6.24%200 show your work?
2 answers:
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Answer:
a) Expected value = 6.406
Variance = 4.905
Standard deviation = 2.45
b) The probability is 0.08547
Step-by-step explanation:
a) Let's suppose that:
X₁ = number of 6´s
X₂ = number of Jack, Queen, King or Aces
The mean of X₁ is:
MeanX₁ = n * p = 20 * (1/6) = 3.33
The variance of X₁ is:
The mean of X₂ is:
MeanX₂ = 10 * (16/52) = 3.076
The variance of X₂ is:
The expect value of X is:
Xexp = MeanX₁ + MeanX₂ = 3.33 + 3.076 = 6.406
The variance of X is:
VarX = VarX₁ + VarX₂ = 2.775 + 2.13 = 4.905
The standard deviation is:
Xdevi = 4.905/2 = 2.45
b) The probability of drawing at least five six out of 20 rolls is equal to:
∑(1/6)ˣ(5/6)²⁰⁻ˣ = 0.231 with x = 5
The probability of at least 4 Jack, Queen, Kings or Aces is:
∑(16/52)ˣ(1-(16/52))¹⁰⁻ˣ = 0.37 with x = 4
The probability of given event is equal to:
P = 0.231 * 0.37 = 0.08547
Answer:
The answer to your question is
Step-by-step explanation:
Data
Foci (-2, 2) (4, 2)
Major axis = 10
Process
1.- Plot the foci to determine if the ellipse is vertical or horizontal. See the picture below.
From the graph we conclude that it is a horizontal ellipse.
2.- Determine the foci axis (distance between the foci)
2c = 6
c = 6/2
c = 3
3.- Determine a
2a = 10
a = 10/2
a = 5
4.- Determine b using the Pythagorean theorem
a² = b² + c²
-Solve for b
b² = a² - c²
b² = 5² - 3²
b² = 25 - 9
b² = 16
b = 4
5.- Find the center (1, 2) From the graph, it is in the middle of the foci
6.- Find the equation of the ellipse
