Andre and Kara are collecting food for the food pantry in their neighborhood. For every person they ask to donate, they receive an average of 13 items. Create a table and graph an arithmetic sequence to model this scenario. What would be the most appropriate label for the y-axis?(1 point)

Question

Andre and Kara are collecting food for the food pantry in their neighborhood. For every person they ask to donate, they receive an average of 13 items. Create a table and graph an arithmetic sequence to model this scenario. What would be the most appropriate label for the y-axis?(1 point)
Responses

number of people asked to donate
number of people asked to donate

number of items donated
number of items donated

food pantry
food pantry

neighborhoo

GPT-4o mini · Answer

To model the scenario of Andre and Kara collecting food donations in an arithmetic sequence, we can create a table and a graph. Since they receive an average of 13 items for every person they ask to donate, we can set up our table based on the number of people asked (x) and the number of items donated (y).

Table of Values

| Number of People Asked to Donate (x) | Number of Items Donated (y) | |---------------------------------------|------------------------------| | 0 | 0 | | 1 | 13 | | 2 | 26 | | 3 | 39 | | 4 | 52 | | 5 | 65 |

Explanation

Each time they ask one more person, they receive an additional 13 items. This creates an arithmetic sequence where the first term is 0 (when no one is asked) and each subsequent term increases by 13.

Graphing

If you were to graph this, you would plot points on a Cartesian plane where the x-axis represents the number of people asked to donate and the y-axis represents the number of items donated. The points from the table would be:

(0, 0)
(1, 13)
(2, 26)
(3, 39)
(4, 52)
(5, 65)

Most Appropriate Label for the Y-Axis

Given the context of the problem, the most appropriate label for the y-axis would be:

number of items donated

This clearly represents the outcome of the number of people they ask to donate, based on the average items they receive.

adaleta · Answer

Eric has $27.00 and wants to buy comic books. If each comic book costs $4.00, create a table and graph the arithmetic sequence to display how much money Eric has left after each comic book purchase. Which graph is an accurate representation of the problem?(1 point)
Responses

Four points showing a decrease in money remaining with an increase in number of comic books are plotted on a coordinate plane. The y-axis is labeled money remaining. The x-axis is labeled number of comic books.
Image with alt text: Four points showing a decrease in money remaining with an increase in number of comic books are plotted on a coordinate plane. The y-axis is labeled money remaining. The x-axis is labeled number of comic books.

Four points showing a decrease in money remaining with an increase in number of comic books are plotted on a coordinate plane. The y-axis is labeled money remaining. The x-axis is labeled number of comic books.
Image with alt text: Four points showing a decrease in money remaining with an increase in number of comic books are plotted on a coordinate plane. The y-axis is labeled money remaining. The x-axis is labeled number of comic books.

Four points showing a decrease in money remaining with an increase in number of comic books are plotted on a coordinate plane. The y-axis is labeled money remaining. The x-axis is labeled number of comic books.
Image with alt text: Four points showing a decrease in money remaining with an increase in number of comic books are plotted on a coordinate plane. The y-axis is labeled money remaining. The x-axis is labeled number of comic books.

Four points showing a decrease in number of comic books with an increase in money remaining are plotted on a coordinate plane. The y-axis is labeled number of comic books. The x-axis is labeled money remaining.
Image with alt text: Four points showing a decrease in number of comic books with an increase in money remaining are plotted on a coordinate plane. The y-axis is labeled number of comic books. The x-axis is labeled money remaining.
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ABC or D

GPT-4o mini · Answer

Let's create the table for Eric's purchases and see how much money he has left after buying comic books.

Table of Values

| Number of Comic Books Bought | Money Remaining ($) | |------------------------------|---------------------| | 0 | 27.00 | | 1 | 23.00 | | 2 | 19.00 | | 3 | 15.00 | | 4 | 11.00 | | 5 | 7.00 | | 6 | 3.00 | | 7 | -1.00 |

Explanation

Each comic book costs $4.00, so after each purchase, Eric's remaining money decreases by $4.00.
The table shows that the money remaining decreases by a consistent amount (i.e., $4) for each additional comic book purchased, forming an arithmetic sequence where the first term represents the initial amount of money and decreases by $4 each step.

Graph Representation

In terms of the graph, you would plot the data points where:

The x-axis represents the number of comic books bought.
The y-axis represents the money remaining.

