Determine which equations below, when combined with the equation 3x-4y=2, would form a system with no solutions. Choose all that
2 answers:
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Given:
The power generated by an electrical circuit (in watts) as function of its current x (in amperes) is modeled by:
To find:
The current that will produce the maximum power.
Solution:
We have,
Here, leading coefficient is negative. So, it is a downward parabola.
Vertex of a downward parabola is the point of maxima.
If a parabola is , then
In the given function, a=-12 and b=120. So,
Putting x=5 in the given function, we get
Therefore, 5 watt current will produce the maximum power of 300 amperes.
Answer:
The population does not need to be normally distributed for the sampling distribution of to be approximately normally distributed. Because of the central limit theorem. The sampling distribution of
is approximately normal.
Step-by-step explanation:
We have a random sample of size from a population with
and
. Because n is large enough (i.e., n > 30) and
and
are both finite, we can apply the central limit theorem that tell us that the sampling distribution of
is approximatelly normally distributed, this independently of the distribution of the random sample.
is asymptotically normally distributed is another way to state this.