Hi

In a board of directors composed of nine people, 

how many ways can a chief executive officer, a director, and a treasurer be selected?

 Order Important:  9P3 = 9!/6! =  ways

 

Hi

select 5 malls from a total of 9 malls 

   9C5 =  =  = 126 }}}

 

Hi





   or 75

  

 

Hi,

Find the area under the standard normal curve between z = 0 and z = 3 

 %

For the normal distribution: 

one  standard deviation from the mean accounts for about 68.2% of the set 

two standard deviations from the mean account for about 95.4%

and three standard deviations from the mean account for about 99.7%.





Important to Understand z -values as they relate to the Standard Normal curve:

Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and 50%  to the right

 

Hi,

Find the z-scores for which 90% of the distribution's area lies between -z and z.

z = ± 1.751

 	a	a/2	2-tailed crtical regions	

80%	0.2	10%	z <-1.28155	z >+1.28155

90%	0.1	5%	z <-1.645	           z >+1.645

92%	0.08	4%	z <-1.751	           z >+1.751

95%	0.05	2.50%	z <-1.96	           z >+1.96

98%	0.02	1%	z <-2.326	           z >+2.326

99%	0.01	0.50%	z<-2.576	           z >+2.576





Important to Understand z -values as they relate to the Standard Normal curve:

Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and 50%  to the right

 

Hi,

r the standard normal curve, find the z-score that corresponds to the 90th percentile?

Excel function NORMSINV(.90) = 1.2816



Important to Understand z -values as they relate to the Standard Normal curve:

Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and 50%  to the right

 

Hi,

How many different signals using three distinct flags can be made if there are five different flags from which to select?

Order Important: 5P3 = 5!/2! =  

 

Hi,

In how many ways can  different cars be displayed along the circumference of a parking area?

As in a 'circle'  (12-1)! = 11!

 

Hi,

An inspector must select three tests to perform in a certain order on a manufactured part.

He has a choice of seven tests. 

How many ways can he perform three different tests? 7P3 = 7!/4! = 

 

Hi,

How many different codes can be made using the letters of the word BEAUTY if each code  must contain 3 letters?

  ways if no letter is to be repeated

  ways if repetition is allowed

 

Hi,

How many different 4-digit numbers can be formed from the  digits 2, 3,4,5,6,7, and 8 if: 

a. Repetition of digits is not allowed?  

b. Repetition of digits is allowed? 

c.How many of them are odd numbers? Refer to letter a.

d. How many of them are even numbers?Refer to letter b.

 

Hi,

How many different ways can a visiting nurse see seven patients if she sees them all in one day.

 7!  ways

 

Hi,

ways in which nine books can be arranged in a shelf if four particular books are to be kept together.

 4 books as one Unit  or 24 ways they can sit together on the shelf

ALL nine:  = 17,280 ways

 

Hi,

8x^4-50= 2(4x^2 - 25) = 2(2x-5)(2x+5)

 

 

Hi,

D=ABC ⇒  B= D/AC

 

Hi,

the idea is to have the base numbers the same ⇒ Exponents are Equal

a) 7^x=49   ⇒  7^x = 7^2   ⇒  x = 2

b) 243 = 9^2x+1  ⇒    ⇒  5 = 2(2x+1), x = 3/4

c) 2^2x * 4^4x +8 = 64  ⇒  , x= -1

d)9^x-1 * 81 ^2x-1 = 27^3x-2  ⇒  x = 0 

 

Hi,

x ≥  -2

Draw an arrow to the right with a closed circle on the -2

 

Hi,

Find the z-scores for which 90% of the distribution's area lies between -z and z. 

 -1.6449 < z < 1.6449    Excel function: NORMSINV(.05) = 1.64485    

For the normal distribution: 

one  standard deviation from the mean accounts for about 68.2% of the set 

two standard deviations from the mean account for about 95.4%

and three standard deviations from the mean account for about 99.7%.

Important to Understand z -values as they relate to the Standard Normal curve:

Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and 50%  to the right



	a	a/2	2-tailed crtical regions	

80%	0.2	10%	z <-1.28155	z >+1.28155

90%	0.1	5%	z <-1.645	           z >+1.645

92%	0.08	4%	z <-1.751	           z >+1.751

95%	0.05	2.50%	z <-1.96	           z >+1.96

98%	0.02	1%	z <-2.326	           z >+2.326

99%	0.01	0.50%	z<-2.576	           z >+2.576

 

Hi, Previously Posted

From a group of 6 men and 8 women, 5 people are chosen at random.

P(more men than women) = P(3M&2W)  + P(4M&1W)

                       =

                       = 

 

Hi,

From a group of 6 men and 8 women, 5 people are chosen at random.

P9more men than women) = P(3M&2W)  + P(4M&1W)

                       =

                       = 

 

Hi,

3, -6, 12, -24, 48,...,   Geometric Series, r  = -2

  

  

 

Hi, 

3x-4y=0  OR = y = (3/4)x





    x^2 = 16

    x = ± 4   and y = ± 3

(4,3) and (-4,-3) the solutions to this system of EQs

 

Hi,

 x- 3z = -5    | x = 3z- 5

Have a relationship between x and z, so...eliminating y from the other two EQs

2x- y + 2z= 16      |mulitplying 1st by 3 and subtracting it form the 2nd EQ

7x – 3y -5z =19

   x  - 11z =  -29 

 (3z- 5 - 11z = -29

         -8z = -24

           z = 3  and x = 4  and y = 

 

Hi,



Find the coordinates of the vertex for the parabola 

f(x)= -2x^2-2x.   

| completing the Square to find the Vertex: y = ax^2 + bx + c   ⇒ y = a(x -(-b/2a)^2) - a(-b/2a)^2 + c

f(x) = -2(x+1/2)^2 + 1/2    V(-1/2,1/2)

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

where(h,k) is the vertex  

 

Hi,

Re TY, one may use either of the 2 formulas*** to find the sum

3, 7, 11, 15, 19...,   Arithmetic sequence, d = 4

For sums of an arithmetic sequence one can use:

***  OR

***



  |Using the Latter after finding 

  ⇒    

 

Hi,

 ⇒   

 ⇒  d = 8/20 = 2/5



{ -8/5,  -6/5, -4/5, -2/5, 0, ... }

 

Hi, Previously Posted

f(x, y) = x^2 + 2xy + 2y^2 -6y + 2

∂ f/∂ x = 2x + 2y

∂ f/∂ y = 4y + 2x - 6

 2x + 2y = 0

 2x + 4y = 6

    2y = 6

     y = 3   and x = -3

 = 2

 = 2

 = 4

D =  

f(x,y) has minimum at (-3,3) 

f(-3, 3) = 9 -18 +18 -18 + 2 = - 7

 

Hi,

f(x, y) = x^2 + 2xy + 2y^2 -6y + 2

∂ f/∂ x = 2x + 2y

∂ f/∂ y = 4y + 2x - 6

 2x + 2y = 0

 2x + 4y = 6

    2y = 6

     y = 3   and x = -3

 = 2

 = 2

 = 4

D =  

f(x,y) has minimum at (-3,3) 

f(-3, 3) = 9 -18 +18 -18 + 2 = -7

 

Hi,

z = f (x, y) = e2x−3y

z needs to be clarified using parenthesis

∂f/∂x 

 (1,2)

∂f/∂y         

 (-2,3)

Second-order partial Derivatives

 



 

 

Hi,

the idea is to find a perfect square in 98...

 

Hi,

Re TY, 

as to as i^2 = -1

x^2+7x+14 = 0





  |Note 2 is the denominator for both terms