Math Answers

1.Show that if d ≠ 0, then d | (-a) and -d | a.
2.Show that it is false that a>b implies a|b.
3.Is 980637 divisible by 7? Show.
4.Determine whether of the following are divisible by 3, 5, 7, 9, or 11 using the methods described int he text:
A. 1969
B. 28350
C. 1421
D. 17303
E. 116424
F. 1089
5.Classify each of the following as true or false:
A. 6 is a divisor of 24.
B. 40 is a multiple of 8.
C. 0 divides 10.
D. 13 is a factor of 33.
E. 12 divides 6.
6.Show that 23n -1 is divisible by 7.
7.Show that 5n - 1 is divisible by 4.

Q. Define the following terms
Series
Conditionally convergent series
Completeness property

In a University, 20% of all students are graduates and 80% are undergraduates.
The probability that a graduate student is married is 0.5 and the probability that an
undergraduate student is married is 0.1. One student is selected at random. What
is the probability that (i) he/she is married (ii) the student is a graduate if he/she is
found to be married?

A sample of 25 items is selected from a very large shipment. It is found to have a mean weight of 310 gm and standard deviation equal to 9 gm. State and compute the 95% confidence limits for the population mean weight.

A random sample of male employees is taken at the end of a year and the mean
number of hours of absenteeism for the year is found to be 63 hours. A similar
sample of 50 female employees has a mean of 66 hours. Could these samples be
drawn from a population with the same mean and standard deviation of 10 hours?
(Use α = 5%)

Like two situations where systematic sampling is appropriate. Justify your choice
of situations. Also explain how it is different from stratified sampling. Justify

Assuming that it is true that 2 in 10 industrial accidents are due to fatigue, find the
probability that exactly 2 of 8 industrial accidents will be due to fatigue.

The mean salary paid to 500 employees working in a firm was found to be Rs. 180.40. After disbursement of salaries for a certain month, it was discovered that the salary of two employees was wrongly entered as Rs. 297 and Rs. 165 against their correct salary of Rs. 197 and Rs. 185, respectively. Find the correct mean salary.

The regression equation of y on x and that of x on y are 8x-10y+66=0 and 40x-18 y = 214 respec tively, and the variance of x is 9.
i) What are the mean values of x and y?
ii) Find σy.
iii) Find the coefficient of correlation between x and y.

The 15 stocks had the following percentage changes in value over the past year:
3 0. 6 -5 -2
5 -18 20 14 18
-10 10 50 -20 18
Compute the range, median, 20th percentile, inter-quartile range.

Consider a random variable X having the uniform density function f ( x ) with a = 20 and b= 30
i) Define and graph the density function f(x).
ii) Verify that f(x) is a probability density function.
iii) Find P(22≤x≤30). iv) Find p( x= 25)

If the second moment of a Poisson distribution is 6, find the probability p ( x≥ 2)