A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 90​% of the time when the person has the virus and ​15% of the time when the person does not have the virus.​ (This 15​% result is called a false positive​.) Let A be the event​ "the person is​ infected" and B be the event​ "the person tests​ positive." ​(a) Using​ Bayes' Theorem, when a person tests​ positive, determine the probability that the person is infected. ​(b) Using​ Bayes' Theorem, when a person tests​ negative, determine the probability that the person is not infected.

Answers

Answer 1

Answer:

a)  P[A/B] = 0,019     or     P[A/B] = 1,9 %

b)  P[A- /B-] = 0,9996       or    P[A- /B-] = 99,96 %

Step-by-step explanation:

Bayes Theorem :

P[A/B]  =  P(A) * P[B/A] / P(B)

The branches of events are as follows

Condition 1        real infection     1/300        and     not infection  299/300

Then

1.-    1/300      299/300

When the test is done   (virus present)  0,9 (+)    0,15 (-)

2.-   299/300

When the test is done  ( no virus )   0,15  (+)     0,85 (-)

Then:

P(A) = event person infected          P(B)  =  person test positive

a) P[A/B]  = P(A) * P[B/A] / P(B)

where   P(A)  = 1/300  =   0,0033   P[B/A] = 0,9    

Then P(A) * P[B/A] =  0,0033*0,9  =  0,00297

P(B)   is    ( 1/300 )*0,9  +  (299/300)*0,15

P(B) = 0,0033*0,9 + 0,9966*0,15    ⇒  P(B) = 0,1524

Finally

P[A/B] =  0,00297 /0,1524

P[A/B] = 0,019     or     P[A/B] = 1,9 %

b) Following sames steps:

P[A- /B-] = (299/300) * 0,85  / (299/300) * 0,85 + (1/300 * 0,1)

P[A- /B-] = 0,8471 /0,8474

P[A- /B-] = 0,9996       or    P[A- /B-] = 99,96 %


Related Questions

Is everything correct and how do you do the last part?

Answers

Answer:

5 terms

Step-by-step explanation:

Yes, that's correct.  For the last part, set b₊₁ less than or equal to the error.

1 / (5ⁿ⁺¹ (n+1)!) ≤ 0.000005

5ⁿ⁺¹ (n+1)! ≥ 200,000

Use trial and error to find the value of n (notice that n starts at 0).

n = 0, 5ⁿ⁺¹ (n+1)! = 5

n = 1, 5ⁿ⁺¹ (n+1)! = 50

n = 2, 5ⁿ⁺¹ (n+1)! = 750

n = 3, 5ⁿ⁺¹ (n+1)! = 15,000

n = 4, 5ⁿ⁺¹ (n+1)! = 375,000

n = 4 is the fifth term.  So it takes 5 terms.

5) Boat World charges an initial price of $20 plus $12.50 per hour for canoe rentals, which is
represented by the expression 20 + 12.5h.
• Complete each statement to describe the terms.

Answers

Answer:

The variable "h" represents: The number of hours

The constant 20 represents: the initial rental price

The variable term 12.5h represents: the hourly rental amount

Step-by-step explanation:

−18x+21>−15 OR 20x−13≥27

Answers

Answer:

I dont know what is your question, but I solved this.

Step-by-step explanation:

-18x>-15-21

-18x>-36

x<2

20x>=27+13

20x>=40

x>2

is 1.36 a rational number or irrational number

Answers

Answer:

No an irrational number

Step-by-step explanation:

An irrational number is a number that cannot be expressed as a fraction of two integers . -1.36 can be expresed as -136/100

Answer:

Rational!

Step-by-step explanation:

Any number that can be written in fraction form is a rational number. This includes integers, terminating decimals, and repeating decimals as well as fractions. So, any terminating decimal is a rational number. Any decimal number that is repeating can be written in the form a/b with b not equal to zero so it is a rational number.

I hope this helps you understand what a rational number is! Have a wonderful day!

