An opinion poll asked a random sample of adults whether they favor the US Food and Drug Administration banning food color additives in the United States. A commentator believes more than 40% of all adults favor such a ban. Which null and alternative hypotheses should be used to test this claim?

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.

Amass weighing 16 pounds stretches a spring 8/3 feet. the mass is initially released from rest from a point 2 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. find the equation of motion if the mass is driven by an external force equal to f(t)=cos(2t).

Describe a pattern in each sequence what are the next two terms of each sequence -5, 5, -5, 5 a. subtract 10 from the previous term; -5,5 b. multiply the previous term by 1; 5, 5 c. add 10 to the previous term; -5, -15 d. multiply the previous term by -1; -5, 5