Melody

If you have already asked this question then you should include a link to the original question and ask people to answer it on the original. Otherwise you may get two answers and this annoys answerers. 

How many ways are there for 8 people to sit around a circular table if none of Alice, Bob, and Eve (three of the 8 people) want to sit next to each other? Two seatings are considered the same if one is a rotation of the other.

Anyway, I'd just seat the 5 first.  Sit one anywhere and then there are 4! = 24 ways to seat the others.

Now we have 5 between spots where we can sit the other 3 people.  So that woud be 5P3 = 60 ways

So that is  24*60 = 1440 ways I think. 

GP      37, ...   925

925/37=25

So the common ratio must be a factor of the form    25 to the power of some number

The obvious ones to try are    \(\pm25\;\;or\;\; \pm5\)

-185/37 = -5    could be that one

-4625/37 = -125 = (-5)^3  or that one

-925/37 = -25  = (-5)^2   or that one, no that cannot work, just by inspection.

481/37 = 13    not that one

37,    37*-5,    37*-5*-5,.....

37,    -185,         925,     -4625,  

so there are two answers and both have the common ratio of  -5

Bob has 45 coins in her piggy bank. She has one fewer nickel than she has dimes, and one fewer quarter than three times the number of nickels. If Bob has only nickels, dimes, and quarters, how many nickels does she have?

N=number of nickels

D=number of dimes

Q=number of quarters

N+D+Q = 45

N=D-1

Q=3N+1

  = 3(D-1)-1

  = 3D-3-1

  = 3D - 4

so

N=D-1

Q=3D-4

D= D

D-1 + 3D - 4 + D = 45

                5D - 5 =  45

                      5D = 50

                        D = 10

N = 10-1 = 9

She has 9 nickels

Say you buy no steak at all then all the money goes on chicken 100/1.29 = 77.5 lbs of chicken

Say you buy no chicken and all the money goes on steak 100/3.49  = 28.6 pounds of steak.

I can graph this. You can purchase any amount of the 2 types of meat that lies inside the triangle

Hi, I can help you :)

The points A (6,1) and B(-2,5) are on the line with equation y=-1/2x+4 

M is the midpoint of AB

Find an equation of the line through M that is perpendicular to y=-1/2x+4

the gradient of the line   y=-1/2x+4   is    \( -\frac{1}{2}\)

The gradient of the line that is perpendicular is the negative reciprocal which is    \( +\frac{2}{1}=2\)

So 2 will be the gradient of the new line.

The midpoint of AB is simply  the average of the xes and the average of the ys     

\(midpoint=(\frac{6+-2}{2},\frac{1+5}{2})\\ midpoint=(\frac{4}{2},\frac{6}{2})\\ midpoint=(2,3)\\\)

So you want the equation of the line through (2,3) with a gradient of 2

there are lots of methods to do this.

Here is one, my start is a bit different from normal, I think it makes it easier because it is the same for many different questions. You just need 2 different ways to express the gradient to make it work.

\(\begin{align} gradient &=gradient\\ m&=\frac{y-y_1}{x-x_1}\\ 2&=\frac{y-3}{x-2}\\ 2(x-2)&=y-3\\ 2x-4&=y-3\\ 2x-1&=y\\ y&=2x-1 \end{align} \)

I hope all that helps :)

The numbers  are written down and some of them are colored blue. A coloring is called factorific if there is at least one blue number, and for each blue number, all of its divisors are also blue.

If Grogg randomly colors some, all, or none of the numbers from 1 to 6 blue, what is the probability that his coloring is factorific?

I have made an assumtion here. The likelihood that any individual number is blue is 50%

For this to work number 1 must be blue because it is a factor of all the others.

Since 1is blue, it really doesn't matter whether 2,3 or 5 are blue as their only factor other then themselves is 1.

6 blue , 3blue, 2 blue, 1 blue others don't matter.   Prob = 0.5^4 = 1/16

6 not blue, 4 blue, 2 blue, 1 blue others don't matter  Prob = 1/16

6 not blue, 4 not blue, 1 blue and others don't matter  Prob = 1/8

1/16  +  1/16  +  1/8 = 4/16  = 1/4 

I think that the chance that his colouring is factoric is  1/4

Here is a correction to you answer guest :)

Simplify the following:

(-125)^(1/3)

(-125)^(1/3) = (-1×125)^(1/3) = (-1×5^3)^(1/3):

(-5^3)^(1/3)

(-5^3)^(1/3) = (-1)^(1/3) (5^3)^(1/3) = (-1)^(1/3)×5^(3/3) = (-1)^(1/3)×5:

= -1*5

= -5

(-1)^(1/3) = -1 becasue  (-1)^3=-1

(-125)^1/3

since 

 (-5)^3=-125

(-125)^(1/3) = -5    

A fair, twenty-faced die has 19 of its faces numbered from 1 through 19 and has one blank face. Another fair, twenty-faced die has  of its faces numbered from 1  through 8 and10 through 20 and has one blank face. When the two dice are rolled, what is the probability that the sum of the two numbers facing up will be 24.  Express your answer as a common fraction.

P(sum is 24)= 15/(20*20) = 15/400 = 3 /80

25%+35% = 60%