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| Section | Objectives |
|---|---|
| Exponential and Logarithmic Concepts | - Logarithmic Basics
|
| Polynomial and Rational Expressions | - Polynomials
|
| Linear Functions and Systems | - Systems of Equations
|
| Foundations of Algebra | - Equations and Inequalities
|
| Functions and Graphs | - Graphing Functions
|
>> Vce Applied-Algebra Format <<
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NEW QUESTION # 37
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 # 38
The number of property sales in a region this year is expected to be 8 times the number of property sales in the region last year. The function H(x)represents the number of property sales this year, where xrepresents the number of properties sold last year.
Which notation represents the number of property sales this year, given that the number of properties sold last year was 360?
Answer: D
Explanation:
We are told that the number of property sales this year is expected to be 8 times the number of property sales last year.
Let:
x= " number of properties sold last year "
and
H(x)= " number of property sales this year "
Since this year's sales are 8 times last year's sales, the function rule is:
H(x)=8x
The question says that last year's property sales were:
x=360
Substitute 360into the function:
H(360)=8(360)
H(360)=2,880
So the correct notation is:
H(360)=2,880
This means: if 360 properties were sold last year, then 2,880 property sales are expected this year.
Therefore, the correct answer is:
# ( " C " )
NEW QUESTION # 39
The graph shows functions modeling the spread of two diseases within the same population.
Which conclusion is valid?
Answer: D
Explanation:
This problem compares two logistic growth curves. Each curve shows the percentage of the population affected by a disease over time. To determine which conclusion is valid, compare when each disease reaches the same percentage level. From the graph, Disease B reaches the 70% population level before Disease A reaches 70%. This means Disease B affects 70% of the population earlier in time. For other listed percentages, the graph does not support the same timing relationship as clearly or correctly. Logistic curves can cross or change relative position, so it is important to compare the same output level on both curves. Based on the graph, the valid conclusion is that Disease B affects 70% of the population before Disease A does. The answer is D.
NEW QUESTION # 40
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: C
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 # 41
The figure displays the graphs of two functions representing the heights, h_1and h_2, in feet, of two balls tseconds after being launched.
Which ball was lower 0.9seconds after being launched?
Answer: D
Explanation:
This question asks us to compare the heights of two balls at a specific time:
t=0.9
The graph shows:
Ball 1 as the solid blue curve.
Ball 2 as the dashed blue curve.
To determine which ball was lower at t=0.9, we look at the vertical positions of both curves when the time is
0.9seconds.
At approximately t=0.9:
" height of Ball 1 " < " height of Ball 2 "
This means Ball 1 is lower than Ball 2 at that time.
The correct reasoning must say both:
Ball 1 was lower, and
Ball 1's height was less than Ball 2's height at t=0.9.
That matches option A.
NEW QUESTION # 42
......
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