On a given week, the classical literature section in a certain library had 40 different books, all of which were in stock on the shelf on monday morning. if 50 percent of the books that were borrowed during the week were returned to the library on or before saturday morning of that same week, and if there were at least 22 books on the shelf that saturday morning, what is the greatest number of the books that could have been borrowed during the week?

The greatest number of the books that could have been borrowed during the week are 36.

Step-by-step explanation:

Let the total number of books or N = 40

Let the number of borrowed books be = B

As given, the number of books available are greater than 22.

We get the following equation as per scenario:

=>

=>

Substituting N = 40, we get ;

Therefore, the maximum possible number of borrowed books will be 36.

33

step-by-step explanation: g=6

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}