%3D If there exist integers r and s such that ra + sb = d. then d = (a, b). lgn hi O

Q: In ADEF, m LF = 42, DE = 12. Find EF to the nearest integer. (Use the table on page 311.) m LE = 90,…

A: The length of DE=12 units. An angle ∠F=42∘ The objective is to find the length of EF.

Q: A. Which of the following have integer solutions? Why? 1. 21x – 7y = 88 2. 55x + 44y = 99 3. 42x +…

A: Since you have asked  multiple questions  so as per guidelines we will solve the first question for…

Q: For positive integers a, b, c, if a|6 and 6|c, then a c. O True O False

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

Q: a|b_ then a|bc for all integers c. ulgn İhi

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Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 92n-3 6 cn-4 ac? n=3 C -

A:

Q: a|b then albc for all integers c.

A: From the question, a|b means that a divides b, and similarly, a|bc means that a divides bc. We need…

Q: Find the value of x if O 1.84 O 1.77 O 1.32 O None of these O 1.52 metazaf =7

A:

Q: Find n if: a) P(n, n) = 5040. b) 66= C(n, 2). c) P(n+1, 5)= 5P(n,1) Note: n is a…

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Q: For all real numbers a and b, |a + b| < ]a| + |bl. Select one: OTrue False

A: Answer

Q: Find the quotient q and the remainder r if a = bq + r. (a) a = 582 and b= 25 (b) a = 614 and b= 43…

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Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 62n–3 19 cn-4 ac² с — В n=3

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Q: If P(A) = 0.7, find the complement. %3D

A:

Q: Z/mZz Zm

A: We need to prove that Z / mZ is isomorphic to Zm .

Q: Suppose that m and n are positive integers with m 7 n. If a = m2 - n2, b = 2mn, and c = m2 + n2 ,…

A: Given: m&gt;0, n&gt;0 and m&gt;n, a=m2-n2b=2mnc=m2+n2 To show that a,b, and c are the sides of the…

Q: Let c, a, B be nonzero real numbers such thatc + B. Find a given that 42n-3 E12 ac? cn-4 с — В n=3

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Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 122n-3 2 cn-4 ac? n-D3 с — В…

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Q: (b) Show that įn is real, even though i or 9i is not.

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Q: (b) If a, b and c are integers such that b| a and b| c, then b | (2a – 3c).

A: We have to proof

Q: (c) Let n be a positive integer and assume that there are integers a and b ab. Show that a < yn or b…

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Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 132n-3 8 cn-4 ac? с — В n=3

A: To find the value of a from the given summation

Q: (cg)" QI: Evaluate dg. where both c and ß are integers.

A: We will first reduce the denominator and then then solve the indefinite integral. Then we will put…

Q: alb then albc for all integers c.

A: Since, a|b, a divides b or there exists an integer k such that b=ak.

Q: Find conditions on a, b, c, and d such that AB = BA

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Q: Determine the numbers a such that x a (p) is solvable for p = 7, 11, and 13. %3D

A: Given, x3≡amod p At p=7 We know that suppose p is rational prime p≡1mod 3 then x3≡a mod p is…

Q: let a and b be integers. Show: if a * b is odd, then a is odd and b is odd

A: A number is even, if it is divisible by 2. A number is odd, if it is not divisible by 2. The odd…

Q: ex: Find the humber of integers between 4 and loo that end with 3 or 5 Date. No.

A: To find:- Number of integers between 4 and 100 that end with 3 or 5

Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 72n 3 E17. 00 ac? c -B' cn 4…

A: Sum f infinite numbers of gp is a1-r

Q: 1. For each pair of integers a and b, find d = gcd(a, b) and find x and y su (a) a = 356, b = 48 (b)…

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Q: If b is a positive integer not divisible by the prime p, then (р-1)b 2b 3b + %3D ...

A: We have to find the required summation value.

Q: If P(-a < z < a) = 0.4314, find a.

A: Given that, P(-a &lt; z &lt; a) = 0.4314  We to find the value of a

Q: If k is an integer: exp[(i)(2pi)(k)] =

A: Solution) ei 2ℼ k As we know eia = cos a + i sin a a = 2ℼk  ei 2ℼ k= cos 2ℼk  + i sin 2ℼk  K =…

Q: If o? = 625, X = 66.3, and Zo.025 = 1.96, %3D %3D %3D then the size n is O 10. None of all. 20. O…

A: None of all

Q: 'ind integers s and t such that s · 35 +t · 78 = 1. Show your work.

A:

Q: Let R = Z10 O Z100- (a) How many units does R have? (b) How many zero divisors does R have?

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Q: alb then albc for all integers c. ylgn O ihi O

A: Correct answer False  Explanation

Q: Suppose that E and F are points on the number line If EF = 10 and E lies at , where could F be…

A: Distance between two points in a number line  is to  subtract the smaller number from the larger…

Q: For each pair of integers a and b, find integers x and y such that ax + by = gcd(a, b) 1. a = 207, b…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Let a, b be positive integers, and let p be a prime integer. Let the notation n|m means m divides n…

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Q: Let M=( 3 Find formulas for the entries of M", where n is a positive integer. Mn = =

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Q: Assume a, b and c are real numbers greater than 1. Find p, q and r so that the following equality…

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Q: Let n be a positive integer and M %3D Then M"

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Q: -t/25 /O Find t if Ans 296:4

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: If B: = {XERI0S X3 = [0,:] for each non-negative integer i, find the following a. B,UB.UB, UB, b.…

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Q: If x-p() is such that (4= p(x = 3) = 4px, then ? = (2 = p(x) 0.418 ( c) 0.148 b) 0.184 0.481 (

A: Given: P(X = 3) = 4P(X = 4)   Formula Used: If a random variable X follows poisson distribution,…

Q: Find the value of x in the regular octagon. (4x-3) O 57 o 12 O 45 O 54

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Q: The number ofunits in Z23 [x] is O 22 O 28 None O30

A: Consider the given information: To find the number of units in ℤ23x.

Q: For all integers a, b and c, if a divides b and a divides c, then a divides (4b - 3c). True False

A: Answer is TRUE

Q: Let -2 М- -16 Find formulas for the entries of M", wheren is a positive integer. M" =

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Q: The QRT states that for any integers n and d (d non-zero), we can find unique integers q and r such…

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Q: Let М- Find formulas for the entries of M", where n is a positive integer. M" =

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.