Directly proportional, both increase/decrease, Multiple k(constant you needed to solve for)..
Inversely --one increases as the other decreases, increase the denominator & fraction gets smaller.... So
 
Problem: 
Dirextly to X (× by X)
 
Inversely to Y, (÷ by Y) 
 
Z= k X/Y
 
Solve, working backwards: Z =5 becomes
 5 = k (X) ÷ (Y). And 
X=15 and Y =9 becomes
 
5= k(15)/(9). Undo ÷9, ×9 both sides
45= k(15). Now undo ×15 by ÷15 both sides
 
45/15 = 3. So k=3, (also called your constant of variation)....and your Equation/Proportion becomes...
 
Z = 3X/Y
 
Use the new #s.... X=23, Y=14
 
Z= 3×23÷14 = 69/14. If they want spirochete answer divide and round to corresponding # if decimals
 
        
             
        
        
        
For the first part:Every shirt she grabs, will cost her dollars, so if she grabs 3 shirts, then the cost of the shirts is:

With the same rationale, if she grabs 2 pairs of jeans, the cost of the jeans is:

So, her total is:

If you subtract 3 from the total, then the expression is:
 For the second part:
For the second part:If she's paying 3 less for each shirt, then the cost of 3 shirts will become:

In the same fashion, for the two jeans:

So the expression for the total cost is:
 For number three:
For number three:The amounts are different because the cost of the total purchase is different than the cost of each element that makes up the total purchase.
For number four:If you're the owner, you want to give the smallest amount of discount (the one in part 1/a).
So you could clarify by saying there's 3 dollars of the TOTAL purchase's cost.
 
        
             
        
        
        
Let
x--------> the amount you have left to spend
y--------> the cost of a shirt you want
z------> the amount of the gift card
we know that
 --------> equation
 --------> equation 
 --------> equation
 --------> equation 
 --------> equation
 --------> equation 
Substitute the equation  and equation
 and equation ![3 in the equation [tex] 1](https://tex.z-dn.net/?f=%203%20in%20the%20equation%20%5Btex%5D%201%20) [/tex]
 [/tex]

 
 
therefore
<u>the answer is the option</u>
x+15 is less than or equal to 60
 
        
                    
             
        
        
        
Answer:
0.0025 = 0.25% probability that both are defective
Step-by-step explanation:
For each item, there are only two possible outcomes. Either they are defective, or they are not. Items are independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which  is the number of different combinations of x objects from a set of n elements, given by the following formula.
 is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.
5 percent of these are defective. 
This means that 
If two items are randomly selected as they come off the production line, what is the probability that both are defective
This is P(X = 2) when n = 2. So


0.0025 = 0.25% probability that both are defective