What is the volume of the geometric solid produced by the triangle below
1 answer:
Answer:
The volume of the geometric solid produced is 391 cubic cm ⇒ A
Step-by-step explanation:
<em>When a </em><em>right triangle is rotated about its vertical leg 360°</em><em>, then it formed </em><em>a cone</em><em> its radius is the horizontal leg of the triangle and its height is the vertical lege of the triangle.</em>
The rule of the volume of the cone is V = π r² h, where
- r is the radius of its base
- h is the length of its height
∵ Triangle XYZ is rotated 360° about the vertical side YZ
∴ It formed a cone with a radius = XZ and a height = YZ
∵
∵ YX = 6√3
∴
∵ tan(60) = √3
∴ = √3
→ By using cross multiplication
∴ 6√3 = XZ(√3)
→ Divide both sides by √3
∴ 6 = XZ
∵ XZ = r and YZ = h
∴ r = 6 and h = 6√3
→ By using the rule of the cone above
∵ V = (π) (6)² (6√3)
∴ V ≅ 391 cm³
∴ The volume of the geometric solid produced is 391 cubic cm
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Answer:
Explained below.
Step-by-step explanation:
The complete question is:
Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.30 and P(B) =0.40.
What is P(A and B)?
What is P(A | B)?
Is P(A | B) equal to P(A)?
Are events A and B dependent or independent?
A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate?
What general conclusion would you make about mutually exclusive and independent events given the results of this problem?
Solution:
The probability of the two events <em>A</em> and <em>B</em> are:
P(A) = 0.30 and P(B) =0.40
(a)
Compute the value of P (A ∩ B) as follows:
This is because mutually exclusive events are those events that cannot occur together.
(b)
Compute the value of P (A | B) as follows:
Thus, the value of P (A | B) is 0.
(c)
No, P (A | B) is not equal to the P (A).
(d)
As mentioned in part (a), mutually exclusive events are those events which cannot occur together.
That is, .
Events A and B are independent if the chance of their concurrent happening is equivalent to the multiplication of their distinct probabilities.
That is, .
The concepts of mutually exclusive events and independent events are not the same.
(e)
As the it is provided that A and B are mutually exclusive events, we know that .
Now compute the value of as follows:
Thus, the events A and B are not independent.
Thus, if two events are mutually exclusive events they cannot be independent.