Question
The equation is y= 0.58755X + 7.16117
If the systolic pressures of two patients differ by 19 millimeters, by how much would you predict their diastolic pressures to differ? Round the answer to three decimal places.
If the systolic pressures of two patients differ by 19 millimeters, by how much would you predict their diastolic pressures to differ? Round the answer to three decimal places.
Answers
Answer
Predict the diastolic pressure for a patient whose systolic pressure is 125 millimeters. Round the answer to one decimal place.
Answered by
GPT-4o mini
To solve this problem, we can start with the given equation for \( y \), which represents diastolic pressure in terms of \( X \), which represents systolic pressure:
\[
y = 0.58755X + 7.16117
\]
Given that the difference in systolic pressures of two patients is \( 19 \) mm, we can express their systolic pressures as \( X_1 \) and \( X_2 \):
\[
|X_2 - X_1| = 19
\]
Let's find the difference in diastolic pressures (\( y_2 - y_1 \)) corresponding to the difference in systolic pressures \( X_2 - X_1 \).
The diastolic pressures can be expressed as:
\[
y_1 = 0.58755X_1 + 7.16117
\]
\[
y_2 = 0.58755X_2 + 7.16117
\]
Now, subtract the two equations to find the difference in diastolic pressures:
\[
y_2 - y_1 = (0.58755X_2 + 7.16117) - (0.58755X_1 + 7.16117)
\]
This simplifies to:
\[
y_2 - y_1 = 0.58755(X_2 - X_1)
\]
We need to calculate \( |y_2 - y_1| \):
\[
|y_2 - y_1| = 0.58755 |X_2 - X_1|
\]
With \( |X_2 - X_1| = 19 \):
\[
|y_2 - y_1| = 0.58755 \times 19
\]
Calculating this gives:
\[
|y_2 - y_1| = 11.15645
\]
Finally, rounding this to three decimal places:
\[
|y_2 - y_1| \approx 11.156
\]
Thus, the predicted difference in diastolic pressures is approximately **11.156** mm.
\[
y = 0.58755X + 7.16117
\]
Given that the difference in systolic pressures of two patients is \( 19 \) mm, we can express their systolic pressures as \( X_1 \) and \( X_2 \):
\[
|X_2 - X_1| = 19
\]
Let's find the difference in diastolic pressures (\( y_2 - y_1 \)) corresponding to the difference in systolic pressures \( X_2 - X_1 \).
The diastolic pressures can be expressed as:
\[
y_1 = 0.58755X_1 + 7.16117
\]
\[
y_2 = 0.58755X_2 + 7.16117
\]
Now, subtract the two equations to find the difference in diastolic pressures:
\[
y_2 - y_1 = (0.58755X_2 + 7.16117) - (0.58755X_1 + 7.16117)
\]
This simplifies to:
\[
y_2 - y_1 = 0.58755(X_2 - X_1)
\]
We need to calculate \( |y_2 - y_1| \):
\[
|y_2 - y_1| = 0.58755 |X_2 - X_1|
\]
With \( |X_2 - X_1| = 19 \):
\[
|y_2 - y_1| = 0.58755 \times 19
\]
Calculating this gives:
\[
|y_2 - y_1| = 11.15645
\]
Finally, rounding this to three decimal places:
\[
|y_2 - y_1| \approx 11.156
\]
Thus, the predicted difference in diastolic pressures is approximately **11.156** mm.
Answered by
GPT-4o mini
To predict the diastolic pressure for a patient with a systolic pressure of \(X = 125\) mm, we can use the given equation:
\[
y = 0.58755X + 7.16117
\]
Substituting \(X\) with \(125\):
\[
y = 0.58755(125) + 7.16117
\]
Calculating the first part:
\[
0.58755 \times 125 = 73.44375
\]
Now, adding the constant:
\[
y = 73.44375 + 7.16117 = 80.60492
\]
Rounding this to one decimal place:
\[
y \approx 80.6
\]
Therefore, the predicted diastolic pressure for a patient with a systolic pressure of 125 mm is **80.6 mm**.
\[
y = 0.58755X + 7.16117
\]
Substituting \(X\) with \(125\):
\[
y = 0.58755(125) + 7.16117
\]
Calculating the first part:
\[
0.58755 \times 125 = 73.44375
\]
Now, adding the constant:
\[
y = 73.44375 + 7.16117 = 80.60492
\]
Rounding this to one decimal place:
\[
y \approx 80.6
\]
Therefore, the predicted diastolic pressure for a patient with a systolic pressure of 125 mm is **80.6 mm**.
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