Well, we could try adding up odd numbers, and look to see when we reach 400. But I'm hoping to find an easier way.
First of all ... I'm not sure this will help, but let's stop and notice it anyway ...
An odd number of odd numbers (like 1, 3, 5) add up to an odd number, but
an even number of odd numbers (like 1,3,5,7) add up to an even number.
So if the sum is going to be exactly 400, then there will have to be an even
number of items in the set.
Now, let's put down an even number of odd numbers to work with,and see
what we can notice about them:
1, 3, 5, 7, 9, 11, 13, 15 .
Number of items in the set . . . 8
Sum of all the items in the set . . . 64
Hmmm. That's interesting. 64 happens to be the square of 8 .
Do you think that might be all there is to it ?
Let's check it out:
Even-numbered lists of odd numbers:
1, 3 Items = 2, Sum = 4
1, 3, 5, 7 Items = 4, Sum = 16
1, 3, 5, 7, 9, 11 Items = 6, Sum = 36
1, 3, 5, 7, 9, 11, 13, 15 . . Items = 8, Sum = 64 .
Amazing ! The sum is always the square of the number of items in the set !
For a sum of 400 ... which just happens to be the square of 20,
we just need the <em><u>first 20 consecutive odd numbers</u></em>.
I slogged through it on my calculator, and it's true.
I never knew this before. It seems to be something valuable
to keep in my tool-box (and cherish always).
Answer:
d = 11t - 20
Step-by-step explanation:
Hope it helps and have a great day! =D
~sunshine~
Simple interest= prt
=806.68 (.0525)(1)
=42.35
Balance=investment + interest earned
806.68+42.35=$849.03
Answer:
12/4 i really hope this helps i took the test and got a 100
Step-by-step explanation:
Say Terry read at the rate of 75 pages per day for d days.
Now, in d days she read 75d pages, and since after that 690 pages were left, then the number of pages in the book is 75d+690.
Next, we also know that she had d+6 days for the assignment. Since Terry planned to read 90 pages per day for this number of days, then the number of pages in book is also equal to 90(d+6).
So, we have that 75d+690 = 90(d+6). Solving the linear equation, we get d = 10.
Thus, the total number of days that she has to complete the assignment on time is d+6 or 10 + 6 = 16 days.