I'm quite confused with the racetrack principle and need on this problem. . suppose that f(t) is continuous and twice-differentiable for t> = 0. further suppose f''(t) > = 3 for all t> = 0 and f(0) = f'(0) = 0.. using the racetrack principle, what linear function g(t) can we prove is less than f'(t) (for t> = 0)? . g(t) = . then, also using the racetrack principle, what quadratic function h(t) can we prove is less than than f(t) (for t> = 0)? . h(t) = .

What are the critical values that correspond to a 95% confidence level and a sample size of 93? a. 65.647, 118.136 b. 59.196, 128.299 c. 57.143, 106.629 d. 69.196, 113.145

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.

Which of the following would be a reasonable estimate for the weight of a pencil? a. 1 × 10^-20 lb b. 1 × 10^20 lb c. 1 × 10^2 lb d. 1 × 10^-2 lb