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The sample mean is the average and is computed as the sum of all the observed outcomes from the sample divided by the total number of events.







Variance and Standard Deviation: Step by Step
Calculate the mean,.


Write a table that subtracts the mean from each observed value.
------- -------
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------- -------
------- -------
------- -------
------- -------
------- -------
------- -------
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Total:

Divide by where is the number of items in the sample.
This is the .
To get the we take the square root of the variance.

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...if you have , just multiply exponents and you will have

=

=

=...if you have , just add exponents and you will have
=

=

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evaluate the ............ degrees

...=> cot will be same as degrees
write as
=

=

=

=

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evaluate the ............ degrees

...=> cot will be same as degrees
write as
=

=

=

=

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.....factor

.....factor

the LCM is:

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length :
length :
length :
It follows that: given perimeter , then



...factor

solutions:
If , then , and it is not a solution for because must be less than .
If , then .

Hence, .
so,
length :
length :
length :

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...write as

...group

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if a car travels for , then the car is traveling ....=>

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where and are the coordinates of the center


, ,; so, the center is at (,)
...=> ....the semi-transverse axis is unit
long
...=> ...the semi-conjugate axis is units
long
focus:



and .....The foci are units right and left of the center:
(,)=(,)
and (,)=(,)

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The radius of a circle is .
the area of a sector bounded by a ° arc is equal of area of the full circle or equal to a semicircle area

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1.
What is percent of ?
%=
and you have ; so, % of is

2.
What is percent of ?

and you have ; so, % of is

3.
What percent of is ?
you are looking for %= of that is equal to
so,



......so, is % of
4.
is percent of what?





......... is percent of

5.
is percent of what?





......... is percent of
6.
What is percent of ?
%=
and you have ; so, % of is

7.
What percent of is ?







8.
What percent of is ?






......... is % of

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given:

$
find


















solution:
we need only positive solution since we are looking for number of books

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....first multiply

....now isolate variable ; add to both sides

...cancel and on right side

.....add to both sides
...cancel and on left side

...solution for variable and it is only solution that makes true

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...if so, then

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Solved by pluggable solver: FIND EQUATION of straight line given 2 points

hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (-3, 5) and (x2, y2) = (5, -3). Slope a is . Intercept is found from equation , or . From that, intercept b is , or . y=(-1)x + (2) Your graph:

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Use only a non-collapsible compass and a straight-edge (not a ruler), construct a square with sides AB.
1. Have the compass length as AB.
2. Draw a straight line XY with a straight edge of length much greater than AB.
3. Now mark a point P on XY.
4. With P as center cut an arc on line XY for Q. Now PQ = AB.
5. With P as center cut two arcs on either side of line XY.
6. With Q as center cut two arcs on either side of line XY, so that they make two points with the arcs drawn with P as center.
7. Mark those points as R and S.
8. Now join P, R, Q, S.
9. Now we have a parallelogram PRQS. PR = RQ = QS = SP parallelogram with all sides equal is a rhombus.
10. The Diagonals of the rhombus are perpendicular to each other
11. Now Draw a line UV with points R ans S.
12. Now mark the point at which RS cuts PQ as A.
13. With A as center cut an arc on UV to get the point C.
14. With A as center cut an arc on XY to get the point B.
15. With B as center cut an arc on one side of XY.
16. With C as center cut an arc which cuts the ac drawn with B as center to get the point D.
17. Now ABCD is the required Square with side AB.

or
use compass and ruler

1.
Draw a line from the left side of your paper to the right using a ruler. Draw and label two endpoints. End point A will be on the left and end point B on the right. The distance from point A and point B will be labeled r. Distance r will be the length of each side of your square. Extend the line further to the right from point B to help in finding a new line that will be perpendicular to Line AB.
2.
Draw a perpendicular line upwards from point B. Using distance r, mark and label a new end point C. This will be the second side of the square at an exact 90 degree angle.
3.
Draw an arc with end point A as the center and r as the distance using a compass. Draw a second arc using end point C as the center and r as the distance. Mark and label where these two arcs meet as point D. This is the final corner for your square.
4.
Connect end point A to point D with your ruler. Connect end point C to point D.

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An isosceles triangle is a triangle with (at least) two equal sides, then base angles are congruent.
let the two equal angles be and
so,
third angle is

if the third angle of an isosceles triangle is dgree less than the sum of the two equal angles, then
......since , we have
..solve for

we know that the sum of all three angles in triangle is
then we have:
.......substitute and
....solve for





then
and

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Solved by pluggable solver: FIND EQUATION of straight line given 2 points

hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (2, -1) and (x2, y2) = (3, 4). Slope a is . Intercept is found from equation , or . From that, intercept b is , or . y=(5)x + (-11) Your graph:

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....write as
...group