CPhill

Good job, catmg   !!!!

As long as  we  have no restrictions ( some boxes  may  be empty)  the  number of  ways  =

S ( 5 , 1)    +  S (5, 2)  + S (5,3)   =  1  + 15  + 25   =    41

Where  "S"  represents  a Stirling number of the   2nd kind 

csc  =  1 /   sin

Part A. 

Carmen purchased a 16-ounce can of Nut Munchies and counted 100 peanuts.

What is the z-score for this can of peanuts?

(100 -  93.6)  /   4.2   =  1,52        translates  to  .9357

Part B

Angelo purchased a 20-ounce can of Gone Nuts and counted 116 peanuts.

What is the z-score for this can of peanuts?

(116 - 111.8 )  / 3.4   =  1.23       translates  to   .8907

Part C

Carmen declares that purchasing her can of Nut Munchies with 100 peanuts is less likely than Angelo purchasing a can of Gone Nuts with 116 peanuts. Is Carmen’s statement correct? Use the definition of a z-score to support or refute Carmen’s claim

What we  can say  is  that  purchasing  a can of Nut Munchies with  less than  100  peanuts  is  more likely  than purchasing a can of Gone Nuts  with less  than 116 peanuts

See the  graph here  :  https://www.desmos.com/calculator/jn9lm00kci

The  pairs are

(1, 1)      (2, 1)

(1, 2)      (2, 2)

(1, 3)      (3, 1)

Since  the perimeter of two  such  rectangles =  90.....the  perimeter of one must  be  45

So

2 ( W + L)  = 45

2 ( (2/3)L  +  L)   = 45  

2  ( (5/3)L )  =  45

(10/3)L  =   45

L =  45 (3/10)  =   13.5

W  =  (2/3) (13.5)   =   9

sqrt  (7x - 5)   =  -2(sqrt (x - 2)      square  both sides

7x  - 5   =  (4) (x - 2)      simplify

7x  - 5  =   4x  -   8

7x - 4x  =  - 8  +  5

3x  =   -3

x  =  -1

However......tis  makes  both expressions under  the roots  negative......and  the  value of a negative  square root  is not  real....so....

No real solutions

Note  that if  x  =    2.8   we  have

Floor  [2.8 ]   +  2.8    =

      2           +    2.8   =

          4.8

Note   the  the "floor"  will  increase  by  one  everytime we  encounter  a perfect square

Floor  ( sqrt 1)  =  1

Floor  (sqrt 4)  =  2

Floor  (sqrt 9) =   3

Floor  ( sqrt 16)  =  4

Floor (sqrt 25 )  =  5

So...we will  have  the following sium

1(3)  + 2(5)  + 3(7)  + 4 ( 9)  +   5   =    75

8b^2c^5−4a^7b^3+10a^5c^4

Hint  :  add   the  exponents in  each  term

The  greatest of these  three  sums  is the  degree

If  you give me an  answer, I will check it......