Answer:
9.09%
Step-by-step explanation:
To find percent decrease you have to use this equation:
Initial = 49.5
New = 45
Plug in and solve:
The percent decrease is 9.09%
<em>Hope this helps!!</em>
<em>- Kay :)</em>
Find the coordinates of the vertices of the figure formed by each system of inequalities. x + y < 9 x - 2y < 12 y < 2x
+ 3 a. (0, 0), (0, 1), (2, 0) c. (9, 1), (2, 3), (5, 6) b. (10, -1), (-6, -9), (2, 7) d. (0, -1), (2, -1), (3, 6)
2 answers:
Answer:
b. (10, -1), (-6, -9), (2, 7)
Step-by-step explanation:
One way to solve this problem is by graphing (see attachment). In fact, that actually is the easiest way to do this.
First, graph x + y < 9 (red part on the attachment). To do this, isolate the y so that it's like a regular linear equation: y < -x + 9. Graph the line y = -x + 9 first, and then choose a point either on the left or right of the line to plug in for x and y.
Let's just choose (0, 0), which is on the left of the line: 0 < -0 + 9 ⇒ 0 < 9. Since this is a true statement, we know that we should shade the left side of the equation, and not the right side.
Now, graph x - 2y < 12 (blue part on the attachment). It's the same process here as the first inequality. For this one, we find that we also shade to the "left" of the line (it's more "up" than "left", but you get the idea).
Finally, graph y < 2x + 3 (green part on the attachment). Again, it's the same process. For this, we shade to the right.
Now look at the three points that they intersect at: they are (2, 7), (-6, -9), and (10, -1). The answer is thus B.
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Answer:
Null hypothesis:
Alternative hypothesis:
(1)
Since the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of adults prefer window seats when they fly is significantly higher than 0.5 .
Step-by-step explanation:
1) Data given and notation
n=778 represent the random sample taken
X=492 represent the people that chose a window seat.
estimated proportion of people that chose a window seat.
is the value that we want to test
represent the significance level
Confidence=99% or 0.99
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the majority of adults prefer window seats when they fly:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statisitc, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
4) Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided . The next step would be calculate the p value for this test.
Since is a right tailed test the p value would be:
5) Conclusion
Since the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of adults prefer window seats when they fly is significantly higher than 0.5 .