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Let d = OP.  Then cos POA = a/d and cos POB = b/d, so POA = acos(a/d) and POB = acos(b/d).

You can then write cos(acos(a/d) + acos(b/d)) = cos(60) = 1/2.

Since cos(x + y) = cos(x) cos(y) - sin(x) sin(y), you can then plug into this formula to solve for d.

Nvm, I found out my mistake on the bonus question!!! So, you guys don't need to help on that one anymore. Thank you once again :D

Thank you guys :D

Thank you, Electric Pavlov, this problem seemed easy to me at first, but I'm not very good at "Counting and Probability". Thank you :D

If this is drawn proportional to scale, it would be C. Also, I remember there is a thereom to solve this, but I'm sorry I forgot.

 p = pennies        1p  = value of pennies

n = nickles..... this equals  3p  ( this is given in the Q)  ....value of nickles =  5 (3p) 

                 summed thes equal 1568

1p      +      5(3p)        = 1568

16p = 1568                       solve for p, the number of pennies      then  # nickles = 3 * p

   126 students   *   2 slices / student   *   1 pizza/ 8 slices    =  31.5 ~~ 32 pizzas    

                                                     See how things 'canel out' and you are left with only 'pizzas' ?

                                                               THAT is often the easy way to 'figure' these types of problems  !  

52 students total

   soccer has   'x' students   and  f has   x+12  students  ( f has 12 more than s    <------ given in the equation)

       they sum to 52

x       +    x+12     = 52     solve for 'x' <--- the number of soccer students     then f = x + 12    the number of field hockey students

If you need more help than what has been given, you are in a class too far above you current knowledge level and need some remedial work to get you up to speed........please let someone know this. 

just kinding but thanks for the help

:( Please I need help

On an ordinary day, the boat can cover the distance of 4 miles in:

4 /12 =1/3 of an hour, or 1/3 x 60 = 20 minutes.

But, on some particular day, it took the boat: 20 + 15 = 35 minutes to travel that 4 miles.

So: 4 / x =35/60

x =4 / (35/60)

x =6  6/7 mph - the speed of the boat on that particular day.

12 - 6  6/7 = 5 1/7 mph - the rate of the current on that day.

  You have to finish the math ....   and YOU have to select one of the letters !  

Look across the table and see where f(x) = (g(x)    

      at x = -1     f(x) = 1    g(x) = -7     not equal  

                      continue on down the table to find all of the values of x that result in f(x) = g(x)   

                                             ( there are more than one value of x where this is true!)

you have to select one of the letters

Slope = rise/run =   y1-y2  /  x1-x2

     =   (2-4) / ( -1 -3) 

     = -2    /   -4   =    .......

I almost never look at questions with unnecessary $ signs. It shows me how lazy the asker is. 

You have 6 numbers between 10 and 60 =6

You have 13 numbers between 100 and 200 =13

13  x  6 = 78 numbers

You have  1 number for 1000.

So: 6 + 78 + 1 = 85 such numbers.

Hi answering guest,

I think that you have double counted.

lets assume there are 2 prizes. Non americans get both.  there would be 11 ways for the first one to be allocated and 10 ways for the second one.

So that is 110 ways to place the non americans in realtion to EACH OTHER

Now the american has to be slotted in.  There is 4 to choose from and 3 places to chose from (infront, in middle, or at back)

So that is 12 ways the americans can be slotted in

Altogether I think there are    110*12 = 1320 ways.

There are 3 groups of skaters as follows:

4 x 11 x 10 =440 ways. But 1st,  2nd and 3rd prizes can be awarded in 3! =6 ways.

Therefore, there are: 440 x 6 =2,640 ways.

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Hi there...

If there are "126" students on the 6th grade team, and they are planing a party.

Where each student will have two slices of pizza.

That means that they need at least "252" slices of pizza.
If each pizza provides "8" slices each, the following equation will give you the answer.

((126*2)/8)=31.5

That means they roughly need "32" pizzas.
 

Kind regards

BizzyX

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Hi there...

It was badly phrased, and therefore I have removed my original post.
If you got the impression that I was in anyway attacking.
Or bad mouthing..., I'm sorry...
That was not my intention.

Kind regards

BizzyX

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Here is the graph of y=1/x

You can see that as x approaches 0 from the positive side, 1/x approaches infinity.

But

you can also see that as x approaches 0 from the negative side 1/x approaches -infinity.

Therefore  1/0  is undefined.   

I think you can find the area of a trapezoid:

A=(a+b) / 2h

   =(224 + 77) / 2 * 334

   =50,267 mm^2 - the area of the face of the fiddle.