a long box can hold a certain number of comic books. use the graph of the step function to find the number of boxes a collector will need to hold 227 comic books.

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Accepted Answer

# Explanation:
## Step1: Analyze the step function graph
The x - axis represents the number of comic books and the y - axis represents the number of boxes. We need to find the y - value (number of boxes) corresponding to $x = 227$ comic books.

Looking at the graph, we can see the intervals of the step function. We need to identify in which interval 227 lies.

## Step2: Determine the interval for 227
We observe the x - values on the graph. Let's assume the intervals of the step function. From the graph, we can see that we need to find the step where $x = 227$ falls.

Looking at the graph, we can see that as we move along the x - axis, we check the intervals. Let's see the key points:

We can see that for a certain range of comic books, the number of boxes is constant. We need to find the step (the horizontal line) that contains $x=227$.

From the graph, we can see that when we look at the x - value of 227, we check the step function. Let's assume the intervals:

Looking at the graph, we can see that the step function has different levels. Let's find the interval that 227 is in.

We can see that 227 is between 200 and 250? Wait, no, looking at the x - axis labels: 50, 100, 150, 200, 250, 300, 350, 400, 450, 500.

Wait, let's re - examine. Let's list the intervals:

- For $0<x\leq50$, number of boxes $y = 1$
- For $50<x\leq100$, $y = 2$
- For $100<x\leq150$, $y = 3$
- For $150<x\leq200$, $y = 4$
- For $200<x\leq250$, $y = 5$? Wait, no, looking at the graph, the black dots and open circles. Wait, the open circles and closed circles: closed circles mean the point is included, open circles mean not included.

Wait, let's look at the y - axis values. Let's see the steps:

First step: from $x = 0$ (open circle at 0) to $x = 50$ (closed circle at 50), $y=1$

Second step: from $x = 50$ (open circle) to $x = 100$ (closed circle), $y = 2$

Third step: from $x = 100$ (open circle) to $x = 150$ (closed circle), $y=3$

Fourth step: from $x = 150$ (open circle) to $x = 200$ (closed circle), $y = 4$

Fifth step: from $x = 200$ (open circle) to $x = 250$ (closed circle), $y=5$? Wait, no, looking at the graph, when we look at the y - axis, the steps are:

Wait, the y - axis has values 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

Wait, let's count the steps. Let's see the points:

At $x = 0$, open circle at (0,1), closed circle at (50,1)

Then open circle at (50,2), closed circle at (100,2)

Open circle at (100,3), closed circle at (150,3)

Open circle at (150,4), closed circle at (200,4)

Open circle at (200,5), closed circle at (250,5)

Open circle at (250,6), closed circle at (300,6)

Open circle at (300,7), closed circle at (350,7)

Open circle at (350,8), closed circle at (400,8)

Open circle at (400,9), closed circle at (450,9)

Open circle at (450,10), closed circle at (500,10)

Wait, no, maybe I misread. Wait, the y - axis starts at 1, and the first step is from x = 0 (open) to x = 50 (closed) with y = 1.

Then from x = 50 (open) to x = 100 (closed) with y = 2.

x = 100 (open) to x = 150 (closed) with y = 3.

x = 150 (open) to x = 200 (closed) with y = 4.

x = 200 (open) to x = 250 (closed) with y = 5.

x = 250 (open) to x = 300 (closed) with y = 6.

x = 300 (open) to x = 350 (closed) with y = 7.

x = 350 (open) to x = 400 (closed) with y = 8.

x = 400 (open) to x = 450 (closed) with y = 9.

x = 450 (open) to x = 500 (closed) with y = 10.

Now, 227 is between 200 (open) and 250 (closed). So when $200<x\leq250$, the number of boxes $y = 5$? Wait, no, wait, let's check the y - axis. Wait, maybe I made a mistake. Wait, let's look at the graph again.

Wait, the first step: at x = 0, open circle at (0,1), closed circle at (50,1). So for 0 < x ≤50, y = 1.

Then open circle at (50,2), closed circle at (100,2). So 50 < x ≤100, y = 2.

Open circle at (100,3), closed circle at (150,3). 100 < x ≤150, y = 3.

Open circle at (150,4), closed circle at (200,4). 150 < x ≤200, y = 4.

Open circle at (200,5), closed circle at (250,5). 200 < x ≤250, y = 5.

