Question
In a study for a new medicine, supposed 3/8 the participants experience headaches as a side effect 1/20 other participants experience nausea as a side effect and 13/40 of the participant experience both headaches and nausea. Esther affect as part and be below. Determine the fraction of study, put participants who experience either a headache or nausea as a side effect by valuating 3/8+1/20- 13/40expressed to fractions in lowest terms If there were 2400 participants in the study, determine the number who experienced either headache or nausea as a side effect the number of participants that experience either headache or nausea as a side effects is
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Answer to a math question In a study for a new medicine, supposed 3/8 the participants experience headaches as a side effect 1/20 other participants experience nausea as a side effect and 13/40 of the participant experience both headaches and nausea. Esther affect as part and be below. Determine the fraction of study, put participants who experience either a headache or nausea as a side effect by valuating 3/8+1/20- 13/40expressed to fractions in lowest terms If there were 2400 participants in the study, determine the number who experienced either headache or nausea as a side effect the number of participants that experience either headache or nausea as a side effects is
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To determine the fraction of participants who experience either a headache or nausea as a side effect, we can use the principle of inclusion and exclusion. The formula for this is:
P(\text{headache or nausea}) = P(\text{headache}) + P(\text{nausea}) - P(\text{headache and nausea})
Given:
P(\text{headache}) = \frac{3}{8}
P(\text{nausea}) = \frac{1}{20}
P(\text{headache and nausea}) = \frac{13}{40}
Substitute the values into the formula:
P(\text{headache or nausea}) = \frac{3}{8} + \frac{1}{20} - \frac{13}{40}
Now, find a common denominator and compute the sum:
P(\text{headache or nausea}) = \frac{15}{40} + \frac{2}{40} - \frac{13}{40}
P(\text{headache or nausea}) = \frac{4}{40} = \boxed{\frac{1}{10}}
If there were 2400 participants in the study, the number who experienced either a headache or nausea as a side effect would be:
2400 \times \frac{1}{10} = \boxed{240}
Therefore, the number of participants that experience either a headache or nausea as a side effect is 240.
Given:
Substitute the values into the formula:
Now, find a common denominator and compute the sum:
If there were 2400 participants in the study, the number who experienced either a headache or nausea as a side effect would be:
Therefore, the number of participants that experience either a headache or nausea as a side effect is 240.
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