Let m be a positive integer not divisible by 2 or 5. Prove that the decimal expansion of the fraction 1/m is periodic with period equal to the order of 10 modulo m.

Q: b. Let Find and f(x) = if x > 0 if x = 0 -1 if x 0 be given...")

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Q: -10- -15- X TU/4

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Q: 1.1! +2.2!+3·3! ++n・n! = (n + 1)! −1 for all n ≥ 1.

A: We will prove the following result by principle of mathematical induction.

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A: The given function .The aim is to find the derivative of the inverse function.

Q: Sº 2 19. s³ +85² + 7s

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Q: Relative Concentration of Tea Extracts % Inhibition Absorbance 0.25 0.974 2.707 0.5 0.967…

A: Relative Concentration of Tea Extracts, y% Absorbance, XConcetraition 1Concentration…

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Q: 5. Let G be a group, and let HCG be a subgroup. Show that if HG, then there exist elements a, b, a',…

A: According to the question,

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A: The objective of the question is to find the general formula for the given recursive sequence. The…

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A: Since you have posted a multiple question according to guidelines I will solve first(Q12) question…

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Q: For Exercises 1-6, state the 1. f(x, y) = x² + y²-1

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A: We shall prove this using mathematical induction

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Q: d df 12. Show that -(f (g xh))==-(gxh)+f. dt ( x ) + f (gx dt

A: We first prove a lemma and then proceed to solve this problem.

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Q: Give an example of an equivalence relation R on the set Q such that there are exactly three distinct…

A: We take the help of the signum function

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Q: 6. Determine the highest root of f(x)=2x- 11x² + 17.5x −5 with E<0.001% using following methods: (a)…

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Q: Construct the confidence interval for the population mean u. c=0.95, x= 15.3, o=2.0, and n=55 A 95%…

A: The given data  and .The aim is to find the confidence interval for the population mean.

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Q: For a E Z921 we make the following definitions. 1) We call a a Fermat Liar for n = 921 if an-1 = 1…

A: We use some basic results from elementary number theory to solve this problem.

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A: Given function is,   defined as the domain,are symmetric matrices  .To calculate the gradient of…

Q: Find the rule for the geometric sequence given below. :3an-1 2-1 and ao an an - = 3.

A: The objective of the question is to find the rule for the given geometric sequence and to find the…

Q: 10.11. Let C = {x € R : x ≥ 1} and D = R+. For each function f defined below, determine f(C), f…

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Q: Let ƒ : R → R³ be defined by f(x) = (−5x, 6x, 5x). Is ƒ a linear transformation? a. f(x + y) = f(x)…

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Q: 2. Let u find the coordinates of the point at the head of w. 8 6 2 12 • - [³] and = +27. Sketch w…

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Q: Use matrix multiplication to find the contraction of (a, b) with factor k = 1/α, where α > 1.

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Q: Let n ≥ 3 be an odd integer. (a) Show that any two reflections in D are conjugate. (b) Let HCDn be a…

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Q: aRb, cRd and aRd, then bRc.

A: A relation R defined on a set A is i) reflexive if aRa for all a belonging to A.ii) symmetric if aRb…