0.25: Rational
√0.25: Rational (=0.5)
√0.33: Irrational
Let x=ab=ac, and y=bc, and z=ad.
Since the perimeter of the triangle abc is 36, you have:
Perimeter of abc = 36
ab + ac + bc = 36
x + x + y = 36
(eq. 1) 2x + y = 36
The triangle is isosceles (it has two sides with equal length: ab and ac). The line perpendicular to the third side (bc) from the opposite vertex (a), divides that third side into two equal halves: the point d is the middle point of bc. This is a property of isosceles triangles, which is easily shown by similarity.
Hence, we have that bd = dc = bc/2 = y/2 (remember we called bc = y).
The perimeter of the triangle abd is 30:
Permiter of abd = 30
ab + bd + ad = 30
x + y/2 + z =30
(eq. 2) 2x + y + 2z = 60
So, we have two equations on x, y and z:
(eq.1) 2x + y = 36
(eq.2) 2x + y + 2z = 60
Substitute 2x + y by 36 from (eq.1) in (eq.2):
(eq.2') 36 + 2z = 60
And solve for z:
36 + 2z = 60 => 2z = 60 - 36 => 2z = 24 => z = 12
The measure of ad is 12.
If you prefer a less algebraic reasoning:
- The perimeter of abd is half the perimeter of abc plus the length of ad (since you have "cut" the triangle abc in two halves to obtain the triangle abd).
- Then, ad is the difference between the perimeter of abd and half the perimeter of abc:
ad = 30 - (36/2) = 30 - 18 = 12
Answer:
Step-by-step explanation:
Given that 10000 times a fair coin is flipped. Since fair coin prob for head of tail =0.5
If tail comes it will be taken as 1. Hence for the sum to be less than 5000, no of heads <5000
Since trials are large we approximate to normal with mean = np = 5000 and variance = np(1-p) = 2500
Thus no of heads x is normal with (5000, 50)
Since this prob is less than 0.5 only minimum amount to be bet i.e. 1 dollar
If sum of coins <5100, then Z = 
P(Z<2) = 0.9500
This time we can bet maximum of 100 dollars as probability is very high nearer to 1.
Answer:
Two ways you can group them is:
(4+7)+2
4+(7+2)
They will both give you the same answer of 13.
(4+7)+2 4+(7+2)
11+2= 13 4+9= 13
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