Select the correct answer from each drop-down menu.
complete the statements about the closure of sets.

1. the set {0, 2, 5} is (closed; not closed) under addition, as is illustrated by the fact that adding 2 and 5 results in 7, which is not included in the set.

2. the set of all integers is closed under addition, as is illustrated by the fact that adding -20 and 6 result in -14, which is (included; not included) in the set.

3. the set of all polynomials is (closed; not closed) under addition, which is illustrated by the fact that adding 3x2 − 2 and 7x4 + 4x results in 7x4 + 3x2 + 4x − 2, which is in the set.

10 ! a train starts from grand city and travels toward belleville 388 miles away. at the same time, a train starts from belleville and runs at the rate of 47 miles per hour toward grand city. they pass each other 4 hours later. find the rate of the train from grand city.

Write the rational number in lowest terms 99/-15

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.