mwwwppppna tind the Probuce 5) 5122-1)0-22 +32-4)

Q: find the probabi lity of getting 3 on the 2nd olie given the Sum is 8?

A:

Q: Can you use mathematical induction to show that 4 divides 32x + 7 First define the predicate ?(x)

A: given , expression :- 32x+7 we have to prove that given expression is divisible by 4 .

Q: What is the coefficeint of a²b³cª in the expansion of (a + 2b + 3c)® ?

A: In the given question we have to find the coefficient of  a2b3c4 in expansion of a+2b+3c9

Q: Prove the statement. "For any integer n, nº +4 is not divisible by 8." by Contradiction.

A: Given: n be any integer. To prove: n3+4 is not divisible by 8.

Q: 14. Use the indirect method (contrapositive) to show that "If a + b is an odd integer, then a or b…

A:

Q: 1. Underline the addition property for 6 +7 = 7+6. associative property commutative property zero…

A: 6+7=7+6 We need to tell which property is followed by the above equation. associative property…

Q: V nEN, 7"- 3n is a multiple of 4.

A: We have to find   For all n= natural number we have to

Q: Use the ertended pigeonhole principle to show that there is at least 15 ways to choose 4 integers…

A: Extended Pigeonhole Principle:      If there are n pigeons and m pigeonholes and n>m. Then, there…

Q: If p + 2 is a prime number, prove that p² + 3 is divisible by 4.

A:

Q: 23. Prove that any integers a,9(a?-3)

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Q: p + 2 is a prime number, prove that p2+3 is divisible by 4. (2.5

A: Prime and divisibility

Q: how do you find "In (5/2) " on a calcualtor

A: To find ln(5/2)

Q: 9.) Is 9" + 3 is divisible by 4? PROVE IT!

A: Given : 9n+3 is divisible by 4. To Prove: The given statement is true for n=k+1. Consider Tn=9n+3.…

Q: Draw the folowing in Standurd pse 1) 8/0° 2) 590° 3) - 308° 4) - 620

A:

Q: Show by mathematical l Induction y 4n-2 3. +17 can be divided by +22 possitive integers 16 far all

A: To prove the given statement by using mathematical induction.

Q: Consider the following statement. Is there an integer that has a remainder of 2 when it is divided…

A: The statement " Is there an integer that has a remainder of 2 when it is divided by 5 and a…

Q: How do we proof that 2logn = n?

A:

Q: Given any set of 15 integers, must there be two that have the same remainder when divided by 12?…

A:

Q: A 10-98 5678 9 10 -5 -6 -7 -1

A: The perimeter of the triangle = sum of all three sides.

Q: Prove that 3:8 is equivalent to 12:32

A: According to the question, we have to prove that the ratio 3:8 is equivalent to 12:32. A ratio is a…

Q: a) Proe by induction on n3, that 23"-/ is diwisible bu

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Q: the velue of x is fore which What the exponsion of 18-3x)- will be X. valid? SHOT ON REDMI Y3 AI…

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Q: If the product of two integers is 2'3*5?7!" and their great- est common divisor is 2°345, what is…

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Q: 4. Prove by contradiction: VmeZ, 7m+4 is not divisible by 7

A: Contrary suppose that,   m is an integer such that 7 m+4 is divisible by 7. By using the definition…

Q: what two consective odd integers have a product of 63?

A: Find two odd integers.

Q: Suppose a and b are integers that divide the integer c. If a and b arerelatively prime, show that ab…

A: Since a/c   &  b/c  , we know there exists integers K1 & K2  ,with K1 a=K2 b=c--1Also…

Q: Prove 3√3  is irrational

A: See the attachment.

Q: How would you respond to Tawana, who claims that mn is the least common multiple of m and n in every…

A: Consider two natural numbers m, n.   Then, the multiples of m are m, 2m, 3m, 4m   and the multiples…

Q: what is 6squared + 7

A: It is given that 6 squared + 7.

Q: Show that there are no prime triples other than 3, 5, 7.

A:

Q: А. If p 2q 5 is a prime number, prove that p2-q? is divisible by 3.

A:

Q: 4. Find the sum of positive divisor of 5,020 and also find the pair of this number so that they can…

A: We have to find the sum of all divisor of 5020 and then the amicable pair of the number.

Q: Number Theory

A:

Q: 2. Find a counterexample to the statement n2 – 4 - V nonzero integers n, is not an integer.

A: 2. Given statement is, ∀ nonzero integers n, n2-4n is not an integer

Q: 3. All proofs start as conjectures counterexamples converses constructions

A: We have to find the terms

Q: Pave by Induction ari nz2: ス1 < 2-1

A: The detailed solution of the probelm is given in the next steps.

Q: If  n×k divisible by 4, then n is divisible by 4 or k is divisible by 4. Which of the following is…

A:

Q: are Qunctionwrite walltn in the form Waf(z) 242

A: Here, given that: u(x,y)=x2-y2+x, v(x,y)=2xy-yw=u+iv

Q: 1. Use Direct Proof to prove that the product of two consecutive integers is divisible by 2.

A: We have to prove that product of two consecutive integers is divisible by 2.

Q: What does the divisibility rule of 4 and 8 have in common ?

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Q: 27. If m AC = 4x-5 and m BD=2(x+20), what is mZABC? 28. If mAC = 65-2x and mBD=4(2x-5)-5, what is…

A:

Q: Give a counterexample to the statement. The product of 2 primes is always odd.

A: Product of two primes.

Q: Evaluate projba if a = (13, 5, 1) and b= (2, 1, –1). %3D

A: Given, To determine

Q: 1) Write all the following as expansi > 0-2 > V26 V35

A: In this question we have to do expansion.

Q: Prove that if an integer m has the same parity as an integer n, 5m + 7n is even.

A:

Q: Use the Parity Theorem to prove: For all integers n, n2+3n is even

A: Given: n is integer. To show: n2+3nis even.

Q: 4. Suppose that a and b are integers that divide the integer c. If a and b are relatively prime,…

A: Suppose that a and b are integers that divide the integer 'i'If a and b are relatively prime. Show…

Q: A restaurant sell features a burrito bar in which a customergets to choose one of 2 different kinds…

A: As per bartleby guidelines only one question is answered please upload the other one separately…

Q: Use a counting argument to prove the following. (*:) - (9) - C) - + ab 2

A: