Consider the probability distribution of a random variable x. is the expected value of the distribution necessarily one of the possible values of x?

yes. the expected value can never be a value from the exact value of x.
no. the expected value can be a value different from the exact value of x.
no. the expected value will never be one of its possible values of x.
yes. the expected value must always be one of its possible values of x.
explain or give an example.

George is putting trim around his rectangular deck, including the gate. he will need 44 feet of trim to do the entire deck. if the deck is 13 feet long, how wide is the deck?

Write the equation of a line that is perpendicular to the given line and that passes through the given point. –3x – 6y = 17; (6, 3) y = x – 9 y = 2x – 9 y = –2x – 9 y = x + 0 3. is the relationship shown by the data linear? if so, model the data with an equation. x y 1 5 5 10 9 15 13 20 the relationship is linear; y – 5 = (x – 1). the relationship is not linear. the relationship is linear; y – 5 = (x – 1). the relationship is linear; y – 1 = (x – 5). write an equation in point-slope form for the line through the given point with the given slope. (–10, –1); m = y + 10 = (x + 1) y – 1 = (x – 10) y – 1 = (x + 10) y + 1 = (x + 10) 5. write an equation for each translation of . 6.5 units up y + 6.5 = | x | y = | 6.5 x | y = | x | + 6.5 y = | x | – 6.5 6. write an equation for each translation of . 5.5 units right y = | x | + 5.5 y = | x – 5.5 | y = | x | – 5.5 y = | x + 5.5 | 7. which equation translates y = | x | by 8 units to the left? y = | x | – 8 y = | x | + 8 y = | x – 8| y = | x + 8|

Mrs. blake's bill at a restaurant is $42.75. she wants to leave the waiter an 18% tip. how much will she pay in all, including the tip?