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Anchor  Rick and Morty in any two seats

And they can be arranged in 2 ways

And we have  C(7,1)  =  7  ways to pick  the person  to sit between them

And the other members can be arranged in 6! ways  = 720 ways

So......the total arrangements   =

2 * 7  * 720   = 

10080  possible seatings 

The vowels  "ooa"   can be  arranged  in 3 identifiable ways

And they can appear  in 6 possible places within our created "words"

And for each of these, the other letters can be arranged in  ( 5! / 2 )   identifiable ways  =  60 ways

So....the  number  of ways  =  

3 * 6  * 60   =

18 * 60  =

1080  ways

The number of possible seatings is 9!*2*2/9 = 161280.

Thank you so much CPhill!!

thank you!!!!

...AND you asked it   AND already got an answer.....    You need to get an easier class....the one you are in you cannot handle.  You are only 'passing' because you are getting answers here without your trying at all !    

https://web2.0calc.com/questions/this-system-has-one-solution

help

20 is to 120 as 'x' is to 93 ?

20/120 = x/93    Multiply both sides by 93

20/ 120  * 93 = x     ====15.5 lbs

a) Violet has six beads that she wants to assemble into a bracelet. Two of the beads have the same color, and the rest have different colors. How many different ways can Violet assemble her bracelet? (Two bracelets are considered identical if one can be rotated and/or reflected to obtain the other.)

Without the reflection it is straight forward.

5!/2 = 60

With the reflection I am not at all sure.

Since one of the beds must  stay fixed, 

Every permutation would have exactly one reflection permutation so I think maybe you divide by 2

Which would be 30 

Can you please let us know when you have the answer as we can all learn that way.

y = x^2  - 3x + 7

y = 3x  - 2

Set these equal

x^2 - 3x + 7 =  3x  - 2         subtract 3x form both sides, add 2 to both sides

x^2  - 6x  + 9  =  0           factor as

(x - 3)^2  = 0            take the root

x - 3  = 0

x  = 3

Using     3x - 2, then  .....  y  = 3(3) - 2 =  9 - 2  =  7

To  be divisible  by  11  we  must have that   either

8 - X  + 3  - 5  +  7   =   0        simplify

13 - X  = 0

X = 13    [ impossible ]    

or

8 - X  + 3  - 5 +  7   =  11     simplify

13 - X  = 11

X = 2

Check     82357 / 11  =  7487

Seriously, do you actually ever do your own homework?

To find the x intercept, set  y  =  0   and we have that

5x  = 60

x  =12

So.....the x intercept  is  (12, 0)

To  find the  y intercept, ley  x  = 0 and  we have that

12y  = 60

y = 5

So.....the  y intercept is  ( 0, 5)

The distance between these  = 

sqrt  [ ( 12 - 0 )^2  + ( 5 - 0)^2 ]  =

sqrt [ 12^2 + 5^2]  =

sqrt [ 144 + 25 ]  =

sqrt [ 169  ]  = 

13 units

The minimum is, I think, 15.

Suppose that \(f(x)=a+bx+cx^{2}+...\)

then \(|f(0)|=a.\)

Substituting x=5 and x=7 gets you

\(20-a=5b+25c+...\)

and

\(20-a=7b+49c+...\)

For integer a, b and c, it's necessary that 20 - a should be divisible by both 5 and by 7.

The smallest, in magnitude, a, is -15.

The quadratic \(f(x)= -15+12x-x^{2}\) 

works, I haven't looked for a cubic.

Please ask one question

Think about the answer, interact with the answerer. (which you may have done here)

Then

Put the next question in a DIFFERENT post

Just cross-multiply and we get that

8 ( x - 4)  =  24x      simplify

8x - 32  = 24x        subtract  8x from both sides

-32 =  24x - 8x

-32 = 16x       divide both sides  by 16

-32/16  =  x

-2  = x

Not as  hard as it seems

Call the lower left vertex of the  triangle, B

Let the center of the bottom left circle  be A

Let the radius of this circle intersect the base of the triangle at C

So.....triangle  ABC  is a 30 -60 -90   right triangle

And   BC  =  radius  of the circle * sqrt (3)  = 1 * √ (3)   =  √ (3)

So....using symmetry...the side of the  triangle  =

2BC + 8 r  =

2sqrt (3)  +  8 r   =

2sqrt (3)  +  8  =

√12 + 8

So....the area of the  triangle =

(1/2) ( √12 + 8)^2 * (√3/2) =

(√3/4)  ( 12 + 16√12 + 64)  =

(√3/4) ( 76 + 16*2√3)   =

√3 ( 19 + 8√3)  =

19√3 + 24  units^2  ≈  56.9  units^2

Let  E   be the  point on the  circle that also lies on DC

Then     DE  =   sqrt  ( 14^2 - 7^2)  = sqrt [ 7^2  ( 2^2  - 1) ] =  7sqrt (3)

So  the  area of triangle  DEA =  (1/2) (DE)(DA)  = (1/2) (7sqrt (3)) ( 7)   = (49/2)sqrt (3)  units^2    (1)

And the sine of  angle  AED  = sine of  angle  EAB  = 7/14  =  1/2

So

arcsin ( 7/14)  =  arcsin (1/2)  =  30°  =  angle EAB 

So.....the  area of sector AEB  =   pi (r^2) (30/360)  =

pi ( 14)^2 (1/12)  =  (196/12) pi =  (49/3) pi  units^2    (2)

And the area of the  rectangle =  14 * 7  = 98 units^2     (3)

So....the shaded area =  (3) - (2) - (1)  =

98  - (49/2)sqrt (3) - (49/3) pi  ≈   4.252 units^2

With M as a center,   construct a circle  with radius   MS

This circle will pass through  S , X  and R

Since MS  = MX, then angles  MSX   and  MXS  are equal

So  triangle   MSX  is isosceles  .....so angle  SMX  =  [ 180 - 2(77) ]  =  26°

And this is a central angle in the  circle that intercepts minor  arc   SX

And angle XRS  is an inscribed angle in the circle that intercepts this same arc

So....the measure of angle XRS =  (1/2)26°  = 13°

I disagree, XRS is 103 (180-77)-SXR (the last angle of triangle SXR that we haven't mentioned yet). Where did you get the numbers 77 and 60?

Hint: Use trigonometry

What is the trigonometric function that deals with the adjacent side and opposite??

solution:

tan(37)=h/15

15*tan(37)=h

h=11.3

The area of a circle  =  pi * r^2

So....to find the radius of each circle  we have that

10  = pi * r^2

10 / pi  = r^2

The width of the rectangle  = 3r

And  the height = 2r

So.....the area =   3r * 2r  =   6r^2  =  6 (10 / pi)  =  60 /pi  ≈  19.1 units^2  ≈  19  units^2 

EDIT TO CORRECT AN EARLIER ERROR  !!!! 

Angle XRS works out to 77 - 60 = 17 degrees.

Let  angles  ABE and  ECD  = x

And let  angles EBD and ACE  = y

So  in   quadrilateral ABCE  angle BCE  = 360 - 100  = 260°

And in a quadrilateral, the sum of the interior angles = 360°

So  we have that     

80 + 260 + x + y  = 360

340 + x + y = 360

x + y = 20

And in quadrilateral   BECD  we have that

100 + x + y + (360 - angle BDC ) =  360

100 + 20  + 360 - angle BDC  = 360

120  - angle BDC  = 0

Angle BDC  =120°

This is  a geometric series

The sum, S,  is given by

S  =   frst term *   [  1  -  r^n ]  / [ 1 - r ]

Where  r  = the common ratio  =  -(1/4)     and  n  = 6

So we have

S =  48  [  1 - (-1/4)^6 ] / [ 1 - (-1/4) ]   =   48 [ 1 -  1/4096 ] / [ 5/4]  =

48 ( 4/5) [ 4096 - 1 ] / 4096  =

[(48 ( 4)) / 4096] *  ( 4095 / 5) =

[3/64]  * [ 819 ] =

2457 / 64