As a special promotion for its 16-ounce bottles of water, a water company printed a message on the inside of each cap. Some of the caps read, "Better luck next time!" whereas others read, "You won!" The company advertised the promotion with the slogan "One in eight wins a prize!" Suppose the company is telling the truth and that every 16-ounce bottle of water has a one-in-eight chance of being a winner. Nine friends each buy one 16-ounce bottle of water at a local convenience store. Let X equal the number of friends who win a prize. Part A: Explain why X is a binomial random variable. (3 points) Part B: Find the mean and standard deviation of X. Interpret each value in context. (4 points) Part C: The store clerk is surprised when three of the friends win a prize. Is this group of friends just lucky, or is the company's one-in-eight claim inaccurate? Compute P(X ≥ 3) and use the result to justify your answer.

Lorne subtracted 6x3 – 2x + 3 from –3x3 + 5x2 + 4x – 7. use the drop-down menus to identify the steps lorne used to find the difference.

Factor x2 – 8x + 15. which pair of numbers has a product of ac and a sum of what is the factored form of the

The table shows the relationship between the number of cups of cereal and the number of cups of raisins in a cereal bar recipe: number of cups of cereal number of cups of raisins 8 2 12 3 16 4 molly plotted an equivalent ratio as shown on the grid below: a graph is shown. the title of the graph is cereal bars. the horizontal axis label is cereal in cups. the x-axis values are 0, 20, 40, 60, 80,100. the vertical axis label is raisins in cups. the y-axis values are 0, 10, 20, 30, 40, 50. a point is plotted on the ordered pair 40,20. which of these explains why the point molly plotted is incorrect? (a) if the number of cups of cereal is 40, then the number of cups of raisins will be10. (b)if the number of cups of raisins is 40, then the number of cups of cereal will be10. (c) if the number of cups of cereal is 40, then the number of cups of raisins will be 80. (d) if the number of cups of raisins is 40, then the number of cups of cereal will be 80.