Which statements are true about the graph of the system of linear inequalities? Check all that apply. y > 3x – 4 y < x + 1
The graph of y > 3x − 4 has shading above a dashed line. The graph of y < x + 1 has shading below a dashed line. The graphs of the inequalities will intersect. There are no solutions to the system. The graphs of the two inequalities intersect the y-axis at (0, 1) and (0, 4).
2 answers:
Answer:
- The graph of y > 3x − 4 has shading above a dashed line.
- The graph of y < x + 1 has shading below a dashed line.
- The graphs of the inequalities will intersect.
Step-by-step explanation:
y > ... means the shading will be above the corresponding line.
y < ... means the shading will be below the corresponding line.
These lines have different slopes, so the solution spaces <em>must</em> overlap, hence <em>there must be solutions</em> to the system.
_____
<em>Comment on last choice</em>
It isn't clear exactly what is intended by the last offered statement. Both of the listed points are in the solution space of y > 3x-4. Neither point is in the solution space of y < x+1.
Together, the two graphs intersect the entire y-axis. Jointly, they only intersect the y-axis on the interval -4 < y < 1.
The y-intercepts of the two boundary lines are (0, 1) and (0, -4). Neither of these points is in the solution space of the system of inequalities.
You might be interested in
Answer:
Check the explanation
Step-by-step explanation:
The null and alternative hypotheses in symbols and words are as follows:
: p ≤ 0.06 (There has been no change in the contribution rate due to addition of the mailing labels)
: p > 0.06 (The addition of the mailing labels has increased the contribution rate)
Test Statistics
The following information is provided: The sample size is N = 75000, the number of favorable cases is X = 5625, and the sample
The z-statistic is computed as follows:
- (1 -
Test statistic z = 17.297
P-value
P-value corresponding to z = 17.297 for a two tailed test is obtained using standard normal table.
p-value = 0.0000
90% Confidence Interval Calculation
Kindly check the attached image below.
Conclusion
Since p-value = 0.0000 < α = 0.05, we reject null hypothesis .
At 0.05 significance level, there is enough evidence to conclude that the addition of the mailing labels has increased the contribution rate.
Since the 90% confidence interval (0.073, 0.077) does not contain the hypothesized value 0.06, the result is significant and we reject null hypothesis.
In other words, at 0.10 significance level, there is enough evidence to conclude that the addition of the mailing labels has increased the contribution rate.
