Math Answers

The sum of 2440 consists of two numbers 100 and 10. If 100 is six times that of 10. How many 100 are there?

There is a claim that on daily average, students spend 5.5 hours on social media with a standard deviation of 1.25. A researcher wants to test the claim at 5% level of significance.

1. Formulate the null and alternative hypothesis

2. Determine the test statistic to be used

3. Find the corresponding zvalue

4. Identify the rejection region

In the class of Statistics, there are 75 students in total out of which 55 male, 20 female students. 10 students need to be selected for the occasion of freshers' reception.

a. Determine the probability that 4 of the selected students would be girls by using the formula of binomial distribution.

Find the value of a2 for the recurrence relation an=17an-1+30n, where a0=3

Find the value of a3 for the recurrence relation an=17an-1+30n, where a0=3

Find the value of a1 for the recurrence relation an=17an-1+30n, where a0=3

What would be the hypothesis of the mathematical induction for x(x + 1) < x! , where x ≥ 7?

If P(k) = k2(k + 2)(k – 1) is true, then what is P (k + 1)?

Which of the following is a parameter in the situation “A machine which has been regulated dispenses an average of 330 ml fruit concentrate per bottle. A random sample of 49 bottles filled by the machine has a mean content of 320 ml and a standard deviation of 50 ml.”?

A. Determine if 1781 is divisible by 3, 6, 7, 8, and 9. (5 items x 2 points)

B. Determine if each of the following numbers is a prime or composite.

6. 828

7. 1666

8. 1781

9. 1125

10. 107

C. Find the greatest common divisor of each of the following pairs of integers.

11. 60 and 100

12. 45 and 33

13. 34 and 58

14. 77 and 128

15. 98 and 273

D. Find the least common multiple of each of the following pairs of integers.

16. 72 and 108

17. 175 and 245

18. 150 and 70

19. 32 and 27

20. 540 and 504

Consider all samples of size 4 from this population: 3, 6, 10, 13, 15, 20

a. Make a sampling distribution of the sample means

b. Compute the mean of the sample means

c. Compute the variance and standard deviation of the sample means

Let f:[ 0,π/2] → [-1,1] be a function defined by f(x)= cos 2x . Verify that f satisfies the condition of the inverse function theorem. Hence, what can you conclude about the continuity of f^-1?

Prove that the sequence (fn(x)), where fn(x)= nx/(1+ nx^2) is not uniformly convergent in [-2,2]