CPhill

1.  Minimum value is  y  = -6

2.  In the form    y  =  Asin(Bx) + C

A  =  5

Since the y intercept  is  (0, - 2), C  is  -2

To find B we need to solve this

B  =  [ 2pi ] / period  =  [ 2pi  ] / [ 6 pi]  =  1/3

So....the function is :

y = 5sin ( (1/3) x )  - 2

Here's the graph :  https://www.desmos.com/calculator/0s8smsawk2

The midlne is  y  = -2

The first point on the midline  is  (0, - 2)

The next point  [to the right of the first point ]  is a max at  (3pi/2, 3)

First one  :

In the form    Acos(Bx) + C

We can  find this as follows

B  =  pi

B   =  2pi / period   

pi  = 2pi/ period      rearrange

period  =  2pi / pi    =  2

Andd the frequency  is     1  / period  =   1 / 2

Second one :

The period is   π

The frequency  is  :     1  / period    =   1  / π

(b)  P( x < 4)  =     ( 5 + 10 + 2 + 9 )  / ( 5 + 10 + 2 + 9 + 33 + 12 + 15 + 3 + 1 ) =  13/45

(c)  P(x  = 6)  =  15 / (5 + 10 + 2 + 9 + 33 + 12 + 15 + 3 + 1)  =  1/6

(d) P( x ≥ 5 ) =  (12+ 15 + 3 + 1) /  (5 + 10 + 2 + 9 + 33 + 12 + 15 + 3 + 1) =  7/30

1)  Rosala....I  believe  the value of  n  is 8

Reasoning

The first letter can be chosen 3 ways...either A, B or C

But....the second letter can only be chosen 2 ways.....for instance....if A  is the first letter, the second can only be chosen  2  ways, either another  A  or   C

And notice that each successive letter can only be chosen in 2 ways......for instance...if the second letter is B, the third letter can only be another B  or A

So.....we need to solve this  to find the number of additional letters, m, after the first one

 3 * 2^m  =  384       divide by 3

2^m  = 128

And m  =  7  makes this true

So....the the number of total letters  is

First one + m additional    =  1  + 7  =  8

Another way to see this is

3 * 2 * 2 * 2 * 2 * 2 * 2 * 2  =  384

Number 3

Rosala....here's the explanation for the book's answer :

Note...if fthe leading digit cannot be 0, we have 9 choices for this

And for the next two digits, we have 10 ways to choose each

But note....that  the last digit must be even if the number is divisible by 2....so....we only have 5 choices for this  2,4,6, 8 or 0

So..... we have    9 * 10 * 10 *  5  =    4500 

Hope that helps....!!!!

tan (2pi / 3)  = - tan (60°)   = -√3

cos ( 11 pi / 6 )  =  cos (30°)  =  √3 / 2

So....substituting, we have

-√3 +  4 (√3 / 2 )  =

-√3  + 2√3  =

√3

The number of permutations  is   6!  =  720

cos θ  =  - √ [  1  -  sin^2  θ ] =

- √ [  1  -  (4/7)^2 ]   =

- √ [  1  -  16/ 49 ]   =

- √   [ 49 - 16]  / 7  =

- √33 /  7

We take the negative root  because the cosine i negative in quadrant 2

10!  ways  =  3,628,800  ways  !!

We need to find r =   √  [  (-3)^2  + 7^2 ]  =  √ 58

So...sin  θ  =   7 / √ 58   =  7√ 58 / 58

We take the positive root because the terminal side of the angle is in quadrant 2 and the sine is positive there