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3 years ago

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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Step-by-step explanation:

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3 years ago

According to a study done by a university student, the probability a randomly selected individual will not cover his or her mou

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Complete Question

The complete question is shown on the first uploaded image

Answer:

$P(X = 8) = 0.0037$

$P(X < 5) = 0.805$

$P(X > 6) = 0.0206$

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

Hence for a randomly selected variable X we have that

$X \ \ \~ \ \ { B ( p , n )}$

The probability distribution function for binomial distribution is

$P(X = x ) = ^nC_x * p^x * (1 -p) ^{n-x}$

Considering question a

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

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

$P(X = 8) = 0.0037$

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

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

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

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

=> $P(X < 5) = 0.805$

Considering question c

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

$P(X > 6) = 1 - p(X \le 6)$