Step 1 ) Move all terms right side of the equation.
Step 2 ) Apply quadratic formula. (Note: There are 2 solutions)
,
Step 3 ) Simplify.
,
,
Since the options only provide one of the answer we found, the answer is...
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- <em>Marlon Nunez</em>
On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 2) and (4, 0). Everything below and to t
he left of the line is shaded. Which point is a solution to the linear inequality y < Negative one-halfx + 2? (2, 3) (2, 1) (3, –2) (–1, 3)
1 answer:
Answer:
Option C.
Step-by-step explanation:
A dashed straight line has a negative slope and goes through (0, 2) and (4, 0).
The given inequality is
We need find the point which is a solution to the given linear inequality.
Check the given inequality for point (2, 3).
This statement is false. Option 1 is incorrect.
Check the given inequality for point (2, 1).
This statement is false. Option 2 is incorrect.
Check the given inequality for point (3, -2).
This statement is false. Option 3 is correct.
Check the given inequality for point (-1,3).
This statement is false. Option 4 is incorrect.
Therefore, the correct option is C.
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Answer:
If we compare the the p value with the significance level provided , we see that
, so then we can reject the null hypothesis. and there is a significant increase in the miles per gallon from 2017 to 2019 at 10% of significance.
Step-by-step explanation:
Previous concepts
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.
Let put some notation :
x=test value 2017 , y = test value 2019
x: 28.7 32.1 29.6 30.5 31.9 30.9 32.3 33.1 29.6 30.8 31.1 31.6
y: 31.1 32.4 31.3 33.5 31.7 32.0 31.8 29.9 31.0 32.8 32.7 33.8
Solution to the problem
The system of hypothesis for this case are:
Null hypothesis:
Alternative hypothesis:
Because if we have an improvement we expect that the values for 2019 would be higher compared with the values for 2017
The first step is calculate the difference and we obtain this:
d: 2.4, 0.3, 1.7,3,-0.2, 1.1, -0.5, -3.2, 1.4, 2, 1.6, 2.2
The second step is calculate the mean difference
The third step would be calculate the standard deviation for the differences, and we got:
We assume that the true difference follows a normal distribution. The 4th step is calculate the statistic given by :
The next step is calculate the degrees of freedom given by:
Now we can calculate the p value, since we have a right tailed test the p value is given by:
If we compare the the p value with the significance level provided , we see that
, so then we can reject the null hypothesis. and there is a significant increase in the miles per gallon from 2017 to 2019 at 10% of significance.