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Tatiana [17]
3 years ago
12

Need help step by step plz

Mathematics
1 answer:
yulyashka [42]3 years ago
8 0

I'm assuming D is the center of the circle.  See the new figure.

Angle BDC = 106 degrees, that's the definition of arc measure.

Triangle BDC is isosceles (two radii make congruent sides) so the two remaining angles in BDC are equal, DBC=DCB=(180-106)/2=37 degrees.

Angle BAC = 106/2 = 53 degrees, subtending the arc of 106 degrees.

Angle CAD = 53/2 = 26.5 degrees because AD is a bisector, the shared hypotenuse of congruent right triangles AED and AFD.

AFD is also congruent to CFD, so angle DCA is also 26.5 degrees

Angle ACB is the sum of DCA and DCB, ACB = 26.5 + 37 = 63.5 degrees

The angle subtends the arc we seek, whose measure must be double:

10x - 23 = 2(63.5) = 127 degrees

10x = 150

x = 15

Answer: 15

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The complete question is shown on the first uploaded image

Answer:

a

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b

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I would be surprised because the value is very small , less the 0.05

Step-by-step explanation:

From the question we are told that

The probability a randomly selected individual will not cover his or her mouth when sneezing is p = 0.267

Generally data collected from this study follows  binomial  distribution because the number of trials is  finite , there are only two outcomes, (covering  , and  not covering mouth when sneezing ) , the trial are independent

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   X \ \ \~ \ \ { B ( p , n )}

The probability distribution function for binomial  distribution is  

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Generally the  the probability that among 12 randomly observed individuals exactly 8 do not cover their mouth when​ sneezing is mathematically represented as

     P(X = 8) =  ^{12} C_8 *  (0.267)^8 *  (1- 0.267)^{12-8}

Here C denotes  combination

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     P(X = 8) =  495  *  0.000025828 * 0.28867947

    P(X = 8) =  0.0037

Considering question b

Generally the probability that among 12 randomly observed individuals fewer than 5 do not cover their mouth when​ sneezing is mathematically represented as

     P(X <  5 ) =[P(X = 0 ) + \cdots + P(X = 4)]

=>   P(X <  5 ) =[ ^{12} C_0 *  (0.267)^0 *  (1- 0.267)^{12-0} + \cdots +  ^{12} C_4 *  (0.267)^4 *  (1- 0.267)^{12-4} ]

=> P(X <  5 )  =  0.02406 +  0.10516 + 0.21067 + 0.25580 + 0.20964

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Generally the probability that fewer than half(6) covered their mouth when​ sneezing(i.e the probability the greater than half do not cover their mouth when sneezing) is mathematically represented as

      P(X > 6) =  1 - p(X \le  6)

=>    P(X > 6) = 1 - [P(X = 0) + \cdots + P(X =6)]

=>    P(X > 6)=1 - [^{12} C_0 *  (0.267)^0 *  (1- 0.267)^{12-0}+ \cdots + ^{12} C_4 *  (0.267)^6 *  (1- 0.267)^{12-6} ]

=>    P(X > 6)= 1 - [0.02406 + \cdots + 0.0519 ]  

=>    P(X > 6) =  0.0206

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