An orange juice manufacturer advertises a new orange juice product that contains 50% less sugar. This new product is expected to increase profits substantially because they create the 50% less sugar product by replacing 50% of the juice with water while selling it for the same price. An inspector wants to investigate whether the actual percentage of water in the product is within 5% of the intended 50%. He selects a random sample of 500 containers of orange juice and determined the percentage of each that is water. He plans to conduct a significance test at the a = 0.01 level to see if there is convincing evidence that the proportion of water added is different from 0.50. What is the probability that the inspector makes a Type I error?

Write an expression that has three terms and simplifies to 4x - 7. identify the coefficient(s) and constant(s) in your expression

What is the inverse of the function f(x) = 2x + 1?

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.