...random manner. Show that regardless of how the numbers are positioned on the wheel, there are three adjacent numbers whose sum is at least 39. Adding all 25 inequalities, we find that 3∑_(i=1)^25▒xi = 3∑_(i=1)^25▒i < 25(39) = 975. But 3∑_(i=1)^25▒i=(25)(26)/2=325 gives us the contradiction that 988 = 3(325) < 975 7. A lumberjack has 4n + 110 logs in a pile consisting of n layers. Each layer has two more logs than the layer directly above it. If the top layer has six logs, how many layers are there? . . 18. Consider the following four equations: 1) 1 =1 2) 2 + 3 + 4 = 1 + 8 3) 5 + 6 + 7 + 8 + 9 = 8 + 27 4) 10 + 11 + 12 + 13 + 14 + 15 + 16 = 27 + 64 1) 1=1 n = 1 2) 2 + 3 + 4 = 1 + 8 n = 2 3) 5 + 6 + 7 + 8 + 9 = 8 + 27 n = 3 4) 10 + 11 + 12 + 13 + 14 + 15 + 16 = 27 + 64 n = 4 Formula (n-1)²+1, or n²-2n+1+1or n²-2n+2. n²-2n+2 Exercise 4,3 10 & 15 10. If n ∈ Z+, and n is odd, prove that 8|(n2 − 1). 15. Write each of the following (base-10) integers in base 2 and base 16. a)22 b) 527 c) 1234 d) 6923 22) base 2 10110 base 16 = 16 527 base 2 = 1000001111 base 16 = 20F 1234 base 2 = 10011010010 base 16 = 4D2 6923 base 2 = 1101100001011 base 16 = 1B0B Exercise 4.4 (1&14) 1. For each of the following pairs a, b ∈ Z+, determine gcd(a, b) and express it as a linear combination of a, b. 231, 1820 b) 1369, 2597 c) 2689, 4001 a) 231, 1820 a) 231, 1820 1820 = 7 (231) + 203 ...
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...Identifying Good or Bad Statements Anit Maharjan HUMN210-H5WW Meghan Roehll Franklin University 4th April, 2013 a. Nobody in the world today is really good. Yes, I have heard of good people, but not really good people. - Good statement. b. The world is not flat. Well, if you look at a map it is: - in what point of view - bad statement. c. I will need an extended period of laborious cogitation to assimilate the missive. This doesn't make any sense - bad statement. d. The number 2 is odd. Are we talking about an even number? I believe your confusion comes from the fact that 2 is a prime number, but it is still even. It is the only even number that is prime – false statement. e. If you believe in evolution, then your ancestors were filthy apes. There are two kinds of people in the world: - one is god prayer and the next is science believer. If you support the statement from the point of scientific theory of evolution by Darwin, then yes our ancestors are filthy apes, whereas if you think form the side of god’s prayer then the statement is false – good statement. f. Some swans are black. In this statement, I am not sure that some swans are black or not, all swans could be black or white – good statement. g. If you are a human, then you are a person. If you are an individual, then you are alive. Human is a person and of course the person becomes an individual and every individual breaths...
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...Year | Album | Peak chart positions | Sold | | | UK | AUS | GER | SWI | FRA | NZ | AUT | IRE | | 2000 | Bright Lights * Released: August 2000 * Label: Island | 1 | 3 | 2 | 2 | 6 | 3 | 10 | 1 | * UK: 3xPlatinum * AUS: Platinum * GER: Platinum * SWI: Platinum * FRA: Gold * NZ: Platinum * IRE: Platinum | 2001 | Dangerously In Love * Released: October 2001 * Label: Island | 1 | 1 | 1 | 1 | 3 | 1 | 6 | 1 | * UK: 4xPlatinum * AUS: Platinum * GER: Platinum * SWI: Platinum * FRA: Platinum * NZ: Platinum * AUT: Gold * IRE: Platinum | 2003 | All Night Long * Released: August 2003 * Label: Island | 1 | 6 | 5 | 5 | 10 | 6 | 14 | 1 | * UK: 2xPlatinum * AUS: Gold * GER: Gold * SWI: Gold * NZ: Gold * IRE: Platinum | 2004 | Troublemaker * Released: October 2004 * Label: Island | 3 | 12 | 10 | 10 | 14 | 12 | 18 | 3 | * UK: Platinum * IRE: Platinum | Year | Song | Peak chart positions | Sold | Album | | | UK | AUS | GER | SWI | FRA | NZ | AUT | IRE | | | 2000 | | 2 | 12 | 10 | 10 | 14 | 12 | 16 | 2 | * UK: Gold * AUS: Gold * NZ: Gold | | | | 1 | 6 | 4 | 4 | 8 | 6 | 10 | 1 | * UK: Platinum * AUS: Platinum * GER: Gold * SWI: Gold * NZ: Platinum | | 2001 | | 8 | 24 | 22 | 22 | 26 | 24 | 28 | 8 | * UK: Gold | | | | 12 | - | - | - | - | - | - | 12 | | | | | 1 | 8 | 6 | 6 | 10 | 8 | 12 | 1 | * UK: Platinum * AUS: Platinum * GER: Gold * SWI: Gold * NZ: Platinum...
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...receives it. And also some other facts which should be considered like life expectancy, importance, age etc. when deciding on whom to donate the heart to. He’s cause for damage to the heart was the steroids, of which he was unaware of the consequences of taking the steroids at the time he took so there wasn’t any sort of health irresponsibility known otherwise. His chances to live 10-15 more years are very high so it’s one point investing in him. He has a family to take care of, wife and the 3 kids who he has to support till they are on their feet and so forth. He also has been a good supporting father as he’s already being supporting their dreams career wise and the future. So my first choice with all confidence would be Jerry. The number 2 choice is Ozzie because as LONG as he does not get back on his old ways HE does hold out some hope on society as a whole as long he does NOT revert back and does good in society by helping out and he no longer does any drugs - he really can have a useful and a prosperous and productive life. His chances of living after a successful heart transplant are another 10 years but only if he stays off the drugs and which is not really guaranteed but if he does he can be a very good mentor and a coach or a guidance for teens with troubled life as they are on drugs already. Since Ozzie have seen the side effects and losses because of the drugs, he can let the teens know it too and...
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...MON TUE FEB WED THU FRI SAT SUN MON TUE MAR WED THU FRI SAT SUN MON TUE APR WED THU FRI SAT 1 2 3 4 5 6 8 9 10 11 12 13 15 16 17 18 19 20 22 23 24 25 26 27 29 30 31 2012 SUN MON TUE 7 14 21 28 5 6 7 12 13 14 19 20 21 26 27 28 SUN MON TUE 1 2 3 8 9 10 15 16 17 22 23 24 29 JUNE WED THU FRI 4 11 18 25 4 5 6 7 11 12 13 14 18 19 20 21 25 26 27 28 SUN MON TUE 1 2 3 8 9 10 15 16 17 22 23 24 29 30 31 FRI SAT 1 2 3 4 5 6 8 9 10 11 12 13 15 16 17 18 19 20 22 23 24 25 26 27 29 30 AUG SUN MON TUE WED THU FRI 7 14 21 28 MAY WED THU FRI SAT JULY SAT WED THU SAT 6 7 13 14 20 21 27 28 2012 1 2 3 4 5 8 9 10 11 12 15 16 17 18 19 22 23 24 25 26 29 30 31 SEPT WED THU FRI SAT 3 4 5 6 7 10 11 12 13 14 17 18 19 20 21 24 25 26 27 28 OCT SUN MON TUE WED THU 1 8 15 22 29 FRI 2 9 16 23 30 SAT 1 2 3 4 5 6 8 9 10 11 12 13 15 16 17 18 19 20 22 23 24 25 26 27 29 30 31 NOV SUN MON TUE WED THU FRI 7 14 21 28 5 6 7 12 13 14 19 20 21 26 27 28 SUN MON TUE 1 2 3 8 9 10 15 16 17 22 23 24 29 30 31 DEC WED THU FRI 4 11 18 25 SUN MON TUE SAT SAT 2 3 4 5 6 7 9 10 11 12 13 14 16 17 18 19 20 21 23 24 25 26 27 28 30 1 8 15 22 29 7 14 21 28 1 2 3 4 5 6 8 9 10 11 12 13 15 16 17 18 19 20 22 23 24 25 26 27 29 30 31 4 5 6 7 11 12 13 14 18 19 20 21 25 26 27 28 1 2 3 8 9 10 15 16 17 22 23 24 29 30 2 9 16 23 30 3 4 5 6 7 10 11 12 13 14 17 18 19 20 21 24 25 26 27 28 31 1 8 15 22 29...
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... 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 30 29 28 27 26 Dec (12)2011 Nov (11)2011 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 31 30 29 28 27 26 Jan (1)2012 Dec (12)2011 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 31 30 29 28 27 26 25 24 Feb (2)2012 Jan (1)2012 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 29 28 27 26 25 24 23 Mar (3)2012 Feb (2)2012 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 31 30 29 28 27 26 25 24 Apr (4)2012 Mar (3)2012 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 30 29 28 27 26 25 24 23 22 May (5)2012 Apr (4)2012 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 31 30 29 28 27 26 25 24 23 22 Jun (6)2012 May (5)2012 29 28 27...
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...Corridors of Transition between 12 Angry Men and 12 “I have always found that mercy bears richer fruits than strict justice”. Abraham Lincoln “The virtue of justice consists in moderation, as regulated by wisdom”. Aristotle ”Nobody gets justice. People only get good luck or bad luck”. Orson Welles Justice = mid-12c., "the exercise of authority in vindication of right by assigning reward or punishment;" also "quality of being fair and just," from Old French justice "justice, legal rights, jurisdiction" (11c.), from Latin iustitia "righteousness, equity," from iustus "upright, just" . The Old French word had widespread senses, including "uprightness, equity, vindication of right, court of justice, judge." The word began to be used in English c.1200 as a title for a judicial officer. Meaning "right order, equity" is late 14c. Justice of the peace first attested early 14c. In the Mercian hymns, Latin iustitia is glossed by Old English rehtwisnisse. To do justice to (someone or something) "render fully and fairly showing due appreciation" is from 1670s. This word, with such a strong connotation, influenced and formed the basis of many philosophical...
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...Week 2 Learning Team A Paper Parts 4 & 5 Levels of Measurement for Each Variable in the Study In the survey that Debbie Horner, the Human Resource manager, distributed to the company, there are different levels of data available for analysis. The question seeking information about the respondent’s gender is a nominal-level question. “The nominal level of measurement observations of a qualitative variable can only be classified and counted” (Lind, Marchal, & Wathen, p. 10, 2011). For analytical purposes the order in which the data is displayed makes no difference. The question regarding the division of work for the respondent, and the question regarding if the respondent is a member of management or supervision is also nominal. Also, the question pertaining to length is service is nominal because it only seeks one answer. The ten questions relating to how each respondent feels is interval-level data. The ten questions ask each respondent to rate his or her individual feelings on a scale of one to five. One is considered very negative and five is considered very positive. This is known as a Likert Scale. The Likert Scale is the most popular form of survey data collection because it is easy to assemble, the scale is more reliable, and produce more interval-level data (Cooper & Schindler, 2011). Data Coding After collecting the data, Sally, one the office support staff, began the task of coding the data. While some values were pre-determined other...
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...1 www.oldwitchcraft.com 2 www.oldwitchcraft.com 3 INTRODUCTION The science of numerology can be traced back thousands of years. The Chinese, Japanese, Greek, Hebrews, Egyptians, Phoenicians, early Christians, Mayans, and Incas all used some form of numerology to gain a deeper understanding of themselves and the universe. Numerology is perhaps the easiest of the occult arts to understand and use. All you need is the birth date and the complete name of an individual to unlock all of the secrets that the numbers hold. (Most authorities agree that the full birth name as recorded on your birth certificate is the name that must be used for all calculations involving name.) There are eleven numbers used in constructing Numerology charts. These numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, and 22. Larger numbers that occur from adding the numbers in the complete birth date or from the values assigned to each name are reduced by adding the digits together until the sum achieved is one of the core numbers. Merely add the components of the larger number together (repeatedly, if necessary) until a single digit (or the "master" numbers 11 or 22) results. Each of these numbers represents different characteristics and expressions. Master numbers are the only exception to rule of reducing to the single digit. The master numbers 11 and 22 are intensified versions of the single digit number they replace (2 and 4). These numbers suggest a potential for a high degree of learning and/or achievement...
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...Customer number 1 Interested in a Camera Photo • What is your age? 38 • What is your gender? Male • What is your household size? 2 people • What is your household income? $40,000.00 • What is your profession? Handling heavy machinery • What is your education level? High School Diploma Psychographic Questions • What did you find interesting about this product? It’s capability of taking photos • What are your thoughts about the product? It has a great resolution Buying Pattern Questions • Do you ever purchase electronics? YES • Where do you go when you are looking for electronics? On Web • How often do you purchase electronics? Once in a while • How long does it take you to make a buying decision? A few days • What is your typical budget for electronics? $200-$500 • How far would you travel to make the purchase? Around Windsor Benefits Questions • What features do you look for when you purchase electronics? Its quality • What specific benefits do you look for in electronics? Reliability • What motivates you to purchase electronics? Universal Trend • What needs are you trying to meet when you purchase electronics? Enhancing lifestyle • How do you hope electronics will make your life better? Time saving Customer Number 2 Interested in a gaming console • What is your age? 22 • What is your gender? Male • What is your household size? 4 people • What is your household income? $30,000.00 • What is your profession? Student • What is your education...
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...10⁰ 10¹ 10¹ 10² 10² 10³ 10³ 1 1 10 10 100 100 1000 1000 2931 2931 30 30 1 1 2000 2000 900 900 2 2 1 1 3 3 9 9 X X X X 1.1.2 2² 2¹ 2º 4 2 1 1 1 X X X 0 0 1 1 5 5 4 4 0 0 1 1 1.1.3 2² 2¹ 2º 4 2 1 0 0 X X X 1 1 1 1 3 3 0 0 2 2 1 1 1.1.4 24 2³ 2² 2¹ 2º 16 8 4 2 1 1 1 0 0 0 0 1 1 0 0 X X X X X 0 0 2 2 16 16 18 18 0 0 0 0 1.1.5 27 26 25 24 2³ 2² 2¹ 2º 128 64 32 16 8 4 2 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 X X X X X X X X 226 226 128 128 64 64 32 32 0 0 0 0 0 0 2 2 0 0 1.1.6 28 28 156 156 28 28 28 28 12 12 4 4 0 0 0 0 ˅ ˅ ˅ ˅ ˅ ˅ ˅ ˅ 27 26 25 24 2³ 2² 2¹ 2º 128 64 32 16 8 4 2 1 10011100 10011100 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 X X X X X X X ...
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...Week Month August 2012 Su M T W 1 5 12 19 1 26 6 13 20 27 7 14 21 28 8 15 22 29 T 2 9 16 23 30 F 3 10 17 24 31 Sa 4 11 18 25 24 27 Academic Calendar 2012/2013 Public Holidays / Students’ Recess Events (開學禮)Opening Ceremony (開課)First Day of Classes (1st Semester) September 2012 Su M T W T F Sa 1 2 3 4 5 2 9 16 23 30 October 2012 Su 6 7 8 9 10 7 14 21 28 M 1 8 15 22 29 T 2 9 16 23 30 W 3 10 17 24 31 T 4 11 18 25 F 5 12 19 26 Sa 6 13 20 27 2 23 1 (中秋節翌日/國慶節)The day following Mid-Autumn Festival / National Day (國慶節翌日)The day following National Day (重陽節)Chung Yeung Festival 3 10 17 24 4 11 18 25 5 12 19 26 6 13 20 27 7 14 21 28 8 15 22 29 November 2012 Su M T W T 1 11 12 13 14 4 11 18 25 5 12 19 26 6 13 20 27 7 14 21 28 8 15 22 29 F 2 9 16 23 30 Sa 3 10 17 24 2 (追思節)All Soul’s Day December 2012 Su M T W T F Sa 1 15 2 9 16 23 30 3 10 17 24 31 4 11 18 25 5 12 19 26 6 13 20 27 7 14 21 28 8 15 22 29 20-31 1 3-5 6-19 (課堂結束)Last day of classes (1st sem.) (複習/補課)Revision/Make-up Classes (期末考試)Final Examinations of 1st Semester 20 8 10 (聖母無原罪瞻禮)Immaculate Conception (聖母無原罪瞻禮後首個工作日)First Working Day After Immaculate Conception (澳門特別行政區成立紀念日)MSAR Establishment Day (聖誕及新年假期)Christmas / New Year Recess Week Month January 2013 Su Mo Tu 1 1 2 3 4 6 13 20 27 7 14 21 28 8 15 22 29 We 2 9 16 23 30 Th 3 10 17 24 31 Fr 4 11 18 25 Sa 5 12 19 26 5 7 7-8 10-16 25 Academic Calendar 2012/2013 Events Public Holidays (期末考成績公佈)Final Grades Announced (開課)First Day of Classes (2nd Semester)...
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...ON CONTRACT ) INTRODUCTION 1. 2. 3. This booklet gives you detailed information about the Competitive examination for recruitment to the post of Executive (on contract). The selection process consists of (a) Written Examination and (b) Interview. Candidates who qualify in the written examination with high merit rank are eligible to be called for interview. Use of HB Pencil and Ball Pen : You should bring with you two HB pencils, a good quality eraser, a sharpener and a ball-point pen. You are advised to bring two pencils to avoid mending a pencil during the examination as you may lose time. Use ball-point pen for filling up the information only in boxes 1-10 on Side 1. Use HB pencil only, for filling up information in boxes 12-26 on side 1 of the answersheet and box 27 on side 2 of the answersheet. All the answers should also be marked by using HB pencil only. Handling answersheet : Please handle your answersheet carefully. Keep it dust free. If it is mutilated, torn, folded, wrinkled, rolled or dusty, it may not be evaluated. Special attention should be paid to the different objective type tests, since these are different from the usual school/college examinations. 4. 5. HOW TO SHOW YOUR ANSWERS : Each question is followed by answers which are numbered 1, 2, 3, 4 and 5. Select the most appropriate answer. Then by using HB Pencil, blacken the oval bearing the correct answer against the serial number of the question. (Refer to side 2 of the Specimen Answersheet). Please...
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...| | 4+ | 2 + | 0 = | 6 | 1.1.3 21↓ | 20↓ | | 2X | 1X | | 1____ | 1____ | | 2 + | 1 = | 3 | 1.1.4 24↓ | 23↓ | 22↓ | 21↓ | 20↓ | | 16X | 8X | 4X | 2X | 1X | | 1____ | 0____ | 0____ | 1____ | 0____ | | 16 + | 0 + | 0 + | 2 + | 0 = | 18 | 1.1.5 27↓ | 26↓ | 25↓ | 24↓ | 23↓ | 22↓ | 21↓ | 20↓ | | 128X | 64X | 32X | 16X | 8X | 4X | 2X | 1X | | 1____ | 1____ | 1____ | 0____ | 0____ | 0____ | 1____ | 0____ | | 128 + | 64 + | 32 + | 0 + | 0 + | 0 + | 2 + | 0 = | 226 | 1.1.6 156 | 28 | 28 | 28 | 12 | 4 | 0 | 0 | | 27↓ | 26↓ | 25↓ | 24↓ | 23↓ | 22↓ | 21↓ | 20↓ | | v | v | v | v | v | v | v | v | | 128x | 64x | 32x | 16x | 8x | 4x | 2x | 1x | | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 = | 10011100 | 128 + | 0 + | 0 + | 16 + | 8 + | 4 + | 0 + | 0 = | 156 | 1.1.7 255 | 127 | 63 | 31 | 15 | 7 | 3 | 1 | | 27↓ | 26↓ | 25↓ | 24↓ | 23↓ | 22↓ | 21↓ | 20↓ | | v | v | v | v | v | v | v | v | | 128x | 64x | 32x | 16x | 8x | 4x | 2x | 1x | | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 11111111 | 128 + | 64 + | 21 + | 16 + | 8 + | 4 + | 2 + | 1 = | 255 | 1.1.8 200 | 72 | 8 | 8 | 8 | 0 | 0 | 0 | | 27↓ | 26↓ | 25↓ | 24↓ | 23↓ | 22↓ | 21↓ | 20↓ | | v | v | v | v | v | v | v | v | | 128x | 64x | 32x | 16x | 8x | 4x | 2x | 1x | | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 11001001 | 128 + | 64 + | 0 + | 0 + | 8 + | 0 + | 0 + | 1 = | 255 | 1.1.10 | 2^7 | 2^6 | 2^5 | 2^4 | 2^3 | 2^2 | 2^1 | 2^0 | | 128...
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...perform more productively? Try proven, specific techniques designed to keep even your most cynical employees satisfied and productive. The first step? Back off. Nobody likes a micromanager. Ads by Google Options Trading Lessons With just these 3 Free reports you could be trading by day's end. wealthdaily.com/Options_Trading Step 1 Set specific goals, and trust your employees to reach them. According to Forbes, nothing makes enthusiasm vanish faster than a micromanager who doesn't trust her employees to do their work properly. Force yourself to let go by setting a clear and achievable goal; for example, "I want to beat increase our sales by 5 percent over the next 60 days." Ask for feedback, then back off and see what happens. Step 2 Reward top performers publicly and meaningfully. Inc. magazine suggests that letting employees share in success keeps them happy and motivated. It also increases the work ethic of those who aren't top performers. Financial incentives are always appreciated,...
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