Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p​ dollars, the revenue R​ (in dollars) is R(p)=-2p squared + 4000 p. ​(a) At what prices p is revenue​ zero? ​(b) For what range of prices will revenue exceed ​$800, 000 ​? ​(a) At what prices p is revenue​ zero? The revenue equals zero when p is ​$0 , 2000 . ​(Use a comma to separate​ answers, but do not use commas in any individual​ numbers.) ​(b) For what range of prices will revenue exceed ​$800, 000 ​? nothing

The weight of an object in a particular scale is 175.2 lbs. the measured weight may vary from the actual weight by at most 0.1 lbs. what is the range of actual weights of the object

For problems 29 - 31 the graph of a quadratic function y=ax^2 + bx + c is shown. tell whether the discriminant of ax^2 + bx + c = 0 is positive, negative, or zero.

Carla was trying to decide what to do saturday evening. she has $100 available to spend for the evening. she has narrowed her choices down to these events: braves game, a concert of an artist she likes, or the georgia aquarium. admission to the braves game is $25, hot dogs cost $10, sodas cost $5. the concert costs $25 for admission, $20 for a souvernir t-shirt, and $10 for a soda. the georgia aquarium has the show of a lifetime with an all you can eat and drink that costs $100. carla does not want to take any driving chances, so in addition to the cost of the aquarium, she will also need to pay for her uber/lyft, which is $15 each way. which option should carla choose if she wants to spend the least? based on that choice, what then is carla's oppotunity cost? fully explain your answer in at least one paragraph.