A diagnostic test for a disease is such that it (correctly) detects the disease in 90% of the individuals who actually have the disease. Also, if a person does not have the disease, the test will report that he or she does not have it with probability 0.9. Only 3% of the population has the disease in question. If a person is chosen at random from the population and the diagnostic test indicates that she has the disease, what is the conditional probability that she does, in fact, have the disease

Answers

Answer 1

Answer:

0.2177 = 21.77% conditional probability that she does, in fact, have the disease

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Test positive

Event B: Has the disease

Probability of a positive test:

90% of 3%(has the disease).

1 - 0.9 = 0.1 = 10% of 97%(does not have the disease). So

[tex]P(A) = 0.90*0.03 + 0.1*0.97 = 0.124[/tex]

Intersection of A and B:

Positive test and has the disease, so 90% of 3%

[tex]P(A \cap B) = 0.9*0.03 = 0.027[/tex]

What is the conditional probability that she does, in fact, have the disease

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.027}{0.124} = 0.2177[/tex]

0.2177 = 21.77% conditional probability that she does, in fact, have the disease


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Step-by-step explanation:

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If 2 boys ate 6 cookies each, how many cookies did they eat?

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Answer:

12 cookies

Step-by-step explanation:

If each boy ate 6 cookies that's 2 boys times 6 cookies each.

2x6=12

So, they ate 12 cookies total

WILL GIVE BRAINLIEST!!


Rewrite the equation by completing the square.

2x^2 -11 x +14 = 0

Answers

Answer:

( x − 2 ) ( 2 x − 7 )

Step-by-step explanation:

Answer:

(x-11/4)^2=9/16

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Khan

9.1(3) + 8.7(4) = ?

Answers

Answer:

62.1

Step-by-step explanation:

PEMDAS!

9.1 * 3 = 27.3

8.7 * 4 = 34.8

27.3 + 34.8 = 62.1

1/3 of the students in Mr. Wilson's class play basketball and 1/2 play football. What combined fraction of students in Mr. Wilson's class plays either basketball or football?

Answers

1/3+1/2

2/6+3/6=5/6

Answer=5/6

Please help I don’t understand

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Answer:

the answer is B

Step-by-step explanation:

Answer:

A. 6 cm, 8cm, and 10 cm

Step-by-step explanation:

There are 6 bookshelf's that hold 72 books per shelf. if 1/3 of the total number of books are non-fiction,how many fiction books are there.​

Answers

Answer:

288 fiction books

Step-by-step explanation:

If the other 2/3 are fiction, then I believe that you would multiply 72 by 6 then divide by 3 or multiply by 1/3 giving you 144. Multiply 144 by 2 and you should get 288, but this is if there are only fiction and non fiction. Sorry if this is wrong..

Two sides of a triangle have lengths 10 and 30. The third side has a length that is

Answers

Answer:

2h4o

Step-by-step explanation:

You are offered a 30--day trial period at your dream job. However, the owner of the company is a little unusual so the pay options are non-traditional. They offer you two different pay options for the 30 days:
Option 1: You make $60,000 per day.
Option 2: You make 1 penny the first day, 2 pennies the second day, 4 pennies the third day, 8 pennies the fourth day, etc.
Which is $5,368,709.12 after 30 days of working.

Answers

Answer:

The question is not complete but from the flow of thought, the question seems to be about what your choice will be between option 1 and option 2.

The correct answer is

option 2

Step-by-step explanation:

The question is asking you to choose an option that pays more after 30 days. In other to determine the more beneficial option, we will compare both options and select the one that pays more. This is done as follows:

option 1: $60,000 per day, after 30 days =

60,000 × 30 = $1,800,000

option 2 = $5,368,709.12 after 30 days

From the total amounts after 30 days of the two options listed above, option 2 is higher than option 1 by $3,568,709. Therefore, option 2 is a better choice.

Write an equation. Use the variables given in the question . a magazine cost $3.00 and a book cost $7.00. If you want to spend exactly $45.00 on reading this month and you need to buy 8 magazines , how many book can you buy ? Write an equation in standard form modeling this situation. PLEASE HELP NEED ASAP !!!! DUE IN 10 MINS !

