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ab=ba, so 23*22/2=253 handshakes

Oh shoot how did I forget the most important part!!! 

They are 

 \(x^4+7x^3+9x^2-17x-20\)

\(x^3-2x^2+3x-6\)

\(x^6-x^4-x^2+1\)

real sorry about that!

Bag1          Bag2         Bag3

4                 0                  0.....................1

3                 1                  0.....................2

2                 2                  0.....................3

1                 3                  0.....................4

0                 4                  0.....................5

3                 0                  1.....................6

2                 0                  2.....................7

1                 0                  3.....................8

0                 0                  4.....................9

0                 3                  1.....................10

0                 2                  2.....................11

0                 1                  3.....................12

1                 2                  1.....................13

1                 1                  2.....................14

Here is the actual distribution!!!!. Or, did I forget something???

The order of the sequence is in the order that the uestion gave it in.

For which polynomials ??/

8)ABCD is a cyclic quadrilateral. Angle A, angle B, and angle C form an arithmetic sequence in this order. What is angle D in degrees?

What is the order of the arithmetic sequence   ???

9)Points A and B are on circle O such that arc AB is 80 degrees. A circle is constructed that passes through A, B, and O. Find the measure of arc AOB on this circle.

AOB  in the smaller circle is also 80°

So.....it's intercepted ard  is  twice this  = 160°

1)Given angle APS = 77 degrees and arc AP = 123 degrees, find the degree measure of arc PS.

If angle APS  = 77°, then  arc AS is twice this = 154°

So...arc PS  = (360 - 123 - 154)   =   83°   

2)In the figure below, EF is a diameter of the circle. Arc AE = 35 degrees and arc CF = 80 degrees. What is the measure of angle ABC, in degrees?

Angle AFE  =  (1/2)(35°)  = 17.5°

Angle CEF  = (1/2)(80°)  =  40°

So ....angle EBF  = angle ABC  =  (180 - 17.5 - 40)   = 122.5° 

3)In the diagram, angle A = 30 degrees, arc DE = 170 degrees, and arc BC = 110 degrees. Find the measure of arc CE, in degrees.

The sum of arcs CE + DB  = (360 - 110 - 170)  = 80”

And  angle A  = (1/2) (arc CE - arc DB).....so....

30  = (1/2)(arc CE - arc DB)

60 = CE - DB

So

CE + DB  =  80

CE - DB   =  60      add these

2CE  =  140     divide both sides by 2

arc CE  = 70°

4)In circle O, AP is a diameter of length 17 and PS is chord of length 8. What is the length of chord AS?

AS  will form a leg of a right triangle with AP  the hypotenuse and PS the other leg....so

AS  =  √ [ 17^2  - 8^2 ] =  √ [ 289 - 64 ]   =  √ [ 225]  =   15 units

5)Grogg draws the following figure. It so happens that angle SAP is 174 degrees less than 4 times angle SOP. Find the degree measure of angle SAP.

SAP + 174  = 4*SOP

But SAP  and SOP  intercept the same arc PS...so they are equal

So...substituting

SAP  + 174  = 4*SAP   subtract SAP from both sides

174   = 3*SAP         dvide both sides by 3

58° = SAP

6)In the diagram, minor arc AB : minor arc BC : major arc CA = 1 : 3 : 5. What is angle ABC in degrees?

There are  1 + 3 + 5  =  9 equal arcs in the circle....and angle ABC  spans 5/9  of these

So  major arc  CA  =  (5/9) (360)  =  (360/9) * 5  =  40 * 5  =  200°

And since angle ABC is an inscribed angle intercepting this arc, it is 1/2 of this  = 100°

7)In the figure, if MR = MK, the measure of arc MK is 130 degrees, and measure of arc MQ is 28 degrees, then what is angle RPK, in degrees?

Since MR = MK, then arc MR  = arc MK,,,,and the sum of these arcs is 260”

So minor arc RK   =  360 - 260  = 100°

So...since angle RMK intercepts this arc it has 1/2 of its measure  = 50°

And since arc MQ is 28, then angle QKM  = 14

So in triangle PKM angle KPM  =  180 - 14 - 50  = 116°.....and angle RPK is supplemental to this  = 180 - 116  =  64°

Thanks, guest...14 is correct....

See the answer here, if you can understand it:

https://www.quora.com/In-how-many-ways-can-4-distinct-balls-be-distributed-into-3-identical-boxes

is this homework?

#5   Three sides are 2x2    so 3 x 2 x2  = 12 cm^2

        the ends are equalateral triangles with sides= 2    area =  2 sides x  sqrt3/4 x (2^2) =3.464

3.464 + 12 = 15 . 464  cm^2

or    12 + 2 sqrt(3)     cm^2        

Thank you, CPhill! Amazing!

Thanks, everyone! Do you what the answer for 5 is?

I think it's because the items are distinguishable? 

1. Four friends agree to split the cost of a rental car equally. One of the friends decided to take a taxi, so the remaining three friends each paid $11 more. What was the cost of the rental car, in dollars?

Let the cost of the rental car = C

So....the amount that each would pay before one left is  C / 4

So.....after one lleft.....the amount each pay is  C/4  + 11

So

3 (C/4 + 11)  =  C       simplify

(3/4)C + 33  = C

33  =  1/4C     multiply both sides by 4

$132   =  C 

#4      x miles/ (40 m/g)  +   x miles/(30 m/g) =  2x miles/ ?m/g

divide by x      1/40 +1/30 = 2/?      solve for ? = 34.3 m/g

#3    D=1  A=9 B=4  C=5

4) EP's answer is the CORRECT one!.

2)

10:30 PM in New York is 3:30 AM in London

3:30 AM + 6 hours, 35 minutes

10:05 AM - in London the following morning, when the plane lands.

Notice that  the 23rd person can shake hands with 22 other people

And the 22nd person can shake hande with 21 people [ this person has already shaken hands with the 23rd person]

And the 21st person can shake hands with 20 people[ this person has already shaken hands with the first two ]

So....the total possible handshakes are

22  +  21  + 20  + ......+  1  =

 1 + 2 + 3 +  ......+ 20 + 21 + 22

Which is just the sum of the first 22 positive integers and is given by :

(22)(23) / 2   =   11 * 23  =  253 handshakes

1)

Let the cost of rental car = C

Let the share of each = S, then:

C/4 =S - original share of each

3[S + 11] =C, solve for C, S

C = $132 - cost of the rental car.

S = 33 - original share of each

It says the answer's wrong...... 

...but you have to select from the multiple choice answers given...hence the correct answer is - pi/6

We have the points  (2,1)  and (3, -1)  on the graph

The slope is    [ - 1 - 1 ] / [ 3 - 2 ]  =  -2/1  =  - 2

Using either point to write the equation of a line, we have

f(x)  = -2 (x - 2) + 1

f(x)  =  -2x + 4 + 1

f(x)  = -2x  + 5    .....correct Julius  !!!!