PLEASE HELP!!! ILL GIVE BRAINLIEST THIS IS WORTH 10 POINTS PLEASE (ignore where it says 8&2 points it’s how much the question adds up to in the grade book)

Answers

Answer:

Since the points X , Y and Z are collinear:

For the diagram, you just have to draw a line and mark the end-points of the line as X and Z and mark the mid-point of the line as Y

Since we are given that XY = YZ,

We will replace with the provided values:

XY = YZ

4(x + 5) = 2(x + 11)

4x + 20 = 2x + 22

2x = 2

x = 1

Since x = 1 and XY = YZ,

We can say that:

XZ = XY + YZ

XZ = XY + XY   or       XZ = 2XY

Now, replacing the variables for the value of XZ

XZ = 2XY

XZ = 2(4x + 20)

XZ = 2(4 + 20)              (Since x = 1)

XZ = 48 units

what is 3/4r+2r+1/2r

Answers

13/4r

Hope this helps you!!

Find the equation of the line
passing through the points. (5, 2) and (10, 6).??

Answers

Answer: y=(4/5)x-2

Assuming this is a liner function, you must first find the slope through the point slope formula [(y2-y1)/(x2-x1)]. When you plug in the corresponding values [(6-2)/(10-5)], your slope value should be 4/5.

After this, apply the slope to the x-values to find the intercept. For example, 10 x 4/5 is 8. To get to 6, you must subtract 2. This means your intercept value is -2

Therefore, your equation is y=(4/5)x-2

Can someone explain how to solve these? I have 10 questions I need to answer for problems like this & I can't go on until I solve it, so I just need the answer for this one and how to solve it. I need it finished fast because I need to bring up a low grade. Any help would be appreciated.

Answers

the value of x is 32°. i believe they’re called internal inverses? it’s because lines m and n are parallel. i’m not sure how else to explain, hope this helped!

The perimeter of a rectangular solar panel is 540 cm. The ratio of the length to the width is 3 : 2. What are the length and width?

Answers

Total number of parts = 3 + 2 = 5 parts

[tex]each \: part \: = \frac{(540 \div 5)}{2} \: m[/tex]

[tex] \\ each \: part \: = \frac{108}{2} m \: \\ \\ each \: part \: = 54 \: m[/tex]

Then , the length of this triangle :

[tex]54 \times 3 \: m[/tex]

[tex] = 162 \: m[/tex]

Then , the width of this triangle will be :

[tex]54 \times 2 \: m[/tex]

[tex]108 \: m[/tex]

∴ The length of this rectangle is 162 m and the width of this rectangle is 108 m .

pls help rn if possible

Answers

Answer:

I would type these in Math-Way, then select Solve the system of equations (or inequalities, I forget which one). (4, -1, 0) would be the answer.

I WILL GIVE BRAINLIEST TO WHOEVER HELPS ME!!

Answers

Answer:

it changes by -4 pounds each month

Step-by-step explanation:

20 pounds in 5 months

20/5 is 4 pounds per month

the elephant loses 4 pounds a month

Ten years ago, Lisa bought a hair salon for 182000 dollars. She built up the business and it is now
worth nine times what she paid for it. She decides to sell half of the business to a friend, and they
become partners. Express the amount Lisa's friend must pay Lisa to buy half the business.

Answers

Answer: 819,000

Step-by-step explanation:

182000×9=1638000÷2=819000

Lisa's friend must pay Lisa $819,000 to become her partner in the business, half the worth of Lisa's business today.

What do we mean by the worth of an object?

The worth of an object is the price of that object currently. The worth of almost every object in this world is variable (not fixed) with time and use.

How do we solve the given question?

In the question, we are said that ten years ago, Lisa bought a hair salon for $182,000. Her business is now worth nine times what she paid.

Worth of the business 10 years ago = $182,000.

Worth of the business now = 9*$182,000 = $1,638,000

We have been informed that Lisa has decided to sell half of her business to a friend. We are asked to find the amount her friend needs to pay, to become her partner.

As we have been told, she is selling half of her business, her friend will need to pay half of her business' worth at the present date.

∴ Her friend pays the amount = 1/2 * worth of the business now

or, Her friend pays the amount = 1/2 * $1,638,000

or, Her friend pays the amount = $819,000.

∴ Lisa's friend must pay Lisa $819,000 to become her partner in the business, half the worth of Lisa's business today.

Learn more about the worth of an object at

https://brainly.com/question/1877466

#SPJ2

HELP ME QUICK PLEASEE!!
4. (03.03 HC)
The table shows the outputs, y, for different inputs, x:
Input (x) 3 4 5 6
Output (y) 3 4 5 6
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Part B: Compare the data in the table with the relation f(x) - 2x + 16. Which relation has a greater value when x = 6? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) - 40? (5 points)
(10 points)

Answers

Answer:

  A) is a function

  B) f(x) is greater

  C) x = 12

Step-by-step explanation:

A) Yes, the relation is a function.

A function has a unique input value for each output value. There are no repeated x-values, so this relation is a function.

__

B) The table says y=6 for x=6.

  f(6) = 2(6)+16 = 28

f(x) has a greater value for x=6.

__

C) Substituting the given information, we have ...

  40 = 2x +16

  24 = 2x

  12 = x

The value of x is 12 when f(x) is 40.

Some students are planning to sell gourmet popcorn at a school fundraiser. They plan to offer cheese popcorn and peanut butter popcorn. The table shows the cost of the ingredients for each type of popcorn and the price at which the students plan to sell the popcorn.

The students want to make and sell 100 containers of popcorn. They can spend at most $50 for the ingredients for each type of popcorn and the price at which the students plan to sell the popcorn.

Answers

Answer : 5 Step-by-step explanation:

2c + y = 7 solve for y​

Answers

Answer:

y = 7 - 2c

Step-by-step explanation:

Step 1:

2c + y = 7      Equation

Step 2:

y = 7 - 2c    Subtract 2c on both sides

Answer:

y = 7 - 2c

Hope This Helps :)

Answer:

y = 7 - 2c

Step-by-step explanation:

2c + y = 7

=> y = 7 - 2c

the national debt is $22,000,000,000,000 and the population is 280,000,000. what is the amount of debt per person?

Answers

Answer:

78571.43 dollars

Step-by-step explanation:

brainliest appreciated

I think of a number.

I multiply this number by 8, then subtract 66
The result is twice the number that I was thinking of.

What is the number I was thinking of?

Answers

8x-66=2x (write it out as algebra)
6x=66(put the x’s on one side)
x=11 (simplify)

Answer:

11

Step-by-step explanation:

Set up:

8x - 66 = 2x -> Subtract 2x from either side

8x - 2x = 66 -> Simplify

6x = 66 -> Divide either side by 6

x = 66/6 = 11

The number is 11

A green grocer has 180 mangoes to sell. She has to arrange them in piles of 9, 10 or 12mangoes.
In which ways would she arrange the mangoes without any remaining?​

Answers

Answer:

in piles of 9,10 &12

Step-by-step explanation:

this is because if you divide 180 by each number there is no remainder hence the green grocer can arrange in any way.

It is possible to arrange the total of mangoes by using 20 piles of 9 mangoes, 18 piles of 10 mangoes, or 15 piles of 12 mangoes.

What is division?

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

The conditions for mangoes to be arranged are that the piles should have either 9, 10 or 12 mangoes and reminders are not allowed. This means you need to fit all the mangoes and no mangoes can be left.

Based on the conditions and the total number of mangoes (180 mangoes), here are the possibilities that you can determine using division:

9 mangoes piles: 180/ 9 = 20 piles (9 x 20 = 180 with no remainders)

10 mangoes piles: 180/10 = 18 piles (10 x 18 = 180 with no remainders)

12 mangoes piles: 180/12 = 15 piles (12 x 15 = 180 with no remainders)

Hence, It is possible to arrange the total of mangoes by using 20 piles of 9 mangoes, 18 piles of 10 mangoes, or 15 piles of 12 mangoes.

Learn more about division in

brainly.com/question/369266

#SPJ2

Retailers will buy 45 Wi-Fi routers from a wholesaler if the price is $10 each but only 20 if the price is $85. The wholesaler will supply 56 routers at $46 each and 70 at $50 each. Assuming that the supply and demand functions are linear, find the market equilibrium point.

Answers

I believe it’s is 1000

PLZ HELP 100PTS!!! An explanation is welcome

Find the value of t, when d(t)=-24

d(t)=t/2

Answers

Answer:

[tex]t=-48[/tex]

Step-by-step explanation:

We have the function:

[tex]d(t)=\frac{t}{2}[/tex]

And we want to find t when:

[tex]d(t)=-24[/tex]

So, let's substitute -24 for our first equation and solve for t:

[tex]-24=\frac{t}{2}[/tex]

Multiply both sides by 2:

[tex]t=-48[/tex]

So, the value of t when d(t)=-24 is -48.

Answer:

Step-by-step explanation:

Simultaneous Equations
2x+3y=3750, 4x+y=4250

The answer is x=900 and y=650
I just need the steps

Answers

Answer:

It's long but you use Substitution!

