A swimming pool in the shape of a right rectangular prism measures 24 feet by 16 feet and is 4.5 feet deep across the entire poo
2 answers:
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Answer:
y = 8 is the equation of tangent.
Step-by-step explanation:
The equation of the tangent to the circle at (-6,8) is of the form:
y = mx + c
where m is the slope of the tangent and c is the y-intercept.
The point (-6,8) lies on the circle and the tangent line as well.
Hence (-6,8) satisfies the line equation:
8 = m(-6) + c ⇒ c-6m = 8 -------------1
We know that slope of two perpendicular lines are related as:
At any point on the circle, the normal line at a point is always perpendicular to the tangent line at that point.
Hence :
We can find the slope of the normal at point (-6,8) as it passes through the centre of the circle (-6,4) by using the two-points formula for slope.
= ∞
Slope of the normal is infinity and hence slope of tangent is -1/∞ = 0
Hence m=0
Putting m=0 in equation 1 we get:
c = 8
The equation of tangent line at (-6,8) is:
y = 8
Using the z-distribution, we have that:
a) A sample of 601 is needed.
b) A sample of 93 is needed.
c) A. Yes, using the additional survey information from part (b) dramatically reduces the sample size.
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, we have the following confidence interval of proportions.
In which z is the z-score that has a p-value of .
The margin of error is:
95% confidence level, hence, z is the value of Z that has a p-value of
, so
.
For this problem, we consider that we want it to be within 4%.
Item a:
- The sample size is <u>n for which M = 0.04.</u>
- There is no estimate, hence
Rounding up:
A sample of 601 is needed.
Item b:
The estimate is , hence:
Rounding up:
A sample of 93 is needed.
Item c:
The closer the estimate is to , the larger the sample size needed, hence, the correct option is A.
For more on the z-distribution, you can check brainly.com/question/25404151