The key features of a quadratic graph that can identified are; x and y intercepts, axis of symmetry and vertex
<h3>Keys features of a quadratic graph</h3>
The key features are the x-intercepts, y-intercepts, axis of symmetry, and the vertex.
If we add units we can move this function upwards, downwards leftwards and rightwards.
- If we add a positive number to the x-variable, then the graph will move to the left.
- If we add a negative number to the x-variable, then the graph will move to the right.
- If we add a positive number to y-variable, then the graph will move upwards.
- If we add a negative number to y-variable, then the graph will move downwards.
Hence, if we compare the rules we use before with linear function, there's no distinction between horizontal and vertical movements, because if we add to x-variable, then y-variable will be also affected.
Learn more about quadratic graphs here:
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Answer:
See the proof below.
Step-by-step explanation:
Assuming this complete question: "For each given p, let Z have a binomial distribution with parameters p and N. Suppose that N is itself binomially distributed with parameters q and M. Formulate Z as a random sum and show that Z has a binomial distribution with parameters pq and M."
Solution to the problem
For this case we can assume that we have N independent variables 
with the following distribution:
bernoulli on this case with probability of success p, and all the N variables are independent distributed. We can define the random variable Z like this:
From the info given we know that 
We need to proof that 
by the definition of binomial random variable then we need to show that:
The deduction is based on the definition of independent random variables, we can do this:
And for the variance of Z we can do this:
![Var(Z)_ = E(N) Var(X) + Var (N) [E(X)]^2](https://tex.z-dn.net/?f=%20Var%28Z%29_%20%3D%20E%28N%29%20Var%28X%29%20%2B%20Var%20%28N%29%20%5BE%28X%29%5D%5E2%20)
![Var(Z) =Mpq [p(1-p)] + Mq(1-q) p^2](https://tex.z-dn.net/?f=%20Var%28Z%29%20%3DMpq%20%5Bp%281-p%29%5D%20%2B%20Mq%281-q%29%20p%5E2)
And if we take common factor 
we got:
![Var(Z) =Mpq [(1-p) + (1-q)p]= Mpq[1-p +p-pq]= Mpq[1-pq]](https://tex.z-dn.net/?f=%20Var%28Z%29%20%3DMpq%20%5B%281-p%29%20%2B%20%281-q%29p%5D%3D%20Mpq%5B1-p%20%2Bp-pq%5D%3D%20Mpq%5B1-pq%5D)
And as we can see then we can conclude that
Commutative because your switching the order
This question is incomplete, the complete question is;
For what value of a is the volume of the tetrahedron formed by the coordinate planes and the plane (x/a) + (y/10) + (z/6) = 1 equal to 10?
Answer: the value of a is 1
Step-by-step explanation:
Given that;
Volume of tetrahedron bounded by plane (x/a) + (y/10) + (z/6) = 1
and coordinate plane is; V = 1/6|abc|
(x/a) + (y/10) + (z/6) = 1
volume = 10
so
10 = 1/6 | a × 10 × 6 |
60 = a × 10 × 6
60 = 60a
a = 60 / 60
a = 1
Therefore the value of a is 1
Answer:
backflip cartwheel
Step-by-step explanation:
