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| Section | Weight | Objectives |
|---|---|---|
| Algebraic Expressions and Operations | 20% | - Operations with polynomials - Variables, constants, and coefficients - Simplifying and evaluating expressions - Order of operations |
| Exponents, Radicals, and Quadratic Relationships | 15% | - Basic quadratic graphs - Simplifying radical expressions - Solving quadratic equations - Properties of exponents |
| Systems of Equations and Inequalities | 15% | - Graphical solutions - Solving by substitution and elimination - Applications of systems |
| Linear Equations and Inequalities | 25% | - Solving single-variable equations - Solving and graphing inequalities - Real-world applications |
| Graphing and Functions | 25% | - Function notation and evaluation - Coordinate plane and plotting points - Linear functions and their graphs - Slope and equations of lines |
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NEW QUESTION # 88
The graphed function v(t) represents the number of vehicles, v, stopped at a toll booth t hours after 6:00 a.m.
The coordinates of points A and B are (1,49.4) and (4,45.8), respectively.
What is the average rate of change of the number of vehicles from point A to point B?
Answer: C
Explanation:
The average rate of change measures how much the output changes per one unit of input. Here, the input is time in hours after 6:00 a.m., and the output is the number of vehicles stopped at the toll booth. The two given points are A=(1,49.4) and B=(4,45.8). Use the average rate of change formula: (y
2
#y
1
)/(x
2
#x
1
). Substituting the coordinates gives (45.8#49.4)/(4#1). The numerator is #3.6, and the denominator is 3, so the average rate of change is #1.2. The negative sign means the number of vehicles decreased over the interval.
NEW QUESTION # 89
The function p(t)represents the number of active players, p, in a game thours after 11:00 a.m. The graph of p(t) is shown.
What is one example of an interval for which the number of players is decreasing faster and faster?
Answer: B
Explanation:
The graph represents:
p(t)= " number of active players "
where:
t= " hours after 11:00 a.m. "
The phrase "decreasing faster and faster" means two things are happening:
The graph is going downward, so the number of players is decreasing.
The graph is becoming steeper downward, so the rate of decrease is increasing.
This corresponds to a graph that is decreasing and concave down.
Looking at the graph, the number of active players reaches a maximum around:
t#9
After that, the graph begins decreasing. Near the far right side of the graph, especially around:
t=11.2 " to " t=11.5
the curve is dropping more and more steeply.
That means the number of players is decreasing faster and faster on that interval.
NEW QUESTION # 90
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: C
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 # 91
The data in the scatterplot represents the number of monthly train crossings at a particular intersection over time.
Which type of function should be used to model the data?
Answer: C
Explanation:
The scatterplot shows a decreasing pattern.
At first, the number of monthly crossings decreases quickly. Then the values begin to level off.
This type of pattern is characteristic of an exponential decay model.
A linear model would show points decreasing at a constant rate, forming an approximately straight line. Here, the decrease is not constant; it is steep at first and then slows down.
A logistic model usually has an S-shaped pattern, which is not shown here.
A polynomial model may curve, but the long-term leveling behavior shown in the scatterplot is best represented by an exponential decay function.
Therefore, the correct answer is:
# ( " D " )
NEW QUESTION # 92
The function P(t)represents the yearly profit, in millions of dollars, for a streaming service since opening. The graph of P(t)is shown.
What is the correct interpretation of the maximum value?
Answer: C
Explanation:
The graph represents yearly profit as a function of time:
P(t)= " yearly profit "
where:
t= " years since opening "
The graph is a downward-opening curve, so its maximum value occurs at the highest point, also called the vertex.
From the graph, the highest point occurs at approximately:
t=10.5
So the maximum yearly profit happened approximately:
10.5 " years after opening "
The vertical axis measures yearly profit in millions of dollars. From the graph, the maximum value is approximately:
1.41
Since the units are millions of dollars:
1.41×1,000,000=1,410,000
So the maximum yearly profit was approximately:
$1,410,000
Therefore, the correct answer is:
# ( " C " )
NEW QUESTION # 93
......
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