...Generalization is useful in research because the more data that is in hand, the more accurate a generalization can be. Generalizing means a few experiences that can signify a category for example because most criminals happen to be males a generalization could be said that only men commit crime. Generalizing could also simplify stereotypes. By using a way to measure numerical approaches with tables or graphs this helps to provide descriptions and this can be known as descriptive statistics. Inferential statistics could be based on predications based on samples from data taken from questions. It could be a hypothesis. And with predictive statistics it’s more of an approach to gather information from data that has already been collected to determine...
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...Microsoft has introduced numerous administrative tools to simplify and enhance management of Windows Server 2008. One of the functions is Active Directory Federation Services. Active Directory Federation Services (ADFS for short) is a software component developed by Microsoft that can be installed on Windows Server operating systems to provide users with Single Sign-On access to systems and applications located across organizational boundaries. It uses a claims-based access control authorization model to maintain application security and implement federated. Claims based authentication is the process of authenticating a user based on a set of claims about its identity contained in a trusted token. Such a token is often issued and signed by an entity that is able to authenticate the user by other means, and that is trusted by the entity doing the claims based authentication. In AD FS, identity federation is established between two organizations by establishing trust between two security realms. A federation server on one side (the Accounts side) authenticates the user through the standard means in Active Directory Domain Services and then issues a token containing a series of claims about the user, including its identity. On the other side, the Resources side, another federation server validates the token and issues another token for the local servers to accept the claimed identity. This allows a system to provide controlled access to its resources or services to a user that...
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...please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the process of download I need to study existing cases.. please simplify the...
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...expression, we need to simplify it. A radical is in simplified form if it meets 3 criteria: * There are no perfect nth-factors inside the radical * There are no fractions inside a radical * There are no radical signs in the denominator of a fraction In this section, we will deal only with the first criterion – that there be no perfect nth factors inside the radical sign. To simplify we will be using the definition of fractional powers: Definition of Fractional Exponents We have worked with the first part of this definition before, but we will use the last part in simplifying. Study the following examples: Example. Use the definition of fractional exponents to rewrite the radical expression in exponential form. 1. By our definition, we can rewrite this as: 2. When we have a square root, the index is understood to be 2. We can write in the index and then proceed as above: Sometimes we can simplify our result after writing in exponential form: 3. Applying the definition we get . If we simplify the exponent, , and so the problem simplifies to 4. Applying the definition and simplifying we get 5. Again, the index of the square root is 2 and so In addition to the definition of fractional exponents, we will also use the following: Rule of Radicals 1: This rule can either be used from left to right or from right to left. Simplifying Square Root Expressions In order to simplify a square root, we need...
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...MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Find the x coordinates of all relative extreme points of[pic]. |A)[pic] |B) [pic] |C) [pic] |D) [pic] |E) [pic] | [pic] First find the derivative of the function[pic], f ’(x): |[pic] |= |[pic] |apply power rule of differentiation | | |= |[pic] |simplify | | |= |[pic] |finish simplifying by first factoring | | | | |out GCF | | |= |[pic] |next factor the trinomial factor, | | | | |leaving the final simplified form of | | | | |the derivative | Set[pic]and solve for x to find critical point(s): When the derivative is set to zero, [pic]; thus, this implies each factor could be equal to zero...
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...distributive property: 12(6 + 4 + 20) 3. Translate and simplify: The sum of the squares of three and seven. 4. If you spend $3.70 each day in tolls, how much money would be spent in 25 days? 5. Write 124/10 as a mixed number. 6. Write 11 and 4/5 as an improper fraction. 7. Change 9 and 1/8 to decimal form. 8. Round $58.195 to the nearest cent. 9. Write 176, 000, 000 in scientific notation. 10. Write 7.35 x 10^(-7) without exponents. 11. Reduce the fraction 1600/3640 to its simplest form. 12. Simplify (3/10) + (1/18) – (2/15) and express your answer in simplest form. 13. Simplify 17 ¾ – (10 and 8/9). 14. Simplify (6 and 5/7) x (9 and 6/11) 15. Simplify (32/17) / (8/34). 16. Simplify (2/5)[(23/8) – (5/8) x 2] 17. Write 174/11 as a decimal in simplest form. 18. If you join a movie club and you agree to buy 24 movies for $18.63 each and $3.44 postage and handling for each movie, what is the total cost to fulfill this agreement? 19. A recipe calls for 2 and 4/5 lb of light brown sugar and 4 ½ lb of dark brown sugar. How many pounds of sugar are needed for this recipe? 20. Each time a rubber rebounds, it bounces to a height tat is ¾ the height of the previous bounce. If the ball is dropped from 256 feet, approximately how high would it bounce after its third bounce. 21. If D = {-3, -2, 1} , find the values for 87 – x^2. 22. Evaluate y^2 – 3yz + z^2 if y = -5 and z = 3. 23. Evaluate | 11 – 16|. 24. Simplify: 12 + (-21) 25. On a number line, start at 5 and move...
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...CHAPTER 1: FUNDAMENTAL CONCEPTS OF ALGEBRA PREPARED BY : C.F.TAN (MSC) Real Number and Their Properties • The idea of counting goes back to the early days of civilization. When people first counted they used the natural numbers, written in the set notation as: • More recent is the ideal of counting no object, the ideal of the number 0. Including 0 with the set of natural number gives the set of whole numbers, • Later, people came up with the idea of counting backward, for example from 4 to 3 to 2 to 1 to 0. There seemed no reason not to continue this process, calling the new numbers, -1 , -2 , -3 and so on. Including these numbers with the set of whole numbers gives the very useful set of integers, • If m and n are two integers, i.e. , with , we can write a number in the form of • The set which consists of all numbers in the form with , and , is called the set of rational number, • Notice that any integer, , may be written as . For examples, • Thus, every integer is a rational number and, hence, is a subset of . • A rational number is usually called a fraction. • Numbers which are not rational number are known as irrational numbers. Irrational numbers are often found in the solution of algebraic equations. For examples, • The set of natural numbers, integers, rational numbers and set of irrational numbers are the subset of the set of real number. • We can represent real numbers on a straight line called the real number line. The line consist of an arbitrary point, 0...
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...power Negative exponents Exponents with similar bases Power to a power Division with exponents 1 Name _________________________ Date __________________________ Math Period ______ Power to a Power Expand each of the following expressions. 1) (2rm3)2 2) (– 4a2) – 3 3) (– 3m2p3)2 ____________________________________________________________________________________ Simplify. Write all exponents as positive if necessary. 4) (5x2)3 5) (xy3) – 5 (x2)4 • (– 3x6)4 6) ____________________________________________________________________________________ 7) (6x2y3)3 8) (– 2mn5)5 9) (4x2)2 • (3y)2 Mixed Review. Simplify. (All answers must have positive exponents) 10) – (m4)3 11) – 3x0 12) – (xy)0 ____________________________________________________________________________________ 13) xy0 14) (– m4)3 15) ( ) –3 ____________________________________________________________________________________ 16) 42a– 3 17) 6bn2 • – 3bn3 18) 2c • 4c • c4 2 Name _____________________________________ Date______________________________________ Math Period ____ Division with Exponents Simplify. Write each of the following with positive exponents if necessary. 1) 106 2) 1012 3) 80x2y5 ÷ 4xy9 8 15 10 10 4) (– 6)5 (–...
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...3=127x3 C. 14x2y -2=4x2y 2=16x4y2 Evaluating expressions with zero and negative exponents The laws of exponents for division can be summarized, such that aman=am-n ;m>n, a≠0 aman=a0or 1;m=n, a≠0 aman=1am-n;m <n, a ≠0 Since the first law for division has been discussed, concentrate on expressions with zero and negative exponents. Skill can be achieved by consistent practice. Rewriting algebraic expressions with zero And negative exponents When algebraic expressions have zero and negative exponents, they have to be rewritten in a way that all exponents must be positive. In all cases, it is assumed that all denominators are not equal to zero. Examples: A. Simplify: 3x3y 512x5y 5 Solution: 3x3y 512x5y 5=312x3x5y5y5 =14x-2y 0=141x21=14x2 B. Simplify: 144s3t -49r-2s5t-2 Solution: 144s3t -49r-2s5t-2=14491r-2s3s5t-4t-2 =16r2s-2t-2=16r2s2t2 Simplifying exponential expressions Exponential expressions are said to be in simplest form if: 1. All the exponents are positive, 2. There are no...
