Jay has $500 in the bank when he decides to try a savings experiment. On each day i ∈ [1..30], Jay flips a fair coin. If it comes up heads, he deposits i dollars into the bank; if it comes up tails, he withdraws $10. How many dollars should he expect to have in the bank after 30 days?

What is the correlation coefficient between the variables? round to three decimal places. enter your answer in the box

Two line segments are shown in the figure below. suppose that the length of the line along the x-axis is 6, and the length of the hypotenuse of the triangle is 10. what is the equation of the hypotenuse line (shown in red, below)?

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.