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The minimum dosage for a medicine is linearly related to the weight of a person. You find that your dosage at 110 pounds is 48 milliliters, and your brother's dosage at 160 pounds is 63 milliliters.

How many milliliters of dosage is required for a 130-pound person?

Answer :

Final answer:

The dosage for a 130-pound person, based on the linear relationship given, is calculated to be 54 milliliters.

Explanation:

To find the dosage for a 130-pound person based on the linear relationship between weight and dosage provided, we first establish the equation of the line.

We have two points: (110, 48) and (160, 63), where the first number in each pair is the weight in pounds and the second number is the dosage in milliliters.

To find the slope (m) of the line, we use the formula m = (y2 - y1) / (x2 - x1), which gives us m = (63 - 48) / (160 - 110) = 15 / 50 = 0.3. So, the slope of our line is 0.3 mL/pound.

Next, we use the point-slope formula to find the equation of the line. Choosing the point (110, 48), we have y - 48 = 0.3(x - 110). Simplifying, we get y = 0.3x + 15.

To find the dosage for a 130-pound person, substitute 130 for x in the equation: y = 0.3(130) + 15 = 54 milliliters.

Therefore, a 130-pound person would require a dosage of 54 milliliters.

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