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Q: Not every collection of terms has a GCF other than one. O True O False

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Q: o is a) 1-1 b) onto c) Both 1-1 and onto d) None

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Q: Prove by direct proof that any integer n ≥ 3 can be part of a Déjà vu Pair n = [11 · · · 1]b for…

A: Given: Any integer n≥3 can be part of a Déjà vu Pair n=11...1b for some base b≥2.   To prove: The…

Q: (2) (a) Show using set identities that AUBU(AN BNT) = AUBUT (b) Prove by contradiction that if A C…

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Q: Let a, b, x, y ∈Zbe such that ax+by= 11. May we conclude that gcd(a, b) = 11?Why or why not? (Write…

A: Consider the given information:Let a,b,x,y∈ℤ be such that ax+ by=11.

Q: a Which of he pocess e satoay? that in some cases you may not be able to get an eact exresin.In…

A: a) Note that Therefore Yk has a pmf of a Poisson random variable, which implies that it is a…

Q: Let S = Span}( 3 2 3 . Show that dim(S)=2. 3

A: Basis: Let V be a subspace of ℝn. A basis of V is a set of vectors v1, v2, ..., vm in V such that:…

Q: 1. Let, a, = 3, a2 = 4 and for n 2 3, a, = 2an-1+ an-2, express a, in terms of n.

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Q: If a, bEZ such that a b then the numbers a and b are called relatively prime numbers if ged (a, b)…

A: True

Q: The number ways in which leters. f the word Pananged of in which letters PARET Can be So that R is…

A: Given, PARET- all letters are different number of letter in PARET=5

Q: 3. Let, a, = 3, a2 = 4 and for n2 3, a, = 2an-1+ an-2 + nº+ 1, express a, in terms of n.

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Q: ofind all voots ecilmal Places.

A: Use Newton's method to find all roots of the equation correct to 6 decimal places1x=1+x2

Q: If a, b e Z such that a b then the numbers a and b are called relatively prime numbers if gcd(a, b)…

A: Consider the given statement. We'll prove the statement by contradiction. Let's the numbers are not…

Q: It reguired to seub 4 boy s and 6girls in a row so thab Ehe girls acev py the odd places How many…

A: Given: There are 4 boys and 6 girls  Girls occupy odd places

Q: M={all numbers of the form 2^n , for n is a natural number} is the set closed under addition?

A: It is given that, M={all numbers of the form 2n , for n is a natural number}   Note that, a set is…

Q: For all intergers a,if 6|5a,then6|a. Prove or disprove this statement."|"means divides

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Q: Consider the word TORTOISE. Count the number of arrangements of this word (a) such that no two…

A: We have to solve given problem:

Q: Q 3 Prove or disprove each of the following: For all sets A, B and C, (а) (А — В) — О%3 (А- С) — В

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Q: Find two infinite sets A and B so that A UB, AN B,А — В аnd B — А are all infinite sets. Show the…

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Q: Chow that ॥२ + १n + 3 (nt) (2nt3)(2nt5) (nt 4) 36

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Q: Let filN >N be defined by f(n) = Ź v(d) for all nEl din where r(R) is the number of the positive…

A: A multiplicative function on the set of natural numbers is a function T such that Tnm=T(n)T(m)…

Q: rsection of any collection of com

A: This is a real analysis question. Let (X,d) be a complete metric space with X not ∅. Suppose the…

Q: EIf a,,a,,a,.--,a, be an A P of non - zero terms, prove that ------ 1 1 +. 1 n-1 %3D a,a, a,a, a,a,

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Q: uppose that A ⊆ C so that n(A) = 5 and n(C) = 11. How many subset B, with n(B) = 8 are there such…

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Q: 1. Let, a, = 3, a2 = 4 and for n 2 3, a,= 2an-1+ an-2, express a, in terms of n.

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Q: 3. Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 – 5, express an in terms of n.

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Q: Suppose that a student aishes to find out what" Saint Rose students think about! the Saint f Smokina…

A: b) If the sample is selected randomly by using the randomization procedure from the list of all the…

Q: O cf AandB are subsets of X such that A=R 3. then fiA = {cB but the converse is not tiug

A: Let A and B be subset of X and  let f be function from A to X If A=B => f(A)=f(B)   taking both…

Q: Give a mathematical example to chow the follewing: For any rational number n And any pesitive real…

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Q: A(n) __________is a letter used in algebra to represent anynumber from a given set of numbers

A: In algebra, there are different set of numbers such as Real numbers, Complex numbers, Rational…

Q: 4. In Aa group of n omen and n wowen, how many trere to arronge the se þeople are ways in F the men…

A: We'll answer one question since the exact one wasn't specified. Please submit a new question…

Q: 3. Let, a1 = 3, a2 = 4 and for n 2 3, an = 2an-1 + an-2 -5, express a, in terms of n. %3D

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Q: A,B and C such al numbers x and

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Q: 3. Show that 1 > 0. 4. Show that if a > b and c < 0, then ac < bc.

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Q: Show that if h+1 distinct integers are, Chasen from the Set El,2,en.,4n}. then there are always two…

A: To show that choosing n+1 distinct integers from the set {1, 2, 3, ..., 4n} then there are always…

Q: Give numericaL example to represent this rule: a -For any nonnegative mumber a, any integer k, and m…

A: Proceed as shown below

Q: 4. Let, a = 3, a2 = 4 and for n 2 3, a, = 2an-1+ an-2 +n, express a, in terms of n.

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Q: You have two copies of of the letter A and an unlimited number of the the letters B, C and D. How…

A: We have two copies of of the letter A and an unlimited number of the the letters B, C and DWe need…

Q: Say whether the Runction is even, odd, or neither. Give reusans for your dnswer. go0 = x"+x-1

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

Q: t if n is a of by com

A: Given as, n is an integer 3n+2 is even

Q: Suppose A and B are bounded and nonempty subsets of real numbers and 1 E R. In this case: If A CB…

A: If you understand the concept of inf and sup then these statements are obvious. Remember that inf of…

Q: s) Let a and b be positive integers such that b< a < 10b. How many ways are there to place a…

A: In the given problem Balls are labelled and boxes are unlabeled. i.e. we have to distribute a…

Q: (a-b) if a,b,c,d are in continued properties,prove that a (b-c) d

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Q: rix is A = onto R³ 1-2 3 - 1 8 34. Determine whether th 6-6

A: Follow the steps.

Q: (b) Let A = a + 1 and B = b+ 12. Using proof by induction, show that A+B divides An+1 + Bên+1, What…

A: here i used basic condition of divisibility and i used the notation a|b for a divides b .

Q: B. Assume that a, b, c, and d are defined as foliows, and ealeulate the results of th following…

A: Here, the given matrices are: a=21-24, b=-1302, c=21,d=eye(2)=I2=1001

Q: How many extensions of g to A are one-to-one? How manu ou

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Q: The bonary operation s defimed on the set Z of all mtegers by ab= a+b-ab. Which of the followng…

A: Given a binary operation ⊗ is defined as a⊗b=a+b−ab for all integers We have to choose the correct…

Q: "for all n,m ∈Z \ {0} and g ∈ N,  gcd (n,m)= g then there are a,b ∈ Z with an+bm= g" is the…

A: We need to see if the converse of the statement "gcdn,m=g then there are a,b∈Z with an+bm=g" is true…

Q: Let (a,b)=1 Show that (a+b, a-b)=1 or 2. When is this GCD 1? When is 2?

A: Proof:It is given that gcd(a,b) = 1. So ax + by = 1.Let gcd(a + b, a – b) = d, then d|( a + b) and…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.