Answers

(8*3) + (7*x) = 45
(24) + (7*x) = 45
45 - 24 = 21
x = 21

Walt's haircut costs $32. He leaves a 15% tip. How much does he pay for the haircut, including the tip?

Answers

Answer:

Walt pays $47

Step-by-step explanation:

If Walt pays $32 for his haircut, and 15% is his tip,

We know here that in percentages, 15% = 15/100, which equals $15

Then, you would simply do 32 + 15

32 + 15 = 47.

Walt pays $47 for his haircut

hope this helps! <3

Answer: 36.8

Step-by-step explanation:

32 x 115 / 100 or you can find the 15% of 32 which is 4.8 and add it to 32 you get 36.8

Use the distributive property to rewrite each expression in it's equivalent form 9a-3/3 ,Just 3 please

Answers

hahahah i think i already did this for you buttttt

the denominator can be distributed to both parts of 9a and -3

so you can rewrite it as (9a/3) and (-3/3)

to simplify (9a/3) is equal to 3a and (-3/3) is equal to -1

so the answer is 3a-1

I need help asap!!!!

Answers

Answer:

150

Step-by-step explanation:

If both addition and multiplication are used in a single expression, then the ___________ property might apply.

Answers

Answer:

associative property

Step-by-step explanation:

Age If you add Natalie's age and Fred's age, the result is 43. If you add Fred's age to 4 times
Natalie's age, the result is 79. Write and solve a system of equations to find how old Fred and
Natalie are.
Fred is
years old. Natalie is
years old.

Answers

Let’s take fred age as x and Natalie’s age as y.
So,
A/Q
X + Y = 43. Let it be eqution 1
and
X + 4Y = 79. Let it be equation 2


Combining equation 1 and 2, we get

( X + Y) + 3Y = 79
43 + 3Y = 79
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Now, evaluating the value of Y in equation 1 we get,

X + 12 = 43
X = 31

Therefore, Fred is 31years old and Natalie is 12 years old.

pls and this question will mark u the brainliest​

Answers

Answer:

96

Step-by-step explanation:

8 × 9 × 8/2 × 3

8 × 9 × 8/6

576/6 = 96

Answer:

96

Step-by-step explanation:

1) 2^3=2*2*2=8

2)8*9*8=576

3)3*2=6

4)576/6 = 96

Please help! I need as soon as possible.

Answers

Answer:

question 2: squareroot k

question 3: 2b/b^10

Step-by-step explanation:

q2:

using power rules, root k^3 = k^2/3

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q3: same thing

If 3v/7 = 6then v = ?
I’m not sure

Answers

Step-by-step explanation:

3v/7=6

3v=6×7

3v=42

v=42/3

v=14

hope it helps.

Answer:

v=14

Step-by-step explanation:

3v/7=6

  x7  x7

3v=42

/3   /3

v=14

hope this helps:)

In a​ week, 18 hens laid 90 eggs. What is the unit rate for eggs per​ hen?

Answers

Answer:

5 eggs

Step-by-step explanation:

I divided the number of eggs by the number of hens 90 divided by 18 = 5. So the unit rate is 5 eggs per hen.

Pls mark me brainliest

There is a bag filled with 4 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting at least 1 blue?

Answers

The answer you’ll be 1/5 ! I hope this helps

Express sin A, cos A, and tan A as ratios.​

Answers

Answer:

sin(A) = 2rad19/20 = rad20/10

cos(A) = 18/20 = 9/10

tan(A) = 2rad19/18 = rad19/9

Quadrilateral A B C D is shown. Angle A is 128 degrees, angle B is 126 degrees, and angle C is 54 degrees.
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52o
54o
57o
126o

Answers

Answer:

What is the measure of angle D?

52o

Angle D = 360-128-126-54 = 52o

Step-by-step explanation: got it right on edge

Since the sum of the angles in a quadrilateral is 360 degrees then the angle D is 50 degrees.

What is a quadrilateral?

A quadrilateral is a four sided figure. Examples of quadrilaterals include; square, parallelogram, rectangle, kite etc.

