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| Section | Objectives |
|---|---|
| Topic 1: Linear Functions and Systems | - Systems of Equations
|
| Topic 2: Functions and Graphs | - Graphing Functions
|
| Topic 3: Foundations of Algebra | - Equations and Inequalities
|
| Topic 4: Exponential and Logarithmic Concepts | - Logarithmic Basics
|
| Topic 5: Polynomial and Rational Expressions | - Polynomials
|
>> Applied-Algebra Zertifizierungsfragen <<
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50. Frage
In the graph showing the number of new customer accounts, the horizontal axis shows the number of weeks since the beginning of winter and the vertical axis shows the number of new customer accounts. More customer accounts are opened during snowy weeks than during weeks without snow.
When was it likely snowy?
Antwort: C
Begründung:
This question asks us to interpret unusually high values on a graph. The problem states that more customer accounts are opened during snowy weeks than during weeks without snow. Therefore, the likely snowy weeks correspond to the peaks on the graph, where the number of new customer accounts is noticeably higher than surrounding weeks. The graph shows clear spikes at approximately week 7 and week 14. These weeks have higher account openings compared with nearby weeks, making them the best evidence of snowy conditions.
Week 1 and week 5 do not match the main peaks shown in the graph. Since the snowy weeks should correspond to the highest customer-account values, the correct answer is D.
51. Frage
The graphed function n(t)represents the number of animals, n, at a feeding station thours after 5:00 a.m. The plotted points Aand Bhave coordinates (1#10.6)and (8#6.59).
Which statement gives the correct interpretation of the average rate of change of the number of animals over the interval from point Ato point B?
Antwort: B
Begründung:
The average rate of change tells how much the output changes per one unit of input.
Here:
t= " hours after 5:00 a.m. "
and
n(t)= " number of animals "
The two given points are:
A=(1,10.6)
and
B=(8,6.59)
Use the average rate of change formula:
(y_2-y_1)/(x_2-x_1 )
Substitute the coordinates:
(6.59-10.6)/(8-1)
=(-4.01)/7
#-0.573
The negative sign means the number of animals is decreasing.
So the correct interpretation is:
" The number of animals at the station decreases at an average rate of " 0.573 " animals per hour. " Therefore, the correct answer is:
# ( " B " )
52. Frage
The number of comments on a social media post is represented by the logistic function f(x), whose graph is shown, where xrepresents the number of days since the post was created and f(x)represents the number of comments on day x.
How does the number of comments change as time progresses from day 1 to day 17?
Antwort: B
Begründung:
This graph represents a logistic growth function, which has an S-shaped curve.
Key behavior of logistic functions:
Initial phase (early time) # growth is slow
Middle phase # growth speeds up (increasing rate)
Later phase # growth slows down as it approaches a maximum
Analyze the interval from day 1 to day 17:
This interval is in the early part of the graph.
The curve is increasing and getting steeper over this range.
That means the rate of increase is growing over time.
So, the number of comments is:
" increasing faster and faster "
53. Frage
A coach is placing an order for team shirts. The graph shows the total cost based on the number of shirts.
What is the cost of each additional shirt?
Antwort: C
Begründung:
This question asks for the cost of each additional shirt, which means we need to find the rate of change of the linear function.
On a graph, the rate of change is the slope:
" slope " = " change in total cost " / " change in number of shirts "
From the graph, two labeled points are:
(0#33)
and
(10#173)
This means:
When 0shirts are ordered, the cost is $33.
When 10shirts are ordered, the cost is $173.
Now find the slope:
m=(173-33)/(10-0)
m=140/10
m=14
So the cost increases by:
$14
for each additional shirt.
The $33represents a fixed starting cost, not the cost per shirt.
54. Frage
The number of employees under supervisor B is 13 more than the number of employees under supervisor A.
Let F(n)represent the number of employees under the two supervisors, where nis the number of employees under supervisor A and Fis the number of employees under supervisor B.
Which is the correct function to represent this relationship?
Antwort: A
55. Frage
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