Hi, 

In General for Cases where Interest compounds Contiuosly 

A = Accumulated Amount $15000

P= principal = $5000

r= annual rate = .025

t= years = 





 ln3/.025 = t = 43.9 yrs

 

Hi, 

five rational number between -4 ad -2

  -2.25, -2.5,-3, -3.5,-3.75

 

Hi, Re:Your TY

(1, -2) 4x-3Y=10 or 4*1+3*2=10 4+6=10  Yes

x+4y=7 or 1+4*(-2)=7   1+(-8)=7  No:  -7 ≠ 7

Might Check Your Sign in EQ II:  would yield the solution (1,-2) , y = -2 and x = 1

I.  4x-3y = 10

II. x+4y = 7              ||Signs SO important to the Solution

   4x-3y = 10

  -4x-16y = -28

     -19y = -18

        y = 18/19 = 0.947368421052632  and  x = 3.21052631578947

(1,-2) is a Pt on the fist line, not the 2nd line. The Solution for this system

of Two EQ, is as You found: x = 3.21052631578947, y = 0.947368421052632 

 

Hi, 

The sum of the reciprocals of two consecutive positive odd integers is 16/63



  63(n+2) + 63n = 16n(n+2)              |||Multiplying thru by 63n(n+2) so as all denominators = 1

  16n^2 - 94n - 126 = 0



  n = 7, tossing out negative solution

   7 and 9 are the two consecutive positive odd integers

CHECKING our Answer***

1/7 + 1/9 = 16/63

 

Hi, 

triangle ABC: vertices A(-1,2) B(1,5) C(5,2). 

  A = (1/2)bh = (1/2)6·3 = 9 units^2

 

Hi, 

8 cans of soft drinks, 4 different brands with 1 regular and 1 diet for each brand.(4 diet and 4 regular)

4 cans in arranged in a  row randomly.

P(first two are diet and second two are regular)  

 

Hi, 

Find the value of x so that the line joining the points(x,3)and (2,1)is parallel to the line joining (x,5)and (-1,2)

Note:  slopes Equal  

(x,3)and 

(2,1) 



(x,5)and 

(-1,2) 

    ||Cross Multiplying to solve

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

       x = 8

 

Hi, 

An aviary contained 12 birdies and 15 eagles.  BIRDS in all.

seven of them flew out.

P(4 birdies and 3 eagles escaped through the window in alternating order)

P = 

 

Hi, 

33 adult men had a mean weight of 182.5 pounds and a standard deviation of

22.5 pounds

ME = 2.576*22.5/sqrt(33) = 10.1		

CI: 182.5-10.1 < u <182.5 +10.1

  CI: 172.4 < u <192.6	

________________________________________________________________________________

	a	a/2	crtical regions	

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

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<-2.576	        z >+2.576

 

Hi, The Idea is to factor out what the two terms have IN COMMMON...

     ||NOTE: 2x·2x = 4x^2



  2x +2y = 2(x+y)



   5xy-12x = x(5y-12)

 

 

Hi, 



base = in^2, r = 5

 height equal to the radius.

V = 

 

Hi, 

3/20 'of' 64 = = 96/10 = 9.6

 

Hi, 

cone with a basic circumference of 19pi cm and a height 6cm less than twice the radius



C =   r = 19/2  and r^2 = 90.25

V = 

 

Hi,

 log2+logx=1og32

  =   

    2x = 32

     x = 16

Basic facts about Logarithms:

*********



*****

 

Hi, 

Note: Category Change

 A rectangular garden is 9 ft longer than it is wide

Let w and (w+9) represent the width and length respectively

Question states***area is 486 ft2.

   w(w+9) = 486

   w^2 + 9w - 486 = 0 





  w = 18 (throwing out neg(-27) solution for length

 w = 18 ft and length = 27 ft

CHECKING our Answer***

   18*27 = 486

 

Hi, 

Using the vertex form of a parabola,  where(h,k) is the vertex

 y = ax^2

 7 = a(1)^2

 7 = a

  

 

Hi, 

Using the vertex form of a parabola,  where(h,k) is the vertex

V(-2,4);P(3,-1) 

 x = a(y-4)^2 -2

3 = a(-5)^2 -2

 5/25 = a

 1/5 = a

,this is the Vertex form for parabola opening right and or left ( in this case >0, opens right.   

