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| Section | Objectives |
|---|---|
| Polynomial and Rational Expressions | - Polynomials
|
| Exponential and Logarithmic Concepts | - Exponential Functions
|
| Functions and Graphs | - Function Concepts
|
| Linear Functions and Systems | - Systems of Equations
|
| Foundations of Algebra | - Algebraic Expressions
|
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NEW QUESTION # 76
A recipe calls for a constant ratio of water and lemon juice. The graph shows the relationship between the amounts of these two ingredients, where wis the volume of water and lis the volume of lemon juice.
What is the correct interpretation of the rate of change?
Answer: C
Explanation:
The graph shows a linear relationship between:
w= " water in cups "
and
l= " lemon juice in cups "
The line passes through the origin, so the relationship has the form:
l=mw
where mis the rate of change.
From the graph, a clear point on the line is approximately:
(8#5)
This means when there are 8 cups of water, there are 5 cups of lemon juice.
The rate of change is:
m= " change in lemon juice " / " change in water "
m=5/8
So the relationship is:
l=5/8 w
This means the amount of lemon juice must be:
5/8
of the amount of water.
NEW QUESTION # 77
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: B
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 # 78
The graph shows the daily practice duration for a musician, where the number of days since the beginning of the month is along the horizontal axis and the number of minutes practiced per day is along the vertical axis.
What was the practice duration for day 9, based on the graph?
Answer: B
Explanation:
This question asks us to read and interpret a value from a graph.
The horizontal axis represents:
" Days since the beginning of the month "
The vertical axis represents:
" Practice duration in minutes "
We need to find the practice duration for:
" day " 9
To do this, locate 9on the horizontal axis, move upward to the blue graph, and then read the corresponding value on the vertical axis.
From the graph, the point at day 9is approximately:
127
So the musician practiced for:
127 " minutes "
NEW QUESTION # 79
The number of registered voters in a district is modeled by a decreasing exponential function, where x represents the number of years since 2005 and f(x) represents the number of registered voters.
Which interval is associated with the slowest average decrease in the number of registered voters?
Answer: A
Explanation:
A decreasing exponential function falls quickly at first and then levels off over time. The "slowest average decrease" occurs where the graph is flattest, because the output changes by the smallest amount per year.
Earlier intervals, such as 2005 to 2008, occur when the graph is steepest, so those intervals have a faster average decrease. Later intervals occur after the exponential decay has slowed. From the graph, the interval from 2015 to 2025 is farthest to the right and has the least steep downward trend. Therefore, the number of registered voters decreases most slowly during that interval. This is why the correct answer is D.
NEW QUESTION # 80
The graph shows the number of people watching a live video. The number of minutes since the video began is on the horizontal axis, and the number of viewers is on the vertical axis. When were there 432 viewers?
Exhibit:
Answer: A
Explanation:
This problem requires reading a value from a graph. The horizontal axis gives time in minutes, and the vertical axis gives the number of viewers. To solve it, find 432 on the vertical axis, locate where the graph reaches that value, and then move down to the horizontal axis. From the exhibit, the graph reaches 432 viewers at minute 1. That means the ordered pair is approximately (1, 432), so the input is 1 minute and the output is 432 viewers. The other listed minutes correspond to different viewer counts on the graph. In graphical depictions, matching the correct input-output pair is the key step. Therefore, the correct answer is B.
NEW QUESTION # 81
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