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Ymorist [56]
2 years ago
5

PLEASE HELP WILL MARK BRAINLIEST!!

Mathematics
1 answer:
noname [10]2 years ago
5 0

Answer:

m∠A = 91°

m∠B = 146°

m∠C = 89°

m∠D = 34°

Step-by-step explanation:

  • If the four vertices of a quadrilateral lie on the edge of a circle, then this quadrilateral is called cyclic quadrilateral
  • In the cyclic quadrilateral each two opposite angles are supplementary (means the sum of their measures is 180°)
  • The sum of the measures of the interior angles of any quadrilateral is 360°

In quadrilateral ABCD

∵ A, B, C, And D lie on the circumference of the circle

∴ ABCD is a cyclic quadrilateral

∴ The sum of the measures of each opposite angles is 180°

∵ ∠A and ∠C are opposite angle in the cyclic quadrilateral ABCD

∴ m∠A + m∠C = 180°

∵ m∠A = (2x + 3)°

∵ m∠C = (2x + 1)°

- Add them and equate the answer by 180

∴ (2x + 3) + (2x + 1) = 180

- Add the like terms in the left hand side

∴ 4x + 4 = 180

- Subtract 4 from both sides

∴ 4x = 176

- Divide both sides by 4

∴ x = 44

Substitute the value of x in the expressions of angle A, C, D

∵ m∠A = 2(44) + 3 = 88 + 3

∴ m∠A = 91°

∵ m∠C = 2(44) + 1 = 88 + 1

∴ m∠C = 89°

∵ m∠D = x - 10

∴ m∠D = 44 - 10

∴ m∠D = 34°

- ∠B and ∠D are opposite angles in the cyclic quadrilateral ABCD

∴ m∠B + m∠D = 180°

∴ m∠B + 34 = 180

- Subtract 34 from both sides

∴ m∠B = 146°

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avanturin [10]

Answer:

0 < x ≤ 12 and 0 < y ≤ 36

Step-by-step explanation:

Here,  x represents the number of female gazelles and y represents  the number of male gazelles.

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∵ The number of rooms must be more than or equal to the total female gazelles ,

12 ≥ x

Also, number of animals can not be negative,

And, it must be greater than 0.

⇒ 0 < x ≤ 12,

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Hence, the constraints to represent a thriving population of gazelles at the zoo are,

0 < x ≤ 12,

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gladu [14]

4x - y = 5 --> 4x = y + 5

substitute

4x + 4y = -4

(y + 5) + 4y = -4

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The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.4 minutes and a standard deviation of 3.5
Lorico [155]

Answer:

0.6672 is the required probability.            

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 8.4 minutes

Standard Deviation, σ = 3.5 minutes

We are given that the distribution of distribution of taxi and takeoff times is a bell shaped distribution that is a normal distribution.

According to central limit theorem the sum measurement of n is normal with mean \mu and standard deviation \sigma\sqrt{n}

Sample size, n = 37

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P(taxi and takeoff time will be less than 320 minutes)

P( \sum x < 320) = P( z < \displaystyle\frac{320 - 37(8.4)}{21.28}) = P(z < 0.4323)

Calculation the value from standard normal z table, we have,  

P(\sum x < 320) =0.6672 = 66.72\%

0.6672 is the probability  that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

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Answer:

8

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