|z|? |z]? |z]? || IN IN IN | N

Q: Z {a} is a z-a True False

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Q: Find the value for z if P( -z < Z < z ) = 0.7427.     0.37     0.65     1.13     0.33

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Q: Prove P(n,r)=P(n-1,r)+r.P(n-1,r-1)

A: To prove  P(n,r)=P(n-1, r)+r.P(n-1, r-1)

Q: 2. (Proof by Contradiction) For every n E Z, 4 t (n² – 3).

A:

Q: 1. Assume that cin. 8" + c2n · 4" + c3n° . 9" = 0 %3D for all n> 0. Show that then ci = 0.

A: We need to the equation c1n5·8n+c2n·4n+c3n3·9n=0 for all n&gt;0 for the value of c1. The equation…

Q: Let r(n) be the number of n-permutations whose square is the identity permutation. Prove that if n >…

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Q: Let P(n) be the statement that n(n + 1)(2n + 1) 12 +22 + .. +n? for n>0 6. What is P(1)? a. It…

A: The given statement is

Q: nl diverges because an > 0, for all n 2 1. ) True False

A: Given statement is

Q: ind the general so lution of the differlential eguation

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Q: What is the first step to prove that S, 2+4 + 6+...+ 2n = n(2 + 1)? n(n + 1)? O Verify that S, is…

A: Here we have to determine the first step to prove that,  Sn⇒2+4+6+..........+2n=n(n+1)

Q: Prove that E, k2k = (n – 1)2"+1 + 2 for all n > 1. i=1

A: Note that there is a typo in the question. We need to show that,                            We will…

Q: If In z + In(x – 6) = In(5x), then r

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Q: Show that the following claim holds when for all n > 1 n n(n + 1)(n +2) (+i) = 3 i=1

A: The aim is to show that ∑i=1n(i2+i)=nn+1n+23, for all n≥1. Consider the LHS, ∑i=1n(i2+i) and rewrite…

Q: Let a, b, c E Z. Suppose albc and gcd(a, b) = 1. Prove that a|c.

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Q: dr - In(z®) +C + In(z*)+C 6. + In(z) +C 5 O 5z- In(z) +C O 5z'+ In(z®) + C

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Q: Let R = M2(Z12). Then A= g] is a O True O False

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 7. For n > 1, verify that 1? + 3? + 5² + ...+ (2n – 1)? = ( 2" *1 ) %3D -

A: We have to prove that for n&gt;=1 in question number (7) Sum of squares of first n natural numbers…

Q: Q >S, F R -SVR, QvR

A: We have to prove that by using rules of inferences that Given argument is Valid.

Q: Q3. Prove that if ax = ay (mod m) , then x = y (mod m/d) where d = gcd( m, a).

A: According to our policy at Bartleby, I can solve only one question. I am solving Question 3. Let's…

Q: d Use induction to prove that (x") = n· x"-! for all n e N. dx

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Q: 7. Prove: Vn,meZ, if n and m are odd, then n·m is odd.

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Q: Disprove the claim: 3 m E N such that m > 3 and m? – 1 is a prime number.

A: The claim is given : ∃ m∈N such that m≥3 and m2-1 is a prime number Now, m2-1=(m-1)(m+1)--(1) Case…

Q: (3c) Let n E Z. Prove that if n is odd, then 4|(n² – 1)

A: here is the proof

Q: Show that p(x* |¤, S) = stu-t(*Ho+nã n+K n+k+1 (n+k)(n+m+1-d) Eo + (n – 1)S + В.3. K- m +1- d)…

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Q: 16. Conclude the test. p-value > a, therefore reject H, B p-value a, therefore do not reject Ho E…

A: Answer: D. p-value &gt;α, therefore do not reject H0.

Q: 9. (a) Prove: If y>0, then there exists ne N such that n-1s y<n. ☆ (b) Prove that the n in part (a)…

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Q: (a) Show that if x E Q is such that |x|, < 1 for all prime numbers p then x E Z.

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Q: 2. Let A = {n? +n € Z:n e Z} and B = {r e Z : r³ – 3x³ + 2x = %3D O mod 5}. Prove or disprove: A C…

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Q: Let r(n) be the number of n-permutations whose square is the identity permutation. Prove that if n >…

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Q: Show that for any r, n > 1, п! Σ = r". nį!n2!...n,! nį+n2+…+n,=n, n¡ 20 11 (

A: Given information: The sample size is n. The number of categories is r.

Q: O Prove thal P(m, n) - (n,m).

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Q: Give a direct proof of the claim: V n E N, Vk E N, if the last k digits ofn are divisible by 2k then…

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Q: (3a) Let n E Z. Prove that if 3 ł n, then 3|(n² – 1)

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Q: Forthe Benstein felynominte prove that こニ-x)() c} ヒ。 4n

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Q: 33. Use the Squeeze Theorem to prove (sinn/n} c) {3"/n!} b) fn/2"} f by contradiction. a)

A: 33.) use squeeze theorem to prove that each of the following sequences converges a) sinnn  , (b)…

Q: 17. prove that Edln H(n/d)7 and σ(n ) σ(n) Σ %3D

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Q: If k = 0, then cosh(kx) Scosnlax) ax = sinnk) + C Select one: O True O False

A: Do the integration using concept of hyperbolic function.

Q: Prove by mathematical induction that Vn E Nwith n 2 4 2 n3

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Q: Show that for any n EN where n > 1, II (1 = n + 1. k k=1

A: We need to prove that for n≥1, ∏k=1n1+1k=n+1 We will prove by the Principle of mathematical…

Q: Disprove the claim: 3 m E N such that m 2 3 and m? – 1 is a prime number. -

A: Given that ∃m∈ℕ such that m≥3 and m2-1 is a prime number. Take m=4. It is known that 4∈N And 4&gt;3.

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: .3 ). Show that x is O(x*) but that x* is not O(x³).

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Q: prove by inclusion However, Un{kEN: mk<n} = U0=0. n=1m=1 00 00 00 I m=1n=1 nu{kEN: mk<n} = N=N. m=1

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Q: Let n ∈ Z, Is it true 4 | n4 – n? Prove it or counterexample.

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Q: € C(R) for all a ER, th is Commutatve hat

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Q: 2. Suppose that P(A;) 1 for all i = 1, 2, .... Show that P(N A¡) = 1.

A: Given problem Given that

Q: Which of the following are valid witnesses to show that 10n-1 is (n)? O C=1, k=100 O C=10, k=10 O…

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Q: Is there any n n for which U2n = Dn?

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Q: Which of the following sets is open in (R, Tµ)? О а. R { (-1)"3n³ :n E N} 5n+n³ b. O b. [2, 4) U (1,…

A: Option (c) is correct.