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Paraphin [41]
3 years ago
8

Explain how you can use the inscribed angle theorem to justify its second corollary

Mathematics
2 answers:
Aleksandr [31]3 years ago
8 0

Answer:

A circle measures 360 degrees, so a semicircle measures 180 degrees. By using the inscribed angle theorem, the measure of the inscribed angle would be half of 180 degrees, or 90 degrees, which is a right angle.

Step-by-step explanation:

A circle measures 360 degrees, so a semicircle measures 180 degrees. By using the inscribed angle theorem, the measure of the inscribed angle would be half of 180 degrees, or 90 degrees, which is a right angle.

kirill [66]3 years ago
5 0

Answer:

The angle inscribed in a semicircle is a right angle. The inscribed angle theorem states that the angle θ, inscribed in a circle is half the measure of the central angle of the circle. So, if the given is a semi-circle, then the inscribed angle is half of 180, therefore, 90 degrees and a right angle

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Answer:

4 miles

Step-by-step explanation

If your mom can walk 1 mile in 14 minutes then 2 miles would take her 28 minutes 3 miles would take her 42 minutes and finally if she walked 4 miles it would take her 56 minutes.

14 + 14 + 14 + 14 = 56

14 x 4 = 56

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Find the ratio of the given one: 20/200 = 0.1


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Solve the initial-value problem<br><br> y' = x^4 - \frac{1}{x}y, y(1) = 1.
natta225 [31]

The ODE is linear:

y'=x^4-\dfrac yx

y'+\dfrac yx=x^4

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xy'+y=x^5

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(xy)'=x^5

Integrating both sides with respect to x yields

xy=\dfrac{x^6}6+C

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Since y(1)=1,

1=\dfrac16+C\implies C=\dfrac56

so that

\boxed{y(x)=\dfrac{x^5}6+\dfrac5{6x}}

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3 years ago
A new screening test for Lyme disease is developed for use in the general population. The sensitivity and specificity of the new
Anit [1.1K]

Answer:

predictive value of a positive test = 18.18%

predictive value of a negative test = 94.03%

Step-by-step explanation:

Sensitivity = 60% = 0.6

Specificity = 70% = 0.7

Let True Positive = TP

True Negative = TN

False Negative = FN

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

FN = 30/2.5

FN = 12

TP = 1.5 FN = 1.5 * 12

TP = 18

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

81 + TN = 270

TN = 189

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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PPT = \frac{TN}{FN + TN} * 100\\PPT = \frac{189}{189+12} * 100\\PPT = \frac{189}{201} * 100\\PPT = 94.03 \%

7 0
3 years ago
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