3.5. Let n E N. Prove that if n + ÷ < 2, then n² + n2 <4.

Q: 4. Show that if ki = (X; – X)/[Σ(X; – Χ)2], then (a) Σ ki = 0; = (b) Σk? = 1/[Σ(X - X)]; (c) Σk;(X;…

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Q: 2, Choose give Single digit positive in te gor f them' and the mean me

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Q: For any n e N, let An = {x € R | –n <x < n}. Prove that NneN An = A1. (Recall that we define 0 ¢ N.)

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Q: : Answer the following 1- Let s = = {+:n € N}. Find max(s), min(s), sup(s), inf(s).

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Q: 1 Compute the quantity, w, using w= - 1 w•w - 7

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Q: 9.To test a hypothesis involving proportions, both np and n(1-p) should a) Be at least 30 b) Be…

A: In general, ‘for testing the null hypothesis involving proportions np should be equal or greater…

Q: 3. Prove the Archimedean Property, if x ER. then there exists K E N such that r SK.

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Q: Q3: Prove that (9":n e Z) (3":ne Z) but (9":n E Z) (3":n E Z).

A: We have to prove that 9n:n∈ℤ⊆3n:n∈ℤ but 9n:n∈ℤ≠3n:n∈ℤ

Q: 3. Given n > 1, let S = E-1: Show that S, is not k=1 _k° an integer.

A: We are given that   Sn = ∑k=1n1/k   and n&gt;1              ..(i) We have to show that Sn  is not an…

Q: 1. The probability that the interval (x-0/4, + o/4) contains u is equivalent to P(

A: 1. The probability that the interval contains μ is x¯-σ4, x¯+σ4.

Q: Let a, b eR with a < b. Assume that a + <b - for all n e N. Show that n n=1

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Q: (c) Show that a permutation o E S, commutes with r if and only if the permu- tation f(o) commutes…

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Q: Show that for any n E N, 7(15".

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Q: 5) Find the total Ħ of díagonals for af )n=5 b)n=10

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Q: 4. A mail-order computer business has six telephone lines. Let X denote the number of lines in use…

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Q: 9.To test a hypothesis involving proportions, both np and n(1-p) should a) Be at least 30 b) Be…

A:

Q: 9.To test a hypothesis involving proportions, both np and n(1-p) should a) Be at least 30 b) Be…

A: From the given information,

Q: n the Wechsler Ac e among the highes

A: According to the sum, the scores on the Wechsler Adult Intelligence scale are approximately normal…

Q: 2) Find the z-score in which 93.70% of the z-scores in a population are below that value. 3) Find…

A: Let, F be the CDF of Z 2. To find t such that, P(Z &lt; t) = 93.7% = 0.937  F(t) = 0.937 = F(1.53) […

Q: 5.7.4. Show that the two formulas (r = y) and (S(r) = Š(y)) in N.

A: Hi, since there are 2 questions given, the first one is answered.  Given - The formula  x=y To prove…

Q: that for n > k we Sn+1 ||

A: The expression given is ,  n+1k+1=∑j=knnn-jjk The number of ways to partition n+1 objects into k+1…

Q: 4. Which of the following is the least decimal: 0.01012, 0.0120, 0.00123?

A: Since you have posted multiple questions and we can answer ome question. So, answered first…

Q: (5) Show that T(n)o(n) > n for all n E N. 11

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Q: Suppose m> n. Show that L x"

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Q: Let n e Z. n#-1,3,

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Q: 19. Show that (for n = 0, 1, 2,..) (a) F(-n, b; c; 1) = (c-b)n (c)₁

A: We have to show F-n,b;c;1=c-bncn Solution: By Pochhammer definition cn=Γc+nΓ(c)           (1) and…

Q: If E (ar + br) 2n and n+1 k=1 Σ (ακ-bk) -- 1, then Σa- n+2 k=1 k-1 O 2 3 2 O 1 5. 2 Ο None

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Q: Suppose that 1000 customers are surveyed and 850 are satisfied or very satisfied with a…

A: Given,n=1000x=850sample proportion(p^)=xnsample proportion(p^)=8501000=0.85H0:P=0.9H1:P≠0.9α=0.095

Q: 8. Suppose X ~ N(7, 1). What value of x has a z-score of −1.25? (Enter an exact number as an…

A: We want to find X value

Q: 6- The special sotution 5014tion to the र१पच्दं०n . -ya)=x"e? 1 XP A/ Xex Ğ d/other than that

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Q: 1 Compute the quantity, w, using w = W •W - 4 - 5 LO

A: The given vector is w=2-4-5. We know that if a=a1a2a3 and b=b1b2b3 are two vectors, then the dot…

Q: The average pollen count in a certain city on day x of the pollen season is P(x) = 6x − 0.2x2  (for…

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Q: 2. Prove or disprove the following. (a) For all r, y E Z, if xy + x is odd, then x and y have…

A:

Q: Let T = > Σ - In k. n n=1

A: We will solve here only (a) part of 2.   we have to show that the sequence Tk is monotone…

Q: Suppose m=nd where n is odd and 1<n<m. Prove that 2m+1 is composite.

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Q: Find all values of x for which ∑ (n=0 to ∞) 1/(1+x)^n equals 4

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Q: Show that for any n E N, n(n + 1)(2n + 1) %3D k=0

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Q: 2. (a) Evaluate e²-dr, where a > 0.

A: Let, I=∫0∞e-x2-a2x2dxI=∫0∞e-x2e-a2x2dx Let F(x,a)=e-x2-a2x2DaF=-2ax2e-x2-a2x2DxF=-2x+2a2x3e-x2-a2x2

Q: 8. Prove 3n e R|n? – n < 0

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Q: For any n e N, let Bn = (n, ∞0). {B„}1 is descending. Show that Bn = 4. %3D n=1

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Q: (b) How many arrangements are there of the letters in STATISTICIANS such that • the Is are…

A: Given information: STATISTICIANS Total number of letters in given word = 13(3S, 2A, 3T, 3I) Total…

Q: 2) Find the z-score in which 93.70% of the z-scores in a population are below that value. 3) Find…

A: It is known that standard normal distribution follows mean 0 and standard deviation 1. Z ~ N(0, 1)…

Q: (-1) is where n is an integer. equal to the above e(1+2n)i where n is an integer. equal to the abov…

A: We know from eular formula e^iθ = cos θ + isin θ

Q: 9. Suppose  X ~ N(2, 3).  What value of x has a z-score of −0.67? (Enter an exact number as an…

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Q: 3. Use the Simpson's rule to estimate 7e 2xdx with n = 6

A: Since you have asked multiple questions we will solve the first question for you. If you want to be…

Q: 3. Let E beE E. Suppose th

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Q: For n>2, let an=5n/n2-2 ,Determine for which n, |an| < 1

A: Given, an=5nn2-2|an|&lt;1 Use the given inequality for an and find the quadratic equation for n and…