A test for checking computations is called casting out nines. Consider the sum 612+301 + 500 = 1473 The remainders when 672, 301, and 500 are divided by 9 are 6, 4, and 5, respectively. The sum of the remainders, 15, has a remainder of 6 when divided by 9, as does 1473 Find the following sum and use casting out nines to check 398+476 + 182 398 476 182

Q: If you want to check that 613 is a prime number using the test for primality, what is the minimum…

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Q: The number of factors of prime numbers are None of the mentioned O 30 Depends on the prime number

A: No. Of factor of prime no. Means how many divisor consist of a prime no.

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 .

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Q: If n has a prime factorization n = pi*p2² ... p" then the sum Eajn d³P(d) is equal to: a1. az

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Q: Show that 7 divides (1111)³³³³ + (3333)¹¹¹¹

A:

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

A: Yes we can use mathematical induction for Natural number x.

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A: Suppose we have three positive integer a , b and c where a=p1x1·p2x2·⋯⋯ ·pmxm , b=q1y1·q2y2·⋯⋯ ·qnyn…

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Q: he notions of the greatest common divisor and the least common multiple extend naturally to more…

A: Solution Given

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A:

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A: Partition of positive integer is a way of writing n as a sum of positive integer.

Q: The integers 77 and 105 are relatively prime. صواب İhi

A: By finding the factors of given numbers you can find the solution :

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Q: The prime factorization of 7007 is 7.113.13 O 73.11.13 7.11.13 72.11.13

A: We need to find prime factorization of 7007.

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A: First let us formulate the problem in a different way. Look! we have to find the total number of…

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Q: Q4: Consider the 5-digit can be formed using the digits 0-9 mbers, with distinct digits (no…

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Q: Suppose that n=24.35.112.133. How many divisors does n have?

A: Given,  n = 24 35 112 133 Then (4+1)(5+1)(2+1)(3+1) = 5×6×3×4=360 It has 360 number of divisors

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A: Answer: Option b)  666600

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A:

Q: In the Sieve of Eratosthenes for numbers less than 100, explain why, after crossing out al the…

A: Given In the sieve of Eratosthenes for the numbers less than 100 , Explain why, After crossing out…

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A: Note: As per Bartleby’s guideline for more than one questions only first is to be answered please…

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A:

Q: Choose the prime factorization of 12 O 2.3 10 O 23.3.5 o 10 12 O2.5.12

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A:

Q: The prime factorization of 7007 is 7.11.13 72.11.13 73.11.13 7.11³.13 o

A:

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A: Given n=100

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A:

Q: Show that the sum of twin primes p and p + 2 is divisible by 12, provided that p> 3.

A: Let p, p + 2 be twin primes. Then p *(p+1) + 1 = p^2 + 2p + 1 = (p+1)^2 ,  a perfect square.

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A: Detailed Solution and Explanation is given below....

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A: Given: a=21·32·72b=23·33·71c=31·52·73

Q: D. Using the digits 2, 4, 6, 7 and 9, how many five-digit numbers can be formed if the number is…

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A:

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: