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).
6 can only go into 6 once
<h3>
Therefore, in =15 ways can these 2 position be filled .</h3>
Step-by-step explanation:
Given a club has 6 members. From these member ,the position of president and vice president have to be filled.
Therefore, in =15 ways can these 2 position be filled
Answer:
Cant see
Step-by-step explanation:
So let's say that the second angle is x.
Then we can say that the third angle is .
So then we have three angles:
1) 66°
2) x°
3) ()°
So then we can add these together and solve for x by setting it equal to the total degrees left in the triangle after subtracting the known angle:
So now we know that the measure of the second angle is 38°. So then we can use this value to solve for the third angle:
So the values of the angles are:
1) 66°
2) 38°
3) 76°