The operation * is defined as a*b=a+b-2ab Evaluate i) 2*(3 * 5) ii) (2 * 3) * 5 Compare your answers in (i) and (ii). What property is that?

Q: 1. Write a regular expression for all strings on {a, b, c} which contain a², b² and as substrings.…

A: It is given that

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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 .

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A: We are given that a and b are positive integers, that means, a≥0 and b≥0 Now, the square of any…

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Q: Quse The rules of Boolean algebra and Demorgon's Theorem to Sim plify

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Q: 3. Let, a, = 3, a2 = 4 and for n2 3, a, = 2an-1+ an-2 + nº+ 1, express a, in terms of n.

A:

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

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

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A: Let the twelve digits be d1,d2,d3, d4,d5,d6,d7,d8,d9,d10,d11,d12 from left to right. Let a1=d1…

Q: Determine whether the statement is true or false. Prove the statement directly from the definitions…

A:

Q: Find integers ? and ? such that 3220? + 6006? = gcd(3220,6006).

A: Remark: The greatest common divisor (gcd) of two integers is the greatest integer that divides both…

Q: Let, a, = 3, a2 = 4 and for n2 3, a,= 2an-1+ an-2 + n + 1, express a, in terms of n. %3D %3D %3D

A: The nth term of A.P is given by an=a+n-1d we have,  a=3,d=4-3=1an=3+n-11=2+n we get,…

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.…

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A: Solution:- In the given problem, we will find how many 4-digits number have all their digits in…

Q: Let n be a number with 3 digits. (i.e 100sns 999) Show that if the sum of digits of n is divisible…

A:

Q: Show that (n + 1)!)" < 2! · 4! - (2n)!.

A: The objective is to prove the given statement using induction

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.

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A:

Q: 2. What is the quotient of and?

A:

Q: 75. If f(7) = 13 and fis one-to-one, what is f(13)?

A: For a function domain is set of values for which the function is defined. The range of a function is…

Q: (i) Deduce that the difference in the number of integers in the numerator and denominator of (* 2N N…

A: Properties of floor functions will be used.

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A:

Q: ken two at a ken three at a

A: 1 2 3 4 5 6 j o y f u l The different arrangements formed from the 6 letters word = 6!

Q: a) How can you find a linear combination (with integer coefficients) of two integers that equals…

A:

Q: 3. Let, a1 = 3, a2 = 4 and for n 2 3, an = 2an-1 + an-2 -5, express a, in terms of n. %3D

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Q: What is the use of Boolean identities?

A: Boolean algebra has a number of useful identities. Here an "identity" so called "rules" is a…

Q: 4. Let, a = 3, a2 = 4 and for n 2 3, a, = 2an-1+ an-2 +n, express a, in terms of n.

A:

Q: (7+2)^2

A: (a+b)2 = a2 + 2ab + b2

Q: Show that (n + 1)! > 2"+3, for n > 5.

A:

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A: We will solve the problem using recurrence relation

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Q: Show that N-, (x) = (-1)"N„(x). Nó(x) = -N1(x). with open steps and explained pls

A:

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A:

Q: 2- w = - w

A: We have given a complex number property;

Q: 20. (gof)(x) and it's domain.

A: Topic = Functions

Q: 4. Use a combinatorial argument to show that () n 1 -2) n + 22 n 2 3 -

A: Given: nn-2=n3+12n2n-2n

Q: If A #8 then

A:

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A: To prove that whether the given statement is true or false

Q: EXERCISE 2.2A Write an expression for the total number of counters in each of these cases. Jse…

A:

Q: 2. Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 + 5n, express an in terms of n.

A:

Q: How many positive integers less than 2ˆ{20} are not divisible by 7, 11 or 13. Use…

A: The solution is given below

Q: rix is A = onto R³ 1-2 3 - 1 8 34. Determine whether th 6-6

A: Follow the steps.

Q: 2. Let, a, = 3, a2 = 4 and for n 2 3, an= 2an-1+ an-2 + 5, express a, in terms of n.

A:

Q: how is 0.46= .32276 because on the z table it's 32.64 so where does the .32276 come from

A: The z-score is -0.46.

Q: Do you  know anything about boolean algebra?

A: Please rate and feel free to ask any query about any part of the question.

Q: prove that if a>4 then (a-2)^2>4

A:

Q: Use a combinatorial argument to show that n 1 2 - 2 3 2 2

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.