Adam needs both small and large cones to set up for a soccer practice. he knows there are fewer than 30 cones in the storage room. he needs at least a dozen large cones. let x represent the number of small cones and y represent the number of large cones. select all inequalities that model this situation.
x> 0
y≥12
x+y≤30
y> 12
x≥0
x+y< 30

X:  the number of small cones
y:  the number of large cones

a "dozen" means 12.

"Adam needs both small and large cones to set up for a soccer practice" mean that x must not be 0, and y must not be 0.

"there are fewer than 30 cones in the storage room." mean that : x+y<30

"He needs at least a dozen large cones." means that y≥12

so we have:

i) x≠0, y≠0, that is x>0, y>0

ii) x+y<30

iii) y≥12

now let's check all choices we have:

    x>0         True by i
   y≥12         True by iii
 x+y≤30       Not True by ii  (x+y is smaller than 30, the sum cannot be 30)
  y>12          Not true by iii (y may be = 12)
  x≥0             Not true by i, Adam needs small cones to (so we are assuming there are some in the storage room. Though this is open to interpretation)
 x+y<30      True