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Answer:
We need a sample size of at least 75.
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
So it is z with a pvalue of , so
Now, we find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
The standard deviation is the square root of the variance. So:
With a .95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is
We need a sample size of at least n, in which n is found when M = 5. So
We need a sample size of at least 75.
Question 1:
The generic equation of the line is given by:
Where,
m: slope of the line
b: cutting point with the y axis
Substituting values we have:
Answer:
an equation for the line with slope 2/3 and y-intercept is:
Question 2:
The standard equation of the line is given by:
Where,
m: slope of the line
(xo, yo): ordered pair that belongs to the line
The slope of the line is:
Substituting values:
We choose an ordered pair:
Substituting values:
Rewriting:
Answer:
An equation in slope-intercept form for the line that passes through the points (1, -3) and (3,1) is:
Question 3:
For this case, since the variation is direct, then we have an equation of the form:
Where,
k: constant of variation.
We then have the following equation:
Rewriting we have:
Therefore, the constate of variation is given by:
Answer:
the constant of variation is:
Question 4:
For this case, since the variation is direct, then we have an equation of the form:
Where,
k: constant of variation.
We must find the constant k, for this we use the following data:
y = 24 when x = 8
Substituting values:
Clearing k we have:
Therefore, the equation is:
Thus, substituting x = 10 we have that the value of y is given by:
Answer:
the value of y when x = 10 is:
The generic equation of the line is given by:
Where,
m: slope of the line
b: cutting point with the y axis
Substituting values we have:
Answer:
an equation for the line with slope 2/3 and y-intercept is:
Question 2:
The standard equation of the line is given by:
Where,
m: slope of the line
(xo, yo): ordered pair that belongs to the line
The slope of the line is:
Substituting values:
We choose an ordered pair:
Substituting values:
Rewriting:
Answer:
An equation in slope-intercept form for the line that passes through the points (1, -3) and (3,1) is:
Question 3:
For this case, since the variation is direct, then we have an equation of the form:
k: constant of variation.
We then have the following equation:
Answer:
the constant of variation is:
Question 4:
For this case, since the variation is direct, then we have an equation of the form:
k: constant of variation.
We must find the constant k, for this we use the following data:
y = 24 when x = 8
Substituting values:
Therefore, the equation is:
the value of y when x = 10 is: