Solution
Robert answered on
Dec 26 2021
Assignment 3
1) The total number of handshakes at a party of n guests, where everyone is shaking
everyone’s hands only once: s = n(n-1)/2
a) Explaining the formula: let’s try to imagine the situation if we went to a party and
everyone shakes everyone else’s hands only once! However, no one shakes their own
hand so every person ends up having n-1 handshakes, so there would be total n(n-1)
handshakes, but it includes each handshake twice because if A is handshaking with B,
then we have also considered the same handshake when B is handshaking with A. we
have counted twice the handshakes as it should be, Therefore, the total number of
handshakes = (1/2)*n*(n-1)
) In the question, it’s given; n =12
So, total number of handshakes would be = 12*(12-1)/2 = 12*11/2 =132/2 = 66
2) A
anging the catering for wedding feast:
a) Formula for total catering cost: Let’s assume that number of guests = n (including the
family and ourselves)
And, we know that it costs $25 per person, so we got 25*n for guests, now we are
going to have to add the booking cost which is $120.
Therefore the total catering cost for the wedding = $(120 + 25*n)
) To fill the table we just have to use the formula, we define above: cost = $(120 +
25*n); n= number of guests.
No. of Guests 20 40 60 80 100
Catering Cost($) 620 1120 1620 2120 2620
c) Plotting the Graph:
d) Look at the graph below that we have plotted, and the trend line we have got, for
every next 20 guests, cost of catering increases by 500, and hence it’s a linear graph,
for every next 10 guests, cost of catering would increase by 250. So, for 110 guest,
cost of catering = 2620 + 250 = 2870
e) Given the cost of catering = $2000
We will simply apply the formula we derived in the first part, cost = $(120 + 25*n)
Therefore, 2000 = 120 + 25*n
And, 1880/25 = n = 75.2
Because people can’t be expressed in decimal point (obviously); total number of
guests = 75 (including the family and us)
3) Looking at the graph given which is how income per person has changed in north and
south Korea from 1960 to 2013
a) Income per person in South Korea in 1960 = $1190
In 2013 = $32,000
620
1120
1620
2120
2620
y = 500x + 120
0
500
1000
1500
2000
2500
3000
3500
4000
20 40 60 80 100
C
at
e
i
n
g
C
o
st
Number of Guests
No. of Guests Vs. Catering Cost
) Percentage change in income from south Korea from 1960 to 2013 = 100*(Income
per person in South Korea in 2013 - Income per person in South Korea in 1960)/
Income per person in South Korea in 1960
= 100*(32,000 – 1190)/1190 = 2589.08 %
c) Comparison of 2013 income per person for north and south Korea by division:
2013 income per person for South Korea/2013 income per person for North Korea
= 32,000/1390 = 168.42
That means compared to income per person for North Korea, South Korean income
per person is 168.42 times higher.
Comparison of 2013 income per person for north and South Korea by subtraction:
2013 income per person for South Korea - 2013 income per person for North Korea =
32,000 – 1390 = $30,610
That means compared to income per person for North Korea, South Korean income
per person is $30,610 more.
4)
a) Let’s assume the person gets paid $100 every fortnight and let’s assume further that
he pays $40 each month towards the repayment of that loan.
So, we can create an imaginary bank balance:
Period(Date) Balance($) Loan Payment($) Balance Remained($)
15th Jan 100 0 100
30th Jan 200 40 160
15th Feb 260 0 260
29th Feb 360 40 320
15th March 420 0 420
30th March 520 40 480
15th April 580 0 580
) We will try to understand how the balance changes from looking at the graph we
just drew.
There are continuous dips in the graph at the end of each month, which shows some
money has been taken out to towards the repayment of loan, it goes up again and
then again a dip at the end of the month. So, if the person has a balance of $100 at
15th Jan, it will be $200 on 30th jab but he will have to give $40 towards loan
epayment, so it will be a dip in the graph.
5)
a) From the given graph, we can see, the x-intercept = 4
The y-intercept = -2
) We can see from the graph that the line passes through (0, -2) and (4, 0). So, the
slope of the line would be: m = The equation of the line would be = [0-(-2)]/[4-0] =
1/2
Therefore, the equation of the line would be: y-0 = (1/2) * (x-4)
Or, 2y = x - 4
Or, x - 2y - 4 = 0
c) If the another line is parallel to this one, then slope of that line would also be 1/2
And, it’s passing from (0, 1). Therefore the equation of that line would be:
y - 1 = (1/2) * (x - 0)
0
100
200
300
400
500
600
700
15th jan 30th jan 15th feb 29th feb 15th march 30th march 15th april
B
al
an
ce
R
e
m
ai
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Date
Or, 2y-1 = x
Or, x-2y-1 = 0
6) y=4- 3x
It fits in the format of y= mx +c, where m is the gradient and c is the y-intercept
So in this given equation, we have gradient = -3, intercept = 4
7)
a) It’s given that the gradient of the line is -1, i.e. it’s making a 135 degrees angle with...