HELP. ME

Sorry if I’m wrong but is it ... 90???

Step-by-step explanation:

Work Shown:

The given list is {95, 89, 99, 85, 82, 81, 99}

Sort this list from smallest to largest.

We then have this: {81, 82, 85, 89, 95, 99, 99}

Next we will erase the first and last items in that sorted list above

Doing so leads to this smaller list: {82, 85, 89, 95, 99}

Repeat the step from before. Erase the first and last items

We now have {85, 89, 95}

One more time lets erase the first and last items getting {89}

This shows that 89 is the very center item

Going back to {81, 82, 85, 89, 95, 99, 99} we see that 89 is at the center with three items below it (81,82,85) and three items above it (95,99,99)

Therefore, the median is 89.

Another route to take is to count the number of items in {81, 82, 85, 89, 95, 99, 99}. You should count 7 items.

Add 1 and divide by 2 to get (7+1)/2 = 8/2 = 4

The median is in slot 4, which is exactly where 89 is located in the list {81, 82, 85, 89, 95, 99, 99}

Note: this trick only works if you have an odd number of items in a set.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!