BA3005 Using and managing data and information
You are a manager at a local gym where customers are encouraged to use a three digits lock for their locker.
One day, you discover that a user has left his/her bag in the locker for over a week. This is illegal
You want to open and empty the locker
You try all possible set of three digits in order to find the correct one
Required
Explain why you cannot apply the classic formula for combinations or permutations in this case.
What formula do you apply to find the maximum number of set of three digits to use the find the correct one.
Calculate this number of possible sets of three digits.
Task 2
The number of hours spent in paid employment by a cohort of 9 students during the autumn semester is recorded in the table below:
Student
1
2
3
4
5
6
7
8
9
No. of hours ()
12
9
0
5
8
11
15
17
4
Required:
Calculate the average number of hours spent in paid employment among this cohort. You may use the following formula:
You need to calculate the quantity
Write down the full extended expression representing this quantity using the numbers in the table. At this stage, you do not need to calculate the final value.
Calculate the final value for this quantity.
Note: You need to follow the same structure 1., 2. and 3. for your answer.
Task 3
A bathroom has a rectangular floor shape.
The total area of the bathroom is given by the formula:
The bathroom has been modified in such a way that the length of the bathroom has increased by 20% and the width has decreased by 30%.
You do not know the original length or width of the old bathroom, therefore, you should not use them in your calculations.
Required:
Write down the formula, studied in class, that you will use to find the percentage change for the total area of the bathroom?
Explain every step in your reasoning and calculations.
Has the total area increased or decreased? By what percentage?
The average cost, per square metre, for tiling the bathroom is given by the formula:
The total cost for tiling the new bathroom has increased by 15% compared to the cost of tiling the old bathroom.
Write down the formula, studied in class, that you will use to find the percentage change for the average cost, per square metre?
Use the formula above to calculate the percentage change in the average cost, per square metre. Give your answer correct to the nearest percentage point.
You need to show all your reasoning and calculations using equations written on equation editor.
Guidance: Your answers should follow the structure 1., 2., 3., and 4. Do not mix your answers if you want to gain the full marks.
Task 4
For this task, you need to show all your workings, step by step. Stating only the final answers will not gain full marks.
Scenario:
You invest £300 at the beginning of each calendar month in a cash ISA account that pays 4% per year. This investment continues for the whole year (12 months).
The formula below calculates the total accrued amount in the fund after 12 months.
Required:
Show that the total accrued amount over 12 months can be written mathematically in the form:
You need to refer to your lecture slides and in particular the formula for the sum of the geometric progression.
Calculate this accrued amount of this investment using the formula above. Give your answer correct to 2 decimal places