ElectricPavlov

A:   Let x = sin (theta)

then   2x^2 +x -1 = 0     then use quadratic formula to find x  (which is sin(theta))

B: Use your answer from A to determine theta possibilities

|-7|   = 7      you can use the web2 calculator to find such things.....

This is the calculator output:

|-7| = 7

I > M > n    should be pretty obvious....but let's just pick some numbers to put in there...

I = 10   M = 5     then      I > M     because   10 > 5

Now suppose   we pick '2' for n    then   M>n  because   5>2

Now what do you find for the relationship between  I  and n ?     I =10   n = 2

According to the bar graph there are    6+4 +1 + 9 = 20 outcomes

Pink has 6 outcomes     6/20 = .3

  green   4                      4/20 = .2

  yellow   1                      1/20 = .05

   blue     9                       9/20 = .45   probability       

I think answer 'a' shows the probabilities correctly

    answer 'd' shows the frequencies correctly  

First find the angle next to 123     123 + angle1 = 180

   then fin the ngle next to 114       114 + angle2= 180

Now you can compute the third angle in the bottom tringle

  Angle 3 = 180 - angle 2 - angle 1

this will also be the bottom angle in the right triangle

 then the other angle in the right triangle will be   180 - 90 - angle 3

   this will also be the angle in the bottom of the TOP triangle

     the other two angles in the top triangle are = (and this includes 'x')

               so subtract this bottom angle from 180    and divide by 2 to find 'x'       Give it a try !

You are multiplying 12 by a fraction....which makes it a fraction of its original self....i.e. smaller......

Richard rate = 1 driveway / 8 hours

Ayanna rate = 1 driveway / xhours

Their combined rate completes the job in 3 hours

3 = 1 driveway / (1driveway/8hours + 1 driveway/xhours)

3 = 1 /(1/8 + 1/x)

3/8 + 3/x  = 1

3/x = 5/8

3 / (5/8) = x

x = 24/5 = 4 4/5 hr for Ayanna 

Ya omitted something: 

"....must be at least ???  women included?"

You can do it 'long hand' with a pencil and paper......the hard part will be finding the squre root of the denominator!

 i can get to here just 'in my head'

-30 / sqrt(1050)      then it gets more involved  You can estimate the square root in your head as 32 point someithing....but then you have to do the division long hand......

I'll do it in parts using the Web2.0 calculator:

2250-0.75*40*40 = 1050

1050^(.5) = 32.4037034920393012

-30/ 32.4037034920393012 = -0.9258200997725514603