Find the mode 9,10,15,17,15,14,37,45,42,13
2 answers:
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Answer: The solution is (2, 2)
Step-by-step explanation:
We have the system of equations:
y = 2*x - 2
x + y = 4
The first step is to write both equations as linear equations in the slope-intercept form.
y = 2*x - 2
y = -x + 4
Now we have two lines, and we can just graph them, the easiest way is the replace the value of x and obtain two points that belong to the line, and then draw a line that passes through both lines.
For example with the first one, we can firt replace x by 0 to get:
y = 2*0 - 2
y = -2
Then the point (0, -2) belongs to this line.
Now we can replace x by 1 to get:
y = 2*1 - 2 = 0
y = 0
The point (1, 0) belongs to this line.
Then we can draw these two points in the graph, and just draw a line that passes through these two points.
Once you have your two lines drawn, the solution of the system will be the point in which the lines intersect.
Below, you can see the two lines graphed (the green is the first one and the red is the second one)
And we can see that they intersect in the point (2, 2)
Then the solution of the system is (2, 2)
Answer:
From the question we are told that
The population mean is
The sample size is n = 30
The sample mean is
The population standard deviation is
The level of significance is
Step 1: State hypotheses:
The null hypothesis is
The alternative hypothesis is
Step 2: State the test statistic. Since we know the population standard deviation and the sample is large our test statistics is
=>
=>
Generally the degree of freedom is mathematically represented as
=>
=>
Step 3: State the critical region(s):
From the student t-distribution table the critical value corresponding to is
Generally the critical regions is mathematically represented as
Step 4: Conduct the experiment/study:
Generally the from the value obtained we see that the t value is outside the critical region so the decision is [Reject the null hypothesis ]
Step 5: Reach conclusions and state in English:
There is sufficient evidence to show that the filling weight has to be adjusted
Step 6: Calculate the p-value associated with this test. How does this the p-value support your conclusions in Step 5?
From the student t-distribution table the probability value to the right corresponding to at a degree of freedom of
is
Generally the p-value is mathematically represented as
=>
=>
Generally looking at the value obtained we see that hence
The decision rule is
Reject the null hypothesis
Step-by-step explanation: