Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Problem 19

$$ 0.27(a+b)=0.15 a+0.35 b $$ An athletic trainer is attempting to produce a carbohydrate-electrolyte solution that is at \(27 \%\) carbohydrates by mass, which is the maximum amount of saturation allowed by her league. A supply company provides solutions that are at \(15 \%\) and \(35 \%\) carbohydrates by mass, respectively. Based on the equation above, if the trainer uses 10 quarts of the \(15 \%\) solution, how many quarts of the \(35 \%\) solution will she need? A) 180 B) 90 C) 30 D) 15 $$ f(x)=(x-b)^2-4 $$

Short Answer

Expert verified
The trainer needs 15 quarts of the 35% solution.

Step by step solution

01

Substitute for a in the equation

From the problem, we know that the trainer is using 10 quarts of the 15% solution. This corresponds to \( a \) in the equation. So we replace \( a \) with 10: \( 0.27(10+b)=0.15*10+0.35b \).
02

Simplify the equation

Distribute the 0.27 across the brackets, and simplify the right side to get: \( 2.7+0.27b=1.5+0.35b \).
03

Rearrange the equation for b

To find \( b \), move all terms involving \( b \) to one side of the equation and constants to the other to get: \( 0.08b = 1.2 \).
04

Solve for b

Finally, divide both sides by 0.08 to find \( b \): \( b = 15 \). So the trainer needs 15 quarts of the 35% solution.
05

Evaluate f(x) for a given x

To evaluate the function \( f(x) = (x-b)^2 - 4 \) for a given value of \( x \), substitute that value into the equation and simplify. However, since we're not given a specific value of \( x \) to substitute, this can't be done at this point.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

$$ \begin{array}{|r|r|} \hline x & y \\ \hline-3 b & 18 b \\ \hline-2 b & 13 b \\ \hline 0 & 3 b \\ \hline 2 b & -7 b \\ \hline \end{array} $$ In the table above, \(b\) is a constant. If the \(x y\)-table describes some points on a linear function between \(x\) and \(y\), which of the following equations could represent that function? A) \(5 x+y=2 b\) B) \(x-5 y=-3 b\) C) \(5 x+y=3 b\) D) \(x-5 y=-7 b\)

$$ 650, a, 1550,1750,2300,2650 $$ If the mean of the list above is 1650 , what is the value of \(a\) ?

A) NO CHANGE B) the war saw Harpers Ferry change hands eight times, C) Harpers Ferry changed hands eight times during the war, D) eight was the number of times Harpers Ferry changed hands,

The author would like to combine the two sentences reproduced below: His parents were part of the Jewish cultural elite in Vienna at the time. Stefan was afforded every possible luxury and privilege. Which of the following gives the best combination of the two sentences? A) His parents were part of the Jewish cultural elite in Vienna at the time; Stefan was afforded every possible luxury and privilege. B) Zweig was afforded every possible luxury and privilege because his parents were part of the Jewish cultural elite in Vienna at the time. C) Born to parents who were part of Vienna's Jewish cultural elite, Stefan was afforded every possible luxury and privilege. D) His parents were part of the Jewish cultural elite in Vienna at the time, and so Stefan benefited from their eliteness with luxury.

For the function defined as \(g(x)=\frac{x-2}{3}\), what is the value of \(g(-4)\) ? A) \(-2\) B) \(-\frac{2}{3}\) C) \(\frac{2}{3}\) D) 2
See all solutions

Recommended explanations on English Textbooks

Syntax

Read Explanation

Text Comparison

Read Explanation

Phonetics

Read Explanation

Key Concepts in Language and Linguistics

Read Explanation

History of English Language

Read Explanation

Email

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free