ΔAXY is similar to ΔABC.
1 answer:
The expression that can be used to determine the length of segment AB is: A. AB = (AX × AC)/AY.
<h3>When are Two Triangles Similar to Each Other?</h3>When the corresponding sides of two triangles have ratios that are equal, or have corresponding side lengths that are proportional to each other, both triangles are considered similar triangles to each other.
Given that triangles AXY and ABC are similar triangles sharing a common vertex A, therefore, the corresponding sides will have equal ratio which can be expressed as:
AB/AX = BC/XY = AC/AY
To find the length of segment AB, we would do the following:
AB/AX = AC/AY
Cross multiply
(AB)(AY) = (AX)(AC)
Divide both sides by AY
(AB × AY)/AY = (AX × AC)/AY
AB = (AX × AC)/AY
The expression we can use to find the length of segment AB can be:
A. AB = (AX × AC)/AY
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Answer:
a) The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).
b) The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.
Step-by-step explanation:
Question a:
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 .
Sample of 120 registered voters in order to predict the winner of a local election. The Democrat candidate was favored by 62 of the respondents.
So 120 - 62 = 58 favored the Republican candidate, so:
99% confidence level
So , z is the value of Z that has a p-value of
, so
.
The lower limit of this interval is:
The upper limit of this interval is:
The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).
b. If a candidate needs a simple majority of the votes to win the election, can the Republican candidate be confident of victory? Justify your response with an appropriate statistical argument.
The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.