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natulia [17]
3 years ago
9

The table below shows the number of hours some business people in two states spend in meetings each week: State A 21 23 24 22 24

25 23 23 22 State B 24 22 20 23 23 50 20 46 21 Part A: Create a five-number summary and calculate the interquartile range for the two sets of data. (6 points) Part B: Are the box plots symmetric? Justify your answer. (4 points)
Mathematics
1 answer:
Lera25 [3.4K]3 years ago
6 0
State A:
21,22,22,23,23,23,24,24,25

minimum = 21
Q1 = 22
Q2(median) = 23
Q3 = 24
maximum = 25
IQR = Q3 - Q1 = 24 - 22 = 2

state B:
20,20,21,22,23,23,24,46,50
minimum = 20
Q1 = (20 + 21)/2 = 20.5
Q2(median) = 23
Q3 = (24 + 46)/2 = 35
maximum = 50
IQR = 35 - 20.5 = 14.5

I do not believe they are symmetrical....I think state B is skewed to the right
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Find the equation, (f(x) = a(x - h)2 + k), for a parabola containing point (2, -1) and having (4, -3) as a vertex. What is the s
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Answer:

f(x)=\frac{1}{2}x^2-4x+5

Step-by-step explanation:

A parabola is written in the form

f(x)=a((x-h)^2+k) (1)

where:

h is the x-coordinate of the vertex of the parabola

ak is the y-coordinate of the vertex of the parabola

a is a scale factor

For the parabola in the problem, we know that the vertex has  coordinates (4,-3), so we have:

h=4 (2)

ak=-3

From this last equation, we get that a=\frac{-3}{k} (3)

Substituting (2) and (3) into (1) we get the new expression:

f(x)=-\frac{3}{k}((x-4)^2+k) = -\frac{3}{k}(x-4)^2 -3 (4)

We also know that the parabola  contains the point (2,-1), so we can substitute

x = 2

f(x) = -1

Into eq.(4) and find the value of k:

-1=-\frac{3}{k}(2-4)^2-3\\-1=-\frac{3}{k}\cdot 4 -3\\2=-\frac{12}{k}\\k=-\frac{12}{2}=-6

So we also get:

a=-\frac{3}{k}=-\frac{3}{-6}=\frac{1}{2}

So the equation of the parabola is:

f(x)=\frac{1}{2}((x-4)^2 -6) (5)

Now we want to rewrite it in the standard form, i.e. in the form

f(x)=ax^2+bx+c

To do that, we simply rewrite (5) expliciting the various terms, we find:

f(x)=\frac{1}{2}((x^2-8x+16)-6)=\frac{1}{2}(x^2-8x+10)=\frac{1}{2}x^2-4x+5

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