Show that theorem 1.5 also holds for the interval (x, x+b]. does it hold in general for the intervals [x, x + b) or (x, x+b)?
theorem 1.5. let a, b e z with b > 0, and let x e r. then there exist unique 9,7 € z such that a = bq+r and r € [x, x + b). thereum des de zaman tese and sex e r. then there existuje

Amovie producer conducted a survey after the screening of his movie to find out how the film would be received by viewers from different age groups. the columns in the two-way table indicate the numbers of viewers who rated the film on a four-point scale: excellent, good, average, and poor. viewer's age group excellent good average poor marginal totals 16-25 52 42 12 7 113 26-35 33 50 5 9 97 36-45 58 12 28 34 132 which of these observations is supported by the data in the table? note: a rating of good or excellent means the audience liked the movie, while a rating of poor means the audience disliked the movie. a. the majority of the audience in the 26-35 age group disliked the movie. b. among those who liked the movie, the majority were in the oldest age group. c. among those who disliked the movie, the majority were in the 26-35 age group. d. the majority of the audience in the 16-25 age group liked the movie. e. the majority of the audience from all the age groups disliked the movie