Use the table to answer the question.

Question

Cups of Flour Loaves of Bread
1 12

2 1
3 112

4 2
A bakery is making loaves of French bread. The recipe calls for 2 cups of flour per loaf of bread. The data table shows how much flour the bakery needs depending on the number of loaves it intends to make. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair inside the parentheses provided.

Answer 1

To find the constant of proportionality, we need to determine the ratio of cups of flour to loaves of bread based on the data from the table. The constant of proportionality is the number of cups of flour needed per loaf of bread.

According to the recipe, it requires 2 cups of flour per loaf. We can check the data table to identify which pair of values represents this ratio:

• For 1 cup of flour: 1 loaf * (2 cups/loaf) = 0.5 loaves (not consistent)
• For 2 cups of flour: 1 loaf of bread (2 cups matches 1 loaf, so this does not apply)
• For 3 cups of flour: 112 loaves (this does not match)
• For 4 cups of flour: 2 loaves (4 cups / 2 loaves = 2 cups per loaf, this matches the recipe)

Therefore, the ordered pair that shows the constant of proportionality is (4, 2).

So, the answer is (4, 2).

Answer 2

nope

Answer 3

Let's re-evaluate the data you provided and clarify the ratios properly.

According to the data table:

• 1 cup of flour → 12 loaves of bread
• 2 cups of flour → 1 loaf of bread
• 3 cups of flour → 112 loaves of bread
• 4 cups of flour → 2 loaves of bread

The recipe requires 2 cups of flour per loaf of bread, which means we need to see which entry in the table matches this ratio.

Now, let's calculate the constant of proportionality for each entry:

1. For 1 cup of flour → 12 loaves: \[ k = \frac{1 \text{ cup}}{12 \text{ loaves}} = \frac{1}{12} \]

2. For 2 cups of flour → 1 loaf: \[ k = \frac{2 \text{ cups}}{1 \text{ loaf}} = 2 \]

3. For 3 cups of flour → 112 loaves: \[ k = \frac{3 \text{ cups}}{112 \text{ loaves}} \approx 0.0268 \]

4. For 4 cups of flour → 2 loaves: \[ k = \frac{4 \text{ cups}}{2 \text{ loaves}} = 2 \]

From this assessment, we can see that for the entries (2 cups, 1 loaf) and (4 cups, 2 loaves), the ratio is consistent with the recipe, but the ratios of \(2\) cups of flour per loaf appear at entry (4, 2).

So the correct answer indicating where the constant of proportionality appears is: (4, 2).

If there was confusion about the interpretations of values, my apologies. Please clarify, and I can correct it further!

Answer 4

well the first option is 1, 1/2 and the other option is 1, 1/12

Answer 5

Thank you for your patience. Let's clarify the information correctly about the ratios. Based on your latest message, it appears you want to express the number of cups of flour per loaf of bread in a standard format.

Based on the table you provided, let's simplify and identify the correct ordered pairs and their corresponding ratios.

1. For 1 cup of flour, the bakery makes 12 loaves.

   • Ratio: \( \frac{1 \text{ cup}}{12 \text{ loaves}} = \frac{1}{12} \)

2. For 2 cups of flour, the bakery makes 1 loaf.

   • Ratio: \( \frac{2 \text{ cups}}{1 \text{ loaf}} = 2 \)

3. For 3 cups of flour, the bakery supposedly makes 112 loaves.

   • Ratio: \( \frac{3 \text{ cups}}{112 \text{ loaves}} = \frac{3}{112} \)

4. For 4 cups of flour, the bakery makes 2 loaves.

   • Ratio: \( \frac{4 \text{ cups}}{2 \text{ loaves}} = 2 \)

To identify the correct constants of proportionality (where the ratios correspond to the recipe of 2 cups per loaf):

• From the first option: you have (1, 1/12).
• From the second option: you have (2, 1).

Thus, the correct ratios based on your information are:

• The first valid ratio is indeed (1, 1/12), indicating that for every cup of flour, 12 loaves can be made.
• The second valid ratio (2, 1) indicates that for 2 cups of flour, you can make 1 loaf.

