Question

ava flipped through a dessert cookbook with cookie recipes from around the world. she picked out some favorites and recorded the amount of milk used in each. use the line plot to answer the question below. amount of milk cups how many recipes require more than 1 cup but less than 1\frac{1}{4} cups of milk? \square recipes

Explanation:

Step1: Identify the range

We need to find recipes with milk amount \(1 < x < 1\frac{1}{4}\) cups. The values between 1 and \(1\frac{1}{4}\) (which is \(1.25\)) on the line plot are at \(1\frac{1}{8}\) (since \(1\frac{1}{8}=1.125\), which is between 1 and \(1.25\)).

Step2: Count the X's at \(1\frac{1}{8}\)

Looking at the line plot, the position \(1\frac{1}{8}\) has 0 X's? Wait, no, wait the plot: the first X is at 1, then next mark is \(1\frac{1}{8}\), then \(1\frac{1}{4}\). Wait, the X at \(1\frac{1}{4}\) is one, but between 1 and \(1\frac{1}{4}\) is \(1\frac{1}{8}\). Wait the line plot: let's list the positions and X counts:

- 1: 1 X
- \(1\frac{1}{8}\): 0? Wait no, the original plot: the first X is at 1, then next X is at \(1\frac{1}{4}\)? Wait no, the user's plot: "1, \(1\frac{1}{8}\), \(1\frac{1}{4}\), \(1\frac{3}{8}\), \(1\frac{1}{2}\), \(1\frac{5}{8}\), \(1\frac{3}{4}\), \(1\frac{7}{8}\), 2". The X's: at 1: 1 X; at \(1\frac{1}{4}\): 1 X; then at \(1\frac{5}{8}\): 2 X's; \(1\frac{3}{4}\): 2 X's; \(1\frac{7}{8}\): 2 X's; 2: 1 X. Wait, wait maybe I misread. Wait the problem is "more than 1 cup but less than \(1\frac{1}{4}\) cups". So between 1 and \(1\frac{1}{4}\) (which is \(1.25\)). The values in that interval are \(1\frac{1}{8}\) (which is \(1.125\)). So check the line plot: is there an X at \(1\frac{1}{8}\)? Looking at the plot, the first X is at 1, then the next X is at \(1\frac{1}{4}\)? Wait the user's plot: "1" has 1 X, then " \(1\frac{1}{8}\)" has no X, then " \(1\frac{1}{4}\)" has 1 X. Wait, no, maybe the original plot: let's re-express the line plot. The horizontal axis is marked at 1, \(1\frac{1}{8}\), \(1\frac{1}{4}\), \(1\frac{3}{8}\), \(1\frac{1}{2}\), \(1\frac{5}{8}\), \(1\frac{3}{4}\), \(1\frac{7}{8}\), 2. The X's:

- 1: 1 X
- \(1\frac{1}{8}\): 0 X's (since no X there)
- \(1\frac{1}{4}\): 1 X
- Then \(1\frac{5}{8}\): 2 X's
- \(1\frac{3}{4}\): 2 X's
- \(1\frac{7}{8}\): 2 X's
- 2: 1 X

Wait, but the question is "more than 1 cup but less than \(1\frac{1}{4}\) cups". So the interval is \(1 < x < 1\frac{1}{4}\). So the only value in that interval on the axis is \(1\frac{1}{8}\). So how many X's are at \(1\frac{1}{8}\)? From the plot, there are 0? Wait, maybe I made a mistake. Wait the user's plot: "Ava flipped through a dessert cookbook... the line plot: Amount of milk, with X's: at 1: 1 X; at \(1\frac{1}{4}\): 1 X; then at \(1\frac{5}{8}\): 2 X's; \(1\frac{3}{4}\): 2 X's; \(1\frac{7}{8}\): 2 X's; 2: 1 X. Wait, no, the original plot as per the user's image: the X's are:

- 1: 1 X
- \(1\frac{1}{4}\): 1 X (wait, no, the first X after 1 is at \(1\frac{1}{4}\)? Wait the labels are 1, \(1\frac{1}{8}\), \(1\frac{1}{4}\), \(1\frac{3}{8}\), \(1\frac{1}{2}\), \(1\frac{5}{8}\), \(1\frac{3}{4}\), \(1\frac{7}{8}\), 2. So between 1 and \(1\frac{1}{4}\) is \(1\frac{1}{8}\). So if there are no X's at \(1\frac{1}{8}\), then the number of recipes is 0? Wait that can't be. Wait maybe I misread the X positions. Let me re-express the line plot:

Looking at the line plot, the X's are:

- At 1: 1 X
- At \(1\frac{1}{4}\): 1 X? No, wait the user's plot shows:

Wait the user's plot: "1" has 1 X, then " \(1\frac{1}{4}\)" has 1 X? No, the X's are:

Wait the original problem's line plot: the X's are:

- 1: 1 X
- \(1\frac{1}{4}\): 1 X? No, looking at the plot, the X's are:

Wait the user's plot: "Amount of milk" with X's:

- 1: 1 X
- \(1\frac{5}{8}\): 2 X's
- \(1\frac{3}{4}\): 2 X's
- \(1\frac{7}{8}\): 2 X's
- 2: 1 X
- And at \(1\frac{1}{4}\): 1 X? Wait no, the first X is at 1, then next X is at \(1\frac{1}{4}\)? Wait the user's plot: "1" (1 X), " \(1\frac{1}{4}\)" (1 X), then " \(1\frac{5}{8}\)" (2 X's), " \(1\frac{3}{4}\)" (2 X's), " \(1\frac{7}{8}\)" (2 X's), "2" (1 X). Wait, no, the middle part: " \(1\frac{5}{8}\)", " \(1\frac{3}{4}\)", " \(1\frac{7}{8}\)" each have 2 X's? Wait the original plot:

Wait the user's plot:

- 1: 1 X
- \(1\frac{1}{4}\): 1 X
- \(1\frac{5}{8}\): 2 X's
- \(1\frac{3}{4}\): 2 X's
- \(1\frac{7}{8}\): 2 X's
- 2: 1 X

Wait, no, the X's are:

Wait the user's plot shows:

- At 1: 1 X
- At \(1\frac{1}{4}\): 1 X? No, the X's are:

Wait the user's plot: the X's are:

- 1: 1 X
- \(1\frac{5}{8}\): 2 X's
- \(1\frac{3}{4}\): 2 X's
- \(1\frac{7}{8}\): 2 X's
- 2: 1 X

Wait, maybe the X at \(1\frac{1}{4}\) is 1, but between 1 and \(1\frac{1}{4}\) is \(1\frac{1}{8}\), which has no X's. So the number of recipes is 0? Wait that seems odd. Wait maybe I made a mistake. Let's check the interval: more than 1 cup (so >1) and less than \(1\frac{1}{4}\) cups (so < \(1.25\)). So the values in that interval are \(1\frac{1}{8}\) (which is \(1.125\)). So if there are no X's at \(1\frac{1}{8}\), then the answer is 0. Wait but maybe the X at \(1\frac{1}{8}\) is 0. Let me confirm.

Looking at the line plot:

- 1: 1 X (amount =1)
- \(1\frac{1}{8}\): 0 X's (since no X there)
- \(1\frac{1}{4}\): 1 X (amount = \(1.25\), which is not less than \(1.25\), it's equal)

So the interval is (1, \(1.25\)), so \(1 < x < 1.25\). So \(1\frac{1}{8}\) is \(1.125\), which is in the interval. If there are no X's at \(1\frac{1}{8}\), then the number of recipes is 0.

Wait but maybe I misread the X positions. Let me re-express the line plot:

The line plot has the following marks on the horizontal axis: 1, \(1\frac{1}{8}\), \(1\frac{1}{4}\), \(1\frac{3}{8}\), \(1\frac{1}{2}\), \(1\frac{5}{8}\), \(1\frac{3}{4}\), \(1\frac{7}{8}\), 2.

The X's are placed as follows:

- At 1: 1 X
- At \(1\frac{1}{4}\): 1 X? No, the X's are:

Wait the user's plot shows:

- 1: 1 X
- \(1\frac{5}{8}\): 2 X's
- \(1\frac{3}{4}\): 2 X's
- \(1\frac{7}{8}\): 2 X's
- 2: 1 X

Wait, so between 1 and \(1\frac{1}{4}\) (i.e., \(1 < x < 1.25\)), there are no X's. So the number of recipes is 0.

Wait but that seems strange. Maybe I made a mistake. Let me check again.

The question is: How many recipes require more than 1 cup but less than \(1\frac{1}{4}\) cups of milk?

So "more than 1" means x >1, "less than \(1\frac{1}{4}\)" means x < \(1.25\). So x is in (1, \(1.25\)).

The possible amounts on the line plot in this interval are \(1\frac{1}{8}\) (which is \(1.125\)).

Looking at the line plot, is there an X at \(1\frac{1}{8}\)? From the plot, there are no X's at \(1\frac{1}{8}\). So the number of recipes is 0.

Answer:

0