Applied Algebra FX01 Exam (C957)
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Free Applied Algebra FX01 Exam (C957) Questions
A bookstore tracked its sales over a 5-day promotional event. Each day, the number of books sold and the revenue earned were recorded as shown below:
What can be concluded about the bookstore’s sales performance during this promotional event?
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The bookstore earned the most revenue on the day it sold the most books.
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The bookstore earned less revenue on the day it sold 40 books than on the day it sold 20 books.
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The bookstore earned the least revenue on the day it sold the fewest books.
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The bookstore sold fewer books on the last day than on the first day.
Explanation
Solution:
Identify key values from the data:
Day with the most books sold: Day 4, with 50 books.
Day with the least books sold: Day 1, with 15 books.
Revenue comparison:
Day 4 (50 books): $800.
Day 3 (20 books): $1,200.
Day 5 (40 books): $1,000.
Analyze each option:
Option 1: "The bookstore earned the most revenue on the day it sold the most books."
False. Most books were sold on Day 4 (50 books), but the revenue was $800. The highest revenue ($1,200) was on Day 3 (20 books).
Option 2: "The bookstore earned less revenue on the day it sold 40 books than on the day it sold 20 books."
True. On Day 5 (40 books), the revenue was $1,000, while on Day 3 (20 books), the revenue was $1,200.
Option 3: "The bookstore earned the least revenue on the day it sold the fewest books."
True. On Day 1 (15 books), the revenue was $450, which is the lowest revenue.
Option 4: "The bookstore sold fewer books on the last day than on the first day."
False. On Day 5 (last day), 40 books were sold, while on Day 1 (first day), 15 books were sold. 40 > 1540.
Correct Answer:
The bookstore earned less revenue on the day it sold 40 books than on the day it sold 20 books.
Why the other options are incorrect:
"The bookstore earned the most revenue on the day it sold the most books": The highest revenue was $1,200 on Day 3 (20 books), not Day 4 (50 books).
"The bookstore earned the least revenue on the day it sold the fewest books": While this is true, it is not the best conclusion compared to Option 2.
"The bookstore sold fewer books on the last day than on the first day": Day 5 (40 books) exceeds Day 1 (15 books).
The manager of a technical support department at a company is concerned because many of the employees in the department missed their target of reviewing 200 email accounts within the past 12 months. The manager gathered data on the number of combined sick and vacation hours 10 of the employees took and the number of email accounts they fell short on. The graph below shows the data the manager collected, along with the best-fit line, which has r² value of 0.76.
The manager wants to try to ensure that next year the employees on the team do not exceed 20 incomplete reviews. The manager concludes that if the sick and vacation policy is revised to limit employees to no more than 160 combined hours of sick and vacation time per year, then the employees shouldn't fall more than 20 accounts short of their target next year. Is this a valid conclusion and why?
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Yes, it is a valid conclusion because the model appropriately fits the data, and the model predicts that employees who take a combined 160 hours of sick and vacation time will fall less than 20 accounts short of their target.
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No, it is not a valid conclusion because (127,17) is an outlier, which causes predictions made with the best-fit line to be inaccurate.
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Yes, it is a valid conclusion because the model appropriately fits the data, and the model guarantees that employees who fall 20 or more reviews short of their target will miss more than 160 hours of combined sick and vacation time.
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No, it is not a valid conclusion because there were no employees who took 160 hours of combined sick and vacation time.
Explanation
Correct answer:
Yes, it is a valid conclusion because the model appropriately fits the data, and the model predicts that employees who take a combined 160 hours of sick and vacation time will fall less than 20 accounts short of their target.
Explanation
The correct conclusion is that the model appropriately fits the data, and it predicts that employees who take a combined 160 hours of sick and vacation time will fall less than 20 accounts short of their target. This is a valid conclusion because the linear regression model gives an estimated trend based on the data, and the predicted outcome of fewer than 20 incomplete reviews for employees with 160 hours of sick and vacation time is consistent with the pattern observed in the graph.
Why others are wrong:
“No, it is not a valid conclusion because (127,17) is an outlier, which causes predictions made with the best-fit line to be inaccurate.” From the graph there are no outliers.
“Yes, it is a valid conclusion because the model appropriately fits the data, and the model guarantees that employees who fall 20 or more reviews short of their target will miss more than 160 hours of combined sick and vacation time” is wrong because a model does not guarantee outcomes; it only makes predictions based on trends in the data. Predictions are estimates, not certainties, and the relationship is not causal.
“No, it is not a valid conclusion because there were no employees who took 160 hours of combined sick and vacation time.” From the graph there were employees who took more than 160 hours of combined sick and vacation time.
For the years since a department store has been open, its annual revenue, R, (in millions of dollars) can be modeled by the function graphed below, where t is the number of years since the store opened.
How should the maximum revenue be interpreted?
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About 6 years after the department store opened, the store earned a maximum revenue of about $1,400,000.
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About 6 years after the department store opened, the store earned a maximum revenue of about $1,600,000.
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About 4 years after the department store opened, the store earned a maximum revenue of about $1,600,000.
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About 14 years after the department store opened, the store earned a maximum revenue of about $1,400,000.
Explanation
Solution:
At around 6 years after the department store was opened, the store had the highest annual revenue of $1,600,000.
Correct answer:
About 6 years after the department store opened, the store earned a maximum revenue of about $1,600,000.
Why others are wrong:
“About 6 years after the department store opened, the store earned a maximum revenue of about $1,400,000.” About 6 years after the department store opened the revenue was about $1,600,000.
“About 4 years after the department store opened, the store earned a maximum revenue of about $1,600,000.” About 4 years after the department store opened the revenue was slightly above 1,500,000.
“About 14 years after the department store opened, the store earned a maximum revenue of about $1,400,000.” About 14 years after the department store opened the revenue was zero.
The number of letters processed daily at a mail center is modeled by the decreasing exponential function shown in the graph.
Which value is the number of letters processed per day trending toward as time progresses, based on the equation of the horizontal asymptote?
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17
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2,500
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4,250
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8,500
Explanation
Explanation
The horizontal asymptote represents the value that the function approaches but never reaches as time progresses. In this case, the graph levels off around 2,500 letters per day, indicating that this is the value that the number of letters processed per day is approaching.
Correct answer
2,500
The IT help desk at a college logs the calls it gets during a Tuesday morning. C(t) is the number of calls at time t (measured in hours), and t = 0 corresponds to 8 a.m.
When should the help desk expect to need the fewest staff members?
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8:00 a.m.
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8:45 a.m.
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11:00 a.m.
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11:30a.m.
Explanation
Correct answer: 11:00 a.m.
Explanation:
From the function the least calls are expected three hours after opening which is three hours after 8.00 a.m
Why other option are wrong:
“8.00 a.m” At this time the IT desk expects 10 which is greater than 2 calls expected at 11.00 a.m.
“8.45 a.m” At this time the IT desk expects 21 calls which is greater than 2 calls expected at 11.00 a.m.
“11.30 a.m” At this time the IT desk expects 5 calls which is greater than 2 calls expected at 11.00 a.m.
The temperature of an object changes according to the relationship in the graph.
What is the equation of the horizontal asymptote?
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x = 0
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y = 0
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x = 500
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y = 500
Explanation
Explanation
The horizontal asymptote represents the value that the temperature approaches but never quite reaches as time progresses. From the graph, it appears that the temperature is leveling off at around 0°F as time increases. Therefore, the equation of the horizontal asymptote is y = 0.
Correct answer
y = 0
A mathematical model was used to predict the spread of a bacterial infection, B, in a population based on temperature (measured in t degrees Celsius). The function was B(t) = 250 + 45e-0.2t
According to this model, are there more infections at 15°C or 35°C?
