ElectricPavlov

You THINK??  Be a little more confident in your abilities !        Yes, it is "C"

put the fractions in a common denominator  (110)

99/110 < a/b < 100/110     

  does not help much, huh? There are no integers between 99 and 100   sooooo: Let's double everything (the next common denominator)

198/220 < a/b < 200/220          Now we might guess b to be least at 220  (and a to be 199)

Yes....

and yes...

and yes....

Put in 5 where ' b' is in the equation   and put in -3 where 'c' is in the equation and solve

Remember :  Rate x time = distance     re -arrange as     Time = distance/ Rate

Time =  800 km / 390 km/hr =   you can do this part !

2.  If k is constant .....then as 'x' gets larger the value gets smaller (because 'x' is in the denominator)

       SO....which do YOU think it is ?

3. y = mx is a direct proportion       y is directly proportional to x    by factor m

18 beats/15 seconds   x  60 seconds/ 1 minute = 18 x60 /15 = 72 beats/min

25 beats / 10 sec x 60 sec/1 minute = 150 beats/min

150 beats / min x 3 min      -    72 beats/min x 3 min =

150 x 3       - 72 x 3 =

= 234 beats more

Where is the vector in question?

If you do it correctly, you should find x = 1/2   or  -1     (which is the value of sin(theta) )

The Identity is:

Tan (A+B)  =  (Tan A + Tan B) / (1-TanA TanB)

I'll do the first one....you can do the rest..I'll use exact values rather than calculator values

Tan(30+45) =  (tan30 + Tan 45) / (1-(tanA tanB )

                   =  (1/2/(sqrt3/2) +1)/ (1 -(1/2(sqrt3/2)(1))

                   =  (1 + 1/sqrt3) / )(1-(sqrt3))

                    ((sqrt3 +1)sqrt3) / (sqrt3-1)/sqrt3

                     (sqrt3+1) / ( sqrt3-1)         ~  = 3.73

There are 36 possible combinations of rolls

if B rolls a

1   there are 5 higher rolls that A could roll

2                   4

3                   3

4                   2

5                   1        5 + 4 +3 + 2 + 1     15 out of 36 combinations with A> B      15/36= 5/12

(as an aside: there will be 15 rolls where  A < B   and  6 will be ties    15 + 15 + 6 = 36 possible rolls)