Ah! So 227 is in the interval $200 < x\leq250$. So the number of boxes y = 5? Wait, no, wait 227 is greater than 200 and less than or equal to 250? Wait, 227 is less than 250, so yes. Wait, but let's check the graph again. Wait, maybe the intervals are different. Wait, maybe the closed circles and open circles:

Wait, the open circle means the left - hand endpoint is not included, and the closed circle means the right - hand endpoint is included.

Wait, let's take x = 227. Let's see the step where x = 227 lies.

Looking at the graph, when x is between 200 (open) and 250 (closed), the number of boxes is 5? Wait, no, maybe I messed up the y - axis values. Wait, let's count the steps.

Wait, the first step (y = 1) is from x = 0 (open) to x = 50 (closed).

Second step (y = 2): x = 50 (open) to x = 100 (closed).

Third step (y = 3): x = 100 (open) to x = 150 (closed).

Fourth step (y = 4): x = 150 (open) to x = 200 (closed).

Fifth step (y = 5): x = 200 (open) to x = 250 (closed).

Sixth step (y = 6): x = 250 (open) to x = 300 (closed).

Wait, 227 is in the interval $200<x\leq250$, so the number of boxes is 5? Wait, no, that can't be right. Wait, maybe I misread the y - axis. Wait, the y - axis has 1,2,3,4,5,6,7,8,9,10. Wait, maybe the intervals are:

Wait, let's look at the x - axis labels: 50, 100, 150, 200, 250, 300, 350, 400, 450, 500.

Wait, maybe the first step (y = 1) is 0 - 50, y = 2: 50 - 100, y = 3: 100 - 150, y = 4: 150 - 200, y = 5: 200 - 250, y = 6: 250 - 300, etc.

So 227 is between 200 and 250, so y = 5? Wait, but let's check the graph again. Wait, maybe the closed circle at 250 is for y = 6? Wait, no, the open circle at (250,6) and closed circle at (300,6). So 250 < x ≤300, y = 6.

Ah! I see my mistake. The open circle at (200,5) and closed circle at (250,5) means 200 < x ≤250, y = 5. The open circle at (250,6) and closed circle at (300,6) means 250 < x ≤300, y = 6.

So 227 is in 200 < x ≤250, so y = 5? Wait, no, 227 is less than 250, so yes. Wait, but let's confirm.

Wait, let's take x = 201, it should be in the y = 5 step, x = 250 is in y = 5 (closed circle at (250,5)), and x = 251 is in y = 6 (open circle at (250,6)).

So 227 is between 200 and 250, so the number of boxes is 5? Wait, but that seems low. Wait, maybe the graph is different. Wait, the user's graph:

Looking at the graph, the y - axis has 1,2,3,4,5,6,7,8,9,10. The x - axis has 0,50,100,150,200,250,300,350,400,450,500.

The first step: (0,1) open, (50,1) closed: 0 < x ≤50, y = 1.

Second step: (50,2) open, (100,2) closed: 50 < x ≤100, y = 2.

Third step: (100,3) open, (150,3) closed: 100 < x ≤150, y = 3.

Fourth step: (150,4) open, (200,4) closed: 150 < x ≤200, y = 4.

Fifth step: (200,5) open, (250,5) closed: 200 < x ≤250, y = 5.

Sixth step: (250,6) open, (300,6) closed: 250 < x ≤300, y = 6.

Seventh step: (300,7) open, (350,7) closed: 300 < x ≤350, y = 7.

Eighth step: (350,8) open, (400,8) closed: 350 < x ≤400, y = 8.

Ninth step: (400,9) open, (450,9) closed: 400 < x ≤450, y = 9.

Tenth step: (450,10) open, (500,10) closed: 450 < x ≤500, y = 10.

So for x = 227, which is in 200 < x ≤250, the number of boxes is 5? Wait, that seems incorrect. Wait, maybe the number of comics per box is 50? Wait, no, the first box holds up to 50 comics (y = 1 for 0 - 50), second box up to 100 (y = 2 for 50 - 100), so each box holds 50 comics? Wait, 50 comics per box. Then 227 comics: 227 divided by 50 is 4.54, so we need 5 boxes (since we can't have a fraction of a box). Ah! That makes sense. Because we use the ceiling function (step function) for the number of boxes. So $\lceil\frac{227}{50}
ceil=\lceil4.54
ceil = 5$. So the number of boxes is 5.

# Answer:
5

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QUESTION IMAGE

Question

Explanation:

Step1: Analyze the step function graph

Step2: Determine the interval for 227

Answer: