Do you use data on a cellphone? You may have a maximum amount of data you can use without having to pay more. Suppose a family data plan includes 10 gigabytes of shared data and costs $80 per month. Any additional data usage is billed at $15 per gigabyte. A certain family wants to spend at most $125 on their bill each month. You could use an inequality to find that the family can use at most 3 additional gigabytes of data. When else could you use an inequality to find a range of values?

Determine whether the set of whole numbers is closed under addition. explain why the set is or is not closed. give an example.

Aword processing program requires a 7- digit registration code made up of the digits 1,2,4,5,6,7 and 9 each number has to be used and no number can be used mor than once how many codes are possible

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.