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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Graphing and Functions | 25% | - Coordinate plane and plotting points - Function notation and evaluation - Slope and equations of lines - Linear functions and their graphs |
| Topic 2: Exponents, Radicals, and Quadratic Relationships | 15% | - Simplifying radical expressions - Properties of exponents - Basic quadratic graphs - Solving quadratic equations |
| Topic 3: Systems of Equations and Inequalities | 15% | - Solving by substitution and elimination - Graphical solutions - Applications of systems |
| Topic 4: Algebraic Expressions and Operations | 20% | - Simplifying and evaluating expressions - Order of operations - Operations with polynomials - Variables, constants, and coefficients |
| Topic 5: Linear Equations and Inequalities | 25% | - Solving single-variable equations - Solving and graphing inequalities - Real-world applications |
>> Exam Vce Applied-Algebra Free <<
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NEW QUESTION # 50
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.
Years since 2020 Percent of Customers with Fiber
0 19
1 28
2 40
3 57
What was the approximate number of customers with fiber internet in 2023?
Answer: B
Explanation:
The table gives the percent of customers with fiber internet for each year since 2020.
Since 2023 is:
2023#2020=3
we use the row where:
Years since 2020=3
From the table, the percent of customers with fiber internet in 2023 is:
57%
The company has approximately:
1,050
customers each year.
Now find 57% of 1,050:
0.57×1,050=598.5
The closest answer choice is:
598
So approximately 598 customers had fiber internet in 2023.
Therefore, the correct answer is:
C
NEW QUESTION # 51
The data in the scatterplot represents the number of people working at a research station over time. The graphed regression function has an r
2
value of 0.96. The predicted number of people working at the research station after 18.1 years is 541.
Is this prediction appropriate?
Answer: C
Explanation:
The value r2=0.96 indicates a strong regression fit because it is very close to 1. A strong fit supports prediction better than a weak or moderate fit. However, prediction also depends on whether the x-value is within a reasonable extrapolation range. The prediction is made at x=18.1, which is beyond the maximum observed x-value in the scatterplot. Even though the model fits the data well, the prediction is too far beyond the observed data range.
For a strong model, extrapolation should not go more than about 50% of the range beyond the maximum value. Since x=18.1 exceeds that limit, the prediction is not appropriate. Therefore, the correct answer is B.
NEW QUESTION # 52
The traffic flow on a roadway after 8:00 a.m. is modeled by the graphed exponential function.
Which conclusion is valid, based on the horizontal asymptote?
Answer: A
Explanation:
The graph shows an exponential decay model for traffic flow. A horizontal asymptote represents the long- term value the function approaches. In this case, the graph decreases but levels off above zero. Because the horizontal asymptote is above the horizontal axis, the model predicts that the traffic flow approaches a positive number rather than decreasing all the way to zero. Exponential functions do not change by a constant additive rate; that is a property of linear functions. Instead, exponential models change by a constant factor.
Therefore, statements about constant rate are not valid here. The valid conclusion based on the asymptote is that the traffic flow will not decrease to 0 vehicles per hour. The correct answer is B.
NEW QUESTION # 53
The number of wild horses in a federal park is represented by the logistic function f(x), whose graph is shown, where xrepresents the number of years since the park was established and f(x)represents the wild horse population in a given year.
How does the number of wild horses change as time progresses from year 1 to year 9?
Answer: D
Explanation:
The graph is a logistic growth function.
A logistic function often has an S-shape. It begins by increasing slowly, then increases faster and faster, and later levels off as it approaches a maximum carrying capacity.
From year 1 to year 9, the graph is rising and becoming steeper.
That means:
" the wild horse population is increasing "
and the slope is getting larger, so:
" the population is increasing faster and faster "
Therefore, the correct answer is:
# ( " A " )
NEW QUESTION # 54
The number of new user accounts per day on a website is modeled by a decreasing exponential function. The graph of the function is shown.
Which statement is justified considering the location of the horizontal asymptote?
Answer: A
Explanation:
The graph shows a decreasing exponential function.
The horizontal axis represents:
" Time in months "
The vertical axis represents:
" New user accounts per day "
The graph starts near 7,000new user accounts per day and decreases over time. However, it does not decrease toward 0. Instead, the graph levels off near a horizontal value around:
y=2,500
This horizontal value is the horizontal asymptote.
A horizontal asymptote shows the long-term value the function approaches. Since the asymptote is above 0, the model predicts that the number of daily new user accounts approaches a positive value, not zero.
So the justified statement is:
" The number of daily new user accounts will not decrease to 0. "
NEW QUESTION # 55
......
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