Every positive integer is the sum of distinct powers of two. F b C e Every positive integer is the sum of distinct powers of three.

Q: Let X x b(n,-) and E(3x) = E(3-5.x) find n.

A: Given X ~ B(n, 12) P(X=x)=Cxn px (1-p)n-x; x=0,1,....n…

Q: Show that if a f b, then a +b ab ... 1 a +b ab ... 1 a +b an+1 - 62+1 ... a - b ... ... ... ... ...…

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Q: 3. Suppose that f(n) = 2f(n/2) + 3 when n is an even positive integer, and f(1) = 5. Find a) f(2) b)…

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Q: If a,b,c,d are in distinct real number in A.P. Such that 2(a-b)+c(b-c) +(c-a) =2(a-d)+(b-d) +(c-d)'…

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Q: Given that a and x are integers, a > 1, a | (11x + 3), and a | (55x+52), find a.

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Q: If a is an even positive integer and b is an odd positive integer, then which of the following…

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Q: If both x and ( ++ ) are positive integers, what is the least possible value of x? 10 120 O 90 O 60…

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Q: 1 fn is a positive integer, then (D -a) II

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Q: Which of the following is a binary operation on the set of positive real numbers? a. a*b = √a + √a+…

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Q: If [2x 3] 23 1. 2 13 2. 2 3. 4. - 13 2 23 2 1 2] [x] -3 08 = 0, then the value of x is

A: 2x312-30x8=02x-94xx8=02x2-9x+32x=02x2+23x=0⇒2x2+23x=0x(2x+23)=0⇒x=0 or 2x+23=0⇒x=0 or x=-232

Q: If a = 2a - a² and b =1-(1-a), show that a = b for all natural numbers n. Assume that a, is a fixed…

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Q: Prove that the value of an expression (a - 1)(a - 3)(a - 4)(a - 6) + 10 is positive for every a…

A: To prove that   the value of an expression (a - 1)(a - 3)(a - 4)(a - 6) + 10 is positive for every a…

Q: Which of the following statement is always true? (a) p(2n) = p(n) (b) p(n) is always even. (c) Edin…

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Q: A factor (x − a)k, k > 1, yields a ________ ________ x = a of ________ k.

A: x=a is a repeated zero of multiplicity k, when we have (x-a)k.

Q: Z/mZz Zm

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

Q: Express each of the following as Ax"y", where xy #0, A is a real number and m and n are integers:…

A: we have to express each of the following as Axmyn, where xy≠0.A is real number and m and n are…

Q: If both x and ( + + ) are positive integers, what is the least possible value of x? 10 120 90 60 30

A: Given that, x and  x5+x6+x10 are positive integers. To find: Least possible value of x. And, for…

Q: Let a and b be non-zero real numbers and m and n be integers. Which of the following is not a law of…

A: Consider the laws of exponents: Power of a fraction rule:abn=anbnPower of a Power rule:amn=amn

Q: Let A= {X: X is an integer and r24}then A= {X: X is an integer and X<4} {X: X e N and X<4} a {X: X…

A: A detailed solution is given below. Z --» the set of integers.

Q: Find all possible values of P in x^2+10x+P=(x-A)(x-B) if P, A and B are all whole numbers

A: To find all possible values of P in x2+10x+P=(x-A)(x-B) if P,A and B are all whole numbers.

Q: Do not use a calculator in this question. 3 V3 6+2v3 5- V3 p+qV3 6. find the CS CamScanner value of…

A: This question is based on similar parallelogram properties and rationalisation.

Q: If (2n+1)! An? + Bn + C (2n-1)! determine the integer values of A, B, and C.

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Q: Express O in each figure in terms of x. (a) = (b) 4

A: a) In the right angle triagle opposite side is x and adjacent side is 7 angle is θ.b) In the right…

Q: Find all positive integers a, b such that a | b^2-b+1 and b | a^2-a+1

A: Solution :-

Q: 6.3.6 For each real number x, let Ay = {3, –2} U {y E R : y > x}. Find U Ax and N Ax. xER xER

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Q: If a is a real number and n ≥ 2 is an integer, then which of the following expressions is equivalent…

A: Given expression: an

Q: The value of k such that P2(1) = 2.8 , 2 k 4 1 Is

A: Lagrange's interpolating polynomial is:…

Q: For each positive integer x, Let Ax=(x, x²), Find A1,A2, and A3

A: Given that for any positive integer x, Ax=(x,x2)

Q: If x – 1 is an even integer, which of the following numbers must be odd? I. x(x - 1) II. 3(x - 1)…

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Q: 5) For each + ive integer i, where i is equal to three, then find the union and intersection of…

A: 5 Given that Ai=x∈R|−1i&lt;x&lt;1i=−1i,1i. a We have to find the A1∪A2∪A3 and A1∩A2∩A3. Here,…

Q: If A= xe Z:2" = 1 and B = {x e Z:-4 < 3x-1<11}, then find n(A×B),where Z is a set of integers.

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Q: There exists a real number R which is greater than 5 O R= {7, 42,2t, and 97/3) O R= {1, 2, and T/6}

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Q: The product of 4x and 0 is: O 4x O 4 O None of these

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Q: { O if k is a multiple of 2 r if k is not a multiple of 2 W where r can be any real number

A:

Q: which

A: Explanation : a )  Let the three consecutive positive integers will be n, n+1 , n+2. If we sum all…

Q: If a, b, c are integer powers of 2, prove that equation a° + 64 .3 + 64 = c5

A: Given: Let's take a,b,c are integer powers of 2. Prove that a3+b4 =c5  does not have a solution.

Q: Let a, b and c be positive numbers such that a ^ 2 + b ^ 2 = c ^ 2 Show that a + b> c.

A: Let a, b and c be positive numbers such that a ^ 2 + b ^ 2 = c ^ 2To Show:-  a + b&gt; c.

Q: 7. How many non-negative integer solutions are there to the equation X1 + X2 + X3 + 4 = 16 such that…

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Q: If a_1=5a1​=5 and a_n=a_{n-1}-4an​=an−1​−4 then find the value of a_6a6

A: Given: a1=5an=an-1-4

Q: For all real numbers b and c such that the product of c and 3 is b, which of the following…

A: Let the term c be replaced with c'. The new equation becomes h=-at2+bt+c'. The h intercept is given…

Q: Find all values of x for which |6x – 1| = 1 – 6x. - Select one: O (-00, 1/6] O -1/6 not in the list…

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Q: If h (x) = x - 2.x+5 , then find h ) O 15 -0.5 -10 O 5

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Q: If g and m are positive integers, then which of the following must be equal to ? m (A) g + 5 m + 5…

A: given  g and m are positive integers

Q: Let X = P(2) and E(3x)= E(2-6x) find 2.

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Q: 4 If x is an integer, then xr >x.

A: See the detailed solution below.

Q: Let A  = {x ∈ A  |x =3b +2 for some integer b } and B = {y ∈ B |y = a + 2 for some integer a }  a.…

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Q: If a, b, c all are distinct positive numbers then (a + b) (b + c) (c + a) is

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Q: If n= 2k for some odd integer k, then o(n)= O a. o(k) b. 30(k) O c. 2k d. 20(k) e. None

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Q: For all numbers x , x4 >x true or false

A: Given, All number x We have to find Whether    x4 &gt;x        is true or false

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.