Using the z-distribution, as we are working with a proportion, it is found that 1016 constituents are required.
<h3>What is a confidence interval of proportions?</h3>
A confidence interval of proportions is given by:
In which:
is the sample proportion.
The margin of error is given by:
In this problem, we have a 95% confidence level, hence
, z is the value of Z that has a p-value of 
, so the critical value is z = 1.96.
The estimate is of 
, while the margin of error is of M = 0.03, hence solving for n we find the minimum sample size.
Rounding up, 1016 constituents are required.
More can be learned about the z-distribution at brainly.com/question/25890103
Order 3/8, 3/7, and 3/9 from least to greatest without writing equivalent fractions with a common denominator explain your Strategy
3/9 3/8 3/7
The greater the denominator, the smaller the pieces are. Thus, numbers with equivalent numerators but smaller denominators will be larger than those with larger denominators.
Is 0.7 greater than less than equal to 7/9
Less than. 7/9 is 0.77777....
The function shown is f(x)= -1/2 cos(x).
sin(x) makes the line way more “curverier” So both sin(x) functions are out. It is NOT 1/2 cos(x) because it would make the y-intercept 0, not .5 In the picture it’s starting at .5 so it’s f(x)=-1/2 cos(x)
Answer:
72 feet from the shorter pole
Step-by-step explanation:
The anchor point that minimizes the total wire length is one that divides the distance between the poles in the same proportion as the pole heights. That is, the two created triangles will be similar.
The shorter pole height as a fraction of the total pole height is ...
18/(18+24) = 3/7
so the anchor distance from the shorter pole as a fraction of the total distance between poles will be the same:
d/168 = 3/7
d = 168·(3/7) = 72
The wire should be anchored 72 feet from the 18 ft pole.
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<em>Comment on the problem</em>
This is equivalent to asking, "where do I place a mirror on the ground so I can see the top of the other pole by looking in the mirror from the top of one pole?" Such a question is answered by reflecting one pole across the plane of the ground and drawing a straight line from its image location to the top of the other pole. Where the line intersects the plane of the ground is where the mirror (or anchor point) should be placed. The "similar triangle" description above is essentially the same approach.
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Alternatively, you can write an equation for the length (L) of the wire as a function of the location of the anchor point:
L = √(18²+x²) + √(24² +(168-x)²)
and then differentiate with respect to x and find the value that makes the derivative zero. That seems much more complicated and error-prone, but it gives the same answer.
