Sum means add
sum of the 3 is
n+n+1+n+2
it add to 57
n+n+1+n+2=57
3n+3=57
minus 3 both sides
3n=54
divide both sides by 3
n=15
n+1=16
n+2=17
the integers are 15,16, and 17
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).
Converting observations from original values to standard deviation units is known as standardizing the data values. This is done in order to get values in such a form where we can compare them. For example, if we have the test scores of two different school and we want to compare the result of the students we have to first convert them into standard deviation units.
Converting the values to standard deviation units is also known as converting the values to z scores.
The formula for the z score is:
[tex]z= \frac{x-u}{s} [/tex]
where x is the data value, which is to be standardized.
u is the average of the entire data.
s is the standard deviation of the data.
Answer: 37
Step-by-step explanation:
if n=24
n+13 becomes 24+13
24+13 = 37
