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| Section | Weight | Objectives |
|---|---|---|
| Exponents, Radicals, and Quadratic Relationships | 15% | - Basic quadratic graphs - Solving quadratic equations - Simplifying radical expressions - Properties of exponents |
| Graphing and Functions | 25% | - Slope and equations of lines - Linear functions and their graphs - Function notation and evaluation - Coordinate plane and plotting points |
| Algebraic Expressions and Operations | 20% | - Simplifying and evaluating expressions - Order of operations - Operations with polynomials - Variables, constants, and coefficients |
| Systems of Equations and Inequalities | 15% | - Applications of systems - Graphical solutions - Solving by substitution and elimination |
| Linear Equations and Inequalities | 25% | - Solving single-variable equations - Real-world applications - Solving and graphing inequalities |
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NEW QUESTION # 64
The given function represents the price of a commodity, p, in dollars, based on the number of months, m, since the beginning of 2020.
p(m)=5m+5
What is the average rate of change of the price over the interval m=1to m=10?
Answer: B
Explanation:
The function is:
p(m)=5m+5
This is a linear function in the form:
p(m)=mx+b
For a linear function, the average rate of change over any interval is the same as the slope.
The slope is the coefficient of m:
5
So the price increases at a constant rate of:
$5 " per month "
We can also verify using the average rate of change formula:
(p(10)-p(1))/(10-1)
Find p(10):
p(10)=5(10)+5=55
Find p(1):
p(1)=5(1)+5=10
Now calculate:
(55-10)/(10-1)
=45/9
=5
NEW QUESTION # 65
The scatterplot shows data on the popularity of a blog post over time. The graphed regression function has an r2value of 0.42.
Is it appropriate to make a prediction for the number of daily blog post views after 12.4 days?
Answer: B
Explanation:
Explanation:The regression model has r2=0.42, which indicates a moderate fit. This means the model captures some of the pattern in the data, but it is not strong enough to support distant predictions. The proposed prediction is for x=12.4 days, which lies beyond the largest observed x-value in the scatterplot. Since the model is only moderate, acceptable extrapolation must remain close to the original data range. The value x=12.4 is more than 25% of the range beyond the maximum observed value, so it is too far outside the data for a reliable prediction. Therefore, the prediction is not appropriate. The correct answer is B.
NEW QUESTION # 66
The function f(z) represents the relationship between the number of units in two inventories, where z is the number of units in inventory A and f(z) is the number of units in inventory B. The number of units in inventory B is 2 more than the number of units in inventory A. Which function represents this situation?
Answer: C
Explanation:
This problem translates a verbal statement into function notation. The variable z represents the number of units in inventory A, and f(z) represents the number of units in inventory B. The phrase "2 more than" tells us to add 2 to the number of units in inventory A. That gives the rule f(z)=z+2. For example, if inventory A has
10 units, then inventory B has f(10)=12 units. Option A subtracts 2, option C multiplies by 2, and option D divides by 2, so those do not match the stated relationship. Because inventory B is always exactly 2 more than inventory A, the correct function is f(z)=z+2. Therefore, the answer is B.
NEW QUESTION # 67
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 # 68
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 # 69
......
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