Data
For an ordered set of data containing an odd number of values, the middle value is always ...?
Options: the mean, the median, the mode, the mean and the median, the mean, the median and the mode
The median
Cheryl invests $492800 in a perpetuity. She would then receive $887.04 each fortnight for the rest of her life. At what annual percentage rate is interest earned by this perpetuity?
0.18%
What is the algorithm below called?
Step 1: Choose the edge in the network which has the smallest value. If 2 or more edges are the smallest, choose any of these.
Step 2: Inspect the 2 vertices included so far and select the smallest edge leading from either vertex. Again, if there is a ‘tie’, arbitrarily choose any one.
Step 3: Inspect all vertices included so far and select the smallest edge leading from any included vertex. If there is a ‘tie’, choose any, arbitrarily.
Step 4: Repeat step 3 until all vertices in the graph are included in the tree.
Prim's algorithm/algorithm to find minimum spanning tree
Does sound or light travel faster?
What would the most appropriate graphical tool be to compare the driving speeds of teenagers vs the elderly?
Single back-to-back stem and leaf plot
Sid purchased a new car for $5000 on 1st January 2019. On 1st January each year after 2019, its value is depreciated by 20% using the reducing balance method. What year will the value of the car first drop below $1500 on Jaunary 1st?
2025
What is the algorithm below called?
Step 1: Choose any vertex
Step 2: From that vertex, find the smallest possible path to return to that vertex: this is called a subcircuit o the original network
Step 3: Arising from each vertex in this subcircuit, draw another subcircuit that is the smallest possible path to return to that vertex
Step 4: Repeat Step 3 until there are no more vertices or edges left
Step 5: Join the subcircuits together at their intersection points
Euler circuit algorithm
Define "dummy activity". How do we normally represent it on a network?
A dummy activity is an activity added to a project schedule as a placeholder. It has no activity time associated with it. A dummy activity is intended to show a path of action in a project activity diagram and is employed when a logical relationship between two activities cannot be linked by showing the use of arrows linking one activity to another.
It typically appears as a dashed line that links two tasks.
Sales of matcha in Australia from 2020 can be modelled by the equation below.
matcha sales ($1000s) = 1600 + 180 x year.
Sales of matcha in New Zealand from 2020 can be modelled by the equation below.
matcha sales ($1000s) = 1500 + 100 x year.
Explain the long-term trend in matcha sales between these two countries.
Matcha sales in Australia will always exceed matcha sales in NZ (higher gradient and slope).
Which of these rates will be a better choice for Sam who is planning on depositing his life savings?
One bank offers 6.0%p.a. compounding annually. Another bank offers 3.0% hemiannually, compounding daily.
Which of these rates will offer a better return for Sam and by how much?
3% hemiannually is better by 0.18% per annum.
The migration patterns of Mongolian storks is under investigation. Three winter nesting places have been identified: areas A, B and C.
Every winter, 80% of storks who nested at area A in the previous year return to area A. Equal numbers of the storks which previously nested at area A now nest at areas B and C. Of the storks which previously nested at area B, 70% return the next year and 20% go to area A. Of those previously nesting at C, 60% return the next year while 20% nest at area A the next year. It may be assumed that all storks nest at one of these three locations every year.
Write down a transition matrix that could be used to predict the nesting numbers at the three locations based on the previous year’s figures.
0.8 0.2 0.2
0.1 0.7 0.2
0.1 0.1 0.6
Which globally-dreaded disease did the World Health Organization declared eradicated in 1980?
Smallpox
You are investigating the volume of cars on the road over 24 hours on a typical Wednesday in Melbourne. If you were to plot this data on a histogram, how would you describe the shape of the distribution?
Bimodal distribution
Luke invests $10,000 and earns interest at a rate of 6% per annum compounding quarterly. Every quarter after interest has been added, he withdraws $500. At the end of 4 years, after interest has been added and he has made the $500 withdrawal, what will the value of the remaining investment be?
$3720
A is a 3 x 4 matrix. The rows show the cost of a return flight for each of economy, business then first class (in order). The columns show four different destinations- Hong Kong, Manila, Bangkok, Shanghai.
B is a 4 x 3 matrix. It shows the discounts for three possible membership types Q, R and S with a row for each destination.
Describe the nature of the information that matrix AB provides. What information is described by row 3, column 2?
Shows the cost of 9 different scenarios. Rows are the different flight classes and columns are the three different packages.
Row 3 column 2 is the cost of first class travel under package R.
What mineral can you add to water to make things float more easily?
Salt
A least squares line is fitted to a set of bivariate data. Another least squares line is fitted with response and explanatory variables reversed. Which statistic will not change in value?
The correlation coefficient (r)- measures association between variables not the direction
There are 1000 ducks living in a park in 2025. After 2025, the number of ducks is expected to increase by 15% per year. Every year, 80 ducks are removed from the park by a local restaurant. Let Dn be the number of ducks living in the park n years after 2025.
Find a difference equation to model this situation n years after 2025.
Dn = 1.15Dn-1 - 80, D0 = 1000
A is a 3 x 4 matrix. The rows show the cost of a return flight for each of economy, business then first class (in order). The columns show four different destinations- Hong Kong, Manila, Bangkok, Shanghai.
B is a 4 x 3 matrix. It shows the discounts for three possible membership types Q, R and S with a row for each destination.
Would the matrix product BA be defined and meaningful? If so, explain what its physical significance would be.
BA is defined, is a 4 x 4 matrix. No real meaning as we are just multiplying a different plan by a different flight class.
Outcome A and Outcome B can be plotted on a scatterplot and an r-value of 0.99 is calculated. Does this mean that there is a correlation or a causation between them?
Could be either correlation or causation. We don't know just by looking at the r-value.