Here are the answers to the multiple-choice questions based on the information provided:
Question 1:
- Answer: The graph shows a line through the points 0, 4 and 6, 0.
To convert the equation \(2x - 3y = 12\) to slope-intercept form (\(y = mx + b\)), we rearrange it:
- \(3y = 2x - 12\)
- \(y = \frac{2}{3}x - 4\)
The y-intercept is -4 (at x=0, y=-4), and the x-intercept can be found by setting \(y = 0\):
\(0 = \frac{2}{3}x - 4 \Rightarrow x = 6\)
Thus, it passes through points (0, -4) and (6, 0).
Question 2:
- Answer: Linearly, because the table shows that the daisies increased by the same amount each month.
The increase is \(3.1\) daisies every month over the four months, indicating a linear increase.
Question 3:
- Answer: \( h = 3 \)
Using the trapezoid area formula:
\[ A = \frac{1}{2}(b_1 + b_2)h \]
Plug in the values: \[ 18 = \frac{1}{2}(5 + 7)h \Rightarrow 18 = 6h \Rightarrow h = 3 \]
Question 4:
- Answer: \(0 < x \leq 200\) and \(0 < y \leq 400\)
Since they plan to accept two times as many in-state students as out-of-state students, and there are constraints on the number of out-of-state students.
Question 5:
- Answer: The y-intercept of g(x) is equal to 2 times the y-intercept of f(x).
\(f(x)\) has a y-intercept of \(f(0) = -6\), and since \(g(x)\) at \(x=0\) is -3, we find that \(-3 = 2 \times -6\).
Question 6:
- Answer: Box plot; because the data is numerical.
Grade point averages (GPAs) are numerical data, and a box plot is suitable for visualizing numerical data distribution.
Question 7:
- Answer: \( x \leq 8 \)
This results from rearranging the inequality \(40x + 80 \leq 400\) to find how many employees can be afforded.
Question 8:
- Answer: \({x | −4 ≤ x ≤ 3}\)
The domain describes the set of x-values for which the function is defined.
Question 9:
- Answer: Superman
The highest relative frequency in the table is for Superman (0.31).
Question 10:
- Answer: \(y = \frac{1}{3}x + 20\)
Since he is leaving 20 minutes late and traveling three times faster, he will save time, represented by the equation \(y = \frac{1}{3}x + 20\) (20 minutes added due to leaving late).
Question 11:
- Answer: \(y = \frac{3}{7}x - 3\)
The slope and y-intercept are evidenced by the visual interpretation of the scatter plot which shows an increasing trend.
Question 12:
- Answer: \(6^{\frac{1}{12}}\)
Simplifying \(\frac{\sqrt[3]{6}}{\sqrt[4]{6}} = 6^{\frac{1}{3}} \cdot 6^{-\frac{1}{4}} = 6^{\frac{1}{3} - \frac{1}{4}} = 6^{\frac{4 - 3}{12}} = 6^{\frac{1}{12}}\).
Question 13:
- Answer: The number of dollars it costs to rent the houseboat for 15 days.
Calculating \(f(15) = 15 + 150 \times 15 = 15 + 2250 = 2265\).
Question 14:
- Answer: \((-3, 7); 7 ≤ y < ∞\)
The vertex of the absolute value function \(y = |x + 3| + 7\) is at \((-3, 7)\), and since it opens upwards, the range is \(y \geq 7\).
Question 15:
- Answer: \(f(t) = 101,234(1.03)^t\)
The constants represent a 3% increase each year based on the appreciation shown in the table values.
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