The cost of a small business is given by the expression 3000 plus 12 x, where x is the number of units produced. The business will be profitable whenever its profit y exceeds its cost. If the profit region is shaded in yellow. Draw the graphs corresponds to the given situation?

In the surface area formula for cylinders which expressionrepresents the lateral area

What is the range? can’t seem to find it out

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.