Rewrite the following mixed number as a decimal.
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The random variable x has probability density function f (x) = k(−x²+5x−4) 1 ≤ x ≤ 4 or =0 1 show that k = 2/9 find 2 e(x), 3 the mode of x, 4 the cumulative distribution function f(x) for all x. 5 evaluate p(x ≤ 2.5). 6 deduce the value of the median and comment on the shape of the distribution.

1948 olympics men's 100m freestyle swim finals competitor time wally ris 57.3s alan ford 57.8s géza kádas 58.1s keith carter 58.3s alex jany 58.3s per-olof olsson 59.3s zoltán szilárd 59.6s taha youssef el-gamal 1: 00.5s 2012 olympics men's 100m freestyle swim finals competitor time nathan adrian 47.52s james magnussen 47.53s brent hayden 47.80s yannick agnel 47.84s sebastiaan verschuren 47.88s cesar cielo 47.92s hanser garcia 48.04s nikita lobintsev 48.44s a. calculate the median and interquartile range for each set of data. make sure to label each measurement in your answer. b. make two inferences based on your results from part a. use complete sentences in your answer.

∆abc is mapped onto ∆a'b'c' which is then mapped onto ∆a"b"c". ∆abc and ∆a"b"c" are shown in the diagram. a. describe the sequence of transformations from ∆abc to ∆a"b"c". b. describe a single transformation from ∆abc to ∆a"b"c". c. what is the relationship between ∆abc and ∆a’’b’’c’’? explain your reasoning.