28. Suppose that [E:Q] = 2. Show that there is an integer d such that E = Q(Vd) where d is not divisible by the square of any prime.

Q: Q3 Prove that In Coth x 1

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Q: Let X = {x E Z|x = Y = {y € Z]y = 3n for some integer n}. 6m for some integer m} and let %D a. Prove…

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Q: Calculate M, for f(x) = 6 · In(æ³) over [1, 2]. M6 ||

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Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1 + Z2| < |Z1| + |Z2|

A: Using complex properties.

Q: Let n E Z. Prove that if 3/ (2n² + 1), then 3 | r n.

A: Solution:     Let 3 does not divide n      =&gt; n = 3k ± 1 for some integer k.       =&gt; 2n2 + 1…

Q: Let x, y E R. Prove that if 21x + 35y = 45, then x and y are not both integers.

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Q: Suppose that in the forward difference formula of order O(h) for f'(xo), h = 0.02 and |f"(c)| < 0.5,…

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Q: If var(e) →0 as n→ 0, then 6 is said to be Select one: a. sufficient b. unbiased c. efficient d.…

A: Solution: Note: Hello! As you have posted 2 different questions, we are answering the first…

Q: If n^2+6n+11 = x^2+y^2 for positive integer n, x and y prove [xy/2] is composite. Note: [t]…

A: Given :              n2+6n+11 = x2+y2              t ≤ t

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: For mighe. any integer exyelicsubysoup of osder Show tht /2 has

A: Since, you have posted multiple questions but according to guidelines we will solve first question…

Q: Another means of rejecting Ho is if the p-value is greater than a. O less than a. O less than 0. O…

A: We have to find the another means of rejecting null hypothesis is the the p-value is ?.

Q: (8.20 ds: Find the tayLor seri's expen sian of In Cxri) about XozO

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Q: Suppose: n ≥ 3 and x,y ∈ Rn , |x - y| = d > 0 and r is some +R, Need to show: 2r = d, there is…

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Q: 2. Prove that, for all k E N, 2 can be written as the sum of two squares.

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Q: Show that E [(X-µ)^n]=0 for ∀n, with X~N(µ, σ²) and n≥3 being odd numbers.

A: We need to show; E[(X-μ)n]=0 for ∀n and n≥3 being odd numberswhere;X~Normal(μ,σ2) That is, we need…

Q: Remind yourself what () means. For this class, we will use the convention that () = 0 if n < k or if…

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Q: Suppose a e Z. If a² is not divisible by 4, then a is odd.

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Q: Assume that |Xn] 0. (Hint: first, prove that P(|X|>c+1) = 0.)

A: Answer:

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

A: The solution is given as

Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1+ Z2| < ]Z1] + |z2|

A:

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: Show that for all n E Z, n² 5.

A: Consider the given condition: This shows that whatever will be the values of n, it will always be…

Q: Show that for all n e Z, n? – 3n +17 2. -

A: Given: For all n∈ℤ, n2-3n+1≠2

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: Prove the following in Z[i]: if a y and 3|y with a and B relatively prime then aß | y. in

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Q: Apply Gauss forward interpolation formula to obtained y(39) if 15 30 45 60 75 90 Y : 0.23 0.32 0.33…

A: Thanks for your question. Since your question contains two parts, so we are solving the first part…

Q: 1. Let A = {x E Z | 6 divides x} and B = {x € Z | 3 divides x}. Prove that A C B, and then prove…

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Q: 15. prove that L. d= nd(n)/2

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Q: 1. Prove that fraction where m is z-4

A: Given: zn-1z-1 ⇒zn-1nz-1 ----(1) Let apply the limit in equation (1) limz→1zn-1nz-1 ----(2) Let n=pq…

Q: 20 + 7)* Evaluate the integral dæ + 7)* * by making the appropriate substitution: u = dx (2x + 7)4

A: Let's find integration of given function.

Q: d. What happens if P < M for all t?

A:

Q: 53. Suppose that a + 0. (a) If a · b = a·c, does it follow that b (b) If a X b = a X c, does it…

A: Given a, b, c are three vectors and a ≠ 0.

Q: prove that and = nd(n)/2

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

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Q: es lls ew zeiflucifiib ons einiseen stigesber Show that for neN, (2n)! ' (r!)² ((n −r)!)² - 7=0 2n -…

A: We will use binomial expansion to prove given relation

Q: For xn = 5n² + 9n³ + 1, an = en = n², prove or disprove: an = O(an) (n → 0)?

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Q: (12) If E(X*) is finite with E(X) = µ and Var(X) =o² then prove that E((X – µ)*) > of. %3D

A: Note : Since you have asked multiple questions, we will solve the first question for you. If you…

Q: In Euler's method, wk = y(tx) for k = 1, ..,n. Select one: O True O False

A:

Q: Suppose n (a)= 7a + 4, determine a such that n (a) = 39. %3D

A: GIVEN n(a) = 7a+4 and n(a) = 39

Q: (35 Show that the following grephes are Hameltonian 8) e a) d c) a ol

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Q: 2 O Expand Pn = 2x +3x +) in Term of P.f,.

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Q: (28) Suppose 1 <N < w and h : w → N. Show that there exist a < b < c < d <e<w such that h(a) = h(b)…

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Q: Suppose that X ~ Unif(-1,1). Compute (d) P(X = 0.5), (e) P(X² > 0.5).

A: Let ,  The pdf of X is ,  = 0 ; otherwise Our aim is to find the following :  d) P(X=0.5) e)…

Q: D. Is there guaranteed to exist a value of x = c on -2 < c < 2, such that h'(c) = 0? Give a reason…

A: Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and…

Q: 4. Prove that n(3n – 1)r x + 4x + 7x + ... + (3п - 2)x for n e N.

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Q: Show that yn Z, if n³+5 is odd then n is even

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Q: Let f(n) = 2n – n? + 10n – 7. Show that f(n) is O(n³) using specific values of C and ng-

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Q: Suppose that in the forward difference formula of order O(h) for f'(xo), h = 0.2 and |f"(c)| < 0.5,…

A: hf''(x)/2 ≤0.2×0.5/2 ≤0.05