Given that for 2 cups of flour per loaf, the corresponding ordered pair to reflect that from the data you provided is (2, 1) since you make 1 loaf with 2 cups.

Ultimately, regarding the desired ratio of 2 cups of flour per loaf of bread, the correct ordered pair that shows this relationship is:

(2, 1).

Thank you for your guidance to clarify further, and I hope this meets your expectation!

Answer 6

2,1 isn't correcte either

Answer 7

I apologize for the confusion in my previous messages. Let’s take a fresh look at the information you provided.

The data you gave is:

| Cups of Flour | Loaves of Bread | |---------------|------------------| | 1 | 12 | | 2 | 1 | | 3 | 112 | | 4 | 2 |

The aim is to identify the ratio where the constant of proportionality \( k \) appears when relating cups of flour needed per loaf of bread.

Given the recipe calls for 2 cups of flour per loaf, we’ll evaluate each entry:

1. (1, 12): \[ \text{Cups of flour per loaf} = \frac{1 \text{ cup}}{12 \text{ loaves}} = \frac{1}{12} \text{ cups/loaf} \]

2. (2, 1): \[ \text{Cups of flour per loaf} = \frac{2 \text{ cups}}{1 \text{ loaf}} = 2 \text{ cups/loaf} \]

3. (3, 112): \[ \text{Cups of flour per loaf} = \frac{3 \text{ cups}}{112 \text{ loaves}} = \frac{3}{112} \text{ cups/loaf} \]

4. (4, 2): \[ \text{Cups of flour per loaf} = \frac{4 \text{ cups}}{2 \text{ loaves}} = 2 \text{ cups/loaf} \]

To find the correct constant of proportionality in accordance with the recipe (2 cups per loaf), we should look for a combination where the amount of flour divided by the number of loaves equals \( 2 \).

From this analysis, it appears:

• The entry (2, 1) shows 2 cups of flour for 1 loaf, fully aligning with the recipe requirement. However, this is not the ratio represented in a simpler format.
• The entry (4, 2) also indicates 2 cups of flour per loaf.

Based on the format you specified (1, 1/2) and (1, 1/12), it seems there might have been a misunderstanding in focusing solely on the ratios derived. If we adjust it according to your request:

• The ratio from (1, 1/12) indicates that 1 cup yields 12 loaves.
• The ratio from (4, 2) can also be represented as \( (2, 1) \) (which simplifies to the same ratio of \( 2 \) cups to \( 1 \) loaf).

Thus, if the focus is on identifying the constant of proportionality as it appears in your original content, you are looking for that relationship on the entry (4, 2).

Based on your corrections, I apologize for not straightening it out initially; please confirm the right entry you wish to focus on, maintaining the context of your queries. Would you like to indicate which specific ratio you are considering, or clarify if there’s more detail you’d like to delve into?

Answer 8

the right answer was 1, 1/2

Answer 9

Thank you for your patience, and I apologize for the confusion earlier. Let’s break it down to see why the correct ratio is \( (1, \frac{1}{2}) \).

Given the recipe calls for 2 cups of flour per loaf of bread, we can express this as:

1 loaf = 2 cups of flour This means that for every loaf, you need 2 cups of flour. If we want to express the relationship of cups of flour to loaves:

\[ \text{Cups of flour per loaf} = \frac{\text{Cups of flour}}{\text{Loaves of bread}} \]

In this case, 2 cups of flour for 1 loaf of bread can be rearranged as:

\[ k = \frac{2 \text{ cups}}{1 \text{ loaf}} \rightarrow \text{This means that } \]

If we adjust it to fit as pairs indicating "Cups of flour, Cups of flour per loaf":

For 1 cup of flour, it would yield:

\[ \text{Cups of flour per loaf} = \frac{1 \text{ cup}}{(\frac{1}{2} \text{ loaf})} = (1, \frac{1}{2}) \]

Thus, with 1 cup of flour, you can make half a loaf, or saying it alternatively, 1 cup of flour corresponds to \( \frac{1}{2} \) of a loaf.

Hence, the ordered pair is indeed (1, \frac{1}{2}).

Thank you for your clarification, and once again, I apologize for any misunderstanding in my previous responses. Your persistence in clarifying this is greatly appreciated!