The probability is 1/5, 1:4(favorable), or 4:1 (unfavorable)
Hope this helps
Obtuse, it does not fit Pythagoreans for a right triangle, two sides are not equal to be isosceles
Solve for h: (I'm using the completing the square)
(x - 1) (x + 5) = K + (x - h)^2
(x - 1) (x + 5) = K + (x - h)^2 is equivalent to K + (x - h)^2 = (x - 1) (x + 5):
K + (x - h)^2 = (x - 1) (x + 5)
Subtract K from both sides:
(x - h)^2 = (x - 1) (x + 5) - K
Take the square root of both sides:
x - h = sqrt((x - 1) (x + 5) - K) or x - h = -sqrt((x - 1) (x + 5) - K)
Subtract x from both sides:
-h = sqrt((x - 1) (x + 5) - K) - x or x - h = -sqrt((x - 1) (x + 5) - K)
Multiply both sides by -1:
h = x - sqrt((x - 1) (x + 5) - K) or x - h = -sqrt((x - 1) (x + 5) - K)
Subtract x from both sides:
h = x - sqrt((x - 1) (x + 5) - K) or -h = -x - sqrt((x - 1) (x + 5) - K)
Multiply both sides by -1:
Answer: h = x - sqrt((x - 1) (x + 5) - K) or h = x + sqrt((x - 1) (x + 5) - K)
Solve for h: using the quadratic formula)
(x - 1) (x + 5) = K + (x - h)^2
(x - 1) (x + 5) = K + (x - h)^2 is equivalent to K + (x - h)^2 = (x - 1) (x + 5):
K + (x - h)^2 = (x - 1) (x + 5)
Expand out terms of the left hand side:
h^2 + K - 2 h x + x^2 = (x - 1) (x + 5)
Subtract (x - 1) (x + 5) from both sides:
h^2 + K - 2 h x + x^2 - (x - 1) (x + 5) = 0
h = (2 x ± sqrt(4 x^2 - 4 (K + x^2 - (x - 1) (x + 5))))/2:
<span>Answer: h = x + sqrt(-5 - K + 4 x + x^2) or h = x - sqrt(-5 - K + 4 x + x^2)</span>
Answer:
The probability is 5/11
Step-by-step explanation:
Let's call V the event that the letter taken at random is a vowel.
Let's call E the event that the man is English and A to the event that the man is American.
If 40 percent of the English-speaking men at the hotel are English means P(E)=0.40 and 60 percent are Americans means P(A)=0.60
In ''color'' we have 2 vowels out of 5 letters so P(V/A)=2/5
In ''colour'' we have 3 vowels out of 6 letters so P(V/E)=3/6=1/2
P(E/V)=P(E∩ V)/P(V)
P(V)=P(V|E)P(E) +P(V|A)P(A)
P(V)=(1/2)0.40+(2/5)0.60=0.44
P(E∩V)=P(V|E)P(E)=(1/2)0.40=0.20
P(E/V)=0.20/0.44=0.45454545=5/11
