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1) Regression analysis is the analysis of the relationship between the arithmetic mean and the standard deviation. 2) The central difference formula is preferable to the forward difference formula for approximating a first derivative value, provided that sufficient data is available. 3) When applying Simpson's rule, dividing the interval of integration into 11 subintervals will give a better approximation than dividing it into 10 subintervals. 4) The formula f(t + h) - 2f(t) + f(t - h) gives an approximation of f ' '(t). 5) The secant method is a root-finding method that approximates f (the function whose root is sought) by a line joining two points known to be on the curve of f.
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Answer the following statement true (T) or false (F)
Write a static method blur(double[][] picture) that you could use on a part of a picture file to obscure a detail such as a person’s face or a license plate number. This method computes the weighted averages of the values in picture and returns them in a new two-dimensional array. To find a weighted average of a group of numbers, you count some of them more than others. Thus, you multiply each item by its weight, add these products together, and divide the result by the sum of the weights.
For each element in picture, compute the weighted average of the element and its immediate neighbors. Store the result in a new two-dimensional array in the same position that the element occupies in picture. This new array is the one the method returns. The neighbors of an element in picture can be above, below, to the left of, and to the right of it, either vertically, horizontally, or diagonally. So each weighted average in the new array will be a combination of up to nine values from the array picture. A corner value will use only four values: itself and three neighbors. An edge value will use only six values: itself and five neighbors. But an interior value will use nine values: itself and eight neighbors. So you will need to treat the corners and edges separately from the other cells.
To increase the accuracy of numerical integration methods, the interval is simply subdivided into a larger number of ____________________.
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