Hi,

If Mary can paint one room in 100 minutes, and Jake can paint one room in 150 minutes, 

how long  will it take if they work together?

Question states*** PER min Key

 1/100 + 1/150 = 1/x   |Multiplying thru by 300x so as all denominators = 1

 3x + 2x = 300

    5x = 300

     x = 60min or 1 hr together

 

Hi,

Let C does 1 work in x days, then

 C = 1/x, B = 1/3x, A = 1/6x

 Total work = 1

 or, 12(1/x + 1/3x + 1/6x) = 1

prefer to think of it in this manner: work/day

 (1/x + 1/3x + 1/6x) = 1/12    |Multiplying thru by 12x so as all denominators = 1

 12 + 4 + 2 = x

 Or, x = 18

 So, C = 18 days, B = 54 days, C = 108 days   Yes. Good Work.

 

Hi,

-5x+9y= -45     or  y = (5/9)x - 5

Finding the y-intercept  (, _)  

 + 9y = -45 

      y = -5    || the y-intercept  (, -5) 



Finding the x-intercept  ( _, )   

 -5x -2· = -45

     x = 9     ||   the x-intercept is (9 , ) 

Plot (0,-5) and (9,0) and connect with a Line

 

Hi,

Yes, log2 = .3010   (rounded off to nearest 10-thousandths

Can read it as well off logarithm chart for base 10

Important thing is that  log2 = .3010  because 10^.3010 = 2 (rounded to a whole number)

KNowing   is not only important, makes one better understand what log2 is.

 

Hi,

If Keesha's car averages 25 miles per gallon, 

how much gas did it take for the 310 mile trip?

       |Cross Multiply to solve for x

 

Hi,

You stuffed 108 envelopes in 45 minutes. 

At this rate how many envelopes can you stuff in 2 hours.

Inquiry Sets Up the proportion:

}   Cross Multiply to solve  for x

     (3/4)x = 216

          x = 216(4/3) = 288 envelopes can be stuffed in 2 hours.

 

Hi





  |factoring out cos(x) is the correct idea



   cos(x) = 0

0r  sin(x) = 

Find x below on the (cosx,sinx) unit circle summary



   

 

Hi,

x^3+6x^2-4x-24 = 0    | x= 2 is a root,  8 + 24 -8 - 24 = 0

Synthetic Division...

2	1	6	-4	-24

 	 	2	16	 24

 	1	8	12	  0

Yields:

   x^2 +8x + 12 = 0

 (x + 6)(x + 2) = 0

  x = -6  0r x = -2

Roots:  -6, -2, 2

 

Hi,

4x^4=12x^2

 x^2 = 3

  x = ± 

 

Hi,

x^2 -1=0

 x^2 = 1

  x = ± 1

 

Hi,

Assume you meant:

x^4-30x^2+125=0

(x^2 - 25)(x^2-5) = 0

x^2 = 25

x = ± 5

x^2 = 5

 x = ±

 

Hi,

g(x)=2x^4-5x^3+9x^2-20x+4 

 2i is a zero, therefore so is -2i and  (x-2i)(x+2i) = x^2 + 4



x^2 + 4 |2x^4-5x^3+9x^2-20x+4   



gives: 2x^2  -5x + 1

 the other two roots

 

Hi, Previously Posted

from 68 min to 51 min?   or 25% decrease

 

Hi,

from 68 min to 51 min?   or 25% decrease

 

Hi,



cylinder with top 7m and height 11m

Assuming the 7m is the diameter  ( r = 3.5)

 V =  = 423.1 m^3 (rounded to the nearest tenth 

 

Hi,

A sample of 320 mobile phone batteries contained 16 defective batteries. 

How many defective batteries would you expect to find in a sample of 3000?

 Inquiry sets Up the Proportion

    | Cross Multiply to solve for x

 

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

h = - 16 t^2 + 12x + 10 

  

h = -16(x - 3/8) + 16(9/64) + 10 

h = -16(x - 3/8) + 9/4 + 40/4    \ parabola opening Downward  a = -16 < 0

h = -16(x - 3/8) + 49/4  Vmax(3/8, 12.25)

12.25 ft the maximum height that the ball will reach

 

Hi,

Note: 



 4^1 = x-8

   12 = x

 

Hi,

 

Find the half-life of carbon-14. 

    

   ln(2)/.0121 = t = 57.2849 yrs

the 'ln' function is on scientific calculators

 ln(2) being a symbol for 

Using a caculator, this is the quickest way to do decay problems

 enter 2, hit ln and then / .0121

  

 

Hi,

 

Hi,

x^2- 3x= -5 

x^2 - 3x + 5 = 0    | Putting into ax^2 + bx + c = 0  Format

Quadratic formula







   | Note i^2 = -1



    

 

Hi,

A bag contains  marbles: 8 green, 4 red, 5 yellow, and 6 blue marbles

Four marbles are drawn from the box at the same time. 23C4 = 8855 total possiblities

A. P(all same color) = 8C4+4C4+5C4+6C4/23C4 = 91/8855  Yes!

B. P (non are blue) = 17C4/23C4= 2380/8855   Yes!

C. P (one of each) = = 8*4*5*6/(23C4)= 960/8855  Yes!

D. P (More than 2 green) = 8C3*15C1=840 (3 yellow)

 8C4*15C0=70 (4 yellow)

 840+70/23C4= 910/8855  Yes!

Good work!

 

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

f(x)= 1/4(x+9)²+1 

+ The vertex is  (-9,1) parabola opens Upward:  a = 1/4 > 0

+ The line of Symmetry is  x = -9

+ What is the max/min value of f(x): min value is 1 

+ Is the value of, f (-9)=1, a maximum or a minimum

 

Hi,

h = - 0.44t^2 + 2.2t + 10 

 t-value at the maximum height is = 

 

Hi,

Cows are $20 each, pigs are $6 each and chicks are $1.00 each

buys 100 animals for 100 dollars 

  works

 

Hi,

What is the height of a 15 inch TV with w = 12? (15in being the diagonal of the screen)

Applying the Pythagorean Theorem

 

 

Hi,

f(x) = 0.0037x^2 – 0.46x +36.63

x-value of the minimum pt =  rounded to nearest whole number

 In which year was this average age at a minimum?  1962

 

Hi,

Suppose that an experiment is repeated four times. 

A certain event has probability 1/10 in a single repetition of the experiment.

P = nCx*  where p and q are the probabilities of success and failure respectively. 

In this case p = .1 and q = .9 ,   n = 4   

 P(x = 0) =        | nCx = 

 

Hi,

p(x) = -5x^2 + 600x +100 = 

p(x) = -5(x-60)^2 + 18100  |Completing the Square,   Vmax = (60,18100)

 at 60 units sold, profit is at a maximum



 

 

Hi,



the length of a rectangular garden is 7 feet longer then its width.

Question states***perimeter of the garden is 28 feet 0r L + W = 14ft

      L + W  = 14ft     |  L = W +7

     (W+7) + W = 14

          2W = 7

           W =  7/2 ft of ft

width is 3.5 ft and length is 10.5 ft

and...

 

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