that f is continuous on C. (b) Show that f maps C onto the open disk…

A:

Q: Suppose that the average number of hours spent by senior high school students in your school for…

A: Mean(µ) = 25Standard deviations (σ) = 4Sample size (n) = 12 Also given that it is normally…

Q: Find the critical value za/2 corresponds to 99.5% confidence level.

A:

Q: A classical example of the Poisson distribution involves the number of deaths caused by horse kicks…

A: Given, No of years n = 20 No of corps = 14 No of deaths = 196

Q: Let R* denotes the set of positive real numbers and let f: R+ R+ be the bijection defined by ƒ (x) =…

A: In this solution, we will examine the properties of the binary operation ⊗ on the set of positive…

Q: Find the derivative of: - R(t) = (sin² (3t+1), ln(t² − 1), ²) +1

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Q: Find the derivative using the long method 3 u = t2

A:

Q: 1- 3s Find the Inverse Laplace Transform of G (s) =- s2+ 8s + 21

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Q: Find the derivative using the long method 3-t to

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Q: The author purchased a slot machine that is configured so that there is a 2000 5. probability of…

A: Binomial distribution formula

Q: Determine the minimum sample size if the Margin of error is 0.045, with confidence level 95%, and p…

A:

Q: By using Newton Raphson Method, the repeated root of 4x^3-8x^2-3x+9=0 using 2 as Xn is? O 1.6 1.55…

A: Given equation is 4x3 -8x2 -3x+9=0 Take fx = 4x3 -8x2 -3x+9 First derivative of f(x) is fx = 4x3…

Q: DO NOT use a calculator to answer this question. Show ALL calculations. 3.1 Prove that : tan 480°.…

A: We will solve the following

Q: If there are three candidates for governor and five for mayor, in how many ways can the two offices…

A: We have given that  Candidates for governor = 3 Candidates for mayor = 5 Total candidates = 8

Q: 2. Solve for the margin of error for a 98% confidence level, the sample size is 1230, of which 40%…

A: 2)GivenConfidence level =98%sample size(n)=1230p^=0.40

Q: Find the adjacency matrices for the directed graphs in (a) and (b). (a) For the adjacency matrix,…

A: Two vertices in a graph are adjacent if there exists an edge between them. The entry in row i and…

Q: 2.30 In how many different ways can a true-false test consisting of 9 questions be answered?

A:

Q: If a group G has finitely many subgroups, does this mean that G is finite group? Justify your…

A: Given that  G is a group and G has finitely many subgroup. We have to find G is a finite group or…