If 0 lies in the quadrant IV. What can be the value of cos 0?
2 answers:
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Answer:
It would look like the picture I attached at the bottom.
Step-by-step explanation:
We know that the slope is -3 and the y intercept is (0,4) (plugging in 0 for x will get you that point), and then you can just graph an equation like you normally would, using rise/run to go down 3 units for every one unit you go right, and plugging in easy x values to check your work.
It gets a little tricky because the question then adds the inequality, and we see that y is now less than <em>or equal to </em>the original equation.
Since it is less than, we can shade all the values below the graph.
(Also, you should probably note for future reference that if it was just less than, the shading would look the same while the graph itself would be dotted because the values on the line are nor included in the solution set).
Desmos is a great website to use if you're having trouble graphing in the future :)
Answer:
a)
So on this case the 99% confidence interval would be given by (13.83;28.17)
b)
c)
d) D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Part a
represent the sample mean
population mean (variable of interest)
represent the population standard deviation
n=350 represent the sample size
99% confidence interval
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.99 or 99%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 99% confidence interval would be given by (13.83;28.17)
Part b
The margin of error is given by:
Part c
The margin of error is given by:
Part d
As we can see when we reduce the sample size we increase the margin of error so the best option for this case is:
D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.