Math Answers

Consider the vector space V = C

2 with scalar multiplication over the real numbers R and let W

and U be the subspaces of V defined by

W = {(z1, z2) ∈ V : z2 = z1 + 2z1} and U = {(z1, z2) ∈ V : z2 = z1 − z1}.

2.1 Find a basis for W ∩ U.

2.2 Express (z1, z2) ∈ V as (z1, z2) = w + u where w ∈ W and u ∈ U.

2.3 Explain whether V = W ⊕ U

Consider the vector space V = C

2 with scalar multiplication over the real numbers R and let

W = {(z1, z2) ∈ V : z2 = z1 + 2z1}.

1.1 Use the Subspace Test to show that W is a subspace of V.

1.2 Find a basis for W.

1.3 Explain whether W is a subspace over C

Rose wants to buy a car on hire purchase for N$75,000.00 at the rate of 11% p.a. repayable using monthly installments for a period of 3 years and 10 months. (No deposit was required). Use the given information to calculate the: (a) Total amount of money expected to be paid to the Hire Purchase Company over the years. (5) (b) Monthly installment to be paid by Rose. (5) c) Bank 1 offered her a loan repayable at a certain monthly installment for the same period of time as the car hire company at the rate same rate of 11% p.a. whereas Bank 2 offered to reduce the rate of by 1.5% p.a. What is the: (i) Total amount of money expected to be received by Bank 1. (5) (ii) Monthly instalment to be paid by Rose to Bank 1. (5) (iii) Total amount of money expected to be received by Bank 2 using the reduced interest rate. (5) (iv) Monthly installment to be paid by Rose to Bank 2. (5) (v) How much money will Rose save per month using the cheapest option? (5)

Research says that adult humans should drink 2 liters of water every day. However, the standard deviation is estimated at 0.7 liters. An event manager arranged 110 liters of mineral water for a one-day conference to be attended by 50 people. a. Present the distribution of population and the sample on a graph. b. Calculate the sample mean and standard error of mean. c. Calculate the probability that the event manager has sufficient water during the conference day.

Suppose data collected on rain fall in(mm) of 390 metrological stations were tabulated in frequency distribution and the following result were obtained.

frequency: 6, 25, 48, 72, 116, 60, 38,22,3

CM1=110; CM2=120, where ;CMi is class marks of ith class and assume the size of the class interval(w) are equal.

Determine:-

a. Class interval size, class boundaries and class marks(class mid point) of each class.

b. Compute the mean, median and the modal rain fall of the distribution.

The median and the mode of mesokurtic distribution is 32 and 34 respectively.The fourth central moment is 243 ,compute pearsonian coefficient of skwness and identify type skwness (assume n-1=n).

population consists of N=5 numbers 0, 3, 4, 9, and 15. Draw all possible samples of size n=3 without replacement, from the population and find the sample proportion of even numbers in the samples. Construct the sampling distribution of sample proportion?