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xxMikexx [17]
3 years ago
14

Represent each set of data in a dot plot. Determine the median, mode, and range.

Mathematics
1 answer:
Kitty [74]3 years ago
5 0

Answer:

Median: 52

Mode: 52

Range: 20

Step-by-step explanation:

Median: is the center of the data, and you would find that by writing out each number of the data set from least to greatest and find the center.

But in this case there are two numbers in the center. 52, and 52.

You would then add those up and get 104

Then you would divide that by two and 54 as your median.

Mode: is the number that appears most in the data set. So when you written out the data set from least to greatest you can see what number appears the most. And in this problem I found out the answer was 52 because it appeared four time, which is more than any number that was in the data set.

Range: is the difference between the maximum and minimum number in a data set.

The maximum in this data set is 65

The minimum is 45

So 65 - 45 = 20

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To solve for the missing steps, let's rewrite first the problem.

Given:

In a plane, line m is perpendicular to line t or  m⟂t
                  line n is perpendicular to line t  or  n⟂t


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Prove that line m and n are parallel lines


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We know that line t is the transversal of the lines m and n.

With reference to the figure above, 

∠ 2 and ∠ 6 are right angles by definition of <u>perpendicular lines</u>. This states that if two lines are perpendicular with each other, they intersect at right angles.

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Therefore, line m and line n are parallel lines.
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<em>ANSWERS: perpendicular lines, corresponding</em>

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Find the vertices and foci of the hyperbola with equation quantity x plus one squared divided by sixteen minus the quantity of y
katrin2010 [14]

Answer:

The vertices are (3 , -5) , (-5 , -5)

The foci are (4 , -5) , (-6 , -5)

Step-by-step explanation:

* Lets study the equation of the hyperbola

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  center (h , k) and transverse axis parallel to the x-axis is

  (x - h)²/a² - (y - k)²/b² = 1

- The length of the transverse axis is 2 a

- The coordinates of the vertices are  (h  ±  a  ,  k)

- The coordinates of the foci are (h ± c , k), where c² = a² + b²

- The distance between the foci is  2c

* Now lets solve the problem

- The equation of the hyperbola is (x + 1)²/16 - (y + 5)²/9 = 1

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# a² = 16 ⇒ a = ± 4

# b² = 9 ⇒ b = ± 3

# h = -1

# k = -5

∵ The vertices are (h + a , k) , (h - a , k)

∴ The vertices are (-1 + 4 , -5) , (-1 - 4 , -5)

* The vertices are (3 , -5) , (-5 , -5)

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∴ c² = 16 + 9 = 25

∴ c = ± 5

∵ The foci are (h ± c , k)

∴ The foci are (-1 + 5 , -5) , (-1 - 5 , -5)

* The foci are (4 , -5) , (-6 , -5)

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