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Sloan [31]
3 years ago
12

A major convention center, whose floors are covered by a square carpet tiles with side lengths of 9 inches laid out in a 48 by 9

6 array, held a wild conference over the weekend. A local cleaning company was hired to clean the carpet tiles, given an offer of $0.05 per carpet square. The cleaners accepted the job, but not until after the convention center agreed to their counter of $0.10 per square foot. The cleaners were happy, because they knew they would be getting paid more than the convention center originally offered. How much more exactly?
A. $11.52
B. $28.80
C. $115.20
D. $201.60
Mathematics
1 answer:
bearhunter [10]3 years ago
4 0

Answer:

option B

$28.80

Step-by-step explanation:

Given the question,

side length of one square tile = 9 inches

area of square tile = l² = 9² = 81 inches²

<h3>Step1</h3>

There are 48(96) = 4608 carpet tiles, so the company was making 4608($.05) = $230.40.

<h3>Step2 </h3>

Now, the company countered with square feet. We have a total of 4608(81) = 373,248 square inches.

1 square foot = 144 square inches.

373,248/144 = 2592 square ft.

2592($.10) = $259.20

$259.20 - $230.40 = $28.80

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Answer: The distribution of the data set is positively skewed.

<u>Explanation: </u>

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For symmetric distribution, Mean = Median=Mode

For positively skewed distribution, Mean > Median>Mode

For negatively skewed distribution, Mean < Median

The mean of the given data set is given below:

Mean = \frac{27+23+22+38+43+24+25+23+22+54+31+30+29+48+27+25+29+28+26+33+25+21+23+34+20+23}{26}

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                =28.96

Now, the Median is:

To find the median we need to sort the data in ascending order as:

20,21,22,22,23,23,23,23,24,25,25,25,26,27,27,28,29,29,30,31,33,34,38,43,48,54

Median=\left(\frac{N+1}{2} \right)^{th} item

                   =\left(\frac{26+1}{2}\right)^{th} item

                   =13.5^{th} item

                   =26+0.5 \times (27-26)

                   =26.5

\therefore Median = 26.5

The mode is the most frequently occurring observation. Therefore the mode is:

Mode=23

Since the Mean >Median>Mode, therefore the distribution of the given data set is positively skewed.


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