Math Answers

Activity 2

Directions :Solve the logistics problem. show your solution.

The population of a certain bacteria follows the logistic growth pattern, initially, there are 10 g of bacteria present in the culture. Two hours later, the culture weighs 25 g. The maximum weight of the culture is 100g.

a.Write the corresponding logistic model for the bacterial growth?

b. What is the weight of the culture after 5 hours?

c. When will the culture's weight be 75 g?

Activity 1:

Solve the following problems applying the concepts learned above. Write your answer on a separate sheet of paper. (Show your solution)

1. The rate of change x is proportional to x. When t =0, x0 = 3 and when t =2, x=6. What is the value of x when t =4?

2. A certain plutonium isotope decays at a rate proportional to the amount present. Approximately 15% of the original amount decomposes in 100 years. How much amount of the substance has decayed after 600 years? Also, find the half - life t1/2 of this radioactive substance ; that is, find the time required for this substance to decay to one- half of its original amount.

In a public senior high school, a survey conducted last year showed that 25%

of the students’ parents are farmers. This year, a new survey was conducted

randomly on 150 students from the same school. It was found that 63 of them

have parents who are farmers. Test if the claim was higher at α = 0.01 level.

If P (A|B) = 0.5, P (A) = 0.45 and P (B) = ?

Suppose the random variable Y has a normal distribution with an expected value equal to 12 and variance equal to 16. What is the value of k such as that P(X<k)= 0.25

with the aid of an example, explain how even and odd parity work and give an example application where they may be useful.

. State the converse, contrapositive, and inverse of each of these conditional statements. A positive integer is a prime only if it has no divisors other than 1 and itself.

1. Let X₁, X_{2 ,} and X₃ be independent standard normal random variable. If we defined Y₁=X₂, Y₂=X₁+X₂/2 and Y₃=X₁+ X₂ +X₃/3.Then find then joint pdf of Y₁, Y_2, and Y₃ using the Jacobian method?

1.The waiting time, in hour, between successive speeders spotted by a radar units is a continuous random variable with cumulative distribution function

 derive the characteristic function of x and use it to find the mean of x

Solve the corresponding equation for the appropriate interval by using the following two root finding techniques :

a) algebraic approach

sin(x+ π /2)=ln|x-1|