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Gemiola [76]
3 years ago
9

A bike path crosses a road as shown. Solve for each indicated angle measure or variable.

Mathematics
1 answer:
Vitek1552 [10]3 years ago
3 0
Given:
84° angle
4x angle
angle M  

The angle that measures 84° and the angle that measures 4x are vertical angles. This means that their angle measures are congruent. Thus, the value of x is 21°

84° = 4x
84° / 4 = x
21° = x

Angle M and the angle that measures 84° are supplementary angles. This means that the sum of their measure equals 180°. Thus, angle M measures 96°.

84° + M = 180°
M = 180° - 84°
M = 96°

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Answer:

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Step-by-step explanation:

The first thing is to calculate critical z factor

the alpha and the critical z score for a confidence level of 90% is calculated as follows:

two sided alpha = (100% - 90%) / 200 = 0.05

critical z factor for two sided alpha of .05 is calculated as follows:

critical z factor = z factor for (1 - .05) = z factor for (.95) which through the attached graph becomes:

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Now we have the following formula:

ME = z * (sd / sqrt (N) ^ (1/2))

where ME is the margin of error and is equal to 6, sd is the standard deviation which is 14 and the value of z is 2.58

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solving for N we have:

N = (2.58 * 14/6) ^ 2

N = 36.24

Which means that the sample size was 37.

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Step-by-step explanation:

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