Let (an) be a bounded sequence. Let S = {s ∈ R : ∃ a subsequence (ank ) converging to s}. This is called the set of subsequential limits. Bolzano-Weierstrass theorem implies there is at least one convergent subsequence, so S 6= ∅. Show S is bounded and lim sup an = sup(S).

Ammonia molecules have three hydrogen atoms and one nitrogen atom. how many of each atom arein five molecules of ammonia

Now max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.

One side of a rectangle is 7 centimeters shorter than six times the other side. find the length of the longer side if we also know that the perimeter of the rectangle is 266 centimeters.