davelopez979

26.05.2021 • 

Mathematics

In 2014, the Center for Disease Control and Prevention (CDC) published results from their National Health Interview Survey about circulatory diseases among American adults based on numerous characteristics. The table displays the percentage of adults in four age groups who have been diagnosed with heart disease and the sample sizes for each group. Age (years) Percentage with heart disease Sample size
18−44 4.3% 112,149,000
45−64 12.0% 82,605,000
65−74 24.6% 26,362,000
75 and over 35.0% 18,573,000
What is the standard error (SE) and the margin of error ( ) for a 99 % confidence interval for the difference in proportion of adults ages 65–74 with heart disease and adults ages 75 and over with heart disease? solve for SE and M

Ответ:

jaaiphieaslade

05.03.2023

Mathematics

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We can prove this by doing a statement and reason (more or less). The first thing we need to do is a construction of segment OG which is parallel to BC and touches A. Since it forms a straight line, we can say that m<OAB + m<A + m<GAC is equal to 180° (because it is a straight line). But, by alternate interior angles theorem, we can say that m<B = m<OAB and m<C = m<GAC. Therefore, by transitivity, m<A + m<B + m<C = 180°. Since angles A, B, and C are the interior angles of triangle ABC, we proved that the sum of the interior angles of ABC is 180°.

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