Math / Algebra

Question15. Construct Arguments A baseball team gets 3 outs for each inning it comes up to bat. So far this season, Silvio's team has batted in 45 innings, $n$ , and has made 135 outs, $t$ . What is the dependent variable? Explain.

Studdy Solution

STEP 1

What is this asking? Which quantity depends on the other: the number of innings played or the number of outs made? Watch out! Don't get tricked by the order the information is presented!
Think carefully about which quantity causes the other to change.

STEP 2

1. Define the relationship
2. Identify the dependent variable

STEP 3

Alright, awesome students, let's break this down!
We know that for every inning a baseball team plays, they get $3$ outs.
This tells us how the number of outs relates to the number of innings.

STEP 4

Let's write this relationship as a super cool formula!
If $n$ is the number of innings and $t$ is the total number of outs, then we can say: $t = 3 \cdot n$ This equation tells us that the total number of outs, $t$ , is three times the number of innings played, $n$ .

STEP 5

Now, the big question: which is the dependent variable?
The dependent variable is the one that changes based on the other.
Think of it like this: the number of outs depends on how many innings are played.

STEP 6

Let's imagine Silvio's team plays one inning ( $n = 1$ ).
How many outs do they get?
Using our awesome formula, $t = 3 \cdot 1 = 3$ . Three outs!

STEP 7

Now, let's say they play two innings ( $n = 2$ ).
Now, $t = 3 \cdot 2 = 6$ . Six outs!
See? The number of outs, $t$ , depends on the number of innings, $n$ .

STEP 8

In Silvio's case, the team played $n = 45$ innings, leading to $t = 3 \cdot 45 = 135$ outs.
Again, the number of outs depends on the number of innings played.

STEP 9

The dependent variable is $t$ , the total number of outs, because it depends on the number of innings played, $n$ .

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Question15. Construct Arguments A baseball team gets 3 outs for each inning it comes up to bat. So far this season, Silvio's team has batted in 45 innings, $n$ , and has made 135 outs, $t$ . What is the dependent variable? Explain.

Studdy Solution

STEP 1

What is this asking? Which quantity depends on the other: the number of innings played or the number of outs made? Watch out! Don't get tricked by the order the information is presented!
Think carefully about which quantity causes the other to change.

STEP 2

1. Define the relationship
2. Identify the dependent variable

STEP 3

Alright, awesome students, let's break this down!
We know that for every inning a baseball team plays, they get $3$ outs.
This tells us how the number of outs relates to the number of innings.

STEP 4

Let's write this relationship as a super cool formula!
If $n$ is the number of innings and $t$ is the total number of outs, then we can say: $t = 3 \cdot n$ This equation tells us that the total number of outs, $t$ , is three times the number of innings played, $n$ .

STEP 5

Now, the big question: which is the dependent variable?
The dependent variable is the one that changes based on the other.
Think of it like this: the number of outs depends on how many innings are played.

STEP 6

Let's imagine Silvio's team plays one inning ( $n = 1$ ).
How many outs do they get?
Using our awesome formula, $t = 3 \cdot 1 = 3$ . Three outs!

STEP 7

Now, let's say they play two innings ( $n = 2$ ).
Now, $t = 3 \cdot 2 = 6$ . Six outs!
See? The number of outs, $t$ , depends on the number of innings, $n$ .

STEP 8

In Silvio's case, the team played $n = 45$ innings, leading to $t = 3 \cdot 45 = 135$ outs.
Again, the number of outs depends on the number of innings played.

STEP 9

The dependent variable is $t$ , the total number of outs, because it depends on the number of innings played, $n$ .

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Question15. Construct Arguments A baseball team gets 3 outs for each inning it comes up to bat. So far this season, Silvio's team has batted in 45 innings, nnn, and has made 135 outs, ttt. What is the dependent variable? Explain.

Studdy Solution

STEP 1

What is this asking? Which quantity depends on the other: the number of innings played or the number of outs made? Watch out! Don't get tricked by the order the information is presented!Think carefully about which quantity *causes* the other to change.

STEP 2

1. Define the relationship2. Identify the dependent variable

STEP 3

Alright, awesome students, let's break this down!We know that for *every* inning a baseball team plays, they get 333 outs.This tells us how the number of outs relates to the number of innings.

STEP 4

Let's write this relationship as a super cool formula!If nnn is the number of innings and ttt is the total number of outs, then we can say: t=3⋅n t = 3 \cdot n t=3⋅n This equation tells us that the **total number of outs**, ttt, is **three times** the **number of innings** played, nnn.

STEP 5

Now, the big question: which is the *dependent* variable?The dependent variable is the one that *changes* based on the other.Think of it like this: the number of outs *depends* on how many innings are played.

STEP 6

Let's imagine Silvio's team plays **one** inning (n=1n = 1n=1).How many outs do they get?Using our awesome formula, t=3⋅1=3t = 3 \cdot 1 = 3t=3⋅1=3. **Three** outs!

STEP 7

Now, let's say they play **two** innings (n=2n = 2n=2).Now, t=3⋅2=6t = 3 \cdot 2 = 6t=3⋅2=6. **Six** outs!See? The number of outs, ttt, *depends* on the number of innings, nnn.

STEP 8

In Silvio's case, the team played n=45n = 45n=45 innings, leading to t=3⋅45=135t = 3 \cdot 45 = 135t=3⋅45=135 outs.Again, the number of outs *depends* on the number of innings played.

STEP 9

The dependent variable is ttt, the **total number of outs**, because it depends on the number of innings played, nnn.

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.

Question15. Construct Arguments A baseball team gets 3 outs for each inning it comes up to bat. So far this season, Silvio's team has batted in 45 innings, $n$ , and has made 135 outs, $t$ . What is the dependent variable? Explain.

What is this asking? Which quantity depends on the other: the number of innings played or the number of outs made? Watch out! Don't get tricked by the order the information is presented!
Think carefully about which quantity causes the other to change.

1. Define the relationship
2. Identify the dependent variable

Alright, awesome students, let's break this down!
We know that for every inning a baseball team plays, they get $3$ outs.
This tells us how the number of outs relates to the number of innings.

Let's write this relationship as a super cool formula!
If $n$ is the number of innings and $t$ is the total number of outs, then we can say: $t = 3 \cdot n$ This equation tells us that the total number of outs, $t$ , is three times the number of innings played, $n$ .

Now, the big question: which is the dependent variable?
The dependent variable is the one that changes based on the other.
Think of it like this: the number of outs depends on how many innings are played.

Let's imagine Silvio's team plays one inning ( $n = 1$ ).
How many outs do they get?
Using our awesome formula, $t = 3 \cdot 1 = 3$ . Three outs!

Now, let's say they play two innings ( $n = 2$ ).
Now, $t = 3 \cdot 2 = 6$ . Six outs!
See? The number of outs, $t$ , depends on the number of innings, $n$ .

In Silvio's case, the team played $n = 45$ innings, leading to $t = 3 \cdot 45 = 135$ outs.
Again, the number of outs depends on the number of innings played.

The dependent variable is $t$ , the total number of outs, because it depends on the number of innings played, $n$ .