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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Algebraic Expressions and Operations | 20% | - Order of operations - Operations with polynomials - Variables, constants, and coefficients - Simplifying and evaluating expressions |
| Topic 2: Systems of Equations and Inequalities | 15% | - Graphical solutions - Applications of systems - Solving by substitution and elimination |
| Topic 3: Linear Equations and Inequalities | 25% | - Real-world applications - Solving and graphing inequalities - Solving single-variable equations |
| Topic 4: Graphing and Functions | 25% | - Slope and equations of lines - Linear functions and their graphs - Coordinate plane and plotting points - Function notation and evaluation |
| Topic 5: Exponents, Radicals, and Quadratic Relationships | 15% | - Basic quadratic graphs - Simplifying radical expressions - Properties of exponents - Solving quadratic equations |
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NEW QUESTION # 140
A new company just launched and is using the function M(t)to predict its market share after tyears. The graph of M(t)is shown.
When should the company expect to have a market share of 40%?
Answer: D
Explanation:
The function M(t)represents the company's market share after tyears.
The horizontal axis represents:
t= " time in years "
The vertical axis represents:
M(t)= " market share percentage "
We need to find when the market share reaches:
40%
From the graph, locate 40on the vertical axis. Then move horizontally to the blue curve and read the corresponding value on the horizontal axis.
The curve reaches 40%at approximately:
t=7.4
So the company should expect to have a market share of 40%after about:
7.4 " years "
Therefore, the correct answer is:
# ( " C " )
NEW QUESTION # 141
A new company just launched and is using the function M(t) to predict its market share after t years. The graph of M(t) is shown.
When should the company expect to have a market share of 60%?
Answer: C
Explanation:
This question uses a logistic function, which often models growth that starts slowly, increases rapidly, and then levels off near a maximum value. The input t represents years, and M(t) represents market share as a percent. To find when the company reaches a 60% market share, locate 60 on the vertical axis and identify where the graph reaches that height. Then read the corresponding value on the horizontal axis. From the graph, the curve reaches 60% slightly after 6 years, approximately at t=6.6. The value after 6 years is close but not yet at 60%. Therefore, the company should expect to reach 60% market share after about 6.6 years.
The correct answer is D.
NEW QUESTION # 142
The function P(t) represents the yearly profit, in thousands of dollars, for a virtual store since opening. The graph of P(t) is shown.
What is the time at which the store reached the maximum yearly profit?
Answer: B
Explanation:
The maximum value of a graph is the highest output value the function reaches. Since P(t) represents yearly profit, the maximum value occurs where the store earns its greatest yearly profit. The graph is a downward- opening curve, so its highest point is the vertex. To answer the question, we need the t-value of the vertex, not the profit amount. From the graph, the highest point occurs between 4 and 5 years after opening, closest to 4.5 years. This means the virtual store reached its maximum yearly profit approximately 4.5 years after it opened.
The later values decrease after the vertex, so options involving 7.5 or 14 years are not correct. Therefore, the correct answer is B.
NEW QUESTION # 143
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?
Answer: A
Explanation:
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.
NEW QUESTION # 144
As regulations change, the number of licensed sellers of a product decreases. The graph models the change in the number of licensed sellers over time.
What does the horizontal asymptote mean?
Answer: D
Explanation:
The graph shows a decreasing exponential model.
The vertical axis represents:
" Licensed sellers "
The horizontal axis represents:
" Time in years "
The graph starts near 700 licensed sellers and decreases over time. However, it does not appear to decrease all the way to 0. Instead, it levels off near:
y=100
That horizontal line is the horizontal asymptote.
A horizontal asymptote represents the long-term value the function approaches as time continues.
So the correct interpretation is:
" In the long run, the number of licensed sellers nears 100. "
Therefore, the correct answer is:
# ( " C " )
NEW QUESTION # 145
......
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