 

Hi, 

Points (2,1) and (4,-7) are endpoints of the diameter of a circle.

D =  r = 

Midpoint Pt(x,y):  ( , )

 Midpoint Pt (3,-3)is the Center of this circle

 

 

Hi, understand now You were referring to this Inquiry

monthly phone bill is normally distributed with a mean of $50 and a standard deviation of $10

What is the 25th percentile: (x-50)/10 = -.6745  ||Note: NORMSINV(0.25)= -.6745

 (x-50)/10 = -.6745

    x  = $43.26 

 

Hi

Jane has  stamps: twelve stamps worth 25 cents each and eight stamps worth 13 cents each?

Selects 5

P(3(25¢) and 2(13¢) = 12C3*8C2/20C5 = 220*28/15504 = .3973

 

Hi

Note: The probability of x succesP(0)ses in n trials is: 

P = nCx*  where p and q are the probabilities of success and failure respectively. In this case p= .70 & q = .30 and n = 13

nCx = 

P( making >5) = 1 - [P(0)+P(1)+  P(2) + P(3) + P(4)+ P(5)]

P = 1-( ++++)= .9960

Recommend using TI or stattrek.com for statistical calculations.

Above is an explanatory presenation.  Hope this helps.

 

Hi

40 hours and a standard deviation of 1.2 hours

P(lasts longer than 42 hours) = 1 -P(z ≤ (42-40)/1.2) = 1 -NORMSDIST(1.6667)= .0478    

 

Hi

urn contains  balls:  5 yellow, 6 green and 7 blue balls

two balls are randomly drawn 'without' replacement

 A. P(both balls are green) = 

 B. P(the first ball is blue and the second is yellow) = 

 C. P(there is one green and one yellow ball)= 6C1*5C1/18C2 = 30/153 = 10/51

 

Hi

salary of $24000 per year. About what salary would you need 4 years from now 

to maintain your purchasing power in case the inflation rate stays at 2.9%?

In General 

A = Accumulated Amount 

P= principal = $22400

r= annual rate = .029

n= periods per year = 1

t= years =  1



  A= = $25,725

 

Hi, re TY, please post so as Inquiry is placed in proper section. TY.

'What annual rate of interest would you have to earn on an investment of $2500

 to ensure receiving $152.50 interest after 1 year?'

In General 

A = Accumulated Amount = $2652.50

P= principal = $2500

r= annual rate = 

n= periods per year = 1

t= years =  1



  2650.50/2500 -1 = r

 r = .061  or 6.1%

 

Hi

$6000 is invested 5 years at 4% annual interest,compounded monthly

In General 

A = Accumulated Amount

P= principal = $6000

r= annual rate = .04

n= periods per year = 12

t= years =  5



 A =  = $7181.37

 

Hi

logarithm  = 3, as 7^3 = 343

2log16(x)-6= -5 

 = 1/2

   16^(1/2) = x = 4  

________________________________________________________________________

 

Hi

You draw from bag  times that has 4 red and 6 black balls in it, with no replacement

 P(3 reds) = (4C3*6C2)/10C5 = 4*15/152 = 60/152 = 15/38

 

Hi

Note: The probability of x successes in n trials is: 

P = nCx*  where p and q are the probabilities of success and failure respectively. In this case p & q are = 1/2 or .5

nCx =   14C5 = 2002

P(5) =2002*  = .1222

Can highly recommend stattrek.com for statistical calculations

 

Hi

Light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours

what percentage of light bulbs have a life less than 2500 hours(the mean)? 50%

 

Hi, re TY, see higlighted Percentage (Others were for comparison purposes only)

the lifetime of light bulbs of a particular type are normally distributed with a mean of 370 hours and a standard deviation of 5 hours. 

What percentage of bulbs has life times that lie within 1 standard deviation of the mean on either side? 

****one  standard deviation from the mean accounts for about % 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%.