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What is a regression coefficient?

The regression coefficient can be derived from a data set using the least squares method. Least squares fits a line to a set of points by minimizing the sum of the squared distances of the points from the line, yielding the linear equation mx + b. In this equation, m is the regression coefficient and b is the point at which the line intersects the y-axis, called the intercept.\nThe value of the regression coefficient contains information about the relationship between the variables x and y. When m is large, y tends to increase more rapidly than x. The reverse is also true. When m is small, y t..

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What must one justify to prove that a quadrilateral ABCD is a parallelogram?

According to Wikipedia, in Euclidean geometry, a parallelogram is a simple quadrilateral, with four edges and four corners, characterized by its two pairs of parallel sides. Because of its parallel orientation, the opposite sides of a parallelogram are equal in length. The opposite angles of a parallelogram are also equal in measure. This congruence is proven by Euclid's parallel postulate, also known as Euclid's fifth postulate; it is part of Euclid's "Elements," which serves as the basis for the shortest method of proof previously described.\nThe basic definition of a parallel..

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How do you evaluate algebraic expressions?

The order of operations is parentheses, exponents, multiplication, division, addition and subtraction. For an example expression, take 4x^2 + 3x + 9 where x = 5. Plugging the required value into the equation results in 4(5)^2 + 3(5) + 9. Exponents come first. When simplified, the expression is 4(25) + 15 + 9. Performing the required arithmetic yields the result of this expression to be 124. Remember that if a parenthetical term has an exponent outside it, you should simplify the term first before applying the exponent; exponents do not distribute over addition.\nEvaluating algebraic expression..

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What is a 12-sided polygon called?

A polygon refers to any two-dimensional shape that consists of only straight edges and has a closed shape. The most common polygons are those with a small amount of sides, such as triangles with three sides and squares with four sides. A dodecagon has 12 straight edges in a closed loop along with 12 vertices where the edges meet.

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What is the definition of the term "vector quantity"?

An example of a vector quantity that should be very familiar is an expression like "go 10 miles east" when offering directions. In this example, 10 is the quantity and east is the direction. Both the direction and magnitude of the movement are necessary to get the person needing directions to the right location.\nVector quantities are used extensively throughout physics to describe physical systems and to calculate the effects that different parts of the system have upon one another. Examples of vector quantities used in physics include velocity, acceleration, force, lift and weight.\nIn physi..

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Why do you use graphs and charts?

Statistics helps make data understandable to people. Computers can understand lists easily; humans cannot. While statistical values, like averages and medians, can relay some information, they do not show patterns in a set of data. Charts and graphs do.\nHumans are able to detect complex patterns. In fact, humans are often better able to see patterns than modern computer programs. When presented with a graph or a chart, people can often see trends. These trends can be upward or downward, and they can even be cyclical. If the data is presented on a table, however, detecting these patterns is fa..

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What is the way to find the derivative of 10x?

Applying the power rule to 10x^1, the derivative is given as (10)(d/dx)(x^1) = (10)[ 1x^(1 -1)]. This can be written as 10(d/dx)(x^1) = (10)x^0 = 10. The power x^0 is equal to 1, so that the derivative of 10x is equal to 10.A derivative of a function, such as y = 10x, are useful for finding the slope of the function. In calculus, there are many different rules that apply to finding derivatives.One simple rule is that the derivative of a constant C is zero. Similarly, the derivative of 'x' is 1, or (d/dx)(x) = 1.Another method to solve for the derivative of 10x is to use this last rul..

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What is the square root of negative 4?

Mathematicians use the imaginary number "i" in these kinds of expressions to make simplifying negative radicals and performing other operations on them easier as well. The imaginary unit "i" represents the square root of -1.

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What is the precise definition of a limit in calculus?

A simple way to think of limits is to imagine a triangle in a circle. In the analogy, the circle represents the limit, while the triangle represents the input values or function. As the input changes into a square, then a heptagon, then an octagon, the shape inside the circle begins to look more like the circle around it. In mathematics, the input shape can get infinitely close to being a perfect circle like the limit circle, but it can never completely reach this stage. That is because there are an infinite number of mathematical possibilities to get close to the limit without ever actually r..

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How many degrees are in a hexagon?

If a hexagon has six equal side lengths and six angles that are also equal, then it is a regular hexagon. All other hexagonal-shaped polygons that do not conform to this definition are irregular hexagons. \nHexagons can be either convex or concave polygons. While a convex hexagon has all interior angles that are less than 180 degrees, a concave hexagon can have one or more interior angles that are greater than 180 degrees. Convex hexagons also have vertices that point outward, and concave hexagons can have at least one vertex that points inward.

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