If d is g(a, b) and c is another natural number which also divides both a and b. Then c also divides d. :Select one True False

Q: Determine if the following statement is true or false. bE {b, d, c, a) Choose the correct answer…

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Q: Given: ZDEF is comp. to ZHEF. Conclusion:

A: We will find the conclusion as following.

Q: If m || n, which statement is true?

A: Given Data: Parallel lines: m∥n   There are two lines m and n parallel to each other and a…

Q: Suppose that B and Care points on the number line. If BC = 8 and B lies sat - 5 , where could C be…

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Q: Suppose that B and Care points on the number line. If BC = 13 and B lies at -4, where could be…

A: Suppose that B and Care points on the number line. If BC = 13 and B lies at -4, where could be…

Q: 2. Let n be a natural number and let A, B E Mnxn(C). If AB = 0, does it follow that either A = 0 or…

A: Given :  A, B ∈ Mn×n(ℂ)  with  AB = 0. To find : We have to examine whether  A=0 or  B=0.

Q: b. Write the set of natural numbers less than 23 needed) orete answ ers aS

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Q: For how many ne {1,2, ..., 570} is n a multiple of one or more of 8, 9, or 5? 215

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Q: So A is correct? and you are sure 100%?

A: Yes. Option (A) is correct.

Q: If n(A U B) = 21, n(A n B) = 16, and n(B) = 19, find n(A). n(A) =

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Q: Suppose that ab = ba, i.e., a and b commute. Determine |a^2 b^3 |, i.e., the order of a^2 b^3 .

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Q: Prove thot for 8^-3^ aery Wamos nzL,5 divides

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Q: If n(A) = 45, n(B) = 23, and n(A n B) = 8, find n(A U B).

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Q: If n(A) 102, n(A U B) = 142, and n(A n B) = 44, find n(B). %3D

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Q: If n(A) = 120, n(B) = 110, and n(A U B) = 170, what is n(A n B)? %3D

A: Given;n(A)=120n(B)=110and n(AUB)=170

Q: n(A) = 104, n(A ∪ B) = 144, and n(A ∩ B) = 45, find n(B).

A: The following information has been given: n(A) = 104, n(A ∪ B) = 144,  n(A ∩ B) = 45 We need to…

Q: 4. If P(A) = 0.3867, P(BJA) = 04232, and P(A or B) = 0.5381, find а. Р(А and B) b. P(B) с. Р(АВ)

A: Given data,P(A)=0.3867P(B|A)=0.4232P(A or B)=0.5381

Q: If n(A) = 42, n(B) = 15, and n(AN B) = 1, find n(A U B).

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Q: If n(A) = 62, n(B) = 21, and n(A n B) = 3, find n(A U B).

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Q: Suppose that S = { x | x ∈ N , and 3 ≤ x ≤ 260 }  What is | S |

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Q: A box with a square base and no top is to be made from a square piece of carboard by cutting 5 in.…

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Q: If ACDE AFGH then D 2?] Enter the letter that belongs in the green box.

A: Given, ∆CDE≅∆FGH We have to find ∠D ≅ ?

Q: If n(A) = 45, n(B) = 22, and n(A N B) = 9, find n(A U B).

A: By using inclusion and exclusion formula, we calculate the required value.

Q: Use the union rule to answer. If n(A) = 8, n(B) = 10 and n(AB) = 6, what is n(AUB)?

A: given data,here we have to use union rule of probability n(A)= 8n(B)=10n(A∩B)=6n(A∪B)=?

Q: Deduce from Q2 that if an integer N can be written as N = x² + ny² , and if a prime number q | N can…

A: We will use standard division algorithms to deduce the given statement.

Q: Q)1 a) How many 3 digits passcodes are there if first digit must be a 1 or 2 ?   b) How many 3…

A: Q1) a) There are 10 digits 0,1,2,3,4,5,6,7,8,9. The 3 digit passcodes must be formed such that first…

Q: If n(A) = 67, n(8) = 15, and n(A N B) = 9, find n(A U B).

A: Topic- sets

Q: When gcd(a, b) = 1, prove σ(ab) = σ(a)σ(b) and find σ(200) and σ(720).

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Q: Suppose that B and C are points on the number line. If BC = 10 and B lies at - 4 , where could C be…

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Q: If n(A) = 45, n(B) = 18, and n(A ∩ B) = 7, find n(A ∪ B).

A: Given that  n(A) = 45, n(B) = 18, and n(A ∩ B) = 7. We find n(A ∪ B).

Q: If 125% of x is 80 and x is n% of 400, what is the value of n? dd inages tere

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Q: What is 5% of 360?

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Q: Given that a,b,c,d,ea,b,c,d,e are distinct whole numbers from 11 to 99 inclusive, along with the…

A: Given that a,b,c,d,e are distinct whole numbers from 11 to 99 inclusive, along with the equality…

Q: MR=5(a+9) and MP=13a+42

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Q: If = 72, which equation is true? O n = 72 ÷ 9 %3D O n= 72 x 9 O n= 9÷ 72 O n= 72 +9

A: Given that n/9=72

Q: If n(A) = 41, n(B) = 21, and n(A N B) = 7, find n(A U B).

A: We have to find the value

Q: 17) If a = 4b3 and c = 5a?b*, show that c 80b10

A: Given:a=4b3,c=5a2b4

Q: (b) {an}, where an 1 if n is odd and an = ; if n is even. |

A: Given that an where an=1n if n is odd and an=n2 if n is even.

Q: If n(A) = 62, n(B) = 19, and n(A ∩ B) = 4, find n(A ∪ B).

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Q: How many combinations can be made from ♣, ♠, ♦, and ♥ if taken a) four at a time? b) three at a…

A: The formula for combination is nCr = n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)]/r!. Explanation:…

Q: 3. Let r and y be positive integers. If r divides y and y divides r, then r y. 4. Let a, b, c E Z.…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Write a proof for: "If a = b and c = a -c = b - d" d, then

A: Consider the given equations, a=b and c=d now, by the subtraction law of Equality, a-c=b-c

Q: If n(A) = 64, n(B) = 18, and n(AN B) = 7, find n(A U B).

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Q: 4) Find x if m/DEJ = x + 51, m¿DEF = 160°, and mJEF x+ 131.

A: From figure m∠DEF=m∠DEJ+m∠JEF160=x+51+x+1312x=160-182=-22x=-11°

Q: If P(A) = 0.36%, P(B) = 0.61%, and A and B are mutually exclusive, what is P(A ∩ B)?

A: We have given that,  A and B are Mutually exclusive events and P(A) = 0.36%, P(B) = 0.61% then,  We…

Q: Choose an n and m that satisfies the following statement

A: We need an example such that  n = m! Take n = 24 and m = 4  Then m! = 4! = 24 Hence , n = m!

Q: If n(A) = 101, n(A ∪ B) = 144, and n(A ∩ B) = 49, find n(B).

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Q: show that given two numbers m and n, if m is even and n is even, then the product is even

A: Solve by using product rule

Q: Place either or between this pair of numbers so that the resulting statement is true: |14| -7

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.