A carton is 15 inches long, 10 inches wide, and 12 inches high. Mindy wants to wrap up the carton. What is the minimum area of wrapping paper needed to cover the carton?

For what values of the variable x is the expression square root of 7x+14+ square root of 7-x a real number?

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.

Prove that 16^4-2^13-4^5 is divisible by 11.