consider an experiment that has N outcomes e1,e2,,eN, where it is known that outcome ej+1 is twice as likely as outcome ej for j=1,2,,N-1. let Ek={E1,E2,Ek}. show that P(Ek)=2^k-1/2^N-1?​

Look at arnold's attempt to solve the equation for b: 3b = 12 b = 3 · 12 b = 36 describe the mistake that arnold made.

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.

The table below shows the function f. determine the value of f(3) that will lead to an average rate of change of 19 over the interval [3, 5]. a. 32 b. -32 c. 25 d. -25