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ΔABC has two congruent angles. Therefore, it is an isosceles triangle.
Therefore we have the equation (1) 3x - 5 = y + 12.
All angles of the ΔDBC are congruent. Therefore it is an equilateral triangle.
Therefore we have the equation (2) 3x - 5 = 5y - 4
From (1) and (2) we have the equation:
5y - 4 = y + 12 <em>add 4 to both sides</em>
5y = y + 16 <em>subtract y from both sides</em>
4y = 16 <em>divide both sides by 4</em>
y = 4
Substitute the value of y to (1):
3x - 5 = 4 + 12
3x - 5 = 16 <em>add 5 to both sides</em>
3x = 21 <em>divide both sides by 3</em>
x = 7
<h3>Answer: x = 7 and y = 4</h3>
Answer:
a. The point estimate of the corresponding population mean is of $8213.
b. The margin of error is of $103.
c. The 98% confidence interval for the corresponding population mean is between $7973.5 and $8452.5, which means that for all weedings, we are 98% sure that the true population mean is in this interval.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
a. What is the point estimate of the corresponding population mean?
The sample mean is of $8213. So, by the Central Limit Theorem, the point estimate of the corresponding population mean is of $8213.
b. What is the margin of error for this estimate (use2 standard deviations (divided by Vn) to either side of the mean is used when no specific confidence level is stated).
Sample of 450, standard deviation of $2185. So
The margin of error is of $103.
c. Create and interpret a 98% confidence interval for the corresponding population mean.
The confidence interval is given by:
In which is the sample mean and z is the value related to the confidence level.
98% confidence level
So , z is the value of Z that has a pvalue of
, so
.
Then
The 98% confidence interval for the corresponding population mean is between $7973.5 and $8452.5, which means that for all weedings, we are 98% sure that the true population mean is in this interval.
The easiest way to tell whether lines are parallel, perpendicular, or neither is when they are written in slope-intercept form or y = mx + b. We will begin by putting both of our equations into this format.
The first equation,
is already in slope intercept form. The slope is 1/2 and the y-intercept is -1.
The second equation requires rearranging.
From this equation, we can see that the slope is -1/2 and the y-intercept is -3.
When lines are parallel, they have the same slope. This is not the case with these lines because one has slope of 1/2 and the other has slope of -1/2. Since these are not the same our lines are not parallel.
When lines are perpendicular, the slope of one is the negative reciprocal of the other. That is, if one had slope 2, the other would have slope -1/2. This also is not the case in this problem.
Thus, we conclude that the lines are neither parallel nor perpendicular.
The first equation,
The second equation requires rearranging.
From this equation, we can see that the slope is -1/2 and the y-intercept is -3.
When lines are parallel, they have the same slope. This is not the case with these lines because one has slope of 1/2 and the other has slope of -1/2. Since these are not the same our lines are not parallel.
When lines are perpendicular, the slope of one is the negative reciprocal of the other. That is, if one had slope 2, the other would have slope -1/2. This also is not the case in this problem.
Thus, we conclude that the lines are neither parallel nor perpendicular.