Rock and roll is a form of music that evolved in the United States and quickly spread to the rest of the world. The interest in rock music, like any other genre, has gone through ups and downs over the years. The Recording Industry Association of America (RIAA) reports consumer trends on the basis of annual data on genre, format, age, and gender of purchasers and place of purchase. The accompanying table lists a portion of the percentage (share) of total shipment of music that falls in the category of rock music from 1991-2008. Year Share 1991 1992 34.8 31.6 2008 31.8 Source: www.riaa.com. B Click here for the Excel Data File The data are plotted below. 37- 35- 33 31- 29- 27- 25- 23 1996 1994 1998 2004 2002 1992 2000 200 2008 1990 a. Discuss the presence of random variations. OThe smoother appearance of the graph suggests the presence of random variations. OThe smoother appearance of the graph suggests the absence of random variations. OThe jagged appearance of the graph suggests the presence of random variations. OThe jagged appearance of the graph suggests the absence of random variations. b. Use the 3-period moving average to make a forecast for the share of rock music in 2009. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) 3-period moving average forecast for 2009 c. Use the 5-period moving average to make a forecast for the share of rock music in 2009. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) 5-period moving average forecast for 2009
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
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