2.31. Show that for each of the following values of a and b, there exists x,...

2.31. Show that for each of the following values of a and b, there exists x, y in Z satisfying ax + by = 11. (i) a = 11, b = 0, (ii) a = 22, b = 11, (iii) a = 33, b = 22, (iv) a = 451, b = 33, (v) a = 484, b = 451.

2.39. Prove that gcd(ad, bd) = |d|gcd(a, b).

2.44. Does the Diophantine equation 12x + 33y = 1 have an integer solution? If so, can you list all integer solutions?

2.47. For nonzero integers a, b, c, gcd(a, b, , c) denotes the largest integer that divides all of them. Show that gcd(a, b, c) = gcd(a, gcd(b, c)).

Expert Solution

Colby Messinger answered 1 year ago

(a) What is the percentile values of (i) 2.31 and of (ii) 3.09?

1.25, 1.64,1.91,2.31,2.37,2.38,2.84,2.87,2.93,2.94,2.98,3.00,3.09,3.22,3.41,3.55. Use this dataset two answer the questions below. (a) What is the percentile values of (i) 2.31 and of (ii) 3.09? (b) Find values of 30th30th and 90th90th percentiles for the above data set, i.e., P30P30 and P90P90.

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