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| Section | Weight | Objectives |
|---|---|---|
| Systems of Equations and Inequalities | 15% | - Solving by substitution and elimination - Applications of systems - Graphical solutions |
| Linear Equations and Inequalities | 25% | - Real-world applications - Solving single-variable equations - Solving and graphing inequalities |
| Algebraic Expressions and Operations | 20% | - Order of operations - Simplifying and evaluating expressions - Operations with polynomials - Variables, constants, and coefficients |
| Exponents, Radicals, and Quadratic Relationships | 15% | - Simplifying radical expressions - Properties of exponents - Solving quadratic equations - Basic quadratic graphs |
| Graphing and Functions | 25% | - Slope and equations of lines - Coordinate plane and plotting points - Function notation and evaluation - Linear functions and their graphs |
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NEW QUESTION # 80
The population of fish in a lake is changing according to the function
P(t)=462-35t
where tis the number of months since the beginning of the year and P(t)is the fish population at time t.
Which interpretation of the rate of change is correct?
Answer: D
Explanation:
The function is:
P(t)=462-35t
This is a linear function in the form:
P(t)=mt+b
where:
m= " rate of change "
and
b= " initial value "
In this function:
m=-35
The negative sign means the fish population is decreasing.
The number 35tells us the amount of decrease per month.
So the fish population is decreasing by:
35 " fish per month "
The value 462is not the rate of change. It represents the starting fish population at the beginning of the year, when t=0:
P(0)=462
Therefore, the correct interpretation is:
" The number of fish in the lake is decreasing at a constant rate of 35 fish per month. " So the correct answer is:
# ( " D " )
NEW QUESTION # 81
The data in the scatterplot represents the number of people working at a research station over time. The graphed regression function has an r
2
value of 0.96. The predicted number of people working at the research station after 18.1 years is 541.
Is this prediction appropriate?
Answer: B
Explanation:
The value r2=0.96 indicates a strong regression fit because it is very close to 1. A strong fit supports prediction better than a weak or moderate fit. However, prediction also depends on whether the x-value is within a reasonable extrapolation range. The prediction is made at x=18.1, which is beyond the maximum observed x-value in the scatterplot. Even though the model fits the data well, the prediction is too far beyond the observed data range.
For a strong model, extrapolation should not go more than about 50% of the range beyond the maximum value. Since x=18.1 exceeds that limit, the prediction is not appropriate. Therefore, the correct answer is B.
NEW QUESTION # 82
The function P(t)represents the daily profit, in hundreds of dollars, for a museum since opening. The graph of P(t)is shown.
What is the correct interpretation of the maximum value?
Answer: D
Explanation:
The graph shows a curved, downward-opening function. This type of graph is commonly associated with a quadratic polynomial function.
The maximum value of a downward-opening parabola occurs at its highest point, called the vertex.
From the graph, the highest point occurs at approximately:
t=9.5
This means the museum reaches its maximum daily profit approximately:
9.5 " years after opening "
The vertical axis represents daily profit in hundreds of dollars. From the graph, the maximum P(t)-value is approximately:
16.5
Since the profit is measured in hundreds of dollars:
16.5×100=1650
So the maximum daily profit is approximately:
$1,650
Therefore, the correct interpretation is:
" Approximately 9.5 years after opening, a maximum daily profit of approximately " $1,650 " was earned. "
NEW QUESTION # 83
The graph shows the number of trees sold by a nursery, where the number of days since the beginning of the month is along the horizontal axis and the number of trees sold per day is along the vertical axis. The greatest number of trees are sold when the temperature is over 70°F.
When was the temperature likely over 70°F?
Answer: C
Explanation:
The problem states that the greatest number of trees are sold when the temperature is over 70°F. Therefore, we need to identify the days on the graph when tree sales are highest. The graph shows two major peaks in the number of trees sold per day. These peaks occur around day 2 and day 10. Since higher tree sales are linked to temperatures over 70°F, those two days are the most likely days when the temperature exceeded 70°F. Day 6 appears near a low point, so it is not likely associated with high temperature based on the given relationship.
Day 12 also does not match the main peaks. Therefore, the correct answer is C.
NEW QUESTION # 84
Consider the function
w(t)=0.03t
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