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melisa1 [442]
3 years ago
13

Tim has an encyclopedia in 5 volumesA–C, D–F, G–J, K–N, and O–Z. Other than alphabetically (ascending or descending), how many w

ays can these volumes be arranged?
120

118

25

insufficient data
Mathematics
2 answers:
levacccp [35]3 years ago
8 0

Answer:

B for Plato

Step-by-step explanation:

Ira Lisetskai [31]3 years ago
6 0
The first book can be any one of the 5.
               For each of those . . .
The 2nd book can be any one of the remaining 4.
               For each of those ...
The 3rd book can be any one of the remaining 3.
              For each of those . . .
The 4th book can be either of the remaining 2.
             For each of those . . .
The 5th book is the last one remaining.

Total number of ways to arrange the 5 books is

           (5 · 4 · 3 · 2 · 1)  =  120 .

Cross off alphabetically ascending (1 way), and alphabetically
descending (1 way), and you're left with  (120 - 2)  =  118 ways.
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7 0
3 years ago
A farmer with 5000 feet of fencing wants to enclose a rectangular field and then divide it into two plots by adding a fence in t
matrenka [14]

Answer:

The required width of the field that would maximize the area is = 1250  feet

Step-by-step explanation:

Given that:

The total fencing length = 5000 ft

Let consider w to be the width and L to be the length.

Then; the perimeter of the rectangular field by assuming a parallel direction is:

P = 3L + 2w

⇒ 3L + 2w = 5000

3L = 5000 - 2w

L = \dfrac{5000}{3} - \dfrac{2w}{3}

Recall that:

The area of the rectangle = L×w

A(w) = ( \dfrac{5000}{3}-\dfrac{2}{3} ) w

A(w) =  \dfrac{5000}{3}w-\dfrac{2}{3}  w^2

Taking the differentiation of both sides with respect to t; we have:

A' (w) = \dfrac{5000}{3} - \dfrac{2}{3} ( 2 w)

A' (w) = \dfrac{5000}{3} - \dfrac{4w}{3}

Then; we set A'(w) to be equal to zero;

So; \dfrac{5000}{3} - \dfrac{4w}{3}=0

5000  = 4w

w = 5000/4

w = 1250

Thus; the required width of the field that would maximize the area is = 1250  feet

Also, the length L = \dfrac{5000}{3} - \dfrac{2w}{3} can now be :

L = \dfrac{5000}{3} - \dfrac{2(1250)}{3}

L = (5000 -2500)/3

L = 2500/3 feet

Suppose, the farmer divides the plot parallel to the width; Then  2500/3 feet = 833.33 feet and the length L = 1250 feet.

8 0
2 years ago
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