Answer:
Step-by-step explanation:
Area = pi*r^2
Area = pi*9^2
Area =
Find the coordinate of the points of intersection of the graphs without building them: 20x - 15y = 100 and 3x - 5 =6y
2 answers:
9514 1404 393
Answer:
(x, y) = (7, 2 2/3)
Step-by-step explanation:
We can multiply the first equation by 2/5 to get ...
8x -6y = 40
The second equation gives an expression for 6y that we can substitute.
8x -(3x -5) = 40
5x +5 = 40 . . . . . eliminate parentheses
x +1 = 8 . . . . . . . .divide by 5
x = 7 . . . . . . . . . .subtract 1
Using the second equation, we find ...
3(7) -5 = 6y
y = 16/6 = 2 2/3
The coordinates of the point of intersection are (x, y) = (7, 2 2/3).
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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