Aquality control officer randomly checking weights of pumpkin seed bags being filled by an automatic filling machine. each bag is advertised as weighing 400 grams. a bag must weigh within 2.1 grams in order to be accepted. what is the range of rejected bag, x, for the bags of pumpkin seeds? a. 397.9 b. x < 397.9 and x > 402.1 c. x < 400.0 and x> 402.1 d. 400.0 > x < 402.1

Option: B is the correct answer.

    B. x < 397.9 and x > 402.1

It is given that:

Each bag is advertised as weighing 400 grams.

Also, a  bag must weigh within 2.1 grams in order to be accepted.

Hence, for the bag being accepted the weight must be no less than 2.1 gram from 400 gram and should be no more than 2.1 gram from 400 grams.

i.e. the weight of the bag must be such that:

               400-2.1≤ x ≤ 400+2.1

i.e.

              397.9 ≤ x ≤ 402.1

Hence, if the weight of the bag is less than 397.9 grams or is more than 402.1 grams then the bag will be rejected.

i.e. The range for the bag being rejected is: x<397.9 grams and x>402.1 grams.

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!

step-by-step explanation: