Math Answers

. Define V =

 x

y



: x, y ≥ 0



. Decide if V is a vector space or not and prove

your claim. (Hint: V is the first quadrant in the xy-plane).

 A population consists of the five measurements 2, 6, 8, 0, and 1.

1. What is the mean and the standard deviation of the population? 

Let G be the group of integers under the operation of addition,

and let H = {3k | k ∈ Z}. Is H a subgroup of G

Prove that the set of complex numbers {1,−1,i,−i} under

multiplication operation is a cyclic group.Find the generators of

cycle

what is the illustration of greater than 1.1150

     Two different products P1 and P2 can be manufactured by one or both of two different machines M1 and M2. The unit processing time of either product on either machine is the same. The daily capacity of machine M1 is 200 units (of either P1 or P2 or a mixture of both) and the daily capacity of machine M2 is 250 units. The shop supervisor wants to balance the products schedule of the two machines such that the total number of units produced on one machine is within 5 units of the number produced on the other. The profit per unit of P1 is $10, and that of P1 is $15. Set up the problem as an LP in equation form.

The value of serum sodium in healthy adults approximately follows a normal distribution with a mean of 141meq/l and standard deviation of 3meq/l

(a) What is the probability that a normal healthy adult will have a serum sodium value above 147meq/l ( 5 marks)

(b) What is the probability that a normal healthy adult will have a serum sodium value below 130 meq/l ( 5 marks)

(c) What is the probability that a normal healthy adult will have a serum sodium value between 132 and 150meq/l (5 marks)

Given a sequence ((xn,yn)) is R2 .prove that if ((xn,yn)) is bounded ,then (xn) and (yn) are bounded.

Solve each of the following problems. Follow Polya's four stages of problem solving in your solution.

3. A palindromic number or numeral palindrome is a "symmetrical" number like 16461, which remains the same when its digits are reversed. The term palindromic is derived from palindrome, which refers to a word like rotor that remains unchanged under reversal of its letters. How many palindromes are there between 0 and 1000?

4. Matt is half as old as James will be when Matt is twice as old as James is now. In five years, the sum of Matt's and James' ages will be 100. How old are Matt and James now?

5. Find the digit 120 places to the right of the decimal point in the decimal representation of 9/13

Solve each of the following problems. Follow Polya's four stages of problem solving in your solution.

1. An egg vendor broke all the eggs that he was delivering to a local store. He could not remember how many eggs there were in all. However, he did remember that when he tried to pack them into packages of 2, 3, 4, 5, and 6 he had one left over each time. When he packed them into packages of 7, he had another left over. What is the smallest number of eggs he could have had in the shipment?

2. Edwin has 100 baseball cards. He wants to place the cards in three stacks so that the second stack has twice as many cards as the first, and the third stack has twice as many cards as the second. How many cards will be in each stack? How many will be left over?