10000 digits can be used for 4 digit A.T.M code.
<u>Solution:</u>
Given that A.T.M required 4 digit codes using the digits 0 to 9.
Need to determine how many four digit code can be used.
We are assuming that number starting with 0 are also valid ATM codes that means 0789 , 0089 , 0006 and 0000 are also valid A.T.M codes.
Now we have four places to be filled by 0 to 9 that is 10 numbers
Also need to keep in mind that repetition is allowed in this case means if 9 is selected at thousands place than also it is available for hundreds, ones or tens place .
First digit can be selected in 10 ways that is from 0 to 9.
After selecting first digit, second digit can be selected in 10 ways that is 0 to 9 and same holds true for third and fourth digit.
So number of ways in which four digit number is created = 10 x 10 x 10 x 10 = 10000 ways
Hence 10000 digits can be used for 4 digit A.T.M code.
Well, we know perimeter is just adding all the lengths together.
And we already know 2 of the lengths, so we know the rest. 11 1/2 is the same as the opposite side, and 6 1/3 is the same as the opposite side.
So the sides are 6 1/3, 6 1/3, 11 1/2, 11 1/2.
Add them up:
6 1/3 + 6 1/3 + 11 1/2 + 11 1/2.
Improper fractions:
19/3 + 19/3 + 23/2 + 23/2.
Common denominator, (6):
38/6 + 38/6 + 69/6 + 69/6 = 214/6.
Simplify:
214/6 = 35 2/3
Where <em>x </em>is the number of books sold, <em>i </em>is income, and <em>c </em>is cost:
<em>c = 4x + 3500 </em> ($4 per book plus the 3500 flat marketing fee)
<em>i = 15x </em>($15 per book)
You are looking for the point where these intersect: the intersection is where the income is equal to the cost, and at any point after that the income is greater than the cost. So, set the equations equal to each other:
<em>4x + 3500 = 15x </em>
subtract 4x from both sides
<em>3500 = 11x</em>
divide both sides by 11
<em>x = 318.181818</em>
So, you would have to sell a minimum of 319 books in order to make a profit.
