Math Answers

You have 80 grams of a radioactive kind of tellurium. How much will be left after 8 months if its half-life is 2 months?

You have 80 grams of a radioactive kind of tellurium. How much will be left after 8 months if its half-life is 2 months?

Let P(t) be the population of a certain animal species. Assume the

P(t) satisfies the logistic growth equation,

dP

dt = 0.2P(t) (1 −

P(t)

200) , y(0) = 150

a) Is the above equation autonomous? if yes (explain your answer with

proper reasons), if no (justify you answer).

b) Solve the above initial value problem, and find the value of solution at

time t = 0.5 using separation of variables

Consider the autonomous DE xʹ = x(x − 1)(x+ 2). Determine the

critical points of the equation. Discuss a way of obtaining a phase portrait

of the equation.

in the new apartment, 2k new light bulbs are included in the lighting network. Each light bulb burns out within a year with probability p. Find the probability that less than half of the original light bulbs will have to be replaced with new ones within a year.

Separate the interval in which the function f defined on R by f(x)=2x3-15x2+36x+5 for all x∈R is increasing

4 independent shots are fired from the aircraft at the aircraft. The probability of hitting each shot is 0.3. Two hits are obviously enough to destroy (failure) an aircraft; with one hit, the aircraft is hit with a probability of 0.6. Find the probability that the aircraft will be hit.

What is the probability that 40 or more boxes will be delivered on a particular day?

The average monthly salary of 500 teachers of Candelaria East district is

P26,500. If the monthly salaries of the teachers are normally distributed with

standard deviation of P2,500, approximately how many teachers in the district

are earning more than P30,000 monthly?

The average number of calories in a 1.8-ounce chocolate bar is 230. Suppose

that the distribution of calories is approximately normal with a standard

deviation of 10. Find the probability that a randomly selected chocolate bar will

have less than 200 calories.