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3 years ago

14

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

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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3 years ago

29. For all values of X,

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3 years ago

Solve for x the triangles are similar

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Answer:

x = 13

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

$\frac{DC}{DU}$ = $\frac{CB}{UT}$ , substitute values

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3 years ago

Determine the coordinates of the vertices of the triangle to compute the area of the triangle using the distance formula (round

Karo-lina-s [1.5K]

Answer:

1. D. $50\text{ units}^2$

2. D. 45 units.

Step-by-step explanation:

We have been two graphs.

1. To find the area of our given triangle we will use distance formula.

$\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Upon substituting coordinates of base line of our triangle we will get,

$\text{Base length of triangle}=\sqrt{(15-5)^2+(5-15)^2}$

$\text{Base length of triangle}=\sqrt{(10)^2+(-10)^2}$

$\text{Base length of triangle}=\sqrt{100+100}$

$\text{Base length of triangle}=\sqrt{200}$

$\text{Base length of triangle}=10\sqrt{2}$

Now let us find the height of triangle similarly.

$\text{Height of triangle}=\sqrt{(20-15)^2+(10-5)^2}$

$\text{Height of triangle}=\sqrt{(5)^2+(5)^2}$

$\text{Height of triangle}=\sqrt{25+25}$

$\text{Height of triangle}=\sqrt{50}$

$\text{Height of triangle}=5\sqrt{2}$

$\text{Area of triangle}=\frac{\text{Base*Height}}{2}$

$\text{Area of triangle}=\frac{10\sqrt{2}*5\sqrt{2}}{2}$

$\text{Area of triangle}=\frac{50*2}{2}$

$\text{Area of triangle}=50$

Therefore, area of our given triangle is 50 square units and option D is the correct choice.

2. Using distance formula we will find the length of large side of triangle as:

$\text{Large side of rectangle}=\sqrt{(14-1)^2+(21-8)^2}$

$\text{Large side of rectangle}=\sqrt{(13)^2+(13)^2}$

$\text{Large side of rectangle}=\sqrt{169+169}$

$\text{Large side of rectangle}=\sqrt{338}$

$\text{Large side of rectangle}=13\sqrt{2}$

$\text{Small side of rectangle}=\sqrt{(4-1)^2+(5-8)^2}$

$\text{Small side of rectangle}=\sqrt{(3)^2+(-3)^2}$

$\text{Small side of rectangle}=\sqrt{9+9}$

$\text{Small side of rectangle}=\sqrt{18}$

$\text{Small side of rectangle}=3\sqrt{2}$

$\text{Perimeter of rectangle}=2(\text{Length + Width)}$

$\text{Perimeter of rectangle}=2(13\sqrt{2}+3\sqrt{2}}$

$\text{Perimeter of rectangle}=2(16\sqrt{2}}$

$\text{Perimeter of rectangle}=32\sqrt{2}$

$\text{Perimeter of rectangle}=45.2548339959390416\approx 45$

Therefore, the perimeter of our given rectangle is 45 units and option D is the correct choice.

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