Hi

Note: # of Diagonals = n(n-3)/2

Recommend putting info like this on a 'condensed' fact sheet.

 n = 55

  55(52)/2 = 1430

Hi

Understand completely, recall there was a time I was self taught on most

ALL early math at any rate:  (country school:)

Might recommend checking out the statistic's section on this site: 

great learning tool selecting previous questions answered, of interest to You.

2. Given a level of confidence of 95% and a population standard deviation of 6, answer the following:

(A) What other information is necessary to find the sample size (n)?

   confidence interval or 'margin of error'

(B) Find the Maximum Error of Estimate (E) if n = 84. Show all work. 

            ME = 1.96[6/sqrt(84)] 



3. A sample of 134 golfers showed that their average score on a particular golf course was 93.23 

with a standard deviation of 6.25. 

Answer each of the following (show all work

and state the final answer to at least two decimal places.): 

(A) Find the 98% confidence interval of the mean score for all 134 golfers. 

ME = 2.3263[6.25/sqrt(134)] 

CI: 93.23- ME < u < 93.23 + ME			



(B) Find the 98% confidence interval of the mean score for all golfers if this is a sample of 110 golfers 

instead of a sample of 134.

ME = 2.3263[6.25/sqrt(110)] 

CI: 93.23- ME < u < 93.23 + ME	

(C) Which confidence interval is larger and why? (Points : 6) 

Note: the Larger the sample size, the smaller ME is and therefore the

confidence interval is larger with the smaller sample size.



5. The diameters of grapefruits in a certain orchard are normally distributed

 with a mean of 5.91 inches and a standard deviation of 0.52 inches. Show all work. 

(A) What percentage of the grapefruits in this orchard is larger than 5.86 inches? 

   z = 5.86-5.91 /.52 = -.05/.52 = -.0962 

    P(z > -.0962) = 1 - .4617 = .5383  53.83%

(B) A random sample of 100 grapefruits is gathered and the mean diameter is calculated.

 What is the probability that the sample mean is greater than 5.86 inches? 

      z = -.05/ .52/sqrt(100) = -.05 /.052 = .9615             

    P(z > -.9615) = 1 -.16815 = .83185   83.185%



Folowing is a summary of Levels of Confidence & their critical regions

	a	a/2	crtical regions	

90%	10	5%	z <-1.645	z >+1.645

95%	5	2.50%	z <-1.96	z >+1.96

98%	2	1%	z <-2.33	z >+2.33

99%	1	0.50%	z<-2.575	z >+2.575

Hi

(2t+3)/(6)-(t-9)/(4) = 5 

i used 12 as the common demoninator and multiplied both side by it 

2(2t+3)-3(t-9)=60 

4t+6-3t+(27) = 60  |Good work. However 'watch the signs'

 t + 33 = 60   |combining like terms (this is where it went...wrong)

    t = 27

CHECKING our Answer***

  57/6 - 18/4 = 9.5 - 4.5 = 5

Hi

I.   x+3y-2z=-9

II. 6x-4y+3z=29

III. 2x+2y+z=13

solving by elimination 

I and III

 x+3y-2z=-9

4x+4y+2z=26

 5x + 7y = 17

II and III

6x-4y+3z=29

-6x-6y-3z=-39

    -10y = -10

       y = 1 and x = 2   | 5x = 17-7y,  x = 10/5

x+3y-2z=-9 

OR x+3y+9 = 2z  

   14 = 2z       z = 7

Hi

produce 50 lb of a mixture

Let x and (50-x)represent the amount of the 5$ and $2.50 mixtures respectively 

Question states*** Mixing

 5x + 2.50(50-x) =3*50

Solving for x

     2.50x = .50*50

         x = .50*50/2.50

         x = 10lb, the amount of the $5/lb tea.  40lb of $2.50/lb tea.

CHECKING our Answer***

 50 + 100 = 150

Hi

 



 3x - 2y = 10  OR y = (1/2)x - 5  |m = -2 is slope of line ⊥ to it

New Line:

y = -2x + b  |using order pair Pt(1,1) to solve for b

1 = -2 + b

 3 = b 

y = -2x + 3

 

Hi

Let x represent represent the amount of 10% solution

Question states*** 

Mixing together to form (15L+x) 20% solution

 .10x + .40*15L = .20(15L+x)

Solving for x 

    .20*15L = .10x

     .20*15L/.10 = x = 30L, the amount of the 10% solution



CHECKING our Answer***

   3 + 6 = .20*45 = 9

Hi, Line with slope of -3 is the 'steeper line'.

Note:

m = 2/1 is the blue line

m = -3/1 is the green line

m = -5/1 the purple line

In each case, regardless of the 'way' the line slants, the slope tells

us how much y changes as x changes by one unit. 

