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| Center number (or average of 2 center numbers for even set) |
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| The number that occurs most frequently |
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| The greatest value in the set minus the least value. |
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Gen: is greater the more data are spread away from the mean.
For each number in set, X, (x-mean)2. Add the sum of these numbers. |
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| For each data value in a set, counting the number of its frequency. |
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| A collection of numbers or other objects. S={5,-1,0}; ABS(s)=3. A set can also be a subset of another set. |
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| The elements that are in a OR in b OR in both. Denoted as: aUb |
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| All elements that are contained in both a AND b. The shaded, shared part of a venn diagram. Denoted by A∩B. |
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| for sets S and T, the number of elements in their union (U)= ABS(SuT)=ABS(S)+ABS(T)-(SnT). The intersecting numbers are subtracted so that they aren't counted twice. |
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| Two sets are disjointed or mutually exclusive if they share no elements. Thus, ABS(SuT)=ABS(S)+ABS(T). |
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| Factorial for counting combinations |
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Factorials are useful for the ordering of objects, or permutations (i.e. combinations for A,b,c).
N!=N+(N-1)+(N-2), etc.
Permutation is a selection process in which objects are selected one by one in a certain order. |
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For a set of objects (n) where only some (k) are selected, and order doesn't matter.
The number of possible complete selections of k objects is the # of combinations of n objects taken k at a time, denoted by (n over k).
(n over k)=(n!)/((k!)(n-k)!). or (5 over 2)=5!/(2!3!)=120/(2*6)=10. |
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| (n over k)=(n over (n-k)). Because every set chosen corresponds to a set not chosen. (5 over 2)=10=(5 over 3). |
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| Discrete probability of an event |
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| P(E)=(the number of outcomes in E)/(the total number of possible outcomes). |
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| Outcomes of experiment with two events |
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| For experiment with events E and F: "not E" - set of outcomes that are not outcomes in E. "E or F" - the set of outcomes in E or F or both; union; EUF. "E and F"- outcomes in both E and F: intersection; EnF. |
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| P(E or F)=P(E)+P(F)-P(E and F). If "E and F" is impossible, then it equals 0. |
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P(E and F)=P(E)P(F). Because they are independent, the order of the events does not matter.
P(E or F)=P(E)+P(F)-P(E)P(F). |
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| The same as solving an equation, except that div. or mult. by a neg number reverses the sign. |
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| An expression denoted by f(x), and the variable is given a value. In any function there can be no more than one output for any given input. |
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| GEOMETRY - intersecting lines |
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| any two straight lines that intersect; the opposite angles have the same measure. Two angles on a straight line add up to 180 deg. |
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a closed plane figure formed by three or more line segments. The interior angles of a triangle =180. The int. ang. of a polygon with n sides = (n-2)*180.
[image] |
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| The sum of the lengths of any two sides is greater than the length of the third. |
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| Equilatoral/isoceles triangle |
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Equilatoral - all sides same length
Isocelese - at least two sides the same length
If two sides are same length, then two angles opposite those sides have same measure.
[image] |
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Hypoteneuse is the side opposite the right angle (c). Ratio of 3:4:5 is right triangle. Thus, a2+b2=c2
[image] |
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45-45-90 tri: lengths are 1:1:√2
30-60-90 tri: lengths are 1:√3:2 |
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area=(height X base)*(1/2)
[image] |
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Quadrilateral with two sets of parallel lines. The opposite sides are of equal length.
Area = base x height
[image] |
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Two sides are parallel (but other two are not). Area=(.5)(top+bottom)(height)
[image] |
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Circumference = 2Πr Area = Πr2
Deg=360 |
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Length of arc is x(deg)/360 of the circumference of circle. If x=60, arc is 60/360 * circumference.
[image] |
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| If a triangle in a circle has one side on the diameter, then the circle is a right triangle. |
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Vertex: point where two edges meet. Rec solid has 6 faces, 12 edges, and 8 vertices.
Surface area = sum of all areas of faces.
Volume = LxWxH |
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Two base circles are the same size.
Surface area = 2(Πr2)+2ΠrH
Volume=Πr2*H
[image] |
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four quadrants; the center is the origin.
[image] |
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y=mx+b m= slope= (y2-y1)/(x2-x1) b= y-intercept (value when x=0) To find x-int must set y=0 and solve for x.
After establishing the slope, plug a known coordinate on line into equation to find the equation of the line. |
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If unique solution, then cross at a single point.
If equations are equivalent, then they are the same line.
If no solution, the two lines are parallel and do not intersect. |
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