Stocks The table presents the 2016 percentage change in the stock price for six well-known companies. (Data from: finance.yahoo.com .) Company Percentage Change American Express +10.6% Coca-Cola − 1.0 % ExxonMobil +14.9% Hewlett Packard +63.1% Ford − 5.7 % Red Robin Gourmet Burgers − 8.0 % Suppose that we wish to determine the difference in percentage change between two of the companies in the table, and suppose that we are interested only in the magnitude, or absolute value, of this difference. Then we subtract the two entries and find the absolute value. For example, the difference in percentage change of stock price for American Express and Ford is | 10.6 % − ( − 5.7 % ) | = 16.3 % Find the absolute value of the difference between the two indicated changes in stock price. American Express and Ford
Stocks The table presents the 2016 percentage change in the stock price for six well-known companies. (Data from: finance.yahoo.com .) Company Percentage Change American Express +10.6% Coca-Cola − 1.0 % ExxonMobil +14.9% Hewlett Packard +63.1% Ford − 5.7 % Red Robin Gourmet Burgers − 8.0 % Suppose that we wish to determine the difference in percentage change between two of the companies in the table, and suppose that we are interested only in the magnitude, or absolute value, of this difference. Then we subtract the two entries and find the absolute value. For example, the difference in percentage change of stock price for American Express and Ford is | 10.6 % − ( − 5.7 % ) | = 16.3 % Find the absolute value of the difference between the two indicated changes in stock price. American Express and Ford
Solution Summary: The author calculates the absolute value of the difference between the stock price of American Express and Ford.
Stocks The table presents the 2016 percentage change in the stock price for six well-known companies. (Data from:finance.yahoo.com.)
Company
Percentage Change
American Express
+10.6%
Coca-Cola
−
1.0
%
ExxonMobil
+14.9%
Hewlett Packard
+63.1%
Ford
−
5.7
%
Red Robin Gourmet Burgers
−
8.0
%
Suppose that we wish to determine the difference in percentage change between two of the companies in the table, and suppose that we are interested only in the magnitude, or absolute value, of this difference. Then we subtract the two entries and find the absolute value. For example, the difference in percentage change of stock price for American Express and Ford is
|
10.6
%
−
(
−
5.7
%
)
|
=
16.3
%
Find the absolute value of the difference between the two indicated changes in stock price.
1.
2.
Show that the following are not logically equivalent by finding a counterexample:
(p^q) →r and
(db) V (d←d)
Show that the following is not a contradiction by finding a counterexample:
(pV-q) AqA (pv¬q Vr)
3.
Here is a purported proof that (pq) ^ (q → p) = F:
(db) v (bd) = (db) v (bd)
=(qVp) A (g→p)
= (¬¬q V ¬p) ^ (q→ p)
(db) V (db) =
=¬(a→p)^(a→p)
= (gp) ^¬(a → p)
=F
(a) Show that (pq) ^ (q→p) and F are not logically equivalent by finding a counterex-
ample.
(b) Identify the error(s) in this proof and justify why they are errors. Justify the other steps
with their corresponding laws of propositional logic.
Question 2: When John started his first job, his first end-of-year salary was $82,500. In the following years, he received salary raises as shown in the following table.
Fill the Table: Fill the following table showing his end-of-year salary for each year. I have already provided the end-of-year salaries for the first three years. Calculate the end-of-year salaries for the remaining years using Excel. (If you Excel answer for the top 3 cells is not the same as the one in the following table, your formula / approach is incorrect) (2 points)
Geometric Mean of Salary Raises: Calculate the geometric mean of the salary raises using the percentage figures provided in the second column named “% Raise”. (The geometric mean for this calculation should be nearly identical to the arithmetic mean. If your answer deviates significantly from the mean, it's likely incorrect. 2 points)
Hint for the first part of question 2: To assist you with filling out the table in the first part of the question,…
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