Which system of linear inequalities is represented by the graph? y > One-thirdx + 3 and 3x – y > 2 y > One-halfx + 3 an
2 answers:
Answer:
Step-by-step explanation:
<u><em>The complete question is</em></u>
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, 3) and (3, 4). Everything above the line is shaded. The second dashed line has a positive slope and goes through (0, negative 2) and (1, 1). Everything to the right of the line is shaded. Which system of linear inequalities is represented by the graph?
step 1
Find the inequality of the first solid line
we have the points (0,3) and (3,4)
The slope is
The y-intercept is the point (0,3)
so
The equation in slope intercept form is equal to
Remember that everything above the line is shaded and is a solid line
so
step 2
Find the inequality of the second line
we have the points (0,-2) and (1,1)
The slope is
The y-intercept is the point (0,-2)
so
The equation in slope intercept form is equal to
Remember that everything to the right of the line is shaded and is a dashed line
so
Rewrite
----->
therefore
The system of inequalities is
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Answer:
a.) The mean of the six layered plywood is 30 mm
The standard deviation is 0.49 mm
b.) That the thickness is less than 28 mm has a probability of 0.000022.
Step-by-step explanation:
There are six layers in a plywood that is considered. It is also given that the layers are independent and normally distributed.
The thickness of the layers of the plywood have a mean, = 5 mm
and a standard deviation, = 0.2 mm.
a.) Therefore the mean of the six layered plywood is = 6
= 6 × 5 mmm
= 30 mm
The standard deviation of the six layered plywood = =
= 0.49 mm
b.) We are given to find that the probability of the plywood is less than 28 mm thick.
P( thickness < 28 mm)
P( Z < ) = P(Z <
) ⇒ P( Z < -4.082) = 0.000022
Answer:
If we compare the p value and the significance level given for example we see that
so we can conclude that we to reject the null hypothesis, and the the actual mean starting age of smokers is significantly lower than 19.
Step-by-step explanation:
1) Data given and notation
represent the mean age when smokers first start to smoke varies
represent the standard deviation for the sample
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to determine if the mean starting age is at least 19, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
Calculate the P-value
Since is a one-side lower test the p value would be:
Conclusion
If we compare the p value and the significance level given for example we see that
so we can conclude that we to reject the null hypothesis, and the the actual mean starting age of smokers is significantly lower than 19.