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2 years ago

I need help with this please

Mathematics

1 answer:

Yakvenalex [24]2 years ago

3 0

Answer:

∠BIF = 126°

∠JBC = 63°

∠BJD = 117°

Step-by-step explanation:

adjacent angles in a rhombus add up to 180°

∠IBJ and ∠BIF are adjacent angles in a rhombus

thus,

∠IBJ + ∠BIF = 180°

54° + ∠BIF = 180

subtract 54 from both sides to isolate the variable

∠BIF = 126°

a line is 180°

thus, ∠IBA + ∠IBJ + ∠JBC = 180° as those three angles form a line

as the parallelograms are congruent, and we can visually notice that ∠IBA corresponds to angle ∠JBC, we can say that ∠IBA = ∠JBC

thus,

∠IBA + ∠IBJ + ∠JBC = 180°

54° + ∠JBC + ∠JBC = 180°

54° + 2∠JBC = 180

subtract 54 from both sides to isolate the variable and its coefficient

126° = 2∠JBC

divide 2 from both sides to isolate the variable

∠JBC = 63°

adjacent angles in a parallelogram add up to 180°

∠JBC and ∠BJD are adjacent angles in a parallelogram

∠JBC + ∠BJD = 180°

63° + ∠BJD = 180°

subtract 63 from both sides to isolate the variable

∠BJD = 117°

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The probability that a test is positive, given that the person is sick is 0.9833
The probability that a test is negative, given that the person is not sick is: 0.9899
The probability that a person is sick, given that the test is positive is: 0.4403
The probability that a person is not sick, given that the test is negative is: 0.9998
A 99% accurate test is a correct test

(a) Probability that a person is sick

From the table, we have:

$\mathbf{Sick = 59+1 = 60}$

So, the probability that a person is sick is:

$\mathbf{Pr = \frac{Sick}{Total}}$

This gives

$\mathbf{Pr = \frac{60}{7500}}$

$\mathbf{Pr = 0.008}$

The probability that a person is sick is: 0.008

(b) Probability that a test is positive, given that the person is sick

From the table, we have:

$\mathbf{Positive\ and\ Sick=59}$

So, the probability that a test is positive, given that the person is sick is:

$\mathbf{Pr = \frac{Positive\ and\ Sick}{Sick}}$

This gives

$\mathbf{Pr = \frac{59}{60}}$

$\mathbf{Pr = 0.9833}$

The probability that a test is positive, given that the person is sick is 0.9833

(c) Probability that a test is negative, given that the person is not sick

From the table, we have:

$\mathbf{Negative\ and\ Not\ Sick=7365}$

$\mathbf{Not\ Sick = 75 + 7365 = 7440}$

So, the probability that a test is negative, given that the person is not sick is:

$\mathbf{Pr = \frac{Negative\ and\ Not\ Sick}{Not\ Sick}}$

This gives

$\mathbf{Pr = \frac{7365}{7440}}$

$\mathbf{Pr = 0.9899}$

The probability that a test is negative, given that the person is not sick is: 0.9899

(d) Probability that a person is sick, given that the test is positive

From the table, we have:

$\mathbf{Positive\ and\ Sick=59}$

$\mathbf{Positive=59 + 75 = 134}$

So, the probability that a person is sick, given that the test is positive is:

$\mathbf{Pr = \frac{Positive\ and\ Sick}{Positive}}$

This gives

$\mathbf{Pr = \frac{59}{134}}$

$\mathbf{Pr = 0.4403}$

The probability that a person is sick, given that the test is positive is: 0.4403

(e) Probability that a person is not sick, given that the test is negative

From the table, we have:

$\mathbf{Negative\ and\ Not\ Sick=7365}$

$\mathbf{Negative = 1+ 7365 = 7366}$

So, the probability that a person is not sick, given that the test is negative is:

$\mathbf{Pr = \frac{Negative\ and\ Not\ Sick}{Negative}}$

This gives

$\mathbf{Pr = \frac{7365}{7366}}$

$\mathbf{Pr = 0.9998}$

The probability that a person is not sick, given that the test is negative is: 0.9998

(f) When a test is 99% accurate

The accuracy of test is the measure of its sensitivity, prevalence and specificity.

So, when a test is said to be 99% accurate, it means that the test is correct, and the result is usable; irrespective of whether the result is positive or negative.