Consider sorting n numbers stored in array a by first finding the smallest element of a and exchanging it with the element in . then find the second smallest element of a and exchange it with . continue in this manner for the first − 1 elements of a. write pseudo-code for this algorithm, which is known as selection sort. what loop invariant does this algorithm maintain? why does it need to run for only the first − 1 elements, rather than for all n elements? give the best-case and worst-case running times of selection sort in θ-notation

25 ! the line of best fit is h = 5a + 86. predict the height at age 16. show your work.

If the ratio of sum of the first m and n terms of an ap is m2 : n2 , show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1).

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.