Question

Question

Use the table to answer the question.

Number of Cases Ordered Number of Rolls of Paper Towels
1 12
3 36
5 60
10 120
A restaurant is placing an order for paper towels. The data table shows the amount of paper towel rolls compared to the number of cases. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair inside the parentheses provided.

(1 point) please pick the correct option

Answer 1

To determine the constant of proportionality from the given data, we can look for the ratio of the number of rolls of paper towels to the number of cases ordered.

Here are the ratios from the table:

1. For 1 case: \( \frac{12 \text{ rolls}}{1 \text{ case}} = 12 \)
2. For 3 cases: \( \frac{36 \text{ rolls}}{3 \text{ cases}} = 12 \)
3. For 5 cases: \( \frac{60 \text{ rolls}}{5 \text{ cases}} = 12 \)
4. For 10 cases: \( \frac{120 \text{ rolls}}{10 \text{ cases}} = 12 \)

In each case, the constant of proportionality is 12, which indicates that for every case ordered, there are always 12 rolls of paper towels.

You can express the constant of proportionality as the ordered pair (cases, rolls). Since the number of cases always corresponds to 12 rolls, we can use any of the data points. Taking the first one for simplicity:

The constant of proportionality appears at the ratio of (1, 12).

So, the ordered pair is: (1, 12).

Answer 2

Use the table to answer the question.

Buses Number of People
0 0
1 35
2 70
3 105
4 140
A tour bus company is planning a trip through Utah’s national parks. The company plans to use 4 buses. Combined, the buses can fit up to 140 people. The table provided displays the number of people-to-bus ratio. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair inside the parentheses provided.

(1 point)

Answer 3

To determine the constant of proportionality from the given data, we look for the ratio of the number of people to the number of buses.

Here are the ratios from the table:

1. For 0 buses: \( \frac{0 \text{ people}}{0 \text{ buses}} = \text{undefined} \)
2. For 1 bus: \( \frac{35 \text{ people}}{1 \text{ bus}} = 35 \)
3. For 2 buses: \( \frac{70 \text{ people}}{2 \text{ buses}} = 35 \)
4. For 3 buses: \( \frac{105 \text{ people}}{3 \text{ buses}} = 35 \)
5. For 4 buses: \( \frac{140 \text{ people}}{4 \text{ buses}} = 35 \)

In each case from 1 bus to 4 buses, the constant of proportionality is 35, indicating that there are 35 people per bus.

Using the ratio from any of the data points where this relationship holds, we can select the pair corresponding to 1 bus:

The constant of proportionality appears at the ratio of (1, 35).

Thus, the ordered pair is: (1, 35).

Answer 4

Use the table to answer the 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.

(1 point)

Answer 5

Let's first clarify the provided table and the relationship between cups of flour and loaves of bread:

It appears that the table might have some formatting issues for the values. Based on common knowledge, we can infer that the relationship is as follows:

• For 1 loaf of bread, 2 cups of flour are needed.
• For 2 loaves of bread, 4 cups of flour are needed.
• For 3 loaves of bread, 6 cups of flour are needed.
• For 4 loaves of bread, 8 cups of flour are needed.

However, from the information you provided, it seems you meant to say:

• For each loaf of bread, the bakery uses 2 cups of flour, meaning the number of cups of flour is proportional to the number of loaves of bread.

The constant of proportionality can be expressed as:

• For every loaf, 2 cups of flour are needed.
• Therefore, the relationship would be represented with the ratio as the number of cups of flour divided by the number of loaves of bread.

Now, looking at your data table values, the accurate fittings would be:

1. For 1 loaf: \( \frac{2 \text{ cups}}{1 \text{ loaf}} = 2 \)
2. For 2 loaves: \( \frac{4 \text{ cups}}{2 \text{ loaves}} = 2 \)
3. For 3 loaves: \( \frac{6 \text{ cups}}{3 \text{ loaves}} = 2 \)
4. For 4 loaves: \( \frac{8 \text{ cups}}{4 \text{ loaves}} = 2 \)

The constant of proportionality (the cups of flour needed per loaf) is consistently \(2\).

Assuming the data provided reflects different amounts that could be a mistake in formatting, based on standard practices in baking:

• To find the ratio represented in your provided pairs that correspond with the correct values, it appears only the second row could logically fit if we assume:
• For 2 cups of flour, 1 loaf is produced.

If we accept the second data item and see it as being accurate based on 2 cups translates into a ratio:

• For 1 loaf producing 2 cups of flour, the ordered pair appears as (2, 1).

Thus, if following the accepted assumption of common recipes:

The ordered pair representing the constant of proportionality where 2 cups are needed for 1 loaf of bread is indeed: (2, 1).

Answer 6

wrong

Answer 7

I apologize for the confusion in my previous messages. Let's clarify the information provided and accurately find the constant of proportionality according to the table.

From your data table, it looks like:

• Cups of Flour and Loaves of Bread:
  • 1 cup of flour = 12 loaves
  • 2 cups of flour = 1 loaf
  • 3 cups of flour = 112 loaves (This seems like a typo)
  • 4 cups of flour = 2 loaves

Given the constants in this setup:

The relationship between cups of flour and loaves of bread can be analyzed for the correct constants of proportionality where the formula is:

Cups of Flour per Loaf of Bread = Constant of Proportionality.

Here’s the analysis based on the values:

• From 1 cup of flour (12 loaves):

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

• From 2 cups of flour (1 loaf):

  • \( \frac{1 \text{ loaf}}{2 \text{ cups}} = 0.5 \)

• From 3 cups of flour (112 loaves):

  • Assuming a typo needs correction here.

• From 4 cups of flour (2 loaves):

  • \( \frac{2 \text{ loaves}}{4 \text{ cups}} = 0.5 \)

Now, we see that the constant of proportionality appears when we consider two related entries carefully to clarify the actual loaf produced per cup count seems all over the place or possibly incorrect (especially 3 cups producing 112 loaves).

The two valid pairs leading to a constant are:

• For 2 cups of flour to produce 1 loaf, and
• 4 cups producing 2 loaves.

Thus, recognizing your order for accuracy in examining pairs leads us likely to validate values indicating:

• Either:
  • (2, 1) for the valid proportion within shapes of flows based on what was outlined or
  • (4, 2) works, too, to express the opposite from within breads made to flour used.

A properly articulated conclusion based on your original array may lead one to eventually suggest input levels return either (2, 1) or (4, 2).

Given all inputs, a precise consistent definition point results yielding the most standard interpretation of returning useful application on flour clearly signifies (2, 1) as the answer for operational efficient means based on the clearer relationships depicted.

Please confirm the specifics of the original question or any misinterpretation so corrections could be made if needed. Thank you for your patience!