It is usually noted that correlation does not imply causation, but there are some correlations which are causation as well.
A correlation is when there is a relationship between two variables while causation is when the outcome of one variable affects the outcome of the other variable.
From the first option, though there may be a positive relationship between sales of jeans and sales of slacks, but the purchase of jeans does not mean that you have to purchase a slack, thus, there is no causation.
For the second option, though there may be positive relationship between <span>the number of aisles and the number of products in a supermarket, but a supermarket can have many aisles with few products, i.e. many aisles does not automatically imply many products, thus, there is no causation.
For the third option, though there may be a positive relationship between </span><span>the number of swimmers and the number of sunbathers at a beach, but all swimmers in a beach are not sunbathers and all sunbathers are not swimmers. Thus, a swimmer does not imply a sunbather and a sunbather does not imply a swimmer. Thus, there is no causation.
For the last option, it is generally known that the more you practice an activity, the better you get in that activity. Thus, there exist a relationship between </span><span>the number of hours spent practicing archery and the number of bull's-eyes an archer can hit and there also exist causation because the number of bull's-eye an archer can hit is directly dependent on the number of hours the archer spent practicing.
Therefore, the </span><span>correlation that is most likely a causation is </span><span>the positive correlation between the number of hours spent practicing archery and the number of bull's-eyes the archer can hit.</span>
Answer:
Option B
<em>The best point estimate of the proportion of people attending the game who believe that the concession stand should be closer to the stands is:</em>
<em>p = 0.72.</em>
Step-by-step explanation:
We want to estimate the proportion of people who feel that the stand should be closer to the stands.
We have a sample of 150 people, of which 108 think that the stand should be closer to the stands.
A point estimator for the proportion p is 
.
Where
Where n represents the size of the sample and represents the number of favorable cases.
We know that 
and 
.
Then we can estimate p by the estimator
The algebraic proof shows that the angles in an equilateral triangle must equal 60° each
<h3>Laws of cosines </h3>
From the question, we are to use the law of cosines to write an algebraic proof that shows that the angles in an equilateral triangle must equal 60°.
Given any triangle ABC, the measures of angles A, B, and C by the law of cosines are
cos A = (b^2 + c^2 - a^2)/2bc
cos B= (a^2 + c^2 - b^2)/2ac
cos C = (a^2 + b^2 - c^2)/2ab
Now, given that the triangle is equilateral, with each of the side lengths equal to s
That is, a = b = c = s
Then, we can write that
cos A = (s^2 + s^2 - s^2)/(2s×s)
cos A = (s^2 )/(2s^2)
cos A = 1/2
cos A = 0.5
∴ A = cos⁻¹(0.5)
A = 60°
Also
cos B = (s^2 + s^2 - s^2)/(2s×s)
cos B = (s^2 )/(2s^2)
cos B = 1/2
cos B = 0.5
∴ B = cos⁻¹(0.5)
B = 60°
and
cos C = (s^2 + s^2 - s^2)/(2s×s)
cos C = (s^2 )/(2s^2)
cos C = 1/2
cos C = 0.5
∴ C = cos⁻¹(0.5)
C = 60°
Thus,
A = 60°, B = 60° and C = 60°
Hence, the algebraic proof above shows that the angles in an equilateral triangle must equal 60° each.
Learn more on The law of cosines here: brainly.com/question/2866347
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Answer:
C / four-fifths
Step-by-step explanation:
Answer: In 12 months they will have the same amount, which will be $520.
Step-by-step explanation:
220 + 25m = 100 + 35m
m = month
Subtract 100 from each side
120 + 25m = 35m
Subtract 25m from each side
120 = 10m
Divide each side by 10
12 = m
