The following table shows the number, in millions, graduating from high school in the United States in a given year.t Year Number graduating (in millions) 2001 2003 2.85 2.98 2005 2007 3.11 3.24 (a) Find the slope of the linear function modeling high school graduations. (Round your answer to twio decimal places.) 0.065 v million per year Explain in practical terms the meaning of the slope. The slope means that every year the number graduating increases vv by about 0.085 v million. (b) Find a formula for a linear function that models these data. (Let t be the number of years since 2001 and N the number in millions graduating. Round the values to two decimal places.) N = 0.0651 + 2.85 (c) Express, using functional notation, the number graduating from high school in 2012. N(11 i Calculate that value. (Round your answer to two decimal places.) 3.50 V million students (d) The actual number graduating from high school in 1994 was about 2.52 million. Compare this with the value given by the formula in part (b) and with estimates using a formula derived from the table below. Year Number graduating (in millions) 1985 2.83 1987 2.65 1989 2.47 1991 2.29 Estimated number of graduates using data from this table. (Round your answer to two decimal places.) x million students Estimated number of graduates using formula derived in part (b). (Round your answer to two decimal places.) x million students Which table of data predicts the number of graduates closer to the actual value? O The formula derived from the table from part (d) is more accurate. • The formula derived from the table from part (b) is more accurate.
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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