Math Answers

Calculate T ; N; B; "\\kappa" ; "\\tau" of the curve x(t) = (t; t ² ; t ⁴) at the point (1; 1; 1).

3.10 If U, V are ideals of R, let U + V = {u + v | u ∈ U, v ∈ V }.

Prove that U + V is also an ideal.

3.9 Show that the commutative ring D is an integral domain if

and only if for a, b, c ∈ D with a #= 0 the relation ab = ac implies that

b = c.

3.8 D is an integral domain and D is of finite characteristic,

prove that the characteristic of D is a prime number.

3.7 If D is an integral domain and if na = 0 for some a #= 0 in

D and some integer n #= 0, prove that D is of finite characteristic.

3.6 If F is a field, prove that its only ideals are (0) and F itself.

3.5 If U is an ideal of R and 1 ∈ U, prove that U = R.

A lot consists of 10 good articles, 4 with minor defects and 2 with major defects. i. One article is chosen at random. Find the probability that (a) It has no defects, (b) It has no major defects, (c) It is either good or has major defects. ii. Two articles are chosen (without replacement), Find the probability that (a) Both are good (b) Both have major defects (c) At least one is good (d) at most one is good (e) Exactly one is good (f) Neither has major defects  

the time between busses on stevens creek blvd is 12 minutes. Therefore the wait time of a passenger who arrives randomly at a bus stop is uniformly distributed between 0 and 12 minutes.

a. find the probability that a person randomly arriving at the bus stop to wait for the bus has a wait time of at most 5 minutes.

in the accompanying diagram, the shaded area represents approximately 95% of the scores on a standardized test. If these scores ranged from 78 to 92,

a. what is the mean?

b. what is the standard deviation?

. In a manufacturing organisation, the distribution of wages was perfectly

normal and the number of workers employed in the organisation was 5000.

The mean wages of the workers were calculated at Rs. 800 and standard

deviation was worked out to be Rs. 200. On the basis of the information

estimate:

(i) The number of workers getting salary between Rs.700 and Rs.900.

(ii) Percentage of workers getting salary above Rs.1000

(iii) Percentage of workers getting salary below Rs.600