Prove that the inequality
x(x+ 1)(x+ 2)(x+ 3) ≥ −1
holds for all real numbers x.

Acircle has a radius of 5/6 units and is centered at (3.6, 7.8) write the equation of this circle

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.

For a science project, a high school research team conducted a survey of local air temperatures. based on the results of the survey, the found that the average temperatures were around 10 degrees higher than expected. this result was wrong. the trouble with the survey was that most of the locations were exposed to direct sunlight and located over asphalt or sand, which resulted in higher temperatures than normal. this is a classic example of an error in which phase of inferential statistics?