Worth 30 points

1. anthony has a sink that is shaped like a half-sphere. the sink has a volume of
2000/3π in3. one day, his sink clogged. he has to use one of two cylindrical cups to scoop the water out of the sink. the sink is completely full when anthony begins scooping.
(a) one cup has a diameter of 4 in. and a height of 4 in. how many cups of water must anthony scoop out of the sink with this cup to empty it? round the number of scoops to the nearest whole number.
(b) one cup has a diameter of 8 in. and a height of 4 in. how many cups of water must he scoop out of the sink with this cup to empty it? round the number of scoops to the nearest whole number.

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|