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In order for <em>F</em> to be conservative, there must be a scalar function <em>f</em> such that the gradient of <em>f</em> is equal to <em>F</em>. This means
Integrate both sides of the first equation with respect to <em>x</em> :
Differentiate both sides with respect to <em>y</em> :
But we assume <em>g</em> is a function of <em>y</em>, which means its derivative can't possibly contain <em>x</em>, so there is no scalar function <em>f</em> whose gradient is <em>F</em>. Therefore <em>F</em> is not conservative.
Answer:
47% is the statistic and 31% is the parameter.
Step-by-step explanation:
A parameter is a quantity of a variable representing certain characteristic of a population.
A statistic is a quantity of a variable representing certain characteristic of a sample.
The sample of parents of kindergartners selected is, <em>n</em> = 345.
The School records show that only 31% of parents of kindergartners sent their children to pre-kindergarten.
That is the population proportion is, <em>p</em> = 0.31.
This is the parameter value.
Of the 349 parents, 47% said they sent their children to pre-kindergarten.
That is the sample proportion is, = 0.47.
This is the statistic value.
Thus, the correct option is:
47% is the statistic and 31% is the parameter.