Aroon is asked to choose five integers so that the mode is 2 more than the median and the mean is 2 less than the median. What is the largest possible value of the range of Aroon's five integers?

The relation between Mean, Median and mode is given by

Mode= 3 Median - 2Mean equation1

According to the given condition

Mode= 2+median equation 2

Putting equation 2 in equation 1

2+median= 3 Median - 2Mean

2 Mean= 3 Median - 2- Median

2 Mean= 2 Median - 2

Mean= Median-1

Mean- Median=1Eq. A

According to the second condition

Median- Mode=-2eq. 3

Putting eq. A in eq. 3

Mean -1 - Mode=-2

Mean- Mode=-1

or

Mode- Mean=1equation 4

Adding equation A and equation4

Mode- Mean=1

Mean- Median=1

Mode+ Median =2 equation5

Again Putting equation2 in equation 5

2+median + Median =2

2 Median =2-2

2 Median =0

Median=0

Mean= 0-1

Mean= 0-1=-1

Mode- Mean=1

Mode-(-1)=1

Mode=0

Putting values in the formula of mean

x bar =∑x/5

(-1)5 = 0+0+ x1+x2+0

-5=  x1+x2

So the highest value is 0.

Learn more about mean here

a4 - 3a2 - 1

step-by-step explanation:

step   1   :

equation at the end of step   1   :

  ((a4) -   3a2) -   1

step   2   :

trying to factor by splitting the middle term

2.1     factoring   a4-3a2-1  

the first term is,   a4   its coefficient is   1 .

the middle term is,   -3a2   its coefficient is   -3 .

the last term, "the constant", is   -1  

a) 7x=7

step-by-step explanation: