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sesenic [268]
3 years ago
11

If the sum of the measures of interior angles of a regular convex polygon is 1620° how many sides does a polygon have find the m

easure of one interior angle and one exterior angle
Mathematics
2 answers:
Keith_Richards [23]3 years ago
7 0

Answer:

  • the polygon has 11 sides
  • one interior angle measures 147 3/11 degrees
  • one exterior angle measures 32 8/11 degrees

Step-by-step explanation:

The relation between the number of sides (n) and the total degree measure of interior angles is ...

  angle total = 180° × (n -2)

We can find n by filling in the given total and solving:

  1620 = 180(n -2)

  1620/180 = 9 = n -2

  9 + 2 = 11 = n

The number of sides is 11.

The measure of one interior angle is 1620°/11 = 147 3/11 degrees.

The measure of one exterior angle is 360°/11 = 32 8/11 degrees.

Mila [183]3 years ago
3 0

Answer:

Step-by-step explanation:

(n-2)180=1620

n-2=1620/180=9

n=9+2=11

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the performance score of 10 adults is recorded, and the results are 83 87 90 92 93 100 104 111 115 121 find the standard deviati
luda_lava [24]

Answer:

The standard deviation of the data set is \sigma = 12.7906.

Step-by-step explanation:

The Standard Deviation is a measure of how spread out numbers are. Its symbol is σ (the greek letter sigma)

To find the standard deviation of the following data set

\begin{array}{cccccccc}83&87&90&92&93&100&104&111\\115&121&&&&&&\end{array}

we use the following formula

                                             \sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} }

Step 1: Find the mean \left( \overline{X} \right).

The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:

                                     Mean = \frac{Sum ~ of ~ terms}{Number ~ of ~ terms}

Mean = \frac{Sum ~ of ~ terms}{Number ~ of ~ terms}=\frac{83+87+90+92+93+100+104+111+115+121}{10} \\\\Mean = \frac{996}{10} =\frac{498}{5}=99.6

Step 2: Create the below table.

Step 3: Find the sum of numbers in the last column to get.

\sum{\left(x_i - \overline{X}\right)^2} = 1472.4

Step 4: Calculate σ using the above formula.

\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} }       = \sqrt{ \frac{ 1472.4 }{ 10 - 1} } \approx 12.7906

3 0
3 years ago
A potter can make 24 vases in 8 days. If the potter works 6 hours each day, how long does it take to make one vase?
NikAS [45]
Answer: 2
Explaintion/
24/8 =3
6/3=2
7 0
3 years ago
In a bag of marbles 12% were blue 18% were green and the rest were purple if the bag has 150 marbles how many were blue or green
baherus [9]

Answer:

45

Step-by-step explanation:

12 % of the marbles are blue, and

18 % of the marbles are green, so

30 % of the marbles are either blue or green.

There are 150 marbles.

30 % × 150 = 0.30 × 150 = 45

The number of blue or green marbles is 45.

8 0
3 years ago
the length of a rectangle is 3 units shorter than one -third of the width, x. Which expression represents the perimeter of the r
Mariana [72]

Answer:

A) \frac{8}{3} x - 6

Step-by-step explanation:

Let the width of the rectangle be x units.

\therefore \: length \: of \: rectangle =  \frac{1}{3} x - 3 \\ Perimeter \: of \: rectangle  = 2(l + w) \\  = 2  \bigg( \frac{1}{3} x - 3 + x \bigg)\\  = 2  \bigg( x + \frac{1}{3} x - 3 \bigg)\\  = 2  \bigg(  \frac{3x + x}{3}  - 3 \bigg)\\  = 2  \bigg(  \frac{4x}{3}  - 3 \bigg) \\  = 2  \bigg(  \frac{4x}{3}  - 3 \bigg) \\  =   \frac{2 \times 4x}{3}  -2 \times  3  \\  \purple{ \bold{{Perimeter \: of \: rectangle   =  \frac{8}{3} x - 6}}}

8 0
3 years ago
Which of the following is used only in non-Euclidean geometry?
MatroZZZ [7]

Answer:c

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3 0
2 years ago
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