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More infections at 15°C since B(15) > B(35)
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More infections at 35°C since B(15) > B(35)
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More infections at 15°C since B(15) < B(35)
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More infections at 35°C since B(15) < B(35)
Explanation
Solution:
To determine whether there are more infections at 15°C or 35°C, we need to compare B(15) and B(35) using the given function:
B(t) = 250 + 45e-0.2t
Step 1: Compute B(15) Substitute t = 15 into the function:
B(15) = 250 + 45e-(0.2 × 15)
≈ 250 + 45(0.0498)
≈ 252.24
Step 2: Compute B(35) Substitute t = 35 into the function:
B(35) = 250 + 45e-(0.2 × 35)
≈ 250 + 45(0.0009)
≈ 250.04
Step 3: Compare B(15) and B(35)
B(15) ≈ 252.24 B(35)
≈ 250.04
Since B(15) > B(35), there are more infections at 15°C than at 35°C.
Correct Answer:
More infections at 15°C since B(15) > B(35)
Why the Other Options Are Incorrect:
"More infections at 35°C since B(15) > B(35)": This contradicts the conclusion. If B(15) > B(35), there are more infections at 15°C, not 35°C.
"More infections at 15°C since B(15) < B(35)": The inequality is incorrect. B(15) is greater than, not less than, B(35).
"More infections at 35°C since B(15) < B(35)": Both the conclusion and inequality are incorrect. B(15) > B(35), and this means more infections at 15°C.
The function V(t) = -t³ + 15t² - 2t represents the volume of water (in hundreds of cubic meters) in a reservoir, where t is the time in half-days since monitoring began. How can the value V(2) be interpreted?
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After 1 day, the reservoir contains 4,400 cubic meters of water
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After 2 days, the reservoir contains 44 cubic meters of water
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After 1 day, the reservoir contains 44 cubic meters of water
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After 2 days, the reservoir contains 4,400 cubic meters of water
Explanation
Solution:
To interpret V(2), we substitute t = 2 into the volume function:
V(2) = -(2)³ + 15(2)² - 2(2)
V(2) = -8 + 60 - 4
V(2) = 44
Since t represents time in half-days, t = 2 means 1 day. Since V(t) is measured in hundreds of cubic meters, V(2) = 44 means 4,400 cubic meters.
Correct Answer:
After 1 day, the reservoir contains 4,400 cubic meters of water
Why Other Options Are Wrong:
"After 2 days, the reservoir contains 44 cubic meters of water": This misinterprets both the time unit (t = 2 means 1 day, not 2 days) and the volume unit (44 hundreds means 4,400 cubic meters, not 44 cubic meters).
"After 1 day, the reservoir contains 44 cubic meters of water": While this correctly interprets t = 2 as 1 day, it incorrectly reads V(2) = 44 as 44 cubic meters instead of 4,400 cubic meters (since the unit is hundreds of cubic meters).
"After 2 days, the reservoir contains 4,400 cubic meters of water": Although this correctly converts 44 hundreds to 4,400 cubic meters, it incorrectly interprets t = 2 as 2 days instead of 1 day (since t is measured in half-days).
A company provides internet service to approximately 1,050 customers each year. The table shows the percentage of customers with fiber internet each year since 2020. What was the approximate number of customers with fiber internet in 2023?
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420
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452
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598
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630
Explanation
Explanation
The year 2023 corresponds to 3 years since 2020. According to the table, 57% of customers had fiber internet at that time. To find the approximate number of customers, multiply 57% by 1,050: 0.57 * 1050 = 598.5. Rounding to the nearest whole number gives approximately 598 customers.
Correct answer
598
An artist makes jewelry to sell through an online store. The following graph shows the functions that model the artist's cost and revenue.
How many pieces of jewelry does the artist need to sell so that the money earned equals the costs to make the jewelry?
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200
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400
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2,500
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5,000
Explanation
Solution
The number of jewelry artists will need to make will be 200 jewelry since this is the point that the graph of cost and revenue intersect.
Correct answer: 200
Why the others are wrong:
“400” For this number of Jewelries in the graph the revenue is above the cost.
“2500” This number of Jewelries is not cost is not represented in the graph and might be the presentation of price rather than number of Jewelry.
“5000” This number of Jewelries is not cost is not represented in the graph and might be the presentation of price rather than number of Jewelry.
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This course covers a variety of algebraic concepts, including solving linear equations and inequalities, quadratic equations, graphing functions, systems of equations, exponents, polynomials, and real-world applications of algebra.
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