Math / Data & Statistics

QuestionThis table displays a scenario. \begin{tabular}{|c|c|} \hline Gallons, $\boldsymbol{g}$ & Liters, $\boldsymbol{l}$ \\ \hline 1 & 3.79 \\ \hline 2 & 7.58 \\ \hline 3 & 11.37 \\ \hline 4 & 15.16 \\ \hline 5 & 18.95 \\ \hline 6 & 22.74 \\ \hline \end{tabular}
What can be determined from the table? Check all that apply. The independent variable is the number of gallons. Liters is a function of Gallons. The equation $l=3.79 \mathrm{~g}$ represents the table. As the number of gallons increases, the number of liters increases. This is a function because every input has exactly one output.

Studdy Solution

STEP 1

What is this asking? This is asking us to figure out what's true about the relationship between gallons and liters shown in the table. Watch out! Don't mix up independent and dependent variables!
Also, make sure the equation actually matches the table's data.

STEP 2

1. Check the independent variable.
2. Check if liters is a function of gallons.
3. Check the equation.
4. Check if liters increase with gallons.
5. Check if every input has exactly one output.

STEP 3

The number of gallons, represented by $g$ , is the independent variable because we're using it to determine the number of liters, represented by $l$ .
So, the statement "The independent variable is the number of gallons" is TRUE!

STEP 4

Since each value of gallons, $g$ , corresponds to a specific value of liters, $l$ , we can say that liters is indeed a function of gallons.
So, "Liters is a function of Gallons" is TRUE!

STEP 5

Let's test the equation $l = 3.79 \cdot g$ with a few values from the table.

STEP 6

When $g = 1$ , $l = 3.79 \cdot 1 = 3.79$ .
This matches the table.

STEP 7

When $g = 2$ , $l = 3.79 \cdot 2 = 7.58$ .
This also matches the table.

STEP 8

When $g = 3$ , $l = 3.79 \cdot 3 = 11.37$ .
This matches too!
It looks like the equation correctly represents the relationship, so "The equation $l = 3.79 \cdot g$ represents the table" is TRUE!

STEP 9

Looking at the table, as the number of gallons increases, the number of liters also increases.
So, "As the number of gallons increases, the number of liters increases" is TRUE!

STEP 10

For every value of gallons (input), there's only one corresponding value of liters (output).
This is the definition of a function!
So, "This is a function because every input has exactly one output" is TRUE!

STEP 11

All of the statements are TRUE: - The independent variable is the number of gallons. - Liters is a function of Gallons. - The equation $l = 3.79 \cdot g$ represents the table. - As the number of gallons increases, the number of liters increases. - This is a function because every input has exactly one output.

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Studdy Solution

STEP 1

What is this asking? This is asking us to figure out what's true about the relationship between gallons and liters shown in the table. Watch out! Don't mix up independent and dependent variables!
Also, make sure the equation actually matches the table's data.

STEP 2

1. Check the independent variable.
2. Check if liters is a function of gallons.
3. Check the equation.
4. Check if liters increase with gallons.
5. Check if every input has exactly one output.

STEP 3

The number of gallons, represented by $g$ , is the independent variable because we're using it to determine the number of liters, represented by $l$ .
So, the statement "The independent variable is the number of gallons" is TRUE!

STEP 4

Since each value of gallons, $g$ , corresponds to a specific value of liters, $l$ , we can say that liters is indeed a function of gallons.
So, "Liters is a function of Gallons" is TRUE!

STEP 5

Let's test the equation $l = 3.79 \cdot g$ with a few values from the table.

STEP 6

When $g = 1$ , $l = 3.79 \cdot 1 = 3.79$ .
This matches the table.

STEP 7

When $g = 2$ , $l = 3.79 \cdot 2 = 7.58$ .
This also matches the table.

STEP 8

When $g = 3$ , $l = 3.79 \cdot 3 = 11.37$ .
This matches too!
It looks like the equation correctly represents the relationship, so "The equation $l = 3.79 \cdot g$ represents the table" is TRUE!

STEP 9

Looking at the table, as the number of gallons increases, the number of liters also increases.
So, "As the number of gallons increases, the number of liters increases" is TRUE!

STEP 10

For every value of gallons (input), there's only one corresponding value of liters (output).
This is the definition of a function!
So, "This is a function because every input has exactly one output" is TRUE!

STEP 11

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Studdy Solution

STEP 1

What is this asking? This is asking us to figure out what's true about the relationship between gallons and liters shown in the table. Watch out! Don't mix up independent and dependent variables!Also, make sure the equation actually matches the table's data.

STEP 2

1. Check the independent variable.2. Check if liters is a function of gallons.3. Check the equation.4. Check if liters increase with gallons.5. Check if every input has exactly one output.

STEP 3

The number of gallons, represented by ggg, is the independent variable because we're using it to determine the number of liters, represented by lll.So, the statement "The independent variable is the number of gallons" is **TRUE**!

STEP 4

Since each value of gallons, ggg, corresponds to a specific value of liters, lll, we can say that liters is indeed a function of gallons.So, "Liters is a function of Gallons" is **TRUE**!

STEP 5

Let's test the equation l=3.79⋅gl = 3.79 \cdot gl=3.79⋅g with a few values from the table.

STEP 6

When g=1g = 1g=1, l=3.79⋅1=3.79l = 3.79 \cdot 1 = 3.79l=3.79⋅1=3.79.This matches the table.

STEP 7

When g=2g = 2g=2, l=3.79⋅2=7.58l = 3.79 \cdot 2 = 7.58l=3.79⋅2=7.58.This also matches the table.

STEP 8

When g=3g = 3g=3, l=3.79⋅3=11.37l = 3.79 \cdot 3 = 11.37l=3.79⋅3=11.37.This matches too!It looks like the equation correctly represents the relationship, so "The equation l=3.79⋅gl = 3.79 \cdot gl=3.79⋅g represents the table" is **TRUE**!

STEP 9

Looking at the table, as the number of gallons increases, the number of liters also increases.So, "As the number of gallons increases, the number of liters increases" is **TRUE**!

STEP 10

For every value of gallons (input), there's only one corresponding value of liters (output).This is the definition of a function!So, "This is a function because every input has exactly one output" is **TRUE**!

STEP 11

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? This is asking us to figure out what's true about the relationship between gallons and liters shown in the table. Watch out! Don't mix up independent and dependent variables!
Also, make sure the equation actually matches the table's data.

1. Check the independent variable.
2. Check if liters is a function of gallons.
3. Check the equation.
4. Check if liters increase with gallons.
5. Check if every input has exactly one output.

The number of gallons, represented by $g$ , is the independent variable because we're using it to determine the number of liters, represented by $l$ .
So, the statement "The independent variable is the number of gallons" is TRUE!

Since each value of gallons, $g$ , corresponds to a specific value of liters, $l$ , we can say that liters is indeed a function of gallons.
So, "Liters is a function of Gallons" is TRUE!

Let's test the equation $l = 3.79 \cdot g$ with a few values from the table.

When $g = 1$ , $l = 3.79 \cdot 1 = 3.79$ .
This matches the table.

When $g = 2$ , $l = 3.79 \cdot 2 = 7.58$ .
This also matches the table.

When $g = 3$ , $l = 3.79 \cdot 3 = 11.37$ .
This matches too!
It looks like the equation correctly represents the relationship, so "The equation $l = 3.79 \cdot g$ represents the table" is TRUE!

Looking at the table, as the number of gallons increases, the number of liters also increases.
So, "As the number of gallons increases, the number of liters increases" is TRUE!

For every value of gallons (input), there's only one corresponding value of liters (output).
This is the definition of a function!
So, "This is a function because every input has exactly one output" is TRUE!