The sum of angles in a quadrilateral is 360  degree hence;

A + B + C + D = 360 (sum of angles in a quadrilateral)

128 + 126 + 54 + D = 360

D = 360 - ( 128 + 126 + 54)

D = 50 degrees

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Answers

Answer:

458

Step-by-step explanation:

A cup of coffee contains 140 mg of caffeine. If caffeine leaves the body at 10% per hour, how long will it
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Answers

Answer: 5 hours

Step-by-step explanation:

If 10% of 140 is 14. And if 14 mg of caffeine is leaving per hour then it would take 10 hours to completely leave from ones body, but for half of it to leave it would take 5.

It takes 5 hours to eliminate half of the caffeine from one's body.

Given that, a cup of coffee contains 140 mg of caffeine.

What is the percentage?

In mathematics, a percentage is a number or ratio expressed as a fraction of 100.

Now, 10% of 140

=0.1×140=14 mg

If 10% of 140 is 14 and if 14 mg of caffeine is leaving per hour then it would take 10 hours to completely leave from one's body, but for half of it to leave it would take 5 hours.

Therefore, it takes 5 hours to eliminate half of the caffeine from one's body.

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A horizontal translation is used to move quadrilateral W XYZ onto quadrilateral
W XYZ.
Use the drop-down menus to describe the horizontal translation used.

Answers

Answer:

Quadrilateral WXYZ is translated 10 units  to the left

Step-by-step explanation:

Translation of Shapes in the Plane

The translation is a type of rigid transformation where all the coordinates of the vertices that form the shape are shifted by the same number of units both vertically and horizontally.

The quadrilateral WXYZ has coordinates:

W(2,-3) X(7,-3) Y(6,-7) Z(1,-7)

The quadrilateral W'X'Y'Z' has coordinates:

W'(-8,-3) X'(-3,-3) Y'(-4,-7) Z'(-9,-7)

It can be noted that all the x-coordinates of the vertices are shifted by 10 units to the left.

Answer:

Quadrilateral WXYZ is translated 10 units  to the left.

if y represent the smallest of three consecutive odd integer,expression to represent each of the next two

Answers

9514 1404 393

Answer:

  y+2, y+4

Step-by-step explanation:

Consecutive odd integers differ by 2.

The next two are ...

  y+2

  y+4

__

Additional comment

You may find it simplifies the math in consecutive integer problems if you let the variable represent the middle one. If y is the middle one, the three odd integers are represented by y-2, y, y+2.

HELP! 10 points!!

Sarah has a part time job working as a line cook. She earns $56 a night plus 5% of the tips.

A- write an equation for Sarah’s total earnings, E dollars, when the tips are t dollars.

B- what will Sarah earn when the tips are $350? Explain your strategy

C- what were the nightly tips when Sarah earned $81? Explain your strategy

Thank you :]

Answers

Answer:

A: E = 0.05t +56

B: $73.50

C: $60.05

Step-by-step explanation:

A) I'll just explain the equation in one go

Equation: E = 0.05t + 56

0.05 - This is meant to represent the 5% of tips

5% = 5/100

5/100 = 0.05

56 - This is a set value that has been established as a constant, thus it simply needs to be added to the 5%

B+C) Since we already have the equation set up, we just need to plug in the variable, t.

B) E = 0.05(350) + 56

= 17.5 + 56

= 73.50

C) E = 0.05(81) + 56

= 4.05 + 56

= 60.05

Hope that does something to help, even though this was posted a while ago

What is the solution set for x over 2 = 8

O S=4 and x = - 16
O S=-4 and s=4
O S=-8 and s= 8
O X=-16 and x = 16

Answers

Answer:

x=-16 and X=16 beads "over" means divide

On a piece of paper, graph y< x-1. Then determine which answer choice
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A
B
D
(3,2)
(3,2)
90.-1)
0.-1)
10.-1)
10-15
O A. Graph D
B. Graph A
Ο Ο Ο
C. Graph
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Answers

A and D is the answer

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Step-by-step explanation:

How is the sentence "six more than x is nine" written as an equation?
O A. 6 = x + 9

Answers

Answer: the answer is c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

x+6=9

so C

if my answer helps please mark as brainliest

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