Answer:
x=45
Step-by-step explanation:
Answer:
ABC - AAS
DEF - not enough information
GHI - not enough information
JKL - SAS
Step-by-step explanation:
SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.
AAS postulate states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.
HL postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
ASA postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
SSS postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
1. In triangles MNO and ABC, there are two congruent sides and non-included angle - AAS
2. In triangles MNO and DEF, there are two congruent sides - there is not enough information
3. In triangles MNO and GHI, there are three congruent angles - there is not enough information
4. In triangles MNO and JKL, there are two congruent sides and included angle - SAS
Answer:18/5
Step-by-step explanation:
Answer:
Step-by-step explanation:
The model
, the number of planets found up to time
, as a Poisson process. So, the
has distribution of Poison distribution with parameter 
a)
The mean for a month is,
per month
![E[N(t)]= \lambda t\\\\=\frac{1}{3}(24)\\\\=8](https://tex.z-dn.net/?f=E%5BN%28t%29%5D%3D%20%5Clambda%20t%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B3%7D%3C%2Fp%3E%3Cp%3E%2824%29%5C%5C%5C%5C%3D8)
(Here. t = 24)
For Poisson process mean and variance are same,
![Var[N (t)]= Var[N(24)]\\= E [N (24)]\\=8](https://tex.z-dn.net/?f=Var%5BN%20%28t%29%5D%3D%20Var%5BN%2824%29%5D%5C%5C%3D%20E%20%5BN%20%2824%29%5D%5C%5C%3D8)
(Poisson distribution mean and variance equal)
The standard deviation of the number of planets is,
![\sigma( 24 )] =\sqrt{Var[ N(24)]}=\sqrt{8}= 2.828](https://tex.z-dn.net/?f=%5Csigma%28%2024%20%29%5D%20%3D%5Csqrt%7BVar%5B%20N%2824%29%5D%7D%3D%5Csqrt%7B8%7D%3D%202.828%3C%2Fp%3E%3Cp%3E)
b)
For the Poisson process the intervals between events(finding a new planet) have independent exponential distribution with parameter
. The sum of
of these independent exponential has distribution Gamma
.
From the given information,
and 
Calculate the expected value.

(Here,
and
)
C)
Calculate the probability that she will become eligible for the prize within one year.
Here, 1 year is equal to 12 months.
P(X ≤ 12) = (1/Г (k)λ^k)(x)^(k-1).(e)^(-x/λ)

Hence, the required probability is 0.2149 or 21.49%
The cost should be the same on day 3