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| Section | Weight | Objectives |
|---|---|---|
| Systems of Equations and Inequalities | 15% | - Solving by substitution and elimination - Graphical solutions - Applications of systems |
| Graphing and Functions | 25% | - Function notation and evaluation - Linear functions and their graphs - Slope and equations of lines - Coordinate plane and plotting points |
| Linear Equations and Inequalities | 25% | - Solving and graphing inequalities - Solving single-variable equations - Real-world applications |
| Exponents, Radicals, and Quadratic Relationships | 15% | - Solving quadratic equations - Basic quadratic graphs - Simplifying radical expressions - Properties of exponents |
| Algebraic Expressions and Operations | 20% | - Variables, constants, and coefficients - Simplifying and evaluating expressions - Order of operations - Operations with polynomials |
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NEW QUESTION # 69
The function P(t)represents the weekly profit, in thousands of dollars, for a rental store since opening. The graph of P(t)is shown.
When did the store have its maximum weekly profit?
Answer: D
Explanation:
The graph shows:
P(t)= " weekly profit in thousands of dollars "
where:
t= " years since opening "
The graph is a downward-opening curve, so it has a maximum value at its highest point. In Applied Algebra, the highest point of this kind of polynomial graph is called the vertex.
To answer the question, we need the t-value of the vertex because the question asks when the store had its maximum weekly profit.
From the graph, the highest point occurs between:
t=5
and
t=6
More specifically, it is approximately:
t=5.5
So the store had its maximum weekly profit approximately:
5.5 " years after opening "
NEW QUESTION # 70
The growth of an animal population is shown in the graph. The instantaneous rate of change at point Pis 3.74.
Which interpretation of the instantaneous rate of change is correct?
Answer: B
Explanation:
The graph shows population in thousands, and the horizontal axis represents:
" years since 1995 "
Point Pis located at approximately:
x=12
Since xrepresents years since 1995:
1995+12=2007
So point Pcorresponds to the year:
2007
The instantaneous rate of change at point Pis:
3.74
Because the vertical axis is measured in thousands, this means:
3.74 " thousand animals per year "
Convert thousands to actual animals:
3.74×1000=3740
So in 2007, the population was increasing by approximately:
3,740 " animals per year "
NEW QUESTION # 71
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?
Exhibit:
Answer: C
Explanation:
This question asks for the cost of each additional shirt, which is the slope of the linear graph. The slope tells how much the total cost increases for each increase of 1 shirt. From the exhibit, the graph shows a starting cost near $39 and a point near (10, 139). The increase in cost from 0 shirts to 10 shirts is 139#39=100 dollars.
Dividing by 10 shirts gives a rate of 10 dollars per shirt. The fixed starting cost is not the cost of a shirt; it is the initial fee or setup cost. Since the graph rises by $10 for each additional shirt, the cost per additional shirt is $10.00. Therefore, the answer is B.
NEW QUESTION # 72
The graph shows the weekly profit in hundreds of dollars for a coffee shop. The horizontal axis represents the number of years since the coffee shop opened.
What is the correct interpretation of the minimum value?
Answer: A
Explanation:
The graph shows weekly profit as a function of time.
The horizontal axis represents:
" years since opening "
The vertical axis represents:
" weekly profit in hundreds of dollars "
The graph is an upward-opening curve, so its minimum value occurs at the lowest point, called the vertex.
From the graph, the lowest point occurs at approximately:
t=6
So the minimum weekly profit happened approximately:
6 " years after opening "
The vertical value at this point is approximately:
9.9
Since the profit is measured in hundreds of dollars:
9.9×100=990
So the minimum weekly profit was approximately:
$990
Therefore, the correct answer is:
# ( " A " )
NEW QUESTION # 73
A researcher collected data on the number of books donated per month to a thrift store over time. The results are shown in the scatterplot. A regression function is graphed with r
2
=0.99.
Which range of x-values is appropriate for extrapolation?
Answer: B
Explanation:
The value r
2
=0.99 indicates a very strong regression fit because it is close to 1. A strong fit means the model explains most of the variation in the data, so limited extrapolation can be appropriate. However, extrapolation should stay close to the observed data range. From the scatterplot, the data values appear to run from about x=5 to x=15. A reasonable extrapolation range extends slightly beyond those observed values, not too far outside them. The interval x=2.5 to x=17.5 stays close to the original data and is more appropriate than the wider interval x=0 to x=20. Therefore, the correct answer is B.
NEW QUESTION # 74
......
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