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Elenna [48]
3 years ago
15

Find the coordinates of the point 7/10 of the way from A to B A=(-4,-7) B=(12,5)p

Mathematics
1 answer:
mars1129 [50]3 years ago
4 0

Answer:

a=(-3,-6) and b=(12,4)

from -3 to 12 is 15 units

7/10 * 15=10.5

add 10.5 to -3 to get 7.5 for the x-coordinate

from -6 to 4 is 10 units

7/10 * 10=7

add 7 to -6 to get 1 for the y-coordinate

the point 7/10 of the way from a to b is (7.5,1) ANSWER

graph these points to check your answer (the point (7.5,1) is on the line segment AB))

also, the distance from a to b is 18.0277

7/10 of this is 12.62

the distance from (-3,-6) to (7.5,1) is also 12.62

Step-by-step explanation:

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According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not
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Answer and Step-by-step explanation:

From the question statement we get know that it is Binomial distribution because there are only two possible outcomes so we need to use Binomial Probability Distribution for this question.

Formula for the Binomial Probability Distribution:

P(X)=   p^x q^(n-x)

Where,

  • C_x^n=n!/(n-x)!x!   (i.e. combination)
  • x= total number of successes
  • p=probability of success (p=1-q)  
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Answer and explanation for each part of the question are as follow:

a.What is the probability that among 10 randomly observed individuals exactly 4 do not cover their mouth when sneezing?

Solution:

Given that

n=10  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=4 (number of successes i.e. individuals not covering their mouths)

C_x^n=n!/(n-x)!x!=10!/(10-4)!4!=210

P(X)=C_x^n   p^x q^(n-x)=210×〖(0.267)〗^4×〖0.733〗^(10-4)

P(X)=210×0.00508×0.155  

P(X)=0.165465  

b. What is the probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth when sneezing?

Solution:

Given that

n=10  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=3 (number of successes i.e. individuals not covering their mouths)

C_x^n=n!/(n-x)!x!=10!/(10-3)!3!=120

P(X)=C_x^n   p^x q^(n-x)=120×(0.267)^3×〖0.733〗^(10-3)

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c. Would you be surprised if, after observing 18 individuals, fewer than half covered their mouth when sneezing? why?

Solution:

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n=18  

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q=1-0.267=0.733  

x=9 (x is the number of successes “number of individuals not covering their mouths when sneezing”, if less than half cover their mouth then more than half will not cover), so let x=9

C_x^n=n!/(n-x)!x!=18!/(18-9)!9!=48620

P(X)=48620×(0.267)^9×〖0.733〗^(18-9)  

P(X)=48620×0.00000689×0.0610  

P(X)=0.020  

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