Exercise 4.1 2. Establish each of the following for all n ≥ 1 by the Principle of Mathematical Induction. Solution a) S(n): ==‚ S(1): = = =1‚ So S(1) is true. Assume S(k): = Consider S(k+1) = = +=-1+= -1. Hence‚ it follows that S(k)⇒S(k + 1) is true for all n ∈ Z+ by the Principle of Mathematical Induction. b) S( n) for n=1‚ = 2 = 2+(1-1). So S(1) is true. Inductive Step: assume S(k)is true‚ for some (particular) k ∈ Z+—that is‚ assume that =2+(k-1). For n=k+1‚ = + (k+1)
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CHAPTER 7 THE TWO-VARIABLE REGRESSION MODEL: HYPOTHESIS TESTING QUESTIONS 7.1. (a) In the regression context‚ the method of least squares estimates the regression parameters in such a way that the sum of the squared difference between the actual Y values (i.e.‚ the values of the dependent variable) and the estimated Y values is as small as possible. (b) The estimators of the regression parameters obtained by the method of least squares. (c) An estimator
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Buried Treasure Ashford University MAT 221 Buried Treasure For this week’s Assignment we are given a word problem involving buried treasure and the use of the Pythagorean Theorem. We will use many different ways to attempt to factor down the three quadratic expressions which is in this problem. The problem is as‚ ““Ahmed has half of a treasure map‚ which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the
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Espinosa‚ Richard Anderson A. February 6‚ 2014 AVTE 221 – 4C Mr. Jimmy Marcaida II Assignment: In electronics‚ a flip-flop or latch is a circuit that has two stable states and can be used to store state information. A flip-flop is a bistable multivibrator. The circuit can be made to change state by signals applied to one or more control inputs and will have one or two outputs. It is the basic storage element in sequential logic. Flip-flops and latches are a fundamental
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D.A.V. PUBLIC SCHOOL‚ THANE. 2012-13 WORKSHEET :10 TOPIC: CIRCLES&TANGENTS SUB: MATHEMATICS. STD: X 1. Three circles are described touching each other at two places externally. If the sides of the triangle are 4cm‚ 6 cm and 8 cm‚ find the radii of circles. 2. In the given figure‚ circles with centres O and O’ touch internally at point A. AB is a chord of bigger circle intersecting the smaller one at C. If the smaller circle passes through the centre of the bigger circle ‚ then P.T AC = CB
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variable The variable is the important aspects of the research. In research the concept are measure from variable. Variable are anythings that can take on differing or varing values. it mean that the value of variable vary from person to person‚ time to time or place to place but the meaning of variable are same to all. Thus variable are the charactestics of person‚ groups‚ objects‚ ideas‚ feeling or other thing that researcher want to measure. Variables are thus anything that can take on differing
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Knowledge Evidence for Unit 221 – Use office equipment (for Outcomes 1.1‚ 1.2‚ 1.3‚ 4.1 & 4.3) Type Features or advantages or benefits Why you’d choose to use that type of equipment Potential problems and the action you could take Computer – Mainly used for Microsoft applications‚ email and the internet The computer can be used for many different things. There are many different purposes for a computer‚ they can vary from producing documents‚ sending information to the printer‚ browsing
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Unit 221 Use Office Equipment Outcome 1: know about different types of office equipment and its uses 1.1‚ 1.2‚ 1.3 Equipment | Used for | Features | Why use the Equipment | Fax Machine | Sending messages to another fax machine by a phone line. | Speed‚ Printer‚ Paper Cutter‚ Paper Feed‚ Autodialing. | A fax machine is used to send documents instantly to another fax machine through a standard telephone line. | Photo copier | Photo copying documents. | Scan‚ Copy‚ Print back to back
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| | |College of Information Systems & Technology | | |ENG/221 Version 4 | | |Technical Writing Fundamentals | Copyright © 2011‚ 2010‚
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Timeline Part I Instructions: Complete the matrix by providing the Time Period/Date(s) in column B‚ and the Description and Significance of the People/Event(s) to American History in column C. See complete instructions in the Syllabus for the Module 1 assignment entitled‚ “Timeline Part I.” NOTE: The timeline project does not need to be submitted to turnitin. NOTE: Please write your answers in a clear and concise manner. Limit your submission of the Timeline Part I to a maximum of 13 pages (not
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