The check digit 13 for an ISBN-13 with initial digits 12 … 12is determined by the congruence

(1 + 3 + ⋯ 13) + 3(2 + 4 + ⋯ 12) ≡ 0 (mod 10).

Determine whether the following 13-digit numbers is a valid ISBN-13.

978-0-073-20679-1

Me 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.

Helena lost her marbles. but then she found them and put them in 44 bags with mm marbles in each bag. she had 33 marbles left over that didn't fit in the bags.

The vertices of a triangle are a(7.5), b(4,2), and c19. 2). what is