Math Answers

5. Express as a double integral the area enclosed by one loop of the curve 𝑟 = 3 cos 2𝜃 and

evaluate the integral

Applications of Ordinary Differential Equation

If a varies jointly as b and c and inversely as the square of d, and a = 120 when b = 5, c = 2, and d = 9, find a when b = 12, c = 9 and d = 9.

Applications of Differential Equation of Newton's law of cooling / warming

ACTIVITY 2:  APPLY THE CENTRAL LIMIT THEOREM

1. A Neilsen reported that children between the ages 2 and 5 watch an average of 25 hours of television per week. Assume the variable is normally distributed and the standard deviation is 3 hours. If 20 children between the ages of 2 and 5 are randomly selected, find the probability that the mean of the number of hours they watch television will be greater than 26.3 hours.

2. Assume that the mean systolic blood pressure of normal adults is 120 milliliters of mercury (mmHg) and the standard deviation is 5.6. If the sample of 30 adults is randomly selected, find the probability that the sample mean will be between 120 and 121.8 mmHg. Assume that the variable is normally distributed.

The mean weight of 20-year-old females is 126 pounds and the standard deviation is 15.7. If a sample of 25 females is selected, find the probability that the mean of the sample will be greater than 128.3 pounds. Assume that the variable is normally distributed.

If the area of the t-distribution to the right is 0.01, then find the following:

a. the area to the left of the distribution.

b. the degree of freedom when n=16.

c. the t-value when the confidence level is 99% and df=16

1.     Let p and q be propositions. p: You drive over 65 miles per hour. q: You get a speeding ticket. Write these propositions using p and q and logical connectives.

a.      You do not drive over 65 miles per hour.

b.     You will get a speeding ticket if you drive over 65 miles per hour.

c.      If you do not drive over 65 miles per hour, then you will not get a speeding ticket. 

A population consists of the four numbers 3, 4, 2, 5. Consider all possible 

distinct samples (without replacement) of size two and verify that the population mean 

is equal to the mean of sample means

How many ways can 4 baseball players and 3 basketball players be selected from 12 baseball players and 9 basketball players?