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...We cannot combine 5m and 3b in any simpler way than this because m and b are not like terms – they stand in for different unknown numbers. We can multiply two or more unknowns together. a ϫ b is written as ab. b ϫ a is the same as a ϫ b and is also written as ab. Instead of writing 2a ϩ 3b ϩ 3ab ϩ ba, we can write 2a ϩ 3b ϩ 4ab. We can add 3ab to ba to make 4ab because ab and ba are like terms. Example Simplify the following by collecting like terms: a) 3m ϩ 4m ϩ m ϩ n ϩ 2n b) 4mv ϩ 2z Ϫ 3mv ϩ z ϩ 3m There are eight lots of m and three lots of n. a) 3m ϩ 4m ϩ m ϩ n ϩ 2n ϭ 8m ؉ 3n b) 4mv ϩ 2z Ϫ 3mv ϩ z ϩ 3m ϭ mv ϩ 3z ϩ 3m First look at the mv terms: 4mv Ϫ 3mv ϭ 1mv (which we usually write as mv) Now look at the z terms: 2z ϩ z ϭ 3z Now look at the m terms: you have 3m Exercise 6.1 .......................................................................................... ᕡ Simplify the following expressions by collecting like terms: a) b) c) d) e) yϩyϩyϩyϩy m+m+m+b+m zϩaϩaϩa pϩrϩpϩpϩpϩrϩrϩpϩrϩpϩpϩrϩpϩpϩrϩp tϩtϪqϩtϪqϪq ᕢ Simplify the following expressions by collecting like terms: a) 9p ϩ 3r Ϫ 2p ϩ r ϩ 2r Ϫ p c) b Ϫ t ϩ 3t Ϫ t e) x ϩ y Ϫ x Ϫ y 58 Maths Connect 1R b) 5x ϩ 2y ϩ y Ϫ x Ϫ y ϩ 7x ϩ 3y...
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...SIT190 Assignment 2 – Solutions Total marks: 80 (i) (ii) (iii) Simplify, and express in terms of positive indices: = 3−4 = 3 4−3 −3−1 3 24 �6−1�2 = 24 × 36−2 4 3−2 = 829−4 −4 = 824 −3 = 3�−3� 2−1+−2 3(2−1+−2) =1 2� 22+ � 12 1�2 3�2 (iv) �34�3= � = −3�2 −3�2 = 2 (v) √�2√ − √16� = 2 − 4 = −2 2. Sketch =2 and=2− onthesamesetofaxes. y = 2e−x y 2 x 3. (a) Simplify (by writing as a single exponential): (i) 3+2 = 3+2−(4−3) 4−3 = 5−1 (ii) �+3�2 = 2+6 4−3 4−3 = 2+6−(4−3) = 5+2 (iii) (3−1)2 × 3−6 = 6−23−6 = 1 = 4. (a) Simplify (by expressing as a single natural logarithm): (i) 3ln4−5ln2+ln3=ln43 −ln25 +ln3 (b) Expand and simplify: (i) (3 − −3)2 = (3)2 − 23−3 + (−3)2 (perfect square) = 6 − 2 + −6 (ii) 2(2 + −2)(2 − −2) = 2((2)2 − (−2)2) = 2(4 − −4) (difference of squares) = ln�43×3� 64×3 =ln�25 � = 6 − −2 = ln 6 32 (ii) 2ln(3) − ln(34) + 2 ln(23) = ln(92) − ln(34) + ln(46) = ln �92×46� 34 = ln(124) (iii) 2ln(2) + ln �3� − 4 ln = ln(42) + ln �3� − ln(4) = ln�42×3� 4× = ln(3) (b) Simplify (without using a calculator): (i) log 1 =log 1 4 16 4 42 = log4 4−2 5. Solve for : (i) = 23−1 = −2 �1 (ii)ln�12�= �2 (iii) ln(3+1) = 3 + 1 3 − 1 = 2 ln(3−1) = ln �2� 3 − 1 = l n � 2 � 3 = l n � 2 � + 1 = l n � 2 � + 1 3  (ii) = 1 ln �5+2� 22 ln �5+2� = 2 ln�5+2� 2 2 2= 5+2 = 2 2 5 = 22 − 2 = 22−2 5 (iii) + 3 = 4 − 2+3 2+3 + + 3 = 4 2+3 = 1 − ln(2+3) = ln(1 − ) 2 + 3 = ln(1 − ) =...
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... ____ 3. Simplify a.||c.|| b.||d.|| ____ 4. Which graph below represents a function? a.||c.|| b.||d.|| ____ 5. What is the domain of the given function? a.| |c.|| b.||d.|| ____ 6. Use the distributive property to simplify the expression: . a.|| b.|| c.|| d.|| ____ 7. Which of the following is not a function? a.||c.|| b.||d.|| ____ 8. Choose the correct algebraic translation of “ 3 more than twice a number is three times the sum of the number and 5”. a.|| b.|| c.|| d.|| ____ 9. Which statement illustrate the symmetric property? a.|| b.|If 3 + 2 = 5 and 5 = 4 + 1 thenn 3 + 2 = 4 + 1| c.|If 3 + 2 = 5 then 5 = 3 + 2| d.|3 + 2 = 5| ____ 10. Translate the verbal phrase below into its mathematical representation. “ Six decreased by three times the sum of two and four times a number is one.” a.|6 - 3 + 2 + 4n = 1| b.|6 - 3 2 + 4n = 1| c.|3(2 + 4n) -6 =1 | d.|6 - 3(2 + 4n) = 1| ____ 11. Simplify a.|| b.|| c.|| d.|| ____ 12. A function, has a domain of {-6, -2, 3}. What is its range? a.|{-12, -8, 4}| b.|{-42, -22, 3}| c.|{-8, -6, 12}| d.|{-10, -6, 3}| ____ 13. Which set of numbers represents the domain of the function in the table? a.|{-2, 2, 4}|c.|{-12, -6, 0, 6}| b.|{-12, -6, -2, 0, 2, 4, 6}|d.|{-2, 0, 2, 4}| ____ 14. Simplify . a.||c.|| b...
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...Algebra 2 Name_____________________________ Summer Assignment Period_________Date______________ Ocean Township High School Mathematics Department These are important topics from Algebra 1 that you must be comfortable doing before you can be successful in Algebra 2. This packet is to be completed in full and turned in on the first day of class. It will be graded and counted as your first quiz grade. If you find that you need some assistance, please feel free to Google or YouTube the concepts. Within the directions of each problem, you will see key words that you should be using in your research. Show all work that is required to be performed in order to solve the problem! Partial credit will be awarded for every correct step given even though the final answer might be incorrect. Points will be deducted if your work is messy and illegible. All answers must be exact and simplified unless the problem asks for an approximation! 1) Evaluate the expression. 5xy 6 y if x 3 & y 4 2) Evaluate the expression. 3x 2 2 xy if x 3 & y 4 3) Evaluate the expression. x 3 y y x if x 6 & y 2 4) Evaluate the expression. xy xx y if x 6 & y 2 5) Combine the like terms. 11x 5 y 7 y 4 x 6) Combine the like terms. 13x 2 7 x 8x 2 x Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 1 7) Combine the like terms. 7 xy x 2 y 9 x 2 y 4 xy 8) Combine the like terms. ...
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...a manner that the common items of information are given in the same relative slots. This system also helps to prepare one" Master Documents" embodying information common to all documents, and xerox all the aligned documents by suitable and reproduction techniques. Accordingly the standardized documents for Indian exports are · Invoice · Exchange Control Declaration (GR) Form · Shipping Bill (Dock challan\ Duty Draw back and Port Trust Copy) · Bill of Lading Aligned DocumentationSystem is based on the U.N. layout key. Deriving national document subsets from the UN Layout Key rules simplifies trade documentation on an international scale, bringing considerable benefits to traders Objectives- * To simplify, rationalize and prioritize information. * To provide benefits to every party associated with international trade chain from easier documentation. * Aligned documents simplify document checking and...
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...7 7.1 Introduction to Rational Expressions 7.2 Multiplication and Division of Rational Expressions 7.3 Addition and Subtraction with Like Denominators 7.4 Addition and Subtraction with Unlike Denominators 7.5 Complex Fractions 7.6 Rational Equations and Formulas 7.7 Proportions and Variation Rational Expressions There is nothing wrong with making mistakes. Just don't respond with encores. —ANONYMOUS ne of the most significant problems facing the U.S. transportation system is chronic highway congestion. According to a newly released “Highway Statistics,” Americans drove about 3 trillion miles in 2009. Our ability to keep traffic moving smoothly and safely is key to keeping our economy strong, and traffic congestion costs motorists more than $87 billion annually in wasted time and fuel. A 2007 study found that, collectively, Americans spend as many as 4.2 billion hours stuck in traffic each year. If the amount of traffic doubles on a highway, the time spent waiting in traffic may more than double. At times, only a slight increase in the traffic rate can result in a dramatic increase in the time spent waiting. (See Example 6 in Section 7.1.) Mathematics can describe this effect by using rational expressions. In this chapter we introduce rational expressions and some of their applications. O ISBN 1-256-49082-2 Source: Randy James, “America: Still Stuck in Traffic.” Time.com, July 9, 2009; U.S. Department of Transportation, 2011. 419 Beginning and Intermediate...
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