Answer:
Step-by-step explanation:
Given
See attachment for her sketch
Required
Which equation do not represent the perimeter
From the attached sketch:
--- Length
--- Width
Perimeter (P) is calculated as:
This gives:
---- This represents (A)
Open bracket
---- This represents (B)
In algebra:
means
So, the expression becomes
--- This represents (D)
<em>This implies that (C) does not represent the perimeter</em>
The equation of the line is, .
Given that,
The equation of the line is,
And contains the point (-2, -5).
We have to determine,
What is the equation of the line that is perpendicular to the given line?
According to the question,
The equation of the line is,
On comparing with the standard equation of the line y = mx +c.
The slope of the line is 1/3.
When two lines are perpendicular the relation between these slopes is,
And line contains the point (-2, -5).
Then,
Therefore,
The equation of the line that is perpendicular to the given line and contains the point (-2, -5) is,
Hence, The required equation of the line is, .
For more details refer to the link given below.
Answer:
n=350
Step-by-step explanation:
Notation and definitions
random sample taken (variable of interest)
estimated proportion (value assumed)
true population proportion
Confidence =0.95 or 95% (value assumed)
Me=0.05 (value assumed)
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".
The population proportion have the following distribution
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
And replacing into equation (b) the values from part a we got:
And rounded up we have that n=350
We are asked to prove by the method of mathematical induction that:
where n is a positive integer.
then we have:
Hence, the result is true for n=1.
i.e.
i.e.
<u>To prove:</u>
Let us take n=k+1
Hence, we have:
( Since, the result was true for n=k )
Hence, we have:
Also, we know that:
(
Since, for n=k+1 being a positive integer we have:
)
Hence, we have finally,
Hence, the result holds true for n=k+1
Hence, we may infer that the result is true for all n belonging to positive integer.
i.e.
where n is a positive integer.