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Korolek [52]
3 years ago
15

The measure of five of of the interior angles of a hexagon are 150, 100, 80, 165, and 150. what is the measure of the sixth inte

rior angle?
please help it’s due soon and show the work!!
Mathematics
1 answer:
givi [52]3 years ago
7 0

Answer:

75°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6 , then

sum = 180° × 4 = 720°

let x be the sixth angle, then sum and equate to 720°

150 + 100 + 80 + 165 + 150 + x = 720

645 + x = 720 ( subtract 645 from both sides )

x = 75

The sixth interior angle is 75°

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3 years ago
Consider a sequence defined by the recursive rule f(1) = 15; f(n)=f(n - 1) - 6 for n 2. Choose True or
Shkiper50 [21]

Answer:

The second term of the sequence is 8  False ⇒ B

The third term of the sequence is 3  True ⇒ A

The fourth term of the sequence is -3  True ⇒ A

Step-by-step explanation:

The form of the recursive rule is:

f(1) = first term; f(n) = f(n - 1) + d, where

  • f(1) is the first term
  • f(n) is the nth term
  • f(n - 1) is the term before the nth term
  • d is the common difference

∵ f(1) = 15, f(n) = f(n - 1) - 6 for n ≥ 2

∴ The first term = 15

∴ d = -6

let us find the 2nd, 3rd, and 4th terms

∵ n = 2

∴ f(2) = f(1) - 6

∵ f(1) = 15

∴ f(2) = 15 - 6 = 9

∴ The second term is 9

∴ The second term of the sequence is 8  False

∵ n = 3

∴ f(3) = f(2) - 6

∵ f(2) = 9

∴ f(3) = 9 - 6 = 3

∴ The third term is 3

∴ The third term of the sequence is 3 True

∵ n = 4

∴ f(4) = f(3) - 6

∵ f(3) = 3

∴ f(4) = 3 - 6 = -3

∴ The fourth term is -3

∴ The fourth term of the sequence is -3 True

5 0
3 years ago
A recent survey found that 7575​% of all adults over 50 wear glasses for driving. In a random sample of 4040 adults over​ 50, wh
malfutka [58]

Answer:

Mean = 30

standard Deviation = 2.74

Step-by-step explanation:

Formula

mean = np

Standard Deviation = \sqrt{npq}

from the question = 40

P = 75% or 0.75

q = 1 - p = 1 - 75% or 1 - 0.75

To find mean

mean = 40 x 0.75

           = 30

For Standard Deviation (SD)

Standard Deviation = \sqrt{npq}

       = \sqrt{40 X 0.75 X 0.25

      = \sqrt{7.5}

:. Standard  Deviation       = 2.74

5 0
3 years ago
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