Imagine that we paint a 4x4x4 cube blue on every side. How many of the small cubes have 3 blue faces?how many have 2 blue faces? How many have 1 blue face? How many have not been been painted at all? How many faces would be painted in a cube of any size?

Write the expression in simplified radical form. show all steps and work including any foil method work. (hint: use the conjugate. no decimal answers.) (9-2√3)/(12+√3)

An energy drink company claims that its product increases students' memory levels. to support its claims, the company issues advertisements claiming that 8 out of 10 people (chosen randomly from across the country) who tried their product reported improved memory. the missing component in this study is a .

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.