I research or chooses a random sample of registered voters in Kingsville he found that three out of every five voters surveyed s
aid they would vote for Miguel Miller for mayor if there are 80 eligible voters in Kentsville protects how many of these voters would choose Miguel Miller for mayor
Why would the sample Above be good for which to draw a valid inference?
a. The sample above is taken from a convenience sample there for the people who are easiest to reach answering the questions
B. The sample Bob is not a good one for which to draw a valid inference
C. The sample book was choosing randomly therefore each member of the population had a same chance of being selected
D. The Stemple above was taken from volunteers there for their responses were based on strong opinions
Why would the sample Above be good for which to draw a valid inference?
a. The sample above is taken from a convenience sample there for the people who are easiest to reach answering the questions
B. The sample Bob is not a good one for which to draw a valid inference
C. The sample book was choosing randomly therefore each member of the population had a same chance of being selected
D. The Stemple above was taken from volunteers there for their responses were based on strong opinions
1 answer:
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A suitable vector calculator can perform this arithmetic directly, as can many graphing or scientific calculators that are capable of handling complex numbers. Mine says
(8, 2π/3) - (4, π/3) = (4√3, 5π/6)
The distance is 4√3 ≈ 6.9282.
If you cannot use your calculator for this purpose, you can use the Law of Cosines. You have two sides of the triangle (4 and 8) and the angle between them (2π/3 - π/3), so you have all the information needed.
c² = a² + b² -2ab·cos(C)
c² = 4² + 8² - 2·4·8·cos(π/3)
c² = 16 + 64 - 32 = 48
c = √48 = 4√3
Or, you can simply recognize that the two vectors have the ratio 1:2 and the angle between them is 60°. That is, they are one leg and the hypotenuse of a 30°-60°-90° triangle, so the other leg is 4√3.
(8, 2π/3) - (4, π/3) = (4√3, 5π/6)
The distance is 4√3 ≈ 6.9282.
If you cannot use your calculator for this purpose, you can use the Law of Cosines. You have two sides of the triangle (4 and 8) and the angle between them (2π/3 - π/3), so you have all the information needed.
c² = a² + b² -2ab·cos(C)
c² = 4² + 8² - 2·4·8·cos(π/3)
c² = 16 + 64 - 32 = 48
c = √48 = 4√3
Or, you can simply recognize that the two vectors have the ratio 1:2 and the angle between them is 60°. That is, they are one leg and the hypotenuse of a 30°-60°-90° triangle, so the other leg is 4√3.