Find the slope of the line going through the points (-5, -10)
1 answer:
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Answer:
Range = 2460 dollars, Variance = 516414.6 , Standard deviation = 718.6199 dollars . There are two outliers and they are likely to have much of an effect on the measures of variation.
Step-by-step explanation:
The smallest value in the sample data is min = 50 dollars and the largest value is max = 2500 dollars, therefore, the range is Range = max - min = 2500 - 40 = 2460 dollars. On the other hand, the formula to compute the sample variance is where
is the sample mean, n is the sample size and the
are the sample values. In this case the sample variance is
= 516414.6
, the sample standard deviation is defined as the squared root of the sample variance, so, the sample standard deviation is s = 718.6199 dollars. There are two outliers because 1750 dollars and 2500 dollars are very different compared to the other values, these two numbers are very large and they are likely to have much of an effect on the measures of variation because these measures are sensible to outliers, they are no robust measures.
The characteristic solution follows from solving the characteristic equation,
so that
A guess for the particular solution may be
, but this is already contained within the characteristic solution. We require a set of linearly independent solutions, so we can look to
which has second derivative
Substituting into the ODE, you have
Therefore the particular solution is
Note that you could have made a more precise guess of
but, of course, any solution of the form
is already accounted for within 
.
so that
A guess for the particular solution may be
which has second derivative
Substituting into the ODE, you have
Therefore the particular solution is
Note that you could have made a more precise guess of
but, of course, any solution of the form