CPhill

We have the points  (2,1)  and (3, -1)  on the graph

The slope is    [ - 1 - 1 ] / [ 3 - 2 ]  =  -2/1  =  - 2

Using either point to write the equation of a line, we have

f(x)  = -2 (x - 2) + 1

f(x)  =  -2x + 4 + 1

f(x)  = -2x  + 5    .....correct Julius  !!!!

The bags are indistinguishable, so the only thing we have to worry about is the number of ways to partition 4 items

The partitions are

(4,0,0)  (3,1,0) (2,2,0)  (2,1,1)

We could put all 4 items in one bag  = 1 way

We could put 3 items in one bag and 1 in another  = 1 way

We could put 2 items in 2 of the bags  =  1 way

We could put  2 items in one bag  and one item in each of the other two  =  1 way

So....4 ways

Here's my take

Anchor the Republicans in any 5 seats.....note that it doesn't matter which 5 seats they occupy....if rotated, all of the arrangements will look the same......and they can be arranged in 5!  = 120 ways

So.....the Democrats  occupy the other 5 seats and they can be arranged in the same muber of ways = 5!  = 120 ways

So...the total arrangemets are   (Ways to arrange the Republicans) x ( Ways to arrange the Democrats)  =  120 x 120  =  14,400

To see this..let's suppose that we have A,B,C,D  and AB  must sit as a block and CD must sit as a block

So  we have  2!  = 2 ways to arrange AB  and 2!  = 2 ways to arrange CD  = 2! x 2!  =  4 total  arrangements

So.....the arrangements are

     A                             A                     B                    B

C       B                   D       B            C      A            D     A

    D                             C                     D                    C

Note that any rotations will still look the same with regards to order

Well ....two of the positions are "set"

So.....  we just want to choose any 3 of the remaining  10 players  = C(10,3)  = 120  different lineups

Anchor Alice in any position

And Bob can sit  in  any position except Alice's  and the two positions on either side of her...so this gives 5 possible positions for him.....and for each of these, the other 6 people can be seated in 6!  = 720 ways

So....the total arrangements are    5 * 6!  = 5 * 720  =  3600  ways

a) Represents the positoin of the object at 5 seconds

b) Represents the average velocity between 5 and 22 seconds

c) Represents the average velocity between  -2  and 4 seconds

d)  Represents the instantaneous velocity at  3 seconds

Here's my take  :

Fix the chief in any position

We have two ways to arrange the mother and wife......either the wife is on the left of the chief and the mother on the right, or vice-versa

And the other  5 members of the tribe can be arranged in 5! ways

So...the total possible arrangements are   2 * 5!  =  2 * 120    =  240

P (3,2)   means that  we are choosing any 2 things out of 3 and then permuting (giving all the possible orders  of the things selected )

So...suppose the math books  are  A, B and C

The possible selections we can make is   

{ A, B}   { B , C}  or { A, C}    (1)

But  we can also arrange these as  { B, A}  {C, B}  or   {C, A}.......so we have a total of 6 possible arrangements

Note that   (1)  is  C(3,2) = 3  =   the number of possible sets

But  P(3,2)   =  6  =  the number of posssible arrangements of these sets

[ This stuff is hard for everyone  !!!  ]

The wheel makes one revolution in 10 sec.....it is at 4 ft  at 7.5 sec  and again at 4 ft, 10 seconds later

So...the first statement is false

At  0 sec.....the loading height is 34 ft....but the lowest height is at 4 ft

So....the second statement isn't true, either

The third statement is true

The last statement is also true....the  max height is 64 and the minimum is 4 ft

So....the radius is  ( 64 - 4) / 2   =  60/2  =  30 ft

First one :

The graph is horizontally compressed by a factor of 2 and shifts up 1 unit.

Here are the graphs :  https://www.desmos.com/calculator/umiqrxhmie

Second One

2. Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 5.15 ft at midnight, rises to a high of 10.2 ft, falls to a low of 0.1 ft, and then rises to 5.15 ft by the next midnight.

In the form   y  =  Asin (Bx) + C

C  =  5.15

The amplitude, A, is  [ 10.2 - .1] / 2  =  5.05

And we can find B  as

2pi / 24   =   pi/ 12

So....the function  is  y  =  5.05sin ((pi/12) x )  + 5.15

Here's the graph : https://www.desmos.com/calculator/7k1p2hksdu