An Analysis of The Relationship between Income and Number of Outlets in a Sporting Event

a) Total number of handshakes equal to half of the product of total number of people at the party and total number of people minus one.

b) n = 10

S =  handshakes     

Question 2                                         

a) C = 60 + 20h

Where; C – cost of hall ($) and h – number of hours.

b)

Hours Required

1

2

3

4

5

Cost of Hall ($)

80

100

120

140

160

c)

d) From the graph above the orange line give a cost of $150.

e) The blue dotted line on the graph show that for a budget of $130 the group will occupy the hall for a maximum of 3.5 hours

Question 3

a) 2009

b)

Ø New Zealand from 2002 to 2007

Ø Singapore from 2007 to 2011

c) Fertility rate =

In 1997 the adolescent fertility in USA was 2.7 times higher than in Australia in the same year

d) Fertility rate =

In 2011 the adolescent fertility in USA was 2.3 times higher than in Australia in the same year.

Question 4

a)

b) The grass has different height during every month of the year dependent on both human and climatic conditions. Due to dry conditions the grass grows slowly during the months of January and continues to grow up to a peak height of 6.0mm in April. However, tall grasses are not desired by humans the grass are then cut between May to June (zero height). As the wet seasons approaches the grass again grows rapidly between July to September. However, due to lack of rains and human activity the grass stops to grow in the months of October to December.

Question 5

a) Gradient =

From the graph the following points can be read from the point where the line cut the axes and

Gradient =

The y-intercept is 8 units

b) Equation is given by the formula y = mx + c where m is the gradient and c the y-intercept. Therefore, the equation of this lines is y = -

Question 6

a)   (calculation of gradient)

 y = 4x – 4   Second point (0, -4), substitute for x = 0

b) y = 4x – 4  

c) Blue line

d)  (2, 4)

Question 7

a)

b) As x values increase the y values also increase smoothly

Question 8

a)

Number of outlets (x)

0

4

8

10

12

16

20

Income (I)

0

1280

1920

2000

1920

1280

0

b)

c) The number of outlets in a sporting event cannot be less than zero. There can be zero outlets but not negative outlets.

d) The orange line originates from the maximum point where the company expects an income of $2,000.

e) The blue dotted line points at ten number of outlets required to meet the maximum income in a sporting event.

f) The exist a positive relationship between the income and the number of outlets for the first ten outlets while for more than ten outlets there exist an inverse relationship. The higher the number of outlets the lower the profit (After market saturation at ten outlets).