Hi,

Note:  z-values for various confidence levels

90%	z = 1.645

95%	z = 1.96

98%	z = 2.33

99%	z = 2.576

a) ME =  1.645(44.5/sqrt(10000)= .732

 138.5 - ME <  < 138.5 + ME

b)ME =  1.96(44.5/sqrt(10000)= .873

 138.5 - ME <  < 138.5 + ME

c)ME =  2.576(44.5/sqrt(10000)= 1.146

 138.5 - ME <  < 138.5 + ME

 

Hi,

    || Cross Multiply

  2x = 3(y+1)

   x =    and  y = 

    || Cross Multiply

  2(x+y) = 7(x-y)

 2x + 2y = 7x - 7y

      9y = 5x

         and 

 

Hi,

The idea is... to isolate the radical term on one side of the EQ 

and then square both sides of the EQuation



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

   4x + 4 = x^2 + 2x + 1

    x^2 - 2x -3 = 0

  (x-3)(x+1) = 0

    x = 3  0r  x = -1

 

Hi,

Note:   and 



Will let you finish it up

 

Hi,

Note:  Goal is to isolate the variable on one side of the Equation

That gives a plan of action!

   ||Multiplying thru by 6 so as all denominators = 1

 1 - 3x =2( x-5)    |Distribute the 2 to remove the parenthesis 

 1 - 3x = 2x - 10   |Adding 3x to both sides

    1 = 5x - 10      |Adding 10 to both sides

    11 = 5x 

    

 

Hi,

Note:  Goal is to isolate the variable on one side of the Equation

That gives a plan of action!

3z+5+2z=12+3z   |Subtracting 3z from both sides

   5+2z = 12    |Subtracting 5 from both sides

     2z = 7 

      z = 7/2  0r   0r 3.5

 

Hi,

x2 + 4y2 + 2x - 24y + 33 = 0

(x+1)^2 + 4(y-3)^2 - 1 - 36 + 33 = 0

(x+1)^2 + 4(y-3)^2 = 4



Ellipse:  C(-1,3)

 Standard Form of an Equation of an Ellipse is  

where Pt(h,k) is the center. (a variable positioned to correspond with major axis)

 a and b  are the respective vertices distances from center

 and ±are the foci distances from center: a > b

 

Hi,

 = 

F	First terms   80

O	Outside terms 20   

I	Inside terms  20

L	Last terms    25

 

Hi,

 = 

F	First terms   t

O	Outside terms    ||Note: 

I	Inside terms  -

L	Last terms    -17

 

Hi,

 = 

F	First terms   x

O	Outside terms    ||Note: 

I	Inside terms  

L	Last terms    7

 

Hi,

 = 

F	First terms   6

O	Outside terms -6

I	Inside terms   5

L	Last terms   -5·3

 

Hi,

 = 

F	First terms   40

O	Outside terms -8

I	Inside terms  -5

L	Last terms    10

 

 

Hi,

needing 10 liters of the 15% acid solution... 

How many liters of 10% solution and 30% solution should you use?

Note:  y = 10L - x

 .30x + .10(10-x) = .15·10      |May multiply thru by 100 first, if one wishes

            .20x = .5

               x = 2.5L of the 30%  and 7.5L of the 10%

and...

 

Hi,

The perimeter of a triangle is 90 cm

The lengths of the sides of the triangle are in the ratios 3 : 5 : 7 

 3k + 5k + 7k = 90cm     | Letting k be the constant of the proportion

         15k = 90cm

           k = 6cm

 , the longest side

and...

 

 

Hi,

Mary's mother is 3 times as old as Mary's age

 y = 3x is mary's mother's age

Question states*** 4 yrs ago...

  x-4 = (1/4)(y-4)

  x - 4 = (1/4)(3x-4)

    (1/4)x = 3

         x = 12, Mary's age.  Mother is 36.

and... 4 yrs ago

 

 

Hi,

A cubic polynomial equation with real coefficients has two zeros, 5 and 6 + 2i.

 x^3 - 17x^2 + 100x - 200 = 125 - 425 + 500-200 = 0

 5	1	-17	100	-200

 	 	  6	-60	 200

 	1	-12	40	0

(x^2 - 12x + 40)

 



     

 

Hi,

y = ax^2 + bx + c   ⇒ y = a(x -(-b/2a)^2) - a(-b/2a)^2 + c

P = -25x^2 + 450x.    |  Note: -450/(2*-25) = 9

P= -25(x-9)^2 + 2025

  9 cleks will maximize the daily profit at $2025

 

Hi,

Alex has twice as much money as Jennifer. Jennifer has $6 less than Shannon's

Shannon  x

Jennifer (x-6)

Alex  2(x-6)

 Question states***

 x + (x-$6) + 2(x-$6) = $54

     4x = $72

      x = $18, shannon's amount.  Jennifer $12  and Alex $24

and..

 

 

Hi,

In general, combine like terms and isolate variable on one side of the EQ

-2+y+5=3y+9

  y + 3 = 3y + 9    ||subtracting y and 9 from both sides of EQ

    -6 = 2y

    -3 = y

 

Hi,

what is 2 to the power -3?

    | In general:  

 

Hi,

Note: n^0 = 1     |  you solved for (12xy)^1 

 

Hi,



Note: the vertex form of a Parabola opening up(a>0) or down(a<0),  

where(h,k) is the vertex  and  x = h  is the Line of Symmetry

Parabola opens Upward, V(0,5) , y-axis the line of symmetry (x=0) (2,9) &(-2,9)are Pts on this parabola 

Always good idea to sketch any curve

 

Hi,

triangle that has a base of 2 1/4 yards and height of 4/5 yard.

A = 

 

Hi,

h(x) = -4.9t2 + 34.3t - 49   || Note: 

h(x)= -4.9(x-3.5)^2 + 60.025 - 49

    V(3.5,11.025)

 Takes 3.5 sec to reach maximum height 0f 11.025m

 

Hi,

find a[20] when a[1]=9 and d=2 

Arithmetic Sequence

 

Hi,

The value of a property declines every year by 5%. 

(each year ...worth 95% of previous year's value)

 presently it's value is $350,000.

 = $297,271.30

 

Hi,

The circumference of a circle is 42 pi inches.     r = 21

A =  = 1385.4 in^2

 

Hi,

Note:  Quantitative variables are numerical. They represent a measurable quantity

A. the division holding the meeting 

B. the conference room for the meeting 

C. the length of time for the meeting ****

D. all of the above 

 

Hi,

Note: Quantitative variables are numerical. They represent a measurable quantity.

A. the square footage of the house 

B. the monthly gas bill 

C. the monthly electric bill 

D. all of the above  ****

 

Hi,

A shop offers 17 varieties of bagels, 28 flavors of cream cheese, and 24 flavors of coffee. 

  is the number of different types of orders that can be made

 

Hi,

A surgical technique is performed on eight patients. You are told that there is an 80% chance of success. 

a) Construct a binomial distribution. 

P = nCx*  p= .8 and q = .2  and n = 8

b) Find the 

mean = np =  

variance = npq = 

standard deviation of the probability distribution.

c) P(x = 6) =  =  .2936  or 29.36% 

d) P(x < 6) = 1 - P(x = 8) - P(x = 7) - P(x = 6) 

            =  1 - .1678 - .3355 - .2936  = .2031   or 20.31%