(a) Suppose c is an integer. If c mod 7 = 5, what is 5c mod 7? (b) Write () in factorial form. (c) Write 4 + 8+ 12+ … + 4k as a summation.

Q: 24. Which is the recursive definition of the set of positive integers that are multiples of 4? * aj…

A: We have to find the correct option which represents the set of positive integers that are multiples…

Q: Use the definitions  to show that the following statements are true. For example, to show that 5 |…

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Q: Show that for every integer n, n³ + 2 is not divisible by 4.

A: Here, we use rules of divisibility.

Q: 17. Expand using Pascal's Triangle or the Binomial Theorem. Be sure to show the setup. Then,…

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Q: For: 25, 23, 21, 19, 17, .. Find RECURSIVELY An

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Q: Find each (n+3)(n+2) (4n 5)(3n + 2) (n+7)(n + 5)

A: Since you have posted multiple subparts we solve the first three subparts for you to get the…

Q: The commutator is: Find the commutators if: (a) A = D² and  = x²* (b) A = D and B = x * D [A, B] =…

A: note : As per the standard notations of operator theory, we will treat the operator "D" as a…

Q: 1 The sequence an 2n + 3 (a)decresing (b) increasing (c)not monotonic a b C

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Q: How many strings of 1our decimal digits have all four digits that are different? How many strings of…

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Q: What is the summation notation of this expanded form: A. (1/3)+(3/5)+(5/7)+(7/9) B. 1-4+9-16+25

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Q: let a=2+7i b=4-2i Choose the correct result of a/b*

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Q: 24. Give a recursive definition of a) the set of odd positive integers. b) the set of positive…

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Q: Determine the correct expression for L{6u(t+2)+&e4t – 58(t) Oa. 5 8-4 O b. be-2 - 5e- 8-4 6e2s - 5e-…

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Q: Show that (a) 8n −3n is divisible by 5 for all natural numbers n.  (b) n2 −n +41 is odd for all…

A: expansion of (a+b)n = hco an bo + nc1 an-1 b1 +.......... +ncn ao b n

Q: Malik currently has 39 tulips in his yard. Each year he plants 3 more. (a) Which of the following is…

A: given data  malik havs 39 tulips in his yard each year he plants 3 more  so,  p0= 39 d = 3

Q: on the 4th implication where does the exponents of the i goes please elaborate

A: To find the rectangular form.

Q: Find the product 3/2 (5 /12 + 6/6) and express your answer in the form A/B+ CVD, A, B, C, and D are…

A: Given : 32512 + 66

Q: Pam is a Disc Jockey. Every week she buys 3 new albums to keep her collection current. She currently…

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Q: True or False. Briefly explain why.  The least nonnegative residue of −123 modulo 12 is 3.

A: We recall the definition.

Q: Answers

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Q: If k is a positive integer, what is the remainder when (k+ 2)(k3 - k) is divided by 6? Stilo…

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Q: 2 (a) Work out 14 x 4 – 24 ÷ 2. (b) Find a number between 80 and 90 that is a multiple of both 3 and…

A: We have to solve two subparts in the given problem.                        (a) We need to work out…

Q: Question: Evaluate each following expressions a.) If x =0   evaluate 4x**2 + 5(9 +x) + x **5 b.)…

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Q: [-727] O [435] [-630-21] [-84]

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Q: um 1+4+7+..

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Q: Oscar currently has 43 tulips in his yard. Each year he plants 8 more. (a) Which of the following is…

A: A recursive and explicit formula A recursive formula gives the worth of a particular term that…

Q: Multiply (x2-y?)(x² +y?) using the distributive property and combine like terms. Generalize the…

A: The distributive property of multiplication over addition is as follows         a x (b + c) = (a x…

Q: Give a recursive definition for the following. (c) and (d)

A: In this question, concept of recursive function is applied. Recursive Function A recursive function…

Q: Evaluate the expression using the order of operations. (28 - 18 + 6) - (84 + 6• 2) (28 - 18 + 6) -…

A: Given expression is 28-18÷6-84÷6*2 Since we know the BODMAS rule to solve the Mathematical…

Q: Simplify the following expressions by rewriting without any factorials. A. (n+1)! (n - 1)! (2n+1)!…

A: A)n2+n B)4n2+10n+61​ C) 4n2+2nExplanation:

Q: Obtain the regular expressions for the following: (a) {a4n+3 : n ≥ 0} (b) {a, a4, a8, … }

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Q: could step 2 be explained further? Where did the -3*121 and the -15*375 come from?

A: As  you have asked for step 2 explanation  As we know that root of a quadretic equation ax2+bx+c=0…

Q: Evaluate. (a) - 73 (b) ( – 7)3

A: Given query is to find the value of the expression.

Q: Evaluate the expression using the order of operations. (22 - 9+ 3) - (42+3•5) (22 -9 + 3) - (42…

A: We know that BODMASThat is Bracket-Division-Multiplication-Addition-Subtraction.Given…

Q: Suppose a is a positive integer. Simplify the expression a Σ((n + 2)³ + n³ - 2(n+1)³). n=1 [Explain…

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