A box is filled with green marbles, red marbles, and blue marbles. The ratio of red marbles to green marbles is 3:1. The ratio of green marbles to all of the marbles in the box is 2:11. Write each of the following ratios using the symbol. The ratio of red marbles to blue marbles.

Write the sine and cosine values of a, b, respectively, in the figure for (1) and (2) + explanation.

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.

Use sigma notation to represent the following series for 9 terms.