Hi

26.414 is 28.1% of what number?

Let x represent that number

  28.1% = 28.1/100 = .281

  .281*x = 26.414

       x = 26.414/.281

       x =  94

CHECKING our Answer***

  .281*94 = 26.414

 

Hi

Finding 441% of 612

   441/100 = 4.41

 4.41*612 = 2521.44 

 

Hi

Convert 22/125 to a percent

   |cross multiplying to solve for x

 125x = 22*100

    x = 22*100/125 

    x = 2200/125

    x = 17.6

  = 17.6%

 

Hi

Converting 0.8% to a decimal.

.8% = .8/100 = .008

 

Hi,

Using the point-slope formula, 

(-4,3) and 

(-2,1)  m = 2/-2 = -1

Note: the standard slope-intercept form for an equation of a line y = mx + b  

where m is the slope and b the y-intercept.    

 y = -x + b

 1 = -1*-2 + b

 -1 = b

 y = -x -1

 

Hi,

Using the point-slope formula, 

(5,7) and 

(8,1)  m = 6/-3 = -2

Note: the standard slope-intercept form for an equation of a line y = mx + b  

where m is the slope and b the y-intercept.  

  

 y = -2x + b

 1 = -2*8 + b

 17 = b

 y = -2x + 17

 

Hi,

Using the point-slope formula, 

(2,7) and 

(5,3) m = 4/-3 = -4/3

Note: the standard slope-intercept form for an equation of a line y = mx + b  

where m is the slope and b the y-intercept.  

  

 y = -(4/3)x + b

 3 = -(4/3)*5 + b

 29/3 = b

 y = -(4/3)x + 29/3

 

Hi,

the standard slope-intercept form for an equation of a line y = mx + b  

where m is the slope and b the y-intercept.  

 m = -2 and line contains(3,9)

 y = -2x + b

 9 = -2*3 + b

 15 = b 

 y = -2x + 15

 

Hi,

finding two points: using.. x = 0 and x = 4

 x + 4y=8 

 0 + 4* = 8  Pt(0,) on the line

 4 + 4* = 8  Pt(4,) on the line

Plotting points and connecting with a line:

 

Hi, Note: 

Standard Form of an Equation of an Hyperbola opening "right and left" is  

             

where Pt(h,k) is a center  with vertices 'a' units right and left of center.

 9x^2 - y^2 = 9

 

 

Hi, Note: 

Standard Form of an Equation of an Hyperbola opening "right and left" is  

             

where Pt(h,k) is a center  with vertices 'a' units right and left of center.

These all open right and left with Centers(0,0) and foci along the x-axis

 vertices (-2,0) and (2,0) foci sqrt(20) each side of center

(((x^2/49 - y^2/9 = 1}}} vertices (-7,0) and (7,0) foci sqrt(58) each side of center

 vertices (-6,0) and (6,0) foci sqrt(52) each side of center

Graph of 

 

Hi, Note: 

Standard Form of an Equation of an Hyperbola opening right and left is  

             

where Pt(h,k) is a center  with vertices 'a' units right and left of center.

 x^2-18x-y^2+12y=19

(x-9)^2 -81 -[(y-6)^2-36] = 19

(x-9)^2 -81 -(y-6)^2+36 = 19

(x-9)^2 -(y-6)^2 = 64

  C(9,6) with vertices V(1,6) and V(17,6)

 

Hi

 36x^2/3 + 18x^1/3 + 5

 Let u = x^1/3

 36u^2 + 18u + 5

 

Hi

Note 1m = 3.2808ft

  = 15.24m/sec^2

 

Hi

 For a game,Patricia must roll a die and draw a card from a deck of 26 cards,

 with each one having a letter of the alphabet on it

 1,2,3,4,5,6 (3 evens out of six numbers)

 Patricia letters are a,c,i,p,r,t which are 6 out of the 26 letters

P(odd number and a letter in her name) =  

 

Hi

Each of the numbers 0 through 14 is written on a piece of paper and all of the

 pieces of paper are placed in a hat.  15 Numbers in all.

P(number selected is even) =    (8 even numbers in all - zero an even number)

 

Hi

P(A given B) = P(A|B) = P(A and B)/P(B)

P(Rolling a sum of 9 on two fair six sided dice.) = 4/36 = 1/9

P(queen of diamonds|it's a face card) =  = 1/12

P(Rolling a sum of 11 on two fair six sided dice) = 2/36 = 1/18 

P( king |it's a face card) =  = 4/12 = 1/3

P(Rolling a sum of 10 on two fair six sided dice) = 3/36 = 1/12



___1_2_3__4__5__6

1|_2_3_4__5__6__7

2|_3_4_5__6__7__8

3|_4_5_6__7__8__9

4|_5_6_7__8__9_10

5|_6_7_8__9_10_11

6|_7_8_9_10_11_12

 

Hi

The average years of employee experience at a company with 10,000 employees is

 normally distributed, with a standard deviation of 12 years.

If a sample of 50 employees indicates a mean age of 38, 

calculate 90 percent confidence intervals for the population mean.

ME = 1.645[38/sqrt(50)] = 8.8402		

CI: 	

	

99 percent confidence intervals for the population mean.

ME =2.575[38/sqrt(50)] = 13.8381

CI: 	



	a	a/2	crtical regions	

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

92%	0.8	4%	z <-1.751	z >+1.751

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

98%	0.02	1%	z <-2.33	z >+2.33

99%	0.01	0.50%	z<-2.575	z >+2.575

 

Hi



If P(A) = 0.20, P(B) = 0.40 and P(A ∩ B) = 0.08:

 Note: Two events A and B are independent if and only if Pr(A ∩ B) = Pr(A)Pr(B).

     therefore then A and B are Independent Events

 

Hi

The theoretical P(of undesirable side effects resulting from taking Grebex) is 1 in 20.

 If 100 people take Grebex to lower their blood pressure

how many will encounter undesirable side effects?

 One would expect that 5% would:     Note: 1/20 = .05

    people = 5 People

 

Hi

Note: in red: prize amount - the $5 cost of the ticket

One thousand raffle tickets are sold for $5.00 each. 

One grand prize of $1000 and two consolation prizes of $200 each will be awarded.

 total prize money awarded  = $1000, $200, 200 

E(X)=∑X*P(X) = 

             = .995 + .195 + .195 - 4.985 = -$3.60

 

Hi

 23 Marbles in all of which: 7 are lavender, 11 are turquoise and 5 are rainbow

 P(drawing a turquoise) = 

Turquoise replaced..back to 23 marbles in the bag

 P(drawing a rainbow) = 

 

Hi

september energy consumption levels for a single-family homes are found to be normally distributed

 of 1030kwph and a of 22kwh

probability that for 16 randomly selected homes, 

the average energy consumption in September is less than 1021kWh

  *Note: 

    z = 

   P( z < -1.6364) = .0509        NORMSDIST(-1.6364)per Excel



Point being not much probability of that happening

 

Hi

IQ scores that are normally distributed with a  of 105 and a of 20

Find 

  *Note: 

 lower 14% then z = -1.0803  NORMSINV(0.14)          

 -1.0803 = (x - 105)/20

 105 - 20*1.0803 = 83.394

 top 86% then z = 1.0803     NORMSINV(0.86)

   105 + .20*1.0803 = 126.606



     126.6 - 83.4 = 43 IQ points separating the bottom 14% from the top 86%.

 

Hi

A student is successful 73% of the time when making random guesses on a multiple choice exam.

For an exam that contains 50 questions...

find the mean number of questions answered correctly.



   mean = np = 50*.73 = 36.5

 

Hi

a.  Range = 9-1 = 7

b.  Variance =  =  = 8.5

c.  Standard deviation = 





x	m	diff	diff^2

2	6	-4	16

4	6	-2	4

7	6	1	1

8	6	2	4

9	6	3	9

30			34

 

Hi

If a couple plans to have 9 children

 P(at least one girl) = 1 - P(no girls) =  = .998

 

Hi

Solving for y in the following system of equations.

-2x - 2y = -12 

 2x - 2y = 28 

    - 4y = 16

       y =  



CHECKING our Answer*** note:  x = 10     x =  (-12+2y)/-2

   2x - 2y = 28 

   20 + -2*-4 = 28

 

Hi

 z = (-12)/4 = .5   P(z< .5) = .3085

 

Hi

Find the area bounded by the curves y=x, y=1, x=2 and y=0.

Area(trapezoid) = 

 

Hi

1) x+7y=62 and 

  -x+2y=10   9y = 72, y = 8 and x = 6, (6,7) the solution

2) 3x+4y=12 and 

  -3x+ y=33   5y = 45, y = 9 and x = -8  (12-4*9)/3 ) (-8,9) the solution

3)4x-8y=1 and 

  4x-8y=2



  4x-8y= 1 

 -4x+8y= -2   |Multiplying 2nd Eq thru by -1

     0 ≠ -1  there is NO solution