Math / Algebra

QuestionThe tables below represent a function $C$ that converts ounces to pints and a function $Q$ that converts pints to quarts. Complete parts (a) through (c) below. \begin{tabular}{|r|c|c|c|c|} \hline $\mathbf{x}(\mathbf{o z})$ & 16 & 48 & 80 & 112 \\ \hline $\mathbf{C}(\mathbf{x})(\mathrm{pt})$ & 1 & 3 & 5 & 7 \\ \hline \end{tabular} \begin{tabular}{|r|c|c|c|c|} \hline $\mathbf{x}(\mathbf{p t})$ & 1 & 3 & 5 & 7 \\ \hline $\mathbf{Q}(\mathbf{x})(\mathbf{q t})$ & 0.5 & 1.5 & 2.5 & 3.5 \\ \hline \end{tabular} (a) Evaluate $(Q \circ C)(16)$ and interpret the results. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $(Q \circ C)(16)=$ $\square$ represents the number of quartsin $160 z$ . B. $(Q \circ C)(16)=$ $\square$ represents the number of pintsin $160 z$ . C. $(Q \circ C)(16)=$ $\square$ represents the number of ouncesin $16 q t$ . D. $(Q \circ C)(16)$ cannot be evaluated, which means that 16 oz cannot be converted to quarts. Get more help Clear all Skill builder Check answer

Studdy Solution

STEP 1

What is this asking? We're converting 16 ounces to quarts using two conversion tables, one for ounces to pints and another for pints to quarts. Watch out! Don't mix up the units!
Ounces, pints, and quarts are all different, and we need to keep track of which is which.

STEP 2

1. Convert ounces to pints.
2. Convert pints to quarts.
3. Interpret the result.

STEP 3

We're given that $C(x)$ is the number of pints in $x$ ounces.
We want to find $C(16)$ , the number of pints in 16 ounces.

STEP 4

Looking at the first table, we see that when $x = 16$ , $C(x) = 1$ .
So, $C(16) = 1$ .
This tells us that 16 ounces is equal to 1 pint.

STEP 5

Now, we'll use the second table. $Q(x)$ is the number of quarts in $x$ pints.
We want to find $Q(1)$ , the number of quarts in 1 pint.

STEP 6

From the second table, when $x = 1$ , $Q(x) = 0.5$ .
So, $Q(1) = 0.5$ .
This means 1 pint is equal to 0.5 quarts.

STEP 7

We just figured out that $C(16) = 1$ and $Q(1) = 0.5$ .
We're asked to find $(Q \circ C)(16)$ , which means we first apply $C$ to $16$ , and then apply $Q$ to the result.

STEP 8

So, $(Q \circ C)(16) = Q(C(16)) = Q(1) = 0.5$ .
This means that 16 ounces is equal to 0.5 quarts.

STEP 9

$(Q \circ C)(16) = 0.5$ , which represents the number of quarts in 16 oz.
So the answer is A.

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Studdy Solution

STEP 1

What is this asking? We're converting 16 ounces to quarts using two conversion tables, one for ounces to pints and another for pints to quarts. Watch out! Don't mix up the units!
Ounces, pints, and quarts are all different, and we need to keep track of which is which.

STEP 2

1. Convert ounces to pints.
2. Convert pints to quarts.
3. Interpret the result.

STEP 3

We're given that $C(x)$ is the number of pints in $x$ ounces.
We want to find $C(16)$ , the number of pints in 16 ounces.

STEP 4

Looking at the first table, we see that when $x = 16$ , $C(x) = 1$ .
So, $C(16) = 1$ .
This tells us that 16 ounces is equal to 1 pint.

STEP 5

Now, we'll use the second table. $Q(x)$ is the number of quarts in $x$ pints.
We want to find $Q(1)$ , the number of quarts in 1 pint.

STEP 6

From the second table, when $x = 1$ , $Q(x) = 0.5$ .
So, $Q(1) = 0.5$ .
This means 1 pint is equal to 0.5 quarts.

STEP 7

We just figured out that $C(16) = 1$ and $Q(1) = 0.5$ .
We're asked to find $(Q \circ C)(16)$ , which means we first apply $C$ to $16$ , and then apply $Q$ to the result.

STEP 8

So, $(Q \circ C)(16) = Q(C(16)) = Q(1) = 0.5$ .
This means that 16 ounces is equal to 0.5 quarts.

STEP 9

$(Q \circ C)(16) = 0.5$ , which represents the number of quarts in 16 oz.
So the answer is A.

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Studdy Solution

STEP 1

What is this asking? We're converting **16 ounces** to **quarts** using two conversion tables, one for ounces to pints and another for pints to quarts. Watch out! Don't mix up the units!Ounces, pints, and quarts are all different, and we need to keep track of which is which.

STEP 2

1. Convert ounces to pints.2. Convert pints to quarts.3. Interpret the result.

STEP 3

We're given that C(x)C(x)C(x) is the number of pints in xxx ounces.We want to find C(16)C(16)C(16), the number of pints in **16 ounces**.

STEP 4

Looking at the first table, we see that when x=16x = 16x=16, C(x)=1C(x) = 1C(x)=1.So, C(16)=1C(16) = 1C(16)=1.This tells us that **16 ounces** is equal to **1 pint**.

STEP 5

Now, we'll use the second table. Q(x)Q(x)Q(x) is the number of quarts in xxx pints.We want to find Q(1)Q(1)Q(1), the number of quarts in **1 pint**.

STEP 6

From the second table, when x=1x = 1x=1, Q(x)=0.5Q(x) = 0.5Q(x)=0.5.So, Q(1)=0.5Q(1) = 0.5Q(1)=0.5.This means **1 pint** is equal to **0.5 quarts**.

STEP 7

We just figured out that C(16)=1C(16) = 1C(16)=1 and Q(1)=0.5Q(1) = 0.5Q(1)=0.5.We're asked to find (Q∘C)(16)(Q \circ C)(16)(Q∘C)(16), which means we first apply CCC to 161616, and then apply QQQ to the result.

STEP 8

So, (Q∘C)(16)=Q(C(16))=Q(1)=0.5(Q \circ C)(16) = Q(C(16)) = Q(1) = 0.5(Q∘C)(16)=Q(C(16))=Q(1)=0.5.This means that **16 ounces** is equal to **0.5 quarts**.

STEP 9

(Q∘C)(16)=0.5(Q \circ C)(16) = 0.5(Q∘C)(16)=0.5, which represents the number of quarts in 16 oz.So the answer is A.

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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? We're converting 16 ounces to quarts using two conversion tables, one for ounces to pints and another for pints to quarts. Watch out! Don't mix up the units!
Ounces, pints, and quarts are all different, and we need to keep track of which is which.

1. Convert ounces to pints.
2. Convert pints to quarts.
3. Interpret the result.

We're given that $C(x)$ is the number of pints in $x$ ounces.
We want to find $C(16)$ , the number of pints in 16 ounces.

Looking at the first table, we see that when $x = 16$ , $C(x) = 1$ .
So, $C(16) = 1$ .
This tells us that 16 ounces is equal to 1 pint.

Now, we'll use the second table. $Q(x)$ is the number of quarts in $x$ pints.
We want to find $Q(1)$ , the number of quarts in 1 pint.

From the second table, when $x = 1$ , $Q(x) = 0.5$ .
So, $Q(1) = 0.5$ .
This means 1 pint is equal to 0.5 quarts.

We just figured out that $C(16) = 1$ and $Q(1) = 0.5$ .
We're asked to find $(Q \circ C)(16)$ , which means we first apply $C$ to $16$ , and then apply $Q$ to the result.

So, $(Q \circ C)(16) = Q(C(16)) = Q(1) = 0.5$ .
This means that 16 ounces is equal to 0.5 quarts.

$(Q \circ C)(16) = 0.5$ , which represents the number of quarts in 16 oz.
So the answer is A.