Graph Points:

(0, 27)
(1, 23)
(2, 19)
(3, 15)
(4, 11)
(5, 7)
(6, 3)

Given this context, the correct option is:

Four points showing a decrease in money remaining with an increase in number of comic books are plotted on a coordinate plane. The y-axis is labeled money remaining. The x-axis is labeled number of comic books.

This accurately reflects the scenario, where as the number of comic books bought increases, the amount of money Eric has left decreases.

adaleta · Answer

so what the answer

GPT-4o mini · Answer

The correct response is: **Four points showing a decrease in money remaining with an increase in number of comic books are plotted on a coordinate plane. The y-axis is labeled money remaining. The x-axis is labeled number of comic books.** This option accurately describes the relationship between the number of comic books Eric buys and the money he has left, with the appropriate axes labeled correctly.

adaleta · Answer

A,B,C or D.

GPT-4o mini · Answer

Based on your previous messages, since you provided a description but didn't label them as A, B, C, or D, I cannot reference specific letters. However, I can summarize the correct choice again.

The correct choice is one that describes:

Four points showing a decrease in money remaining with an increase in number of comic books are plotted on a coordinate plane. The y-axis is labeled money remaining. The x-axis is labeled number of comic books.

Please select the option that corresponds to that description. If you provide the letter options again (A, B, C, D), I can help you identify which letter corresponds to that description.

adaleta · Answer

Question
To show that arithmetic sequence formulas have the same structure as linear functions, choose the linear function equation that has the same structure as the arithmetic sequence an=6+(n−1)⋅8
.(1 point)
Responses

y=8x−2
y equals 8 x minus 2

y=8x+6
y equals 8 x plus 6

y=2x−8
y equals 2 x minus 8

y=6x+8
y equals 6 x plus 8
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GPT-4o mini · Answer

To find the linear function that has the same structure as the given arithmetic sequence formula $ a_n = 6 + (n - 1) \cdot 8 $, we can rearrange the arithmetic sequence equation into a linear function form.

Let's simplify the arithmetic sequence formula:

Distribute the 8: \[ a_n = 6 + 8(n - 1) = 6 + 8n - 8 = 8n - 2 \]

So, the arithmetic sequence can be rewritten as: \[ a_n = 8n - 2 \]

This has the same structure as the form $ y = mx + b $, where:

$ m = 8 $ (the coefficient of $ n $)
$ b = -2 $ (the constant term)

Now, looking at your options:

y = 8x - 2
y = 8x + 6
y = 2x - 8
y = 6x + 8

The linear function that matches our derived equation $ a_n = 8n - 2 $ is:

y = 8x - 2

So, the answer is:

y = 8x - 2.

adaleta · Answer

Use the table to answer the question.

x y
2 a
4 b
Use the arithmetic sequence formula an=−8+(n−1)⋅2
to find the missing values in the table.

(1 point)
Responses

a=−15
; b=−13
a equals negative 15 ; b equals negative 13

a=−10
; b=−8
a equals negative 10 ; b equals negative 8

a=−12
; b=−10
a equals negative 12 ; b equals negative 10

a=−6
; b=−2
a equals negative 6 ; b equals negative 2
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GPT-4o mini · Answer

To find the missing values $a$ and $b$ in the given table using the arithmetic sequence formula $a_n = -8 + (n - 1) \cdot 2$, we can calculate the values for $n = 2$ and $n = 4$. ### Step 1: Calculate $a$ (which corresponds to $n = 2$) Using the formula: $$ a_2 = -8 + (2-1) \cdot 2 $$ This simplifies to: $$ a_2 = -8 + 1 \cdot 2 = -8 + 2 = -6 $$ So, $a = -6$. ### Step 2: Calculate $b$ (which corresponds to $n = 4$) Using the formula: $$ a_4 = -8 + (4-1) \cdot 2 $$ This simplifies to: $$ a_4 = -8 + 3 \cdot 2 = -8 + 6 = -2 $$ So, $b = -2$. ### Final Values The calculations give us: - $a = -6$ - $b = -2$ ### Answer Thus, the correct response is: **a = -6; b = -2**.

Andre and Kara are collecting food for the food pantry in their neighborhood. For every person they ask to donate, they receive an average of 13 items. Create a table and graph an arithmetic sequence to model this scenario. What would be the most appropriate label for the y-axis?(1 point)

Table of Values

Explanation

Graphing

Most Appropriate Label for the Y-Axis

Table of Values

Explanation

Graph Representation

Graph Points:

Step 1: Calculate \(a\) (which corresponds to \(n = 2\))

Step 2: Calculate \(b\) (which corresponds to \(n = 4\))

Final Values

Answer