S2 is a set of passwords that has 8 digit numeric pin [0-9] with a possible size of 100,000,000
Task: Assessing hash functions

Let’s try to assess some hashing functions now.
Consider the following hashing algorithm H1 for numeric pincodes in S2:
- Sum the last 4 digits
- Add the result to the number represented by the first 4 digits
- Output the result
Q1. Prove that for any number N in S2, applying the instructions above can not yield a result that is 6 digit large.

Answer:

Step-by-step explanation:

Here the domain is 8 digit number and the range is 5 digit number.

Now for the two different value of inputs let's say 11111111 and 11110004 

H1(11111111) = H2(11110004) 

The output is 1111+4 = 1115 for both the inputs. But, for each value of x there will be unique value of y. A function is a relation which describes that there should be only one output for each input.

Therefore it is a function .

But, this is not a good hash function. For a good hash function there must not be two inputs having the same output.

Therefore it is not a good hash function.

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

The answer is in the image 

The answer is in the image 

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Approximately it is aqual to 1300kg

The answer is in the image 

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.