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sveta [45]
3 years ago
7

Two circles have the same radius. Is the combined area of the two circles the same as the area of a circle with twice the radius

? Explain.
Mathematics
1 answer:
Dimas [21]3 years ago
8 0
Ok so area=pir^2

2 circles with same area=2pir^2

circle with 2 times radius=pi(2r)^2=pi4r^2=4pir^2

is 2 circles with same area equal to circle with 2 times radius?
is 2pir^2=4pir^2?
is 2=4?
no


therfor the answer is no

it is because the radius is squaered so the doubled gets doubled makng it quadrupuled when the first one only gets doubled
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A new screening test for Lyme disease is developed for use in the general population. The sensitivity and specificity of the new
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predictive value of a positive test = 18.18%

predictive value of a negative test = 94.03%

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Sensitivity = 60% = 0.6

Specificity = 70% = 0.7

Let True Positive = TP

True Negative = TN

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Sensitivity = \frac{TP}{TP + FN} \\0.6 = \frac{TP}{TP + FN} \\0.6TP + 0.6FN = TP\\0.4TP = 0.6FN\\TP = 1.5 FN

Specificity = \frac{TN}{TN + FP} \\0.7 = \frac{TN}{TN + FP} \\0.7TN + 0.7FP = TN\\0.7FP = 0.3 TN\\TN  = 7/3 FP

Prevalence = 10% = 0.1

Three hundred people are screened, T_{total} = 300

Total number of people having the disease, T_{disease} = ?

Prevalence = \frac{T_{disease} }{T_{total} } \\0.1 =  \frac{T_{disease} }{300 }\\T_{disease} = 30

T_{disease} = TP + FN\\30 = TP + FN

But TP = 1.5 FN

30 = 1.5 FN + FN

30 = 2.5 FN

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FP + TN = T_{total} - T_{disease} \\FP + TN = 300 - 30\\FP + TN = 270\\FP + \frac{7}{3} FP = 270\\\frac{10}{3} FP = 270\\FP = 27 * 3\\FP = 81

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To calculate the Predictive value of positive test (PPT)

PPT = \frac{TP}{TP + FP} * 100\\PPT = \frac{18}{18+81} * 100\\PPT = \frac{18}{99} * 100\\PPT = 18.18 \%

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