Let e be a positive real number. Prove or disprove that n E N(n²+e).

Q: 1. Show that if f is a bijection from a set X onto a set Y then f is a bijection from Y onto X.

A: Please post the multiple questions separately. Here I answered question (1) only as per our policy.

Q: Theorem. E(X)= Proof: Let X-Po(2), then Var(X)= mx(t) = exp{^ (e¹-1)}

A: X has a Poisson distribution

Q: 2b(6pts). Let f be a function from X into Y. Let S and T be subsets of Y. Show that f-'(SUT)= f-'(S)…

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Q: For a function f: A → B and subsets C and D of A, prove that f(CUD) = f(C) Uƒ(D).

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Q: 2b. Show that if K CR is compact then K is closed.

A: Given that  is compact. we have to show that  is closed .In other words ,it is suffices to show that…

Q: 1. S ef = c f

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Q: A particular coin is biased. Each time it is flipped, the probability of getting a head is P(H) =…

A: Let X be the number of heads shows up follows binomial distribution with n=10 and P(H)=0.7.

Q: O Consider the infinite series where 9 ER. Show using induction or otherwise we have - Σ qk, k=0 Sn…

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Q: If f(x) = 2x – 1 and g(æ) = a – 2 then (f.g )(0) = O a. -2 O b. 1 O c-1 O d. 2

A: Since, we have been given that f(x)=2x-1 and g(x)=x-2Then our aim is to calculate (f.g)(0)=?

Q: Given: PQRS and QDCA and parallelograms are B Prove: AP BS Statements Reasons

A: Given -  PQRS and QDCA are parallelogram.

Q: A. What is the limiting value of the temperature of the coffee? lim T(t) 25 t 00 B. What is the…

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Q: Suppose that f: [a, b] → R is a continuous function, and f f = 0 for every rational number x in the…

A: Suppose, for the sake of contradiction, that there exists a point c in [a, b] such that f(c) is not…

Q: Let f [a, b] R and ro € (a, b). Assume that f is continuous on [a, b]\ {xo} and limx→zo f (x) = L (L…

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Q: Directions: Write your convincing proof. The function f(x) 2/x takes on the value-2 at x--1 and it…

A: Application for Intermediate value theorem.

Q: proof.

A: Under given problem all Xi are iid

Q: Subtract f(x). f(x + h) – f(x) = (4x² + 8xh + 4h² + 3x + 3h – 2) – (4x² + 3x – 2) = 4x2 - x² + 3x -…

A: We can simplify the following expression : f(x+h)-f(x) = 4x2+8xh+4h2+3x+3h-2 - 4x2+3x-2

Q: Let A = {1, 2, 4, 5, 6, 7, 8, 9} Let R be a relation on A defined by R = {(a, b) : a e A. b e A, a…

A: Given set is A=1,2,4,5,6,7,8,9 and R be the relation on A defined by R={(a,b):a∈A,b∈A,a is…

Q: 5. Prove that if a matrix A is invertible and diagonalizable, then matrix A-1 is also diago-…

A: We have to prove that Given statement.

Q: 1. A psychologist is studying learning in rats. The psychologist wants to determine the average time…

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Q: Given: mzQVR = 49° Prove: x = 15 R V (3x + 4)° U Complete the steps of the proof.

A: Given ∠QVR =49°    and ∠TVu =3x×4    We know ∠QVR =∠TVu             ( as both are vertically…

Q: If f(x) = 2a? + x +1, then (f + f )(1) = O a. 8 O b. - 4 O c.-8 O d.4

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Q: Part 2 Given: mZT = 30 MZVUS = 135 Prove: mZS = 105 U S

A: Topic = Geometry   Supplementary angles are two angles whose measures add up to 180° .   The sum of…

Q: 1. Use residual analysis to determine whether any outliers and/or influential observations are…

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Q: Let's assume that we want to do unpaired two-sample t-test for the following summary of samples.…

A: Margin of error is calculated by the combined value of standard error and critical value. It explain…

Q: Complete the proof

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Q: Theorem. E(X) = np If X has a Binomial distribution, then Var(X) = npq mx(t) = (pe¹ + q)

A: A random variable  is defined to have binomial distribution denoted by  if the PMF of  is given by…

Q: Q1. Use numerical evidence to evaluate lim (-2x + 5) based on the table given. X 0 5 .9 .99 1.01 1.1…

A: The answer is in step 2.

Q: 4-7 Practice (continued) 6. Given: AAFD and ABGE are equilateral triangles. ZA ZB, DE = FG Prove: AD…

A: Given: and  are equilateral triangles,Prove that :

Q: Write an equation in which the quadratic expression 2x² – 2x – 12 equals 0. Show the expression in…

A: a) To write the equation of expression 2x2 - 2x - 12 equals 0. b) To express in factored form.  c)…