Given three points, there is one line that can be drawn through them if the points are colinear. If the three points are noncolinear,there are three lines that can be drawn through pairs of points. For three points, three is the greatest number of lines that can be drawn through pairs of points. Determine the greatest number of lines that can be drawn for four points, five points, and six points in a plane. Gerneralize for n points.

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Solution. The greatest number of lines that can be drawn for four points, ...

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The relationship between non-colinear points and lines drawn through them is investigated and generalized. The explanation is concise.

Using Excel, prepare a frequency distribution from the data you've been collecting.
Calculate the Standard Deviation of your data.
Is this a normal distribution?
What are the implications?

Indicate whether the given points below are on line 1, on line 2, on both line 1 and line 2, or on neither one of the two lines:
Line 1: -4x -y+3=0
Line 2: 4x +3y -1=0
(x,y).............Line 1...........Line 2.........Both Lines..........Neither Line
( 1,-1)
(2,-5)
(4, 6)

Consider function
f(x) = -x^2 +2x and points P1 = (0, 0), P2 = (1, 1) and P3 = (2, 0). Find equations
of:
- secant lines to f through every pair of these points (3 pairs), and
- tangent lines to f at each of these points.

Please help me with these problems and please show all work and steps to your solutions. This will help me better understand the problems once I have the answer and the steps for it. Thanks!
Please show work
1. How do we write the equation of a horizontal line? What would be an example?
2. How do we write the equation of

A month of sales data are collected on sales of different types of computer products.
Run the t-tests to determine:
A. Is there a difference in the total sales numbers for laptops versus desktops?
B. Is there a dfifference in the total sales numbers for components versus desktops?
Laptop

1. Construct a model of incidence geometry that has neither the elliptic hyperbolic nor Euclidean parallel properties.
2. Consider a finite geometry where the points are interpreted to be the six vertices of a regular octedron and the lines are sets of exactly two points.
see attached

A single line divides a plane into two regions. Two lines (by crossing) can divide a plane into four regions, three lines can divide it into seven regions. Let psubn be the max number of regions into which n lines divide a plane where n is a positive integer.

Find the possible failures in the column picture and the row picture, and match them up. Success would be 3 columns whose combinations give every vector b, which matches with 3 planes in the row picture that intersect at one point (the unique solution x). Give numerical examples of these two types of failure:
a. 3 columns lie

For the first 5 questions, consider the set of intersection points of two equations, and let a1 be the number of distinct affine real intersections with multiplicity one, let a2 be the number of distinct affine real intersections with multiplicity two, let b be the numberof distint complex non-real affine intersections and let