Aussie Maths & Science Teachers: Save your time with SmarterEd
Each day, members of a swim centre can choose to attend a morning session
The transition diagram below shows the transition from day to day.
The transition diagram is incomplete.
Which one of the following transition matrices represents this transition diagram?
For one particular week in a school year, students at Phyllis Island Primary School can spend their lunch break at the playground
Students stay at the same location for the entire lunch break.
The transition diagram below shows the proportion of students who change location from one day to the next.
The transition diagram is incomplete.
On the Monday, 150 students spent their lunch break at the playground, 50 students spent it at the basketball courts, 220 students spent it at the oval, and 40 students spent it in the library.
Of the students expected to spend their lunch break on the oval on the Wednesday, the percentage of these students who also spent their lunch break on the oval on Tuesday is closest to
Every Friday, the same number of workers from a large office building regularly purchase their lunch from one of two locations: the deli,
It has been found that:
A transition matrix that can be used to describe this situation is
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B. |
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D. |
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In a particular supermarket, the three top-selling magazines are Angel (A), Bella (B) and Crystal (C).
The transition diagram below shows the way shoppers at this supermarket change their magazine choice from week to week.
A transition matrix that provides the same information as the transition diagram is
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B. |
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D. |
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A farm contains four water sources,
Part 1
Cows on the farm are free to move between the four water sources.
The change in the number of cows at each of these water sources from week to week is shown in the transition diagram below.
Let
The state matrix for the location of the cows in week 23 of 2019 is
The state matrix for the location of the cows in week 24 of 2019 is
Of the cows expected to be at
Part 2
Sheep on the farm are also free to move between the four water sources.
The change in the number of sheep at each water source from week to week is shown in matrix
In the long term, 635 sheep are expected to be at
In the long term, the number of sheep expected to be at
Families in a country town were asked about their annual holidays.
Every year, these families choose between staying at home (H), travelling (T) and camping (C).
The transition diagram below shows the way families in the town change their holiday preferences from year to year.
A transition matrix that provides the same information as the transition diagram is
| A. | B. | ||
| C. | D. | ||
| E. |
A new shopping centre called Shopper Heaven (
Market research suggests that each shopping centre will have a regular customer base but attract and lose customers on a weekly basis as follows.
80% of Shopper Heaven customers will return to Shopper Heaven next week
12% of Shopper Heaven customers will shop at Eastown next week
8% of Shopper Heaven customers will shop at Noxland next week
76% of Eastown customers will return to Eastown next week
9% of Eastown customers will shop at Shopper Heaven next week
15% of Eastown customers will shop at Noxland next week
85% of Noxland customers will return to Noxland next week
10% of Noxland customers will shop at Shopper Heaven next week
5% of Noxland customers will shop at Eastown next week
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During the week that Shopper Heaven opened, it had 300 000 customers.
In the same week, Eastown had 120 000 customers and Noxland had 180 000 customers.
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In a country town, people only have the choice of doing their food shopping at a store called Marks (
In the first week that Foodies opened, only 300 of the town’s 800 shoppers did their food shopping at Marks. The remainder did their food shopping at Foodies.
Part 1
A state matrix
A.
B.
C.
D.
E.
Part 2
A market researcher predicts that
A transition matrix that can be used to represent this situation is
There are two fast-food shops in a country town: Big Burgers (B) and Fast Fries (F).
Every week, each family in the town will purchase takeaway food from one of these shops.
The transition diagram below shows the way families in the town change their preferences for fast food from one week to the next.
A transition matrix that provides the same information as the transition diagram is
