Answer:
D.
Step-by-step explanation:
It’s never lupus. Lupus is a medical phenomenon where antibodies that are supposed to attack foreign cells to prevent infections instead see plasma proteins as foreign bodies, leading to a high risk of blood clotting. It is believed that 2% of the population suffer from this disease. The test is 98% accurate if a person actually has the disease. The test is 74% accurate if a person does not have the disease. There is a line from the Fox television show House that is often used after a patient tests positive for lupus: “It’s
never lupus.” Do you think there is truth to this statement? Use appropriate probabilities to support your answer.
L = person has Lupus
~L = person does not have Lupus
P(L) = 0.02 since 2% of the population has it.
P(~L) = 1 - 0.02 = 0.98, ie 98% of the population does not have it.
------------------
If the person has Lupus, then the test will indicate as such 98% of the time, and do so