Jackson has a gift card for $120 to use at a department store. he wants to purchase 2 shirts and 3 pairs of pants with his gift
1 answer:
- The domain of this relationship can be defined as,
0 ≤ x ≤ 60
- The range of this relationship can be defined as,
0 ≤ y ≤ 40
Definition of Domain and Range
The set of all the possible input values for which the provided function is defined is termed as the domain of that function.
The set of all the possible values that a given function can generate as an output is termed as the range of that function.
Forming the Relation
It is given that,
- Jackson wants to purchase 2 shirts and 3 pairs of pants with his gift card
- x represents the cost of the shirts and y represents the cost of the pants
- The limit of the gift card = $120
Thus, the relation formed is given by,
Domain and Range of the Given Relation
We have,
⇒
⇒
Thus, the domain is given by,
⇒
Similarly,
⇒
Thus, the range is given by,
⇒
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Answer:
if repetition is allowed,
if repetition is not allowed.
Step-by-step explanation:
For the first case, we have a choice of 26 letters <em>each step of the way. </em>For each of the 26 letters we can pick for the first slot, we can pick 26 for the second, and for each of <em>those</em> 26, we can pick between 26 again for our third slot, and well, you get the idea. Each step, we're multiplying the number of possible passwords by 26, so for a four-letter password, that comes out to 26 × 26 × 26 × 26 = possible passwords.
If repetition is <em>not </em>allowed, we're slowly going to deplete our supply of letters. We still get 26 to choose from for the first letter, but once we've picked it, we only have 25 for the second. Once we pick the second, we only have 24 for the third, and so on for the fourth. This gives us instead a pretty generous choice of 26 × 25 × 24 × 23 passwords.