Inequalities

 

Question 1: (3 points)
Solve the inequality.
Enter the exact answer in interval notation.
To enter , type infinity. To enter , type U. For example, to enter , type (-infinity, 100].
__________
Question 2: (3 points)
Solve the compound inequality.
Enter the exact answer in interval notation.
To enter , type infinity. To enter , type U. For example, to enter , enter (-infinity, 99) U ([101, infinity).
5x − 13 ≤ 7
∞ ∪ (−∞, 100]
3x + 2 > 2x − 3 > x − 14
∞ ∪ (−∞, 99) ∪ [101,∞)
Southern New Hampshire University – 1/19/21, 4:06 PM
file:///Users/laureenbaddoo/Desktop/Math%20Assignment.webarchive Page 2 of 10
__________
Question 3: (3 points)
A basic cellular package costs /month for minutes of calling with an additional charge of /minute beyond that time. The
cost function for using minutes would be
If you used 60 minutes or less, i.e. if if , then (the base charge).
If you used more than 60 minutes, i.e. minutes more than the plan came with, you would pay an additional for
each of those minutes. Your total bill would be .
If you want to keep your bill at or lower for the month, what is the maximum number of calling minutes you can use?
The maximum calling minutes you can use is ____________ minutes.
Question 4: (6 points)
Answer the functions questions below.
a. Determine whether the relation represents as a function of .
(a) Yes, the relation represents a function.
(b) No, the relation does not represent a function.
b. Determine whether the relation represents as a function of .
(a) Yes, the relation represents a function

 

Sample Solution

As is widely known, economic operators in the internal market are at liberty to make use of their rights under EU law and move freely throughout the Union. However, not all thrive towards the same end; some merely abuse the rights conferred upon them by Union law solely for their own benefit, to the detriment of their home Member States. This makes identifying the line between use and abuse of rights in EU law an often difficult task.

The system of value-added tax in the EU is one which is vulnerable to abuse. Though the area has reached a high level of harmonisation, the EU is still presented with the challenge of constructing a single market consisting of 28 different value-added tax (VAT) systems, which withstands various attempts to obtain benefits for which it was not designed.

The Court has often used the aforementioned principle of abuse of EU law as a tool with which to combat fraud in the form of denying rights relied on from the VAT Directive, where such rights are derived in cases of established tax fraud or where there has been a failure to comply with the conditions of good faith.

Of particular interest to this paper is the extent to which a general principle may emerge, and whether the principle of prohibition of abuse of EU law may be regarded as a constitutional general principle of EU law. This will be done by examining the relevant case law of the Court and the recent trends, which, in the opinion of the author, confirm the notion that there is one general principle of abuse of EU law.

Part I: The Notion of Abuse in EU law
Early linguistic discrepancies notwithstanding, the author contends that there is indeed only one concept of abuse. This will be highlighted by the willingness of the Court to s

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