1. Write A if the quantity in Column A is greater
Write A if the quantity in Column A is greater. Write B if the quantity in column B is greater. Write C if the quantities are equal. Write D if there is not enough information to determine the relationship.
Column A
Column B
z z2
(r+t)2 r<0,t<0 (r-t) 2 3.
4. (x + 2 )2 (x - 1)2

2. Determine if the UPC code is valid.
Find the value of the check digit that will make the UPC code valid. d d
5. Come up with 2 valid UPC codes of your own.
6. Check out 2 real UPC codes and see if they are valid under our formula.

3. Determine if the UPC code is valid.
Not valid
Find the value of the check digit that will make the UPC code valid.
d d = 0
d d = 9
5. Come up with 2 valid UPC codes of your own.
6. Check out 2 real UPC codes and see if they are valid under our formula.

4. Credit cards have 16-digit numbers, of which the first 15 digits identify the credit card and the sixteenth digit is the check digit.
Visa card begin with a 4 and MaterCard cards begin with a 5.
1. MasterCard numbers begin with 51,52,53,54,or 55. What is the maximum number of credit cards that MasterCard can issue?
5[(first two digits] [check digit is determined by the previous digits]=
5(1013)

5. A check digit is used to help validate credit card numbers
A check digit is used to help validate credit card numbers. The credit card companies use the CODABAR method to determine the check digit. This method consists of the following:
Add the digits in the odd-numbered positions and double the total
add how many odd-position digits that are more that 4 to the total
add the even-position digits
choose a check digit that makes this calculation total a number whose final digit is 0.

6. 97 + d needs to equal a number that ends in 0
Visa card d (d=3?)
2( )+ 4 +( d)
2(35)+ 4 +(23+d)
2(35)+ 4 +(23+d)
97 + d
97 + d needs to equal a number that ends in 0
so d = 3

7. 65, so not valid because it does not end in 0.
What is the check digit (d) for the MasterCard number d?
2( )+ 3 +( d)
2(29)+ 3 +(26+d)
87+d so d = 3
4. Show that is an invalid Visa Credit card number.
2( )+ 1 +( )
2(20)+ 1 +(24)
65, so not valid because it does not end in 0.

8. Suppose you entered 8 instead of 9 when recording the credit card number
explain why it will detect this error…
2(9) – 2(8) = 2, so the sum of the weighted sum of the digits will be off by 2 and will not end in 0.
Do you think the Codabar method will detect all such single-digit errors?
YES

9. 7. The codabar method detects 98% of all transposition errors
7. The codabar method detects 98% of all transposition errors. There is one pair of numbers, however, that when transposed will not be detected by the Codabar method. When will it not matter?
if you transpose any of the red numbers with each other or any of the black numbers with each other it will not effect the Codabar method,

10. HW --Determine if the following credit card numbers are valid. 1
HW --Determine if the following credit card numbers are valid Determine the value of d so that the credit card number is valid d d d d