Question

1. which of the following statements best describes the relationship between the data points shown on the scatter plot?

a. there is a positive correlation.
b. there is a negative correlation.
c. there does not appear to be any correlation.
d. it cannot be determined without knowing the values of the data points

1. what are the end behavior of the function y= 3x³ + 15x² - 6x + 5?

a. +∞ for x < 0 and +∞ for x > 0
b. -∞ for x < 0 and -∞ for x > 0
c. -∞ for x < 0 and +∞ for x > 0
d. +∞ for x < 0 and -∞ for x > 0

1. which of the following graphs represents the following inequalities?

y < (2/3)x - 4
y ≥ -3x + 3
a.
b.
c.
d.

Explanation:

38. Step1: Analyze scatter plot trend

Data points show upward trend as x increases → positive correlation.

39. Step1: Identify leading term

Leading term: $3x^3$ (degree 3, positive coefficient).

Step2: Determine end behavior

For odd degree: as $x→-\infty$, $x^3→-\infty$ → $3x^3→-\infty$; as $x→+\infty$, $x^3→+\infty$ → $3x^3→+\infty$.

40. Step1: Analyze first inequality

$y < \frac{2}{3}x - 4$: dashed line, shade below.

Step2: Analyze second inequality

$y ≥ -3x + 3$: solid line, shade above.

Step3: Match to graph

Find graph with dashed line (slope $\frac{2}{3}$, y-int -4, shaded below) and solid line (slope -3, y-int 3, shaded above), overlapping in feasible region.

Answer:

1. a. There is a positive correlation.
2. C. $-\infty$ for $x < 0$ and $+\infty$ for $x > 0$
3. (Assuming the correct graph is the one with a dashed line for $y=\frac{2}{3}x - 4$ (shaded below) and a solid line for $y=-3x + 3$ (shaded above), intersecting to form a feasible region; if option B matches this, then B)