The cantor set is constructed as follows. start with a closed interval [0, 1] and remove the open interval ( 1 3 , 2 3 ). that leaves the two intervals [0, 1 3 ] and [ 2 3 , 1]. remove the middle third of each of these closed intervals, leaving four intervals. continue the process of removing the middle third of each interval that remains from the previous step. the cantor set consists of the numbers that are not removed during the process. (a) show that the total length of the intervals removed is 1. (b) despite the result of part a. there are infinitely many numbers in the cantor set. list three numbers in the cantor set.

The cross-sectional areas of a right triangular prism and a right cylinder are congruent. the right triangular prism has a height of 6 units, and the right cylinder has a height of 6 units. which conclusion can be made from the given information? the volume of the triangular prism is half the volume of the cylinder. the volume of the triangular prism is twice the volume of the cylinder. the volume of the triangular prism is equal to the volume of the cylinder. the volume of the triangular prism is not equal to the volume of the cylinder.

In the diagram, the ratios of two pairs of corresponding sides are equal to prove that almn - axyz by the sas similarity theorem, it also needs to be shown that x 6 z un z zz un = 2x zləzz lezy

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.