CPhill

There are 36 possible outcomes

The number of rolls where Amaya's roll is greater than Bo's  is

5  +  4  +  3  +  2   + 1  =  15

So....the probability is  

15 / 36   =

5  / 12

[ x / 6]  +  2  =  15          Given

[ x / 6 ]  + 2 - 2 =  15 - 2                 Subtraction Property of Equality

[x/ 6]  =  13

6 [ x/ 6]  =  6 * 13                        Multiplication Property of Equality

x  =  78

Fixed now....I'm trying to answer too many questions at once....LOL!!!

These are common reference angles,  Adam

You really just need to memorize this chart :

http://www.analyzemath.com/trigonometry/special_angles.html

Note that the reciprocal  of  √2/2  = 2 / √2  =  √2*√2 / √ 2 =  √2

It's not as bad as it looks...since  csc, sec and cot  are just reciprocals of sin, cos and tan, respectively.....just learn the values for sin, cos and tan......"flip" these over for  csc, sec and tan!!!

This is the way I  had to learn them.....  

Boy-Boy  =  C(5,2)  =  10 games

Girl-Girl = C(5,2)  =  10 games

Boy-Girl  =  5 * 5  =  25 games

So..... Boy - Boy  =

[ 10 ]  /  [ 10 + 10 + 25 ]  =

10 / 45  =

2 / 9

sin (pi/3)  =  √3/2

cos(pi/4) =  √2/2

tan (pi/4)   =  1

csc(pi/3)  =  2/√3  =  2√3 / 3

sec (pi/3)  =  1 / cos(pi/3) =  1 / (1/2)  =   2

cot (pi/6)  =  1 / tan (pi/6)  =  1 / (1/√3)  =   √3

P  +  .04* P   = 

P( 1 + .04)  =

P (1.04) =

(1.04)P

Note that  we have 5 girls....and we want to choose any 2 for a game....so

C (5.2)  =  10  games

-7 pi    is the same angle as  + pi ......  on the unit circle, the coordinates  are  (-1, 0)

cos(−θ) =−3/5       tan θ  > 0  

Note  that  cos(-θ) = cos (θ)  ....so....this angle is is in the 3rd quadrant.......so....the sin (-θ) is

y / r  =   - √ [5^2  - (-3)^2 ]  / 5   =  - √ 16/ 5   =   - 4 / 5

1. A population of bacteria doubles every 12 hours. Initially, the population of bacteria is 80.

What is the population of the bacteria after 30 hours?

We have the following

80 (2) ^t/12     ....so.......when t  = 30....we have

80 (2) ^30/12 ≈   453

2. What type of exponential function is f(x)=0.75(2.1)^x

In the form

f(x)  =  a* b^x      if  b >  1   we have a growth function  as x increases

So......This is a growth function......the rate of change  is  2.10 * 100  =   210 %

3.  Just  put 4 into the function

(4)^4−2(4)^3+5(4)^2−20(4)−4   =

256  - 128 + 80   -  80  - 4   =  

124