Step-by-step explanation:

Let's solve your system by substitution.

2x+3y=3750;4x+y=4250

Rewrite equations:

4x+y=4250;2x+3y=3750

Step: Solve 4x+y=4250 for y:

4x+y = 4250

4x+y+−4x = 4250+−4x (Add -4x to both sides)

y = −4x+4250

Step: Substitute −4x+4250 for y in 2x+3y = 3750:

2x+3y=3750

2x+3(−4x+4250)=3750

−10x+12750=3750 (Simplify both sides of the equation)

−10x+12750+−12750=3750+−12750 (Add -12750 to both sides)

−10x =−9000

−10x = −9000 (Divide both sides by -10)

−10          −10

x=900

Step: Substitute 900 for x in y = −4x+4250:

y=−4x+4250

y=(−4)(900)+4250

y=650 (Simplify both sides of the equation)

Answer:

x=900 and y=650

round 649,418 to the nearest hundred

Answers

Answer:

649,400

Step-by-step explanation:

Answer:

649,420

Step-by-step explanation:

There are 18 girls in Mr. Brimley's math class. If 40% of the students are girls, what is the best estimation for the number of boys in the class?
A. 20
B. 30
C. 40
D. 50

Answers

Answer:Its B I got It right on my test

Step-by-step explanation:

please help me
find dy/dx using implicit differentiation
e^((x+y)/4) +tan(ln(x/y)) = e^sqrt(y)

Answers

Step-by-step explanation:

Taking log both sides :

[tex]( \frac{x + y}{4} ) + \tan( ln( \frac{x}{y} ) ) = \sqrt{y} [/tex]

Differentiate both sides w.r.t x :

[tex] \frac{1}{4} + \frac{1}{4} \frac{dy}{dy} + {sec}^{2} ( ln\frac{x}{y} ) + \frac{y}{x} + \frac{1}{y} - \frac{x}{ {y}^{2} } = \frac{1}{2 \sqrt{y} } \frac{dy}{dx} [/tex]

Rearranging :

[tex]( \frac{4 - 2 \sqrt{y} }{8 \sqrt{y} }) (\frac{1}{4} + {sec}^{2} ( ln\frac{x}{y} ) + \frac{y}{x} + \frac{1}{y} - \frac{x}{ {y}^{2} }) = \frac{dy}{dx} [/tex]

(You can rearrange it further)

Three swimmers competed in a race.
Karen finished 4.367 seconds ahead of Mary.
Brenda finished in 35.04 seconds.
Brenda finished 2.45 seconds behind Mary.
What was Karen’s finish time?

Answers

Answer:

33.123

Step-by-step explanation:

Brenda is at 35.04 seconds which is 2.45 seconds behind Mary so Mary is at 37.49 seconds.

Karen is ahead of Mary by 4.367 seconds which means she is at 33.123

Convert 10 feet into yards. Round your answer to the nearest hundredth.

Answers

Answer:

3.33 Yards

Step-by-step explanation:

divide 10 by 3

Rita charges $50 for 5 tutoring sessions. What is the cost per session?

Answers

Answer:

10

Step-by-step explanation:

Answer:

10$

Step-by-step explanation:

If she charges 50$ per 5 session then you need to do is

50 ÷ 5 = 10

Why?

Because you can to break it down to one session.

Find the distance between the points (-4,0) and (2,1). If necessary,round to the nearest 10th.

Answers

Answer:

square root of 37

Step-by-step explanation:

you would use the formula (X2-X1) squared + (Y2-Y1) squared

Step by step of how to find f(g(x)) and g(f(x))

Answers

Answers:

[tex]f(g(x)) = \sqrt[3]{\frac{x+1}{x^3}}\\\\\\g(f(x)) = \frac{\sqrt[3]{x}+1}{x}[/tex]

===============================================

Work Shown:

[tex]f(x) = \sqrt[3]{x}\\\\\\f(g(x)) = \sqrt[3]{g(x)}\\\\\\f(g(x)) = \sqrt[3]{\frac{x+1}{x^3}}\\\\\\[/tex]

The idea is to replace every x with g(x). Then you'll plug in the definition of g(x).

