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Prove that the sum of two consecutive exponents of the number 5 is divisible by 30.if two consecutive exponents are 5n and 5n + 1, then their sum can be written as 30.

Abag contains 3 red marbles, 2 blue marbles, and 2 green marbles. one marble is picked, then another marble. assume that the selections are made with replacement. a) find the probability of picking two red marbles with replacement. b) find the probability of picking a red marble and a blue marble. assume the selections are made without replacement. c) find the probability of picking two red marbles without replacement. d) find the probability of picking a red marble and a blue marble without replacement.

(05.02) mr. morris is going to save money and replace his sailboat's mainsail himself. he must determine the area of the mainsail in order to buy the correct amount of material. calculate the area of the parallelogram to determine how much material should be purchased. be sure to explain how to decompose this shape into rectangles and triangles. describe their dimensions and show your work.