The rational numbers on the unit interval (that is, QN[0,1]) are countable so they can be enumerated with a sequence of distinct points (r„)nen (that is, QN[0,1] = {rn: nƐN }) Let (r„)nen be any sequence of distinct points that enumerates the rational numbers on the unit interval and let T be the points of the sequence (rn)nen (that is, T= {rn: nƐN }) Find the following and justify the answers without proving. A) lim sup (rn) B) lim inf (rn) C) the accumulation points of T

Q: Sketch the interval (a,b) on the x-axis with the point c inside. Then find the largest value of 8> 0…

A: Choose the correct option.

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Q: Prove that there exist irrational numbers r and s, such that r^s is rational. Do not use the Gelfond…

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Q: Solve the given initial-value problem. The DE is homogeneous. (x² + 2y²) dx 3D ху, у(-1) %3D 2 Ap

A: See the detailed solution below.

Q: Determine mine a conditioN ON | x-4) that will that | 7x²-2 | 4.01

A: We have to determine the condition on  that will assure that

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A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Let a,n∈N. Assume that n≥2. Show that if a^(1/n) is rational, then it is an integer.

A: The detailed solution is as follows below:

Q: To find the P(Z ≤ -1.65) find the row containing ----- in the far left column. Then find the column…

A: Given information- We have given- P (Z ≤ -1.65) We have to find the probability corresponding to…

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A:

Q: Which of the following sets are equal? (Select all that apply.) O A- (3, 4, 5) O 8- (x R| 2 s x « 6}…

A:

Q: ` Prove that positive real numbers a, b, c, d, b 2 + > 3.. a b+zc+3d +c+zd+za+d+za+36 d a+zh+30

A:

Q: Find the length of the graph of f(x) = ² - In(x) for 1 < x < 10. 99 1 a) 4 -In(10) 99 + In(10) b) 4…

A:

Q: Since P+ Q, it follows that [(a1 + a3 + a5) – (a2 + a4)] [(B1 + B3 + B5) + A (82 + B4)]' | P+Q =…

A:

Q: Prove that (a) For all integers m and n, n + m and n - m are either both odd or both even.

A: Since you have posted multiple questions, according to our guidelines we can solve only first…

Q: To find the P(Z > 0.93) find the row containing---- in the far left column. Then find the column…

A: Given that P(Z&gt;0.93).

Q: Let X ~ B (25, 0.30). What R code would calculate: 1. P(X < 15) 2. P(X ≥ 10) 3. P(14 < X ≤ 20)

A: It is given that n=25 and p=0.30. The distribution is binomial.

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A: Given, Graph the set {x|-3≤x≤2}

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A: Let be positive integers with and .Assume are relatively prime.

Q: What function has an acutal rational zero of 7? A.) g(x)=x^3-4x^2-36x+28 B.) g(x)= x^3-4x^2-26x+35…

A:

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A: We have to find the domain of the given function r(t).

Q: 1. What R code will compute P(X125)? 3. What R code will compute P(160<X<170) ?

A: X ~ N(150, 12) Mean(µ) = 150Standard deviations (σ) = 12

Q: 8. Suppose X~N(5,1), find: (а) Р(X 3) (d) Р(\X — 5| > 3)

A: Solution-: Given:  X→N(μ=5,σ2=1) We find following probabilities using R-software: (c) P(X≥3)=? (d)…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.