Taxable income. As a result of several mergers and acquisitions, stock in four companies has been distributed among the companies. Each row of the following table gives the percentage of stock in the four companies that a particular company owns and the annual net income of each company (in millions of dollars): So company A holds 71 % of its own stock, 8 % of the stock in company B , 3 % of the stock in company C .etc. For the purpose of assessing a state tax on corporate income, the taxable income of each company is defined to be its share of its own annual net income plus its share of the taxable income of each of the other companies, as determined by the percentages in the table. What is the taxable income of each company (to the nearest thousand dollars)?
Taxable income. As a result of several mergers and acquisitions, stock in four companies has been distributed among the companies. Each row of the following table gives the percentage of stock in the four companies that a particular company owns and the annual net income of each company (in millions of dollars): So company A holds 71 % of its own stock, 8 % of the stock in company B , 3 % of the stock in company C .etc. For the purpose of assessing a state tax on corporate income, the taxable income of each company is defined to be its share of its own annual net income plus its share of the taxable income of each of the other companies, as determined by the percentages in the table. What is the taxable income of each company (to the nearest thousand dollars)?
Solution Summary: The author calculates the taxable income of each company as A,B,CandD to the nearest thousand dollars.
Taxable income. As a result of several mergers and acquisitions, stock in four companies has been distributed among the companies. Each row of the following table gives the percentage of stock in the four companies that a particular company owns and the annual net income of each company (in millions of dollars):
So company
A
holds
71
%
of its own stock,
8
%
of the stock in company
B
,
3
%
of the stock in company
C
.etc. For the purpose of assessing a state tax on corporate income, the taxable income of each company is defined to be its share of its own annual net income plus its share of the taxable income of each of the other companies, as determined by the percentages in the table. What is the taxable income of each company (to the nearest thousand dollars)?
3. (i) Consider the following R code:
wilcox.test(UK Supermarkets $Salary ~ UKSupermarkets $Supermarket)
(a) Which test is being used in this code?
(b) What is the name of the dataset under consideration?
How would be adapt this code if we had ties? What other command
can be used which deals with ties?
(ii) Consider the following R code:
install packages("nortest")
library(nortest)
lillie.test (Differences)
(a) Assuming the appropriate dataset has been imported and attached,
what is wrong with this code?
(b) If this code were to be corrected, what would be determined by run-
ning it?
[3 Marks]
1. (i) Give the definition of a metric on a set X.
[5 Marks]
(ii) Let X = {a, b, c} and let a function d : XxX → [0, ∞) be defined
as d(a, a) = d(b,b) = d(c, c) 0, d(a, c) = d(c, a) 1, d(a, b) = d(b, a) = 4,
d(b, c) = d(c,b) = 2. Decide whether d is a metric on X. Justify your answer.
=
(iii) Consider a metric space (R, d.), where
=
[10 Marks]
0
if x = y,
d* (x, y)
5
if xy.
In the metric space (R, d*), describe:
(a) open ball B2(0) of radius 2 centred at 0;
(b) closed ball B5(0) of radius 5 centred at 0;
(c) sphere S10 (0) of radius 10 centred at 0.
[5 Marks]
[5 Marks]
[5 Marks]
(c) sphere S10 (0) of radius 10 centred at 0.
[5 Marks]
2. Let C([a, b]) be the metric space of continuous functions on the interval
[a, b] with the metric
doo (f,g)
=
max f(x)g(x)|.
xЄ[a,b]
= 1x. Find:
Let f(x) = 1 - x² and g(x):
(i) do(f, g) in C'([0, 1]);
(ii) do(f,g) in C([−1, 1]).
[20 Marks]
[20 Marks]
Chapter 4 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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