Hi

Standard Form of an Equation of an Ellipse is  

where Pt(h,k) is the center with a and b determining the respective vertices distances from center.

x^2/9+y^2/16=1

Center(0,0)  Vertices: (3,0),(-3,0) and (0,4),(0,4)

foci distance from center along major axis: 

foci: (0,sqrt(7)),(0,-sqrt(7))

Hi

OK on your moving the 'a^-15' to the denominator to 'meet up' with the 'a^13' 

You are then in a position to multiply them by adding their exponents.



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Hi

1100 people

 	      ≥ 1	Both	  1

Microwave	860				

DVD Player	740						

          1600	-590	= 1010

a. how many own either a microwave oven or a DVD player: 1010

b. how many own neither a microwave oven nor a DVD player: 1100-1010 = 90

c. How many own a microwave oven and do not own a DVD player = 860-590= 270

Hi

cosēθ(tanēθ+1)=1         | (tanēθ+1)= secθē = 1/cosēθ 

cosēθ/cosēθ = 1

            1 = 1



 secēθ cotē=1+cotēθ 

 secēθcotē- cotēθ = 1

 cotēθ(secēθ - 1) = 1    | secēθ - 1 = tanēθ

 cotēθtanēθ  = 1         | tanēθ = 1/cotēθ 

 cotēθ/cotēθ = 1

           1 = 1



Sinθ/(1+cos θ) = cscθ-cot θ   |cscθ = 1/sinθ and cotθ = cosθ/sinθ

Sinθ/(1+cos θ) = (1-cosθ)/sinθ

sinēθ  = (1+cos θ)(1-cos θ)

 sinēθ = 1 - cosēθ

  sinēθ + cosēθ = 1      |pythagorean Identity

Hi, nice preentation

Do like completing the table with Totals for more clarity:

	       Favor  Oppose  Total

Democrat	     270	130	400

Republican	     115	220	335

Other	          40	85	125

total  	    425	435	860

a. P(a randomly selected person favors the death penalty) = 425/860

b. P(a randomly selected person is a democrat given that they favor the death penalty) 270/425 

c.P(probability that a randomly selected person favors the death penalty given that they are a republican) 115/335

Hi

Factor the expression

20x^3y^2 + 28x^2y^4

 4x^2y^2(5x + 7y^2)

Hi

 Volume of tank = 5in * 5in * 6in = 150 in^3 of water (or about 2.6 quarts(US))

Hi





using x and y to represent the lengths of the respective sides.

 2x + 2y = 50m

 2x + 2*20 = 50m

    2x = 10m

     x = 5m

Hi

write the first five terms of the sequence: substituting for n = 1 to 5

  {4,5,6,7,8...}

  {3,12,27,48,75...}

 {8,11,16,23,32...}

  {15,12,7,0,-9,...}

Hi,

taking the 1. as a typo:

arithmetic sequence: {1,3,7,11,...}  d = 4

{{a[n]=a[1]+(n-1)*d}}}

{{a[8]= 1 +(7)*4 = 29}}}

Hi

geometric sequence



 



          24/r^3 *r^8 = 768

                  r^5 = 32

                  r = 2  and 

Hi

Arithmetic Series



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  (1-d) + 5d = 27

          4d = 26

           d = 26/4 = 13/2   

CHECKING our Answer***

Hi

survey of 51 pet owners: results described in the chart below:

Find the number of pet owners who owned none of the three lovely animals.

 	>= 1	D&C	D&T	C&T	1

Dog	24				

Cat	28				

Turle	11				

ALL	2				

	65	-12	-7	-3    = 43

 51 - 43 = 8 own none

Hi

sum of two numbers is 25

Let x and (25-x) represent the smaller and larger respectively

Question states***

  3x = 2(25-x)

Solving for x

      5x = 50

       x = 10, the smaller number.  15 the larger  (25-10))

CHECKING our Answer***

    30 = 2*15   

Hi

sum of two numbers is 3

Let x and (3-x) represent the smaller and larger respectively

Question states***

  4x + (3-x) = -48

Solving for x

      3x = -51

       x = -17, the smaller number.  20 the larger  (3-(-17))

CHECKING our Answer***

    -68 + 20 = -48

   

Hi

3x-2y=-24   OR  y= 3/2x + 12 (Green) 

x=0, then y= 12 

y=0 then x =-8    

(0,12)and(-8,0)

-3x-y=6      OR    y=-3x-6 (Blue)

x=0, then y=-6    

y=0  then x= -2   

(0,-6) and (-2,0)

Plotting points and connecting with Line

Lines Intersect at ordered pair Pt(-4,6)

This is the  solution for this system

Hi

 y= -x^2+2x-2   |Note use of ^ for squared term

 y-intercept (when x = 0)  Pt(0,-2)



y= -(x-1)^2 -1   |completing the square  Vertex Pt(1,-1)

 x-intercept (when y = 0)

-(x-1)^2 -1 =0

   (x-1)^2 = -1  NO real roots, Parabola does not cross the x-axis

   x = 1 ą sqrt(-1)  

Hi

y = -2x^2+4x+2    |Note use of ^ for squared term

 y-intercept (when x = 0)  Pt(0,2)



y= -2(x-1)^2 + 4    |completing the square  Vertex Pt(1,4)

 x-intercept (when y = 0)

 -2(x-1)^2 + 4 =0

   (x-1)^2 = 2

   x = 1 ą sqrt(2)  Pt(2.414,0) and Pt(-.414,0) the x-intercepts

Hi

graphing 

 2x-3y=6     OR y =(2/3)x -2 

|when x=0, then y= -2 When y =0 then x = 3  Pts (0,-2) & (3,0) on the line

Graph Points and connect with Line:



Might recommend substituting any possible values for ordered pairs (x,y)that may

be found...into 2x-3y = 6 to see if they would be correct ordered pairs

Hi

If we randomly sample five cards from a standard poker deck, 

find the probability that all five cards selected are clubs.

without replacement:

 P (five being all clubs) = = 154,440/311,875,200 = .000495

with replacement:

 P (five being all clubs) = (1/4)^5 

Hi

a jar contains 7 green, 19 black and 13 pink marbles.

 39 marbles in ALL

ONE marble is drawn at random. 

P(being a green 'or' black) = 7/39 + 19/39 = 26/39

Hi

18x^2+36y^2=648

 18x^2/648 + 36y^2/648 = 1

   x^2/36 + y^2/18 = 1

 sqrt(36-18) = sqrt(18) = 3sqrt(2)

foci are (3sqrt(2),0) and (-3sqrt(2),0)

Hi

MULTIPLE CHOICE QUESTION (consisting of 5 possible answers of which only one is correct)

odds against guessing correctly 4:1

 odds for guessing correctly    1:4    |good work



P(guessing correctly) = 1/5 = .20

Hi

 Volume(cube) = s*s*s where s is the length of each edge

   s^3 = 216 in^3

     s = 6 in

Hi

odds against 4:7

odds for 7:4

 P(event ocurring) = 7/11  |good work

Hi

parabola with a vertex at the origin and a directrix at y = 5

The standard form is , where the focus is (h,k + p) 

p = -5

 parabola opening downward y = -20x^2

Hi, great presentation

......=  PASS   FAIL   TOTAL

MALE  =  28     17     45

FEMALE=  21     19     40

TOTAL =  49     36     85

 P(selecting female 'or' a person who passed) = 40/85 + 49/85 - 21/85 

Hi

factoring

 5n^2-7n+2=0     an^2 + bn + c









   n = 10/10 = 1  and n = 4/10 = 2/5

 5(n-1)(n-2/5) = 0

Note:SUM of the inner product(-n) and the outer product(-2/5n) = -7/5n

                                                     5*-7/5n = -7n

Hi

 2m^2-13m+15=0





   

   x = 20/4  and x = 6/4  = 3/2

    2(m-5)(m-3/2) = 0

   Note:SUM of the outside terms(-5m) and the inside terms(-1.5m) = -6.5m

                                                     2*-6.5m = -13m

Hi

factor each polynomial completely

36qģ+24qē+4q

 4q(9q^2 + 6q + 1)

 4q(3q + 1)(3q + 1)

Note:SUM of the inner product(3q) and the outer product(3q) = 6q

Hi

Factoring by grouping

2x^3 - 10 + 4x^2 - 5x

2x^3  + 4x^2 - 5x - 10

 2x^2(x+2) - 5(x+2)

(2x^2 -5)(x+2)