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The rational function f( 2/-2×-5)



A .Find f¹(×)



B. Find the equation of the line of symmetry of f¹(×) and f(×).


A population consists of six values (6, 9, 12, 15, 18, and 21). (with illustration)

e. Determine the mean, variance and standard deviation of the sample mean.


Determine the area of the given curves


1 . 𝑦2 = 2 𝑥 ; 𝑦 = 𝑥 − 4


2. 𝑦 = 𝑥 − 𝑥2 ; 𝑦 = − 𝑥


1. A population consists of six values (6, 9, 12, 15, 18, and 21). (with illustration)

e. Determine the mean, variance and standard deviation of the sample mean.



2. The scores of individual students on a national test have a normal distribution with mean of 18.6 and a standard deviation of 5.9. At Federico Ramos Rural High School, 76 students took the test. If the scores at this school have the same distribution as national scores, solve for the following: (with illustration)

a. determine the mean and standard deviation of the sampling distribution of the sample mean.


  1. A population consists of six values (6, 9, 12, 15, 18, and 21). (with illustration)

e. Determine the mean, variance and standard deviation of the sample mean.


2. The scores of individual students on a national test have a normal distribution with mean of 18.6 and a standard deviation of 5.9. At Federico Ramos Rural High School, 76 students took the test. If the scores at this school have the same distribution as national scores, solve for the following: (with illustration)

a. determine the mean and standard deviation of the sampling distribution of the sample mean.


According to Nielsen Media Research, the (population) average number of hours of TV viewing per household per week in the United States is 50.4 hours. Suppose the (population) standard deviation is known to be 11.8 hours. A random sample of 42 U.S. households is taken. What is the probability that the sample average is less thank 47.5 hours


A group of four IC chips consists of two good chips and two defective chips. The experiment consists of selecting three chips at random from this group. Write the sample space of the possible outcomes. What is the probability that two are defective?


simplify y= 1+2x/(1-2x)


A population of Grade 11 Arts and Design Students of size N=140 has mean grade of u=83 in Arts Subject and a population standard deviation of 25.




1.) What is the z-score of the the sample mean 80 if the sample size n=30?



2.) What is the area or probability of the sample mean 75 of the sample size n=30?



3.) What is the area greater than the sample mean of 80 if the sample size n=30?

A garment factory distributes two brands of jeans. If it is found that 75 out of 250 customers prefer brand A and that 30 out of 150 prefer brand B, can we conclude at 0.05 level of significance that brand A outsells brand B?


a. State the null and alternative hypothesis

b. Determine the significance level

c. Select the test statistic to be used

d. Compute the test statistic value

e. Determine the critical value

f. Sketch the rejection region

g. Draw the conclusion



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