---------------------------------

Similarly,

[tex]g(x) = \frac{x+1}{x^3}\\\\\\g(f(x)) = \frac{f(x)+1}{(f(x))^3}\\\\\\g(f(x)) = \frac{\sqrt[3]{x}+1}{(\sqrt[3]{x})^3}\\\\\\g(f(x)) = \frac{\sqrt[3]{x}+1}{x}\\\\\\[/tex]

What is the factored form of 5x − 625x4?

Answers

Answer:

I think it's 5 I think

Step-by-step explanation:

hopefully I helped

Answer:

I think it's 5

Step-by-step explanation:

Other Questions
The last part of the Beowulf excerpt recounts how Grendel flees into thedarkness after suffering a fatal wound from Beowulf. What part of Freytag'spyramid best fits this section of the story?A. Falling actionB. Rising actionC. CharacterizationD. Exposition Sheryl got these scores on her spelling tests.95, 89, 99, 85, 82What is the mean absolute deviation of her spelling test scores?(10 point)HELP PLSSSSSSSSS5.617.08990 When lava is expelled from a volcano, it temperature may vary from 700 degrees Celsius to 1200 degrees Celsius. Write an absolute value equation that represents the minimum and maximum temperatures of lava. Use x to represent the temperature.Equation:__ How did the feudal system emerge in Europe? Alex nervously looked at the website of the Soccer Olympic Development Program. The program let in very few soccer players. It was especially challenging for goalies like him. Only the best players in the country were selected to train for a spot on the national team. Would he be one of them? what is the role of each branch of the federal government and explain how the three branches work as a check on each other. 3x= 5 + 2(3 + 4x)How to solve this? I'll be giving brainliest to whoever can help with these! 7/10;1/3;5/6 ayuda es de matemticas If jimmy has 3 billion dollars and subtracts a dollar how much does he have .Protiens contain which atoms? (6 of them) Write down the whole word. What is the value of f(x) when x=3?3214 100 points and brainliestMira and Sasha observed two points, P and Q, on a number line.A number line is shown from negative 2 to positive 2 with increments of 2 over 8. A point P is shown at the seventh tick mark to the left of 0, and a point Q is shown at the seventh tick mark to the right of 0.Sasha said that the absolute values of the numbers represented by the two points are different.Mira said that the absolute values of the numbers represented by the two points are the same.Which of the following explains who is correct? A Sasha, because the points are of different signsB Sasha, because the points are at different locationsC Mira, because each of the two points is 14 over 8 units from 0D Mira, because the distance between the two points is 14 over 8 units What is the name of the highest note in this example?A. the note FB. the note EC. the note CD. the note D Read Edward Corsi's quotation from the book Immigrant Kids by Russell Freedman. The writer Angelo Pellegrini has recalled his own family's detention at Ellis Island: My sister was indeed momentarily rejected; she had been so ill and had cried so much that her eyes were absolutely bloodshot, and Mother was told, "Well, we can't let her in." This quotation adds credibility to the text because it comes from an actual immigrant whose experience agrees with Freedman's statement that one out of every five immigrants was detained. it comes from an actual immigrant whose experience proves that no one was detained on Ellis Island. it comes from a young woman who was held on Ellis Island, which supports Freedman's statement that one out of every five immigrants was detained. it comes from a mother whose daughter was detained because her eyes were red and bloodshot Find the 125% of 600lb I need help, pls answer. from The Five Orange Pipsby Sir Arthur Conan Doyle When I glance over my notes and records of the Sherlock Holmes cases between the years '82 and '90, I am faced by so many which present strange and interesting features that it is no easy matter to know which to choose and which to leave. Some, however, have already gained publicity through the papers, and others have not offered a field for those peculiar qualities which my friend possessed in so high a degree, and which it is the object of these papers to illustrate. Some, too, have baffled his analytical skill, and would be, as narratives, beginnings without an ending, while others have been but partially cleared up, and have their explanations founded rather upon conjecture and surmise than on that absolute logical proof which was so dear to him. There is, however, one of these last which was so remarkable in its details and so startling in its results that I am tempted to give some account of it in spite of the fact that there are points in connection with it which never have been, and probably never will be, entirely cleared up.from The Adventures of Sherlock Holmes by Sir Arthur Conan DoyleFrom which point of view is this story being told? A. first person B. The point of view changes. C. third person Jessie enjoys running every day for exercise. On Monday, he ran 3.30 miles. On Tuesday, he ran 3.09 miles. On Wednesday, he ran 2.98 miles. On what day did Jessie run the farthest? * {5,25,35,45,55,65} Rational numbers