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Anna [14]
3 years ago
8

The manager of the customer service division of a major consumer electronics company is interested in determining whether the cu

stomers who have purchased a media player made by the company over the past 12 months are satisfied with their products. Which of the following questions in the survey will NOT likely induce a measurement error?
A. How many times have you illegally copied copyrighted sporting events?
B. What is your exact annual income?
C. How many times have you failed to set the time on the media player?
D. How many times have you brought the media player back for service?
Mathematics
1 answer:
aniked [119]3 years ago
6 0

Answer:

Option D

Step-by-step explanation:

The objective of the survey is to assess the satisfaction level of the customers.

Out of the options given, option D is the closest to be used as a basis for gauging the satisfaction level of customers. Option A is irrelevant to the subject under discussion, as it is bears no semblance to the topic.

Option B also has this same tendency, and tend to view the satisfaction from the customers annual income, and not from the firm or its products. Using this definitely could give a measurement error.

Option C talks on inability of the user/customer of the media player to set the time. This failure is borne by the user, and not an inherent fault in the media player. As such, using this as a basis could lead to a measurement error.

Option D is the most suited for the survey.

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The Range is the difference between the lowest and highest values.

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Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe
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Answer:

The statement is true for every n between 0 and 77 and it is false for n\geq 78

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: \sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4

For n=1: \sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4

From this point we will assume that n\geq 2

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\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4

Now, we will use the formula for the sum of the first 4th powers:

\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}

Therefore:

\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0

and, because n \geq 0,

465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1

Observe that, because n \geq 2 and is an integer,

n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5

In concusion, the statement is true if and only if n is a non negative integer such that n\leq 77

So, 78 is the smallest value of n that does not satisfy the inequality.

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(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064

(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992

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