Definitions
What is an explanatory variable
The variable that is being investigated or adjusted. It is the x values in set of coordinates, and found on the horizontal axis of a scatterplot.
Which variable is plotted on the y axis?
Response variable.
What does the pronumeral d represent in financial maths formulas
Decide whether this pattern is arithmetic or geometric:
1, 6, 36, 216, 1296
Bonus [100] if you give the common ratio/difference.
Geometric
common ratio = 6
In a critical path network, what information is placed in the nodes?
Earliest start time, latest finish time (for the activity before) and latest finish time (for the activity after).
Explain compounding periods.
Compounding periods are the number of times in a year that compound interest is earnt. For example, if compounding monthly, there are 12 compounding periods.
Identify the value of M and C in this least squares regression line:
y = -4.32x + 13.4
M = -4.32
C = 13.4
Write this reducing balance loan as a recurrence relation:
A $450 000 loan is taken at 7.2% p.a. compounding monthly with monthly payments of $800.
A(n+1) = 1.006*An - 800, A0 = 450000
A ticket service charges $8 booking fee
$35 for every ticket bought in the booking.
Show this as a mathematical model.
Determine the cost of a 10 tickets
t(n) = 8 + 35n
let n = 10
t(10) = 8 + 35(10)
t(10) = 358
Using diagram, identify a:
Eulerian Trail [100]
Semi-Hamiltonian Path [100]
Eulerian Trail = A>B>D>E>F>D>C>A
Semi-Hamiltonian = B>A>C>D>F>E
Determine the 3-point moving averages and 3-point moving median for the following data set of monthly average temperature (degree celcsius)
See table
Refer to answers
Determine the least squares regression line for the following data * Must show equation*
Rainfall (cm) 14 12 20 24 29
Number of Plants 45 41 49 56 64
Use the equation to predict number of plants with 16 cm of rainfall
y = 1.2856x + 25.5457
let x = 16
y=1.2856 (16) + 25.5457
y=46.1153
Determine the effective interest rate for an investment if 7.64% p.a. compounding monthly.
i(effective) = 0.07913
= 7.91%
In a geometric sequence, explain how to find the value of r when:
There is a percentage increase
There is percentage decrease
increase = 1 + % (as decimal)
decrease = 1 - % (as decimal)
What is the local time in Okalahoma City (UTC-6) if it is 8 am Monday in Auckland (UTC +12)
Okalahoma City is 18 hours behind Auckland
2pm Sunday in New York.
Define a Semi-Eulerian Trail.
Starts and stops at different vertices and covers all edges in a network only once.
Bonus. Only 2 vertices can odd degree of vertices and the remaining are even.
Predict the amount of fat (y) in a burger when there is 20 grams of protein (x) using the summary statistics:
r = 0.83 sx=14.0 g (x bar) = 17.2 g
sy=16.4 g (y bar) = 23.5 g
y=0.9723x + 6.7764
let x = 20
y=0.9723(20) + 6.7764
y=26.2224 g fat
How much money must be invested to arrange a perpetuity that pays $5000 every quarter at 4.8% p.a.
A = 5000/(0.048/4)
A = $416666.67
Approx = $416667.00
A state forest is used for logging and in a particular block there are 2000 mature trees. Each year the state allows for a set amount of trees to be logged. After the first 3 years a total of 1440 trees were removed. Determine how many more years the plot can be logged before there are no more trees
1 year = 480 trees
year 3 = 1440 trees
Y4 = 1440 - 480 = 960
Y5 = 960 - 480 =480
Y6 = 480 - 480 = 0
Therefore there are another 3 years before all the trees are logged over a 6 year period.
Using the table:
Construct a project network and identify the critical path using forward and backward scanning. Times shown are in minutes
Activity A B C D E F
Duration 5 4 7 2 9 10
Prerequisite - A A A B, C, D E
--B,4->
0/0-A,5->5/5--C,7->12/12-E,9->21/21-F,10->31/31
--D,2->
Critical Path = A, C, E, F
Minimum completion time = 31 minutes
Explain float time and provide a formula.
How much time a non-critical activity can be delayed before it impacts the critical path. It is calculate by
FT = LST-EST-AT
A bivariate analysis of data found the Pearson Correlation value to be -0.81.
Describe the direction and strength of the relationship.
Using mathematical evidence, justify whether using a linear model is suitable.
Direction = negative
Strength = moderate/strong
The coefficient of determination (r2) is used to explain how much of the data can be represented by the line of best fit. r2 = 0.6561 this means 65.61% of the data is explained by the line of best fit. Although a strong correlation, a linear model may not be as suitable for this data set.
Determine the monthly repayments for a $990 000 home loan that has 4.56% p.a. compounding monthly for 30 years.
M= $5051.54
A lab is testing a new strand of antibiotics. The petri dish covered in bacteria has an area of 21 cm^2. After the first hour the area covered in bacteria was observed to be 16.8 cm^2 and after the second hour it was 13.44 cm^2.
The lab will deem the antibiotics effective if it can reduce the area to less than 2 cm^ in 10 hours.
Evaluate whether the antibiotics is effective.
r = 1-0.2 = 0.8
T(0) = 21, T(n+1)= 21 * 0.8^(n-1)
At n=10 hours t(10) = 2.82 cm^2
therefore this is greater than 2 cm^2 and would mean the antibiotics is not effective.
Town A (28°S, 149°E) is due west from Town B (28°S, 153°E).
Town C (26°S,153°E) is due north of Town B. If you live in Town A and the only way to Town C is via Town B, determine the total distance to the nearest kilometre.
Total = 392.735 + 222.4
Total = 615.14 km