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postnew [5]
3 years ago
8

What is best definition of an exterior angle of a triangle

Mathematics
1 answer:
olga_2 [115]3 years ago
3 0

an angle that forms a linear pair with one of the interior angles of the trinagle.(Apex)

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According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not
Lorico [155]

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)  
  • q=probability of failure (q=1-p)
  • n=number of trials
  • P(X)= probability of total number of successes

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)

P(X)=120×0.01903×0.1136  

P(X)=0.25962  

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

Solution:

Given that

n=18  

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=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  

Yes, I am surprised that probability of less than 9 individuals covering their mouth when sneezing is 0.020. Which is extremely is small.

3 0
3 years ago
Given the regular price of an item and the discount rate, how do you find the discount?
Allisa [31]

Answer:

discount divided by the normal/actual

Step-by-step explanation:

5 0
3 years ago
Factor the expression.<br> 30-4n
zheka24 [161]
Hope this is what you are looking for the answer is 2(15-2n)
7 0
3 years ago
Read 2 more answers
One third of a number x is equal to 22 less the number. Write and solve an equation to find the number. What would be the whole
zheka24 [161]
1/3(x)=22-x
x/3=22-x
(x/3=22-x)3
3x=66-3x
6x=66
x=11
3 0
3 years ago
Mariana wears her winter coat when the temperature is colder than -4^{\circ}\text{C}−4 ∘ Cminus, 4, degrees, start text, C, end
Savatey [412]

Answer:

T < - 4°C

Step-by-step explanation:

Given that Mariana wears her coat only when temperature is colder than - 4°C

Recall that lower temperature values indicate higher degree of coldness ;

Hence, Mariana will only wear her coat when temperature values are lesser than - 4°C ; this means that the temperature at that period is colder than - 4°C.

Hence, the inequality expression which is only true for temperatures when Mariana wears her coat can be written as :

Temperature = T

T < - 4°C

5 0
3 years ago
Read 2 more answers
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