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3 years ago

6

Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the equation of the line con

taining the points of tangency.

1 answer:

almond37 [142]3 years ago

4 0

Answer:

$y=-x+r$

Step-by-step explanation:

we know that

The tangency point on the x-axis is (r,0)

The tangency point on the y-axis is (0,r)

Find the slope of the line containing the points of tangency

$m=\frac{0-r}{r-0}=-1$

Remember that the equation of the line into slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-coordinate of the y-intercept

In this problem we have

$m=-1$

$b=r$

substitute

$y=-x+r$

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Complete Question

The complete question is shown on the first uploaded image

Answer:

a

$P(X = 8) = 0.0037$

b

$P(X < 5) = 0.805$

c

$P(X > 6) = 0.0206$

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

So

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

$P(X = 8) = 0.0037$

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

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

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

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

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

=> $P(X > 6) = 0.0206$

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

8 0

3 years ago