Let the first number of the five we are looking for equal n.
Because the numbers are consecutive, the next four can be expressed as (n+1), (n+2), (n+3) and (n+4).
Our series of 5 numbers is therefore n,(n+1),(n+2),(n+3),(n+4).
We are told the sum of the squares of the first 3 is equal to the sum of the squares of the last 2 therefore:
n² + (n+1)² + (n+2)² = (n+3)² + (n+4)²
expand all the brackets to give
n² + n² + 2n + 1 + n² + 4n + 4 = n² + 6n + 9 + n² + 8n + 16
3n²+6n+5 = 2n²+14n+25
n²-8n-20=0
factorising this gives us
(n+2)(n-10) = 0 so the solutions are n=10 and n=-2
That means that n,(n+1),(n+2),(n+3),(n+4) could be [-2, -1, 0, 1 and 2] or [10, 11, 12, 13 and 14].
Since the question asks for whole numbers, and negative numbers are not classed as whole numbers, the numbers we want must be 10, 11, 12, 13 and 14.
You can check this on a calculator by doing 10² + 11² + 12² (=365) and 13² + 14² (=365).
Bundle (31 , 40) has 40 bananas.
So 40 - 28 = 12 bananas
These 12 banana give the consumer negative utility which will be balance one for one apple.
So we have to need 12 apple to balance it.
So the final utility of apples and banana is 28 + (31 - 12) = 28 + 19 = 43
In second bundle (X , 23) has 23 bananas. We need to get the same utility 43.
Which we will get from 43 - 23 = 20 apples.
So X equal to 23.
Answer:
6 : 12 9 : 18 12 : 24
Step-by-step explanation:
Here all employees get equal amount as bonus, so the standard deviation of the employees income won't change.
if you subtract or add equally to all the data then standard deviation won't change but mean and median would change.
hope this help
