TechWiz Electronics makes a profit of $35 for each MP3 player sold and $18 for each DVD player sold. Last week, TechWiz sold a c
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The given equation of a line is:
It is required to find the equation of a line that is parallel to this line and passes through the point (-5,5).
Recall that the equation of a line in point-slope form is given as:
Where m is the slope of the line, and the line passes through the point (x₁,y₁).
Rewrite the given equation in the point-slope form:
Compare this equation with the standard point-slope form written above, it can be seen that the slope of the line is 3/7.
Recall that the slopes of parallel lines are the same or equal<em>.</em>
It follows that the slope of the required parallel line is also 3/7.
Substitute m=3/7 and the point (x₁,y₁)=(-5,5) into the point-slope form of the equation of a line:
Rewrite the equation in the slope-intercept form and simplify as required:
The required equation of the line is y=3/7 x + 50/7.
Answer:
(a) The sample mean startup cost is 107.3 thousand dollars.
The sample mean startup cost is 107.3 thousand dollars.
(b) The 90% confidence interval for the population average startup costs for candy store franchises is ($89.4, $125.2) thousand.
Step-by-step explanation:
The questions asked related to the data are:
(a) Use a calculator with mean and sample standard deviation keys to find the sample mean startup cost x and sample standard deviation s. (Round your answers to one decimal place.)
x = thousand dollars
s = thousand dollars
(b) Find a 90% confidence interval for the population average startup costs μ for candy store franchises. (Round your answers to one decimal place.)
lower limit thousand dollars
upper limit thousand dollars
Solution:
The data provided is:
X = {100, 170, 133, 93, 75, 94, 116, 100, 85}
(a)
Compute the sample mean as follows:
The sample mean startup cost is 107.3 thousand dollars.
Compute the sample standard deviation as follows:
The sample standard deviation of startup cost is 28.9 thousand dollars.
(b)
As the population standard deviation is not known we will use a <em>t</em>-interval.
The critical value of <em>t</em> for 90% confidence level and (n - 1) = 8 degrees of freedom is:
*Use a <em>t</em>-table for the value.
Compute the 90% confidence interval for population mean as follows:
Thus, the 90% confidence interval for the population average startup costs for candy store franchises is ($89.4, $125.2) thousand.