For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v3. It is believed that migrating fish try to minimize the total energy required to swim a fixed distance. If the fish are swimming against a current u (u < v), then the time required to swim a distance L is L/(v - u) and the total energy E required to swim the distance is given by the formula below, where a is the proportionality constant.
E(v) = av^3 L/(v - u)
Determine the value of v that minimizes E. (Note: This result has been verified experimentally.)

The number of potato chips in a bag is normally distributed with a mean of 71 and a standard deviation of 2. approximately what percent of bags contain between 69 and 73 potato chips? approximately 68% approximately 71% approximately 95% approximately 99.7%

What values of x satisfy the inequality x^2-9x< 0? how is your answer shown on the graph?

People end up tossing 12% of what they buy at the grocery store. assume this is the true population proportion and that you plan to take a sample survey of 540 grocery shoppers to further investigate their behavior. a. calculate the mean and the standard error for the sample proportion p. b. describe the sampling distribution of p in part a. draw a graph of this probability distribution with its mean and standard deviation. what is the probability that your survey will provide a sample proportion more than 15%? c. d. population proportion? what is the probability that your survey will provide a sample proportion within + 0.03 of the