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andre [41]
1 year ago
8

A professor went to a website for rating professors and looked up the quality rating and also the "easiness" of the six full-tim

e professors in onedepartment. The ratings are 1 (lowest quality) to 5 (highest quality) and 1 (hardest) to 5 (easiest). The numbers given are averages for eachprofessor. Assume the trend is linear, find the correlation, and comment on what it means.

Mathematics
1 answer:
Marat540 [252]1 year ago
7 0

We are asked to determine the correlation factor "r" of the given table. To do that we will first label the column for "Quality" as "x" and the column for "Easiness" as "y". Like this:

Now, we create another column with the product of "x" and "y". Like this:

Now, we will add another column with the squares of the values of "x". Like this:

Now, we add another column with the squares of the values of "y":

Now, we sum the values on each of the columns:

Now, to get the correlation factor we use the following formula:

r=\frac{n\Sigma xy-\Sigma x\Sigma y}{\sqrt{(n\Sigma x^2-(\Sigma x)^2)(n\Sigma y^2-(\Sigma y)^2)}}

Where:

\begin{gathered} \Sigma xy=\text{ sum of the column of xy} \\ \Sigma x=\text{ sum of the column x} \\ \Sigma y=\text{ sum of the column y} \\ \Sigma x^2=\text{ sum of the column x\textasciicircum2} \\ \Sigma y^2=\text{ sum of the column y\textasciicircum2} \\ n=\text{ number of rows} \end{gathered}

Now we substitute the values, we get:

r=\frac{\left(6)(70.56)-(25.2)(16.4\right)}{\sqrt{((6)(107.12)-(25.2)^2)((6)(47.82)-(16.4)^2)}}

Solving the operations:

r=0.858

Therefore, the correlation factor is 0.858. If the correlation factor approaches the values of +1, this means that there is a strong linear correlation between the variables "x" and "y" and this correlation tends to be with a positive slope.

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There will be 72 flowers in total in the large arrangement.

Step-by-step explanation:

No. of red flowers in vase = 4

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Using proportion;

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4:5::32:w

Product of extreme = Product of mean

4*w=32*5\\4w=160

Dividing both sides by 4

\frac{4w}{4}=\frac{160}{4}\\w=40

Total flowers in large arrangement = Red flowers + white flowers

Total flowers in large arrangement = 32 + 40 =72

There will be 72 flowers in total in the large arrangement.

Keywords: ratio, proportion

Learn more about ratios at:

  • brainly.com/question/4228574
  • brainly.com/question/4279146

#LearnwithBrainly

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Triangle ABD is congruent to triangle BDC by ASA because angle B in ABD  is 30 degrees. Then they give you BD which equals BD by the reflexive property. And finally angle D in ABD is also 30 degrees. In triangle BCD, angle B is 30 degrees, BD = BD, and angle D in BCD is 30 degress. So we have an angle (B), side (BD), and another angle (D)

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