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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Linear Equations and Inequalities | 25% | - Real-world applications - Solving and graphing inequalities - Solving single-variable equations |
| Topic 2: Algebraic Expressions and Operations | 20% | - Operations with polynomials - Simplifying and evaluating expressions - Variables, constants, and coefficients - Order of operations |
| Topic 3: Graphing and Functions | 25% | - Slope and equations of lines - Linear functions and their graphs - Function notation and evaluation - Coordinate plane and plotting points |
| Topic 4: Systems of Equations and Inequalities | 15% | - Applications of systems - Solving by substitution and elimination - Graphical solutions |
| Topic 5: Exponents, Radicals, and Quadratic Relationships | 15% | - Solving quadratic equations - Properties of exponents - Basic quadratic graphs - Simplifying radical expressions |
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NEW QUESTION # 12
The number of people, P, in a festival audience is represented by the graph, with the number of hours since the beginning of the festival along the horizontal axis and the size of the audience along the vertical axis.
Point Arepresents an audience size of 402 for the first hour of the festival, or P(0)=402.
Which ordered pair represents a point on the graph?
Answer: D
Explanation:
This question is about reading an ordered pair from a graph.
An ordered pair has the form:
(x#y)
where:
x= " time in hours "
and
y= " audience size "
From the graph:
Point Ais at approximately (0#402)
Point Bis at (2#401)
Point Cis at (4#403)
Point Dis at (6#406)
Point Eis at approximately (8#410)
Point Fis at (10#408)
Now compare these graph points with the answer choices.
Choice A says:
(2#401)
This matches point Bon the graph exactly.
The other choices do not match the graph:
(4#404)
is incorrect because at x=4, the graph shows about 403, not 404.
(8#409)
is incorrect because at x=8, the graph is about 410, not 409.
(10#407)
is incorrect because at x=10, the graph shows about 408, not 407.
NEW QUESTION # 13
The scatterplot shows data on the number of shirts sold at a gift shop per week over time. The graphed regression function has an r
2
value of 0.09.
Which range of x-values is appropriate for extrapolation?
Answer: C
Explanation:
The r
2
value tells how closely the regression model fits the scatterplot data. In this problem, r
2
=0.09, which is extremely low. This means the regression model explains only a very small portion of the variation in the shirt-sales data. When r
2
is this weak, the model is not reliable for predictions outside the data range. Extrapolation is already less certain than interpolation because it predicts beyond the observed data. With such a poor fit, extending the model beyond the data would not be appropriate. Since 0.09 < 0.3, the best justification is that extrapolation is not appropriate because r
2
< 0.3. Therefore, the correct answer is C.
NEW QUESTION # 14
The value of an investment portfolio after x years is modeled by the function g(x)=3100(1.059) x
.
What is the value of the portfolio when x=10?
Answer: C
Explanation:
This problem uses an exponential growth model. The initial portfolio value is 3100, and the growth factor is
1.059. Since the growth factor is greater than 1, the portfolio increases over time. To find the value after 10 years, substitute x=10 into the function: g(10)=3100(1.059)
10
First evaluate the exponent, then multiply by 3100. This gives g(10)#5499.4758. Rounded to the nearest cent, the value is $5,499.48. The answer must be written as money because the function models the value of an investment portfolio. Among the choices, only option B matches the correctly evaluated exponential expression. Therefore, the correct answer is B.
NEW QUESTION # 15
The graphed function n(t)represents the number of people, n, at a park thours after 8:00 a.m. The plotted points Aand Bhave coordinates (2#110)and (6#182).
Which statement gives the correct interpretation of the average rate of change of the number of people over the interval from point Ato point B?
Answer: D
Explanation:
The average rate of change measures how much the output changes per one unit of input.
Here:
t= " hours after 8:00 a.m. "
and
n(t)= " number of people at the park "
The two given points are:
A=(2,110)
and
B=(6,182)
This means:
At t=2hours after 8:00 a.m., there were 110people at the park.
At t=6hours after 8:00 a.m., there were 182people at the park.
Now calculate the average rate of change:
" Average rate of change " =(182-110)/(6-2)
=72/4
=18
Because the value is positive, the number of people is increasing.
So the correct interpretation is:
" The number of people at the park increases at an average rate of 18 people per hour. "
NEW QUESTION # 16
Through a local marketplace, a person makes livestock feeders to sell. The graph shows the functions modeling the cost and revenue.
What is the minimum number of livestock feeders that must be sold in order for the revenue to cover the costs?
Answer: B
Explanation:
This question asks for the break-even point, which is the point where:
Revenue=Cost
On the graph:
The solid blue line represents revenue.
The dashed blue line represents cost.
The revenue line starts below the cost line, meaning the person is not yet covering costs. The revenue line eventually crosses the cost line at a little more than 4 units.
Since the question asks for the minimum number of livestock feeders that must be sold, we need a whole number of feeders.
The graph shows the intersection occurs between:
4 and 5
So selling 4 feeders is not enough, but selling 5 feeders is enough for revenue to cover the costs.
Therefore, the correct answer is:
C
NEW QUESTION # 17
......
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