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Obtain the solution of the differential equation
y"+3y'+2y=e^(2t) using the method of variation of parameters
C. Choose a quantity to be represented by a variable, then write a mathematical expression for each.
1. The product of three consecutive integers
2.. Jose's age in 10 years
3. The distance traveled by a man driving at the rate of 45 kph
4. The total amount in pesos of 30 coins consisting of 5-peso coins and 10-peso coins
5. The sum of three consecutive odd integers
6. The fraction of work done by a man who can finish a job in three days
7. The total interest after one year if a fraction of P500 000 is invested at 5% annual interest rate and the remaining part is invested at 7.5% annual interest rate
8. A three-digit number whose hundreds digit is twice its tens digit and the tens digit is 3 more than the units digit
9. The percentage of alcohol in a mixture formed by combining 1.5 liter of pure water and x liters of 30% alcohol solution.
10. The total distance traveled by a boat 1 hour and 20 minutes upstream and 40 minutes downstream if the rate of the current is 3 kph.
Life Insurance A 39-year-old woman purchases a $300,000 term life insurance policy for an annual payment of $450. Based on a period life table for the U.S. government, the probability that she will survive the year is 0.999053Find the expected value of the policy for the insurance companyRound to two decimal places for currency problems
A group of students got the following scores in a test:6,7,8,12,13and 15. Consider samples of size 3thag can be drawn from this population. List all the possible samples and the corresponding mean.
State whether the following statement are true or false and also give the reason in support your answer
In a big hall there are 50 rows and each row has 60 students. A research scholar selects 10 rows randomly and then randomly selects 15; students from each selected row. It is an example of cluster sampling procedure.
State whether the following statement are true or false and also give the reason in support your answer
(1)As we increase the sample size, representativeness of the population by the sample decrease
Problem: A researcher is conducting a study about the effectiveness of a new product to the households in a certain Barangay. His population consists of the numbers 8, 4, 2, 1, 13, and 10. Let us list all possible sample size of 4 from this researcher and compute the mean of each sample.
1. Determine the number of sets of all possible random samples using the combination formula.
2. List all the possible samples and compute the mean of each sample.
3. Construct the sampling distribution.
4. Construct the histogram.
Consider a population consisting the scores of 6 students in a Statistic Test.
18, 22, 25, 28, 32, 36
Suppose samples of size 3 are drawn from this population, describe the sampling
distribution of the sample means following the steps below.
Step 4: List all possible
samples and their
corresponding means.
A company has developed a new battery. The engineering department of the company claims that each battery lasts for 200 minutes. In order to test this claim, the company selects a random sample of 100 new batteries so that this sample has a mean of 190 minutes. Given that the population standard deviation is 30 minutes, test the engineering department’s claim that the new batteries run with an average of 200 minutes. Use 1% level of significance.
4)Given that the level of significance is 0.01 or 1%, what is/are the critical values?
5)Using the appropriate formula, what is the computed test statistic? (Input your answer using 3 decimal places, example: 1.234 if positive or -1.234 if the answer is negative) *
6)What is the decision based from the critical value and the computed test statistic
7)What is the conclusion?
A company has developed a new battery. The engineering department of the company claims that each battery lasts for 200 minutes. In order to test this claim, the company selects a random sample of 100 new batteries so that this sample has a mean of 190 minutes. Given that the population standard deviation is 30 minutes, test the engineering department’s claim that the new batteries run with an average of 200 minutes. Use 1% level of significance.
1)Which is the correct null hypothesis that can be derived in the situation?
2)Which is the correct alternative hypothesis that can be derived in the situation?
3)What test will be used based from the given values in the situation?
