Find AR step by step pleaseeee
1 answer:
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9514 1404 393
Answer:
- late only: 15
- extra-late only: 24
- one type: 43
- total trucks: 105
Step-by-step explanation:
It works well when making a Venn diagram to start in the middle (6 carried all three), then work out.
For example, if 10 carried early and extra-late, then only 10-6 = 4 of those trucks carried just early and extra-late.
Similarly, if 30 carried early and late, and 4 more carried only early and extra-late, then 38-30-4 = 4 carried only early. In the attached, the "only" numbers for a single type are circled, to differentiate them from the "total" numbers for that type.
__
a) 15 trucks carried only late
b) 24 trucks carried only extra late
c) 4+15+24 = 43 trucks carried only one type
d) 38+67+56 -30-28-10 +6 +6 = 105 trucks in all went out
You can see how the difference between two consecutive terms is constantly increasing:
So, for the next terms we'll have to add +9, +11, +13 and so on.
Also, note that is obtained by adding the 2nd odd number to
,
is obtained by adding the 3rd odd number to
, and so on.
So, the recursive formula is
For the explicit formula, recall that the sum of the first n odd numbers is n squared. Taking into account the fact that we're not starting from 1, we have