A children clothing manufacturer has 500 yards of material to make shirts and skirts. A shirt requires 0.5 yards of fabric, and a skirt requires 1 yard of fabric. It takes 1 hour to make a shirt and 1.5 hours to make a skirt. The manufacture has 800 hours available to make shirts and skirts.

Which system of inequalities represent the constraints for this situation? Let x = number of shirts, and let y = number of skirts.

A) x ≤ 0 and y ≤ 0
0.5x + y ≤ 800
x + 1.5y ≤ 500

B) x ≤ 0 and y ≤ 0
0.5x + y ≥ 800
x + 1.5y ≥ 500

C) x ≥ 0 and y ≥ 0
0.5x + y ≤ 500
x + 1.5y ≤ 800

D) x ≥ 0 and y ≥ 0
0.5x + y ≥ 500
x + 1.5y ≥ 800

Step-by-step explanation:

We first denote the inequalities of the number of shirts and skirts.

#Since you cannot make a negative number of shirts or skirts, the inequalities will be written as:

#We then represent the inequality of material.

-The material size is a production constraint as only 500 yards of material is available for use.

-The inequality is therefore  written as:

#We then represent the inequality of time.

-The material size is a production constraint as only 800 hours available for use.

-The inequality is therefore  written as:

We combine the three inequalities to represent the constraints

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages

maya’s expression will generate the wrong sum because she violated the commutative property.

step-by-step explanation: