Huang Yi works as a paleontologist and a sculptor. She earns \$5{,}500$5,500dollar sign, 5, comma, 500 per month as a paleontologist and \$4{,}500$4,500dollar sign, 4, comma, 500 per month as a sculptor. Huang Yi wants to make more than \$50{,}000$50,000dollar sign, 50, comma, 000 this year. In the inequality shown above, PPP represents the number of months Huang Yi can work as a paleontologist and SSS represents the number of months she can work as a sculptor to reach her goal. If Huang Yi worked for 666 months as a paleontologist this year, what is the minimum whole number of months that she must work as a sculptor to reach her goal?

4 months

Step-by-step explanation:

Let P represents the number of months Huang Yi can work as a paleontologist and S represents the number of months she can work as a sculptor to reach her goal.

If she works for P months as an paleontologist, her income would be 5500P while if she works for S months as a sculptor her income would be 4500S.

Her total income = 5500P + 4500S

Since she wants to earn more than $50000, hence:

5500P + 4500S > 50000

Given she worked as a paleontologist for 6 months, therefore:

5500(6) + 4500S > 50000

33000  + 4500S > 50000

4500S > 50000 - 33000

4500S > 17000

S > 17000/4500

S > 3.78

S > 4

The minimum whole number of months that she must work as a sculptor to reach her goal is 4 months

answer: 0+0=0

step-by-step explanation:

that is the only answer that can make 0

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.