B because a negative squared is always a positive and it has to be a negativ number less than -3 is less than 9 and if it is greater than 3 than it would make it untrue.
Answer:
Step-by-step explanation:
Given that :
St = the event that person is statistician
E = the event that person is Economist
Sh = the event that person is Shy
a. Briefly explain what key assumption is necessary to validly bring probability into the solution of this problem?
St and E are exclusive events since a person cannot be both statistician and economist.
Key Assumptions:
P(St) + P(E) = 1
Also;
P (St ∩ E) = ∅
b. Using the St. E and Sh notation, express the three numbers (80%, 15%, 90%) above and the probability we're solving for, in unconditional and conditional probability terms.
Given that :
80 % (0.8) of the statisticians are shy and also 15% (0.15) of the economist too are shy; Then :
![P(Sh|st) = 0.8](https://tex.z-dn.net/?f=P%28Sh%7Cst%29%20%3D%200.8)
![P(Sh|E) = 0.15](https://tex.z-dn.net/?f=P%28Sh%7CE%29%20%3D%200.15)
In the conference; it is stated that there are 90% economist ; Therefore:
P(E) = 0.9
P(St) = 0.1
c) Briefly explain why calculating the desired probability is a good job for Bayes's The- orem
From the foregoing; we knew the probability of
and asked to show that P(st|sh) = 0.37 ; Then using Bayes Theorem; we have:
![P(St|Sh) = \frac{P(St)*P(Sh|St)}{P(E)*P(Sh|E)*P(St)*P(Sh|St)} = 0.37](https://tex.z-dn.net/?f=P%28St%7CSh%29%20%3D%20%5Cfrac%7BP%28St%29%2AP%28Sh%7CSt%29%7D%7BP%28E%29%2AP%28Sh%7CE%29%2AP%28St%29%2AP%28Sh%7CSt%29%7D%20%3D%200.37)
![P(St|Sh) = \frac{0.1*0.8}{0.1*0.8+0.9*0.15} = 0.37](https://tex.z-dn.net/?f=P%28St%7CSh%29%20%3D%20%5Cfrac%7B0.1%2A0.8%7D%7B0.1%2A0.8%2B0.9%2A0.15%7D%20%3D%200.37)
![P(St|Sh) = \frac{0.08}{0.215} = 0.37](https://tex.z-dn.net/?f=P%28St%7CSh%29%20%3D%20%5Cfrac%7B0.08%7D%7B0.215%7D%20%3D%200.37)
As illustrated above; the required probability was determined using Bayes Theorem; Thus, calculating the desires probability is a good job for Bayes's The- orem.
Answer:
You can prove that these triangles are congruent by SSS axiom.
Step-by-step explanation:
- The co-ordinates of points of triangle ABC are: A(-3,4), B(-4,1), C(0,3).
- Measure the length of every side of triangle ABC and DEF by using distance formula i.e. AB, BC, AC, DF, DE and EF.
- The co-ordinates of points of triangle DEF are: D(0,2), E(3,1), F(2,-2).
- By calculating the distance you can see that, BC=DF, AB=DE=AC=EF.
- Hence all three sides are equal that means the triangles are congruent by the SSS (side-side-side) axiom.