Applied-Algebra Deutsche Prüfungsfragen - Applied-Algebra Antworten

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WGU Applied-Algebra Exam Syllabus Topics:

Section	Objectives
Topic 1: Foundations of Algebra	- Algebraic Expressions 1. Simplifying expressions 2. Evaluating expressions 3. Order of operations - Equations and Inequalities 1. Linear equations in one variable 2. Inequalities and interval notation
Topic 2: Functions and Graphs	- Function Concepts 1. Function notation 2. Domain and range - Graphing Functions 1. Transformations of graphs 2. Coordinate plane interpretation
Topic 3: Linear Functions and Systems	- Systems of Equations 1. Substitution method 2. Elimination method - Linear Equations 1. Slope-intercept form 2. Point-slope form
Topic 4: Exponential and Logarithmic Concepts	- Logarithmic Basics 1. Logarithm properties 2. Conversion between exponential and logarithmic form - Exponential Functions 1. Growth and decay models 2. Exponential equations
Topic 5: Polynomial and Rational Expressions	- Polynomials 1. Operations with polynomials 2. Factoring techniques - Rational Expressions 1. Restrictions on variables 2. Simplification

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Applied-Algebra Antworten - Applied-Algebra Testing Engine

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WGU Applied Algebra FXO2 PFXP C957 Applied-Algebra Prüfungsfragen mit Lösungen (Q25-Q30):

25. Frage
The graph shows the progress of a manufacturing team, modeling the number of widgets the team is able to produce each day since the team was formed.

How should the average rate of change from day 16 to day 18 be interpreted?

A. The team increased production by an average of approximately 0.8 widgets each day.
B. Over the 2-day period, the team approximately produced an additional 0.8 widgets in total.
C. The team increased production by an average of approximately 1.7 widgets each day.
D. Over the 2-day period, the team approximately produced an additional 1.7 widgets in total.

Antwort: C

Begründung:
The graph models the number of widgets the manufacturing team can produce each day.
The horizontal axis represents:
" Days "
The vertical axis represents:
" Widgets produced each day "
The two labeled points are:
(16#9.1)
and
(18#12.4)
This means:
On day 16, the team could produce about 9.1widgets per day.
On day 18, the team could produce about 12.4widgets per day.
The average rate of change is:
(12.4-9.1)/(18-16)
=3.3/2
=1.65
Rounded to the nearest tenth:
1.7
So from day 16 to day 18, the team's production increased by an average of about:
1.7 " widgets each day "

26. Frage
A contractor charges a flat rate plus a fixed rate per hour to come and make repairs. For a job that takes 3 hours, the contractor charges $220. For a job that takes 5 hours, the contractor charges $340.
Which function correctly represents the total charge Cfor a job that takes thours?

A. C(t)=60t
B. C(t)=40t
C. C(t)=40t+60
D. C(t)=60t+40

Antwort: D

Begründung:
The contractor charges a flat rate plus a fixed rate per hour, so this situation is modeled by a linear function:
C(t)=mt+b
where:
m= " hourly rate "
and
b= " flat rate "
We are given two points:
(3#220)
and
(5#340)
These mean:
A 3-hour job costs $220.
A 5-hour job costs $340.
First, find the hourly rate using slope:
m=(340-220)/(5-3)
m=120/2
m=60
So the contractor charges:
$60 " per hour "
Now the function has the form:
C(t)=60t+b
Use the point (3#220)to find the flat rate:
220=60(3)+b
220=180+b
b=40
So the function is:
C(t)=60t+40
Check with t=5:
C(5)=60(5)+40
C(5)=300+40
C(5)=340
This matches the given information.

27. Frage
A factory mixes two colors, red and yellow, to create a dye.

The graph shows the relationship between the amounts of each dye, where rrepresents the amount of red dye and yrepresents the amount of yellow dye.
What is the correct interpretation of the rate of change?

A. The amount of yellow dye must be the amount of red dye plus 9/2.
B. The amount of yellow dye must be the amount of red dye plus 2/9.
C. The amount of yellow dye must be 9/2of the amount of red dye.
D. The amount of yellow dye must be 2/9of the amount of red dye.

Antwort: C

Begründung:
The graph shows a linear relationship between the amount of red dye, r, and the amount of yellow dye, y.
The rate of change of a line is the slope:
" slope " =( " change in " y)/( " change in " r)
From the graph, the line goes through the origin and rises steeply. A clear point on the line is approximately:
(2#9)
This means when the amount of red dye is 2gallons, the amount of yellow dye is 9gallons.
So the rate of change is:
9/2
That means for every 2gallons of red dye, the factory uses 9gallons of yellow dye.
The relationship can be written as:
y=9/2 r
So the correct interpretation is:
" The amount of yellow dye must be " 9/2 " of the amount of red dye. "
Therefore, the correct answer is:
# ( " A " )

28. Frage
The temperature of an object changes according to the relationship in the graph.

What is the equation of the horizontal asymptote?

A. y=0
B. y=500
C. x=500
D. x=0

Antwort: A

Begründung:
The graph shows the temperature of an object decreasing over time.
The horizontal axis represents:
" Time in minutes "
The vertical axis represents:
" Temperature in degrees Fahrenheit "
The curve decreases and approaches the horizontal axis as time increases.
A horizontal asymptote is a horizontal line that the graph approaches but may not reach. Horizontal lines have equations of the form:
y= " constant "
From the graph, the curve approaches:
y=0
So the horizontal asymptote is:
y=0
The options x=0and x=500are vertical lines, not horizontal asymptotes.
Therefore, the correct answer is:
# ( " B " )

29. Frage
As regulations change, the number of licensed sellers of a product decreases. The graph models the change in the number of licensed sellers over time.

What does the horizontal asymptote mean?

A. The number of licensed sellers was initially 700.
B. After 11 months, the number of licensed sellers decreased to 100.
C. Over time, the number of licensed sellers will increase back up to 700.
D. In the long run, the number of licensed sellers nears 100.

Antwort: D

Begründung:
The graph shows a decreasing exponential model.
The vertical axis represents:
" Licensed sellers "
The horizontal axis represents:
" Time in years "
The graph starts near 700 licensed sellers and decreases over time. However, it does not appear to decrease all the way to 0. Instead, it levels off near:
y=100
That horizontal line is the horizontal asymptote.
A horizontal asymptote represents the long-term value the function approaches as time continues.
So the correct interpretation is:
" In the long run, the number of licensed sellers nears 100. "
Therefore, the correct answer is:
# ( " C " )

30. Frage
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