A medical study investigated the effect of calcium and vitamin supplements on the risk of older Americans for broken bones. A total of 389 older Americans who lived at home and were in good health were studied over a three-year period. While all of the 389 people took in at least 700 milligrams of calcium and 200 units of vitamin D through their normal diet, 187 of them were given additional supplements containing 500 milligrams of calcium citrate and 70 units of vitamin D daily. Of the 187 who took additional supplements, 11 of them suffered broken bones over the three-year period. Of the 202 older Americans who did not take the additional supplement, 26 of them suffered broken bones over the study period.

What fraction of older Americans who were included in the study suffered broken bones during the three-year period?

Fraction of older Americans who were included in the study and suffered broken bones during the three-year period = (37/389) = 0.0951

Step-by-step explanation:

The fraction of older Americans who were included in the study and suffered broken bones during the three-year period?

This fraction = (Number of older Americans who suffered broken bones recorded during the three year period of the study)/(Total number of older Americans involved in the study)

Number of older Americans who suffered broken bones recorded during the three year period of the study = (11 from those that took the additional supplements) + (26 from those that did not take additional supplements) = 11 + 26 = 37

Total number of older Americans involved in the study = 389

Fraction of older Americans who were included in the study and suffered broken bones during the three-year period = (37/389) = 0.0951

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step-by-step explanation

2r= 2300

r =1150

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°