The numerator of the slope reflects 'the change in y'

the larger that numerator is relative to the denominator('the change in x')

The steeper the line slants. 

 

Hi, previously posted 

recommend showing what work you have done and posting only 1 or 2 two questions that are similar in content. 

"I hope You get to this fast" ...must admit, did put a smile in my heart. :)

1. 7x+3=15x+9   | 8x = -6   |finish to decimal answer

2. (1/2)=(2/3)b+(1/6)b  | b = (6/5)*(1/2) |finish to decimal answer

3. 0.3a+0.7=0.5a-0.1   | .8/.2 = a   |finish to decimal answer

4. 2n-5=8n+7    | 6n = -12   |finish it up

5. 3+4x=3x+6    |x = 3

6. 5(2w-4)=6w   | 4w = 20    |finish it up

7. hike up a hill at 4km/hr.. hike down at 6km/hr. hiking trip took 3 hours. 

       4kmp*t = 6kmph*(3hr-t)   |  10t = 18  |finish it up, t is time uphill

8. length of a rectangle is 8in. More than its width. P = 24in

   2x + 2(x+8) = 24in  |  4x = 8in    |finish it up, x is the width

9. The sum of two consecutive EVEN integers is 118

   x + (x+2) = 118   |  2x = 116  |finish it up, x is the lesser integer

10. Your brothers average speed was 4mi/h faster than your average speed.

together they rode 52mi towards each other and met in 2hrs.

    2x + 2(x-4mph) = 52mi  | 4x = 60  |finish it up, x is the brother's speed

Hi









  n = 1/9

CHECKING our Answer***

 3 /4/9 - 1/12/9 = 6

  3*9/4 - 9/12 = 6

    27/4 - 3/4 = 24/4 = 6

Hi

My recommendation for linear equations is to 'focus' on isolating the

variable on one side of the equation and take the steps that are allowable

to accomplish that.  



For example: Doing allowable steps is for the 'sole purpose' of isolating x

2(x+5) - 4 = 5x + 6(x-1)  |remove parenthsis by applying distributive principle

 2x + 10 - 4 = 5x + 6x - 6  |combining like terms on both sides

 2x + 6 = 11x - 6    |adding 6 to both sides of equation to combine like terms

  2x + 12 = 11x       |subtracting 2x from both sides to combine like terms

      12 = 9x         |dividing both sides of equation by 9 to finish!

      12/9 = x

 OR x = 1 1/3

Hi

One card is selected from a deck of playing cards. 

 What is the probability of selecting a card >9 or a black card?

 5 in each suit >9 (10,jack,queen,king,ace)

 P(>9 'or' black) = P(> 9) + P(black) - P(both >9 and black) 

 P(>9 'or' black) = 20/52 + 26/52 - 10/52 = 36/50 

Hi

(a) Mean = $14,810/13 = $1234.17

(b) Median = 1240       |(1250...1230) 

(c) Mode = 850          |occurs most frequently

(d) midrange = 1375     |(850 + 1900)/2 

850

900

1000

1110

1230

1250

1350

1370

1400

1600

1900

Hi

if you double the width of a square, how much does the area of the square increase?

 width x, then   A = x^2

 width 2x, then  A = 4x^2

Hi

entering the data in an Excel Cloumn and used the stat tool found:

 = 2.623423897  and mean = 15



ME = 1.96*2.6234/sqrt(35) = 5.9161		

CI: 15-5.9161 < u < 15+ 5.9161		

Hi, recommend showing what work you have done and posting only 1 or 2 two questions that are similar in content. 

"I hope You get to this fast" ...must admit, did put a smile in my heart. :)

1. 7x+3=15x+9   | 8x = -6   |finish to decimal answer

2. (1/2)=(2/3)b+(1/6)b  | b = (6/5)*(1/2) |finish to decimal answer

3. 0.3a+0.7=0.5a-0.1   | .8/.2 = a   |finish to decimal answer

4. 2n-5=8n+7    | 6n = -12   |finish it up

5. 3+4x=3x+6    |x = 3

6. 5(2w-4)=6w   | 4w = 20    |finish it up

7. hike up a hill at 4km/hr.. hike down at 6km/hr. hiking trip took 3 hours. 

       4kmp*t = 6kmph*(3hr-t)   |  10t = 18  |finish it up, t is time uphill

8. length of a rectangle is 8in. More than its width. P = 24in

   2x + 2(x+8) = 24in  |  4x = 8in    |finish it up, x is the width

9. The sum of two consecutive EVEN integers is 118

   x + (x+2) = 118   |  2x = 116  |finish it up, x is the lesser integer

10. Your brothers average speed was 4mi/h faster than your average speed.

together they rode 52mi towards each other and met in 2hrs.

    2x + 2(x-4mph) = 52mi  | 4x = 60  |finish it up, x is the brother's speed

Hi

How do you subract with fractional exponents?  2 5/2 - 2 3/2



Recommend using the improper fraction format:

 9/2 - 7/2 = 2/2 = 1

Hi, good work.

16√27 + 7√108 = 90√3 

16√9√3 + 7√36√3 

16 . 3√3 + 7 . 6√3 

(48 +42)√3

    90√3       |yes, right on track!



√600x^4 = √100 . √x^4 . √6 = 10x^2√6    

|note: 'x^4'.. until actually taking the square root when showing your work.

Hi

2x+5y+z=22

3x-3y-z=-22

5x+y+2z=-3



Solving by elimination 

2x+5y+z=22

3x-3y-z=-22

 5x + 2y = 0



6x-6y+2z=-44

5x+y+2z=-3

  11x - 5y = -47



 5x + 2y = 0

11x - 5y = -47



 25x + 10y = 0

 22x - 10y = -94

   47x = -94

     x = -2  and y = 5    ( 5x + 2y = 0, y = -5x/2= 10/2)

AND  z = 22-2x-5y = 1

Hi



   e^y=3

  ln(3) = y

Hi

 (1/8)mi = (1/8)5280ft = 660ft

 660ft/hr = 660/60min = 11ft/min

Hi



  | 1968 -1987



  |1968-2018 

Hi

 



y = (1/9)x+2  |slope of  ⊥ line would be -9 (negative reciprocal of 1/9 )

New Line

 y = -9x + b  |using ordered pair Pt(3,-3) mto solve for b

-3 = -27 + b

 24 = b

 y = -9x + 24

 

Hi

 r = 6cm and h = 8cm

S = = 72*pi cm^2 + 96*pi cm^2 |surface area for top and bottom and side

S = 168*pi cm^2

Hi

using Proportions to determine drawings to scale:

1) 1"/(8') = x/40'  |cross multiply to solve

     8x = 40

      x = 5"

2) 6.5"/78' = 1/x 

     6.5x = 78

        x = 12'  Scale 1":12'

3) (27/8)"/x = 1"/4'

       x= (27/8)*4 = 27/2 = 13.5'



If I am understanding the question properly :)

111+333+777+999: replace five of the digits with 0's so that the sum equals 1,111

  333 + 777 = 1,110

 1,110 + 001 + 000 = 1,111

Hi

Question relates to a Arithmetic Sequence {30,32,34...} where d = 2

and the terms are the enumber of seats in each row.

  |Sum of the seats in the 26 rows.

 = 1430 seats in the ALL 26 rows

Hi

 66km/3hr = 22kmph

Hi

speed of the current is 2 mph

Let (x+2mph) and (x-2mph) represent the speed of the boat down and upstream respectively,

D = r*t  OR t = D/r

Question states*** (total time up and down is 6 hr)

 5/(x+2) + 5/(x-2) = 6  |multiplying thru by (x+2)(x-2)

5(x+2) + 5(x-2)=6(x+2)(x-2)

 10x = 6(x^2 - 4)

   6x^2 -10x - 24 = 0

  2(3x^2 -5x - 12) = 0

   (3x^2 -5x - 12)= 0

factoring

   (3x +4)(x-3)= 0 Note:SUM of the inner product(4x) and the outer product(-9x) = -5x

   (3x +4)= 0 |tossing out negative solution for speed

     (x-3)= 0  x = 3mph, speed of boat in still water



CHECKING our Answer***

   5/5 + 5/1 = 6hr

Hi

10x-7=4x-25

Solving for x

  6x = -18

   x = -3

Hi

 y=12*3^x for x=4

y = 12*3^4 = 972

Hi

f(x)= x^3+2x^2-13x+10 

    x^3+2x^2-13x+10 =0   |Determined x = 1 a root, thus (x-1) a factor

f(x)= (x-1)(x^2+3x-10)   |divided (x^3+2x^2-13x+10) by (x-1)

f(x)= (x-1)(x+5)(x-2)    |factored (x^2+3x-10)

       Note:SUM of the inner product(5x) and the outer product(-2x) = 3x



f(x)= 2x^4+6x^3-2x^2-6x 

f(x)= 2x(x^3+3x^2-x-3)  |factoring out the 2x

(x^3+3x^2-x-3) = 0      |Determined x = -1 a root, thus (x+1) a factor

f(x)= 2x(x+1)(x^2+2x-3) |divided (x^3+3x^2-x-3)by (x+1)

f(x)= 2x(x+1)(x+3)(x-1) |factored (x^2+2x-3)

           Note:SUM of the inner product(3x) and the outer product(-x) = 2x



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