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Prove that every non-trivial sub group of cyclic group has finite index. Hence prove that (Q,+) is not cyclic.


Between z=-1.46 and z=2.15

Task 4 make your own experiment and trial .choose your own random variable X and compute for its mean , variance and standard deviation





A population consists of the five numbers: 2,3,6,8 and 11. Consider samples of size 2 that can be drawn from this population. 1. List all the samples and the correspondinv mean. 2. Construct tha sampling distribution of the sample mean. 3. Draw a histogram of the sampling distribution of the mean.


The numbers of workers of a new fast-food restaurant with 7 outlets are 8, 9, 8, 10, 12, 11, and 7. compute the following: Population mean: Population variance population standard deviation


Find the mean, variance and standard deviation of the following measures: 2,5,6,3,9,10,12, and 15

What is the probability that a market inspector will discover, at most, three violations of the public health code? (Round off your answer in the nearest hundredths if possible)

D. Write in the form " if p then q", then write converse, inverse and contra positive of each of the following implications.


  1. it is necessary to do your homework to get a passing grade.
  2. if you read your lesson everyday, you will pass all your courses.

write the negation of these propositions


  1. Today is Monday
  2. The air in Naic Cavite is hot and polluted.
  3. Summer in Davao is hot and sunny.
  4. 2 + 1 > 5
  5. it is hot.
  6. X + y = 4
  7. 7. sierra madre mountains are denuded.
  8. a x b > 6
  9. it's raining in August.
  10. it is cold in December

If In=int_0 to ♾️ {(e^-x)(sin^n) (x) dx } , prove that (1+n^2)In=n(n-1)In-2 for n≥2 .

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