Suppose that a project manager tested the strength of one tile out of a batch of 3,000 to be used on a building. this one sample measurement was compared with the design specification and, in this case, the sampled tile's strength exceeded that of the specification. on this basis, the project manager accepted the tile shipment. if the sampled tile was defective (with a strength less than the specification), the project manager would have rejected the lot. a. what is the probability that ninety percent of the tiles are substandard, even though the project manager's sample gave a satisfactory result? b. sketch out the operating characteristic curve for this sampling plan as a function of the actual fraction of defective tiles.

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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.

This circle is centered at the origin, and the length of its radius is 6. what is the circle's equation? a. x^2+y^2=36 b x^2+y^2=6 c x+y=36 d x^6+y^6=1