A population of birds walks along the shores of a swampy area eating small crabs. Climatic changes cause the water level in the area to increase. Which genetic variation in the bird population will be at an advantance leading to greater survival in the area?

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k

The weights of bags filled by a machine are normally distributed with a standard deviation of 0.05 kilograms and a mean that can be set by the operator. at what level should the mean weight be set if it required that only 1% of the bags weigh less than 9.5 kilograms? round the answer to 2 decimal places.

The power exerted by a muscle is the product of the force exerted and the velocity of contraction. the area of which of these shaded regions represents the power exerted while a weight is lifted at maximum speed?