Answers:
lower bound = 39001
upper bound = 40999
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Step-by-step explanation:
You'll have to think backwards to find what values round to 690,000 when rounding to the nearest thousand.
It turns out that if x is on the interval
, then x will round to 690,000 when rounding to the nearest thousand. The x refers to the population of Sheffield, so it's some integer in that range.
Through similar logic, if y is on the interval
then it will round to 730,000 when rounding to the nearest thousand. This represents the population of Nottingham.
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Now let's say we go for the smallest possible value of x (689500) and the largest possible value of y (730499). This guarantees the two populations are the most spread out or distant from one another. Subtract those two values:
730,499 - 689,500 = 40,999
This is the largest difference possible of the two populations. It represents the upper bound, i.e. it's the ceiling.
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On the other hand, let's now say x is as big as possible (690499) and y will be as small as possible (729500). Subtract those values:
729,500 - 690,499 = 39,001
This is the lower bound. It's the smallest the difference can be. It's considered the floor.
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Let d be the difference in the populations. In other words, d = y-x
We found that the lower bound was 39,001 and the upper bound was 40,999
Meaning that
or