10. Prove that (n) ≤ n/2 for n ≥ 8.

Q: 7. i) How many functions are there from the set {1, 2, 3, ...,k} where k is a positive integer, to…

A:

Q: Let X~ N(2, 9). Compute P(1 ≤ X < 7).

A: From the provided information, Mean (µ) = 2 Variance (σ2) = 9 X~N (2, 9)

Q: 6) If X is N(45,5) for i = 1, 2,..., 25; find: 25 (a) P (30 < (X-45) < 55) 221 b) P(30< (X -45) 2 <…

A: The objective of the question is to find the probability of two different scenarios for a normally…

Q: 5. Let r > 1 be an integer such that 2" + 1 is prime. Show that r = 2" for some non-negative integer…

A:

Q: Find the supremum and infimum of the set x € R:x = +(-1)" ,n e N} + (-1)" ,n e N}

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

A:

Q: XA and x & f(x)}. Show Cim ƒ.) 38. Let a, b, c, and d be any real numbers such that a < b and c < d.…

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Q: 5.80 Show that these facts are true. Use the definition of binomial coefficients to show that each…

A: We expand left hand side i.e. nCn nCn= n!/n!*(n-n)! We know that 0!= 1 so  nCn = n!/n! = 1 This…

Q: Prove that 6 divides n³ - n whenever n is a nonnegative integer.

A: In this problem we have to prove that  divides  where  is a nonnegative integer.

Q: prove that (1- (1/4))(1-(1/9))(1-(1/16))...(1-(1/ n2)) =(n+1)/2n for all integers n greater than or…

A: We have to prove that  (1- (1/4))(1-(1/9))(1-(1/16))...(1-(1/ n2)) =(n+1)/2 By mathematical…

Q: Let X-x²(18). Given P(7.015 < X <)-029th - then: a) 14.44 b) 10.865 c) 6.265

A: Let X~χα2( 18). GivenP(7,015 &lt;X&lt;χα2)=0.29To find the χ2(α) using the Excel software…

Q: 5. Identify the mistake(s) in the following "proof": Theorem: The sum of any two positive integers…

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Q: Prop (1.23 ≤ x ≤ 1.72) = Prop (-2.50 ≤ x ≤ 0.5) = Prop (x ≥ 3.00)

A: here use normal distribution table

Q: 10. Evaluate | x In(x+12) « dr.

A:

Q: 9.56. In Z11, express the following sums and products as r], where 0 <r<11. a. [7] + [5] b. [7] ·…

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Q: 2. Prove: if an < bn for » 1, and an on Definition 3.3. 00, then bn - 0o. Base the proof

A: SEQUENCE Question

Q: Prove for all integers n, k, and r with n ≥k≥r that (O)(=O(-) Lify both sides.) n n- r

A:

Q: How do I prove the following statements: (a) For all a, b, c ∈ Z, if a a. ● (O2) For all a, b ∈…

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Q: Prove the inequality V1+æ – 1 –+ < 6 on [0, 0). 8

A: Consider the given inequality in the given interval. Use the graphical approach to prove the…

Q: 9. Let A = 0100 001 0 0001 0000 to Show that A" = 0 for n ≥ 4. 6]

A: Solution:

Q: 5) Given f(x) = V1 -x² , the range is: a) O (-∞; -1] b) O [-1, 1] c) O All real numbers d) O [[0,…

A: The graph is shown below: