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**Q1:**If 116 is added to a number, it will be 5 times as large as it was originally. Find the number. The number is XSee Answer**Q2:**Use the information shown in the graph. The graph represents a survey of 1325 office workers and shows the percent of people who indicated what time of day is most productive for them. Most Productive Time of Day After office hours 9% Last few office hours 14% First few working hours 31% Before office hours 25% Late morning/early afternoon 21% Estimate the number of people who feel they are most productive outside normal office hours. Round your answer to the nearest integer. An estimate for the number of people who feel they are most productive outside normal office hours is XSee Answer**Q3:**Use the line graph shown. The graph shows annual cigarette consumption (in billions) for the United States for the years 1900 to 2010. Cigarette Consumption in the United States Billions of cigarettes 700 600 500 400 300 200 100 0 1900 1920 1940 1960 1980 Year 2000 The year(s) in which 400 billion cigarettes were smoked: Estimate the year or years in which 400 billion cigarettes were smoked. If there is more than one answer, separate them with commas. DO 2010 XSee Answer**Q4:**5. a) Calculate possible remainders of a prime p > 3 when divided by 6. 5. b) Prove for any prime p > 3, the number p² + 1 can't be prime.See Answer**Q5:**Exercise 4.3.4 Let p≥ 2 be a prime and prove that any group of order p² is isomorphic to either Zp² or Zpx Zp. Hint: If there exists an element of order p², then GZp², so assume that this is not the case and deduce that every nonidentity element of G has order p. Then prove that for any two elements g, h E G, either (g) = (h) or (g) n(h) = {e}. Finally, prove that there are two nonidentity elements g, h E G so that (g) n(h) = {e}, and apply Proposition 3.7.1.See Answer

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