m□ebd=4 x-8 and m□ebc=5 x+20
This is solvable only if e b is the initial side and b d and b c lies on opposite side of each other and lies on a line i.e c,b,d are Collinear.
∠ebd and ∠ebc will form a linear pair.The meaning of linear pair is that angles forming on one side of a straight line through a common vertex which are adjacent is 180°.
i.e
∠ ebd + ∠ebc = 180°
4 x- 8 + 5x + 20= 180°
adding like terms
⇒ 9 x +12 =180°
⇒ 9 x = 180° - 12
⇒ 9 x = 168°
⇒ x =( 168/9)°=(56/3)°
now m□ebc =5 x +20
= 5 × 56/3 + 20
= 280/3 + 20
=340/3
m□ebc=( 340/3)°
So, solution set is x =(56/3)° and m□ebc =(340/3)°
Answer:
=(k−1)*P(X>k−1) or (k−1)365k(365k−1)(k−1)!
Step-by-step explanation:
First of all, we need to find PMF
Let X = k represent the case in which there is no birthday match within (k-1) people
However, there is a birthday match when kth person arrives
Hence, there is 365^k possibilities in birthday arrangements
Supposing (k-1) dates are placed on specific days in a year
Pick one of k-1 of them & make it the date of the kth person that arrives, then:
The CDF is P(X≤k)=(1−(365k)k)/!365k, so the can obtain the PMF by
P(X=k) =P (X≤k) − P(X≤k−1)=(1−(365k)k!/365^k)−(1−(365k−1)(k−1)!/365^(k−1))=
(k−1)/365^k * (365k−1) * (k−1)!
=(k−1)*(1−P(X≤k−1))
=(k−1)*P(X>k−1)
Answer:
38
Step-by-step explanation:
We can express the 8th term as x and the 12th term as y.
This would mean that 8x=12y
Because the common difference between terms is -2 and term 8 and term 12 are 4 terms apart, this means that the 12th term is 8 less than the 8th term, so x-8=y
Now we can use this to substitute y with x in the first equation. This would give us:
8x=12(x-8)
Which we can expand and solve:
8x=12x-96
-4x=-96
Therefore x=24
This means the 8th term is 24 and the 12th term is 16 (24-8).
To test if this is correct we can do:
8x24=12x16
Which indeed are equal, both sides multiply to 192.
Now that we have our 8th term, we can find the 1st term, which is 7 terms away, therefore we just add 14 to the 8th term 24. (7x2=14)
24+14=38.
The first term is 38.
Hope this helped!
