In an isolated environment, a disease spreads at a rate proportional to the product of the infected and non-infected populations. let i(t) denote the number of infected individuals. suppose that the total population is 3000, the proportionality constant is 0.0002, and that 1% of the population is infected at time t=0. write down the intial value problem and the solution i(t).

Exclude leap years from the following calculations. (a) compute the probability that a randomly selected person does not have a birthday on october 4. (type an integer or a decimal rounded to three decimal places as needed.) (b) compute the probability that a randomly selected person does not have a birthday on the 1st day of a month. (type an integer or a decimal rounded to three decimal places as needed.) (c) compute the probability that a randomly selected person does not have a birthday on the 30th day of a month. (type an integer or a decimal rounded to three decimal places as needed.) (d) compute the probability that a randomly selected person was not born in january. (type an integer or a decimal rounded to three decimal places as needed.)

Which fraction represents the ratio 35 : 42 in simplest form

Use stokes' theorem to evaluate c f · dr where c is oriented counterclockwise as viewed from above. f(x, y, z) = xyi + 5zj + 7yk, c is the curve of intersection of the plane x + z = 8 and the cylinder x2 + y2 = 81.