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2 years ago

The box plots below show the distribution of salaries, in thousands, among employees of two small companies.

Mathematics

2 answers:

Shtirlitz [24]2 years ago

7 0

Answer:

Mean and IQR

Step-by-step explanation:

The measure of centre gives the central or the measure which gives the best mid term of a distribution. Based in the details of the box plot, the median is the value which divides the box in the box plot.

For company A:

Range = 25 to 80 with a median value at 30 ; this means the median does not give a good centre measure of the distribution ad it is very close to the minimum value. This goes for the Company B plot too; with values ranging from (35 to 90) and the median designated at 40.

Hence, the mean will be the best measure of centre rather Than the median in this case.

For the variability, the interquartile range would best suit the distribution. With the lower quartile and upper quartile both having reasonable width to the minimum and maximum value of the distribution.

jeyben [28]2 years ago

3 0

Answer:

Step-by-step explanation:

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Answer:

Part A)

The x-intercepts are (-1/4, 0) and (4, 0).

Part B)

The vertex is a maximum because the leading coefficient is negative.

The vertex is (1.875, 72.25).

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We can plot the zeros and the vertex, and connect them with a curve.

Step-by-step explanation:

The function given is:

$f(x)=-16x^2+60x+16$

Part A)

To find the x-intercepts of the function, set the function equal to 0 and solve for x:

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We can divide both sides by negative four:

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Factor:

$0=(4x+1)(x-4)$

Zero Product Property:

$x-4=0\text{ or } 4x+1=0$

Solve for each case:

$\displaystyle x=-\frac{1}{4}\text{ or }x=4$

Hence, our zeros are:

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Part B)

Note that the leading coefficient of our function is negative.

So, our function will be concave down.

Hence, our vertex will be the maximum.

The vertex is given by:

$\displaystyle \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$

In this case, a = -16, b = 60, and c = 16.

Find the x-coordinate of the vertex:

$\displaystyle x=-\frac{(60)}{2(-16)}=\frac{15}{8}=1.875$

Substitute this back into the function to find the y-coordinate:

$f(1.875)=-16(1.875)^2+60(1.875)+16=72.25$

Hence, our vertex is:

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Part C)

Since we already determined the zeros and the vertex, we can plot the two zeros and the vertex and draw a curve between the three points.

The graph is shown below. Again, to do this by hand, simply plot the three points and connect them with a parabola. If necessary, we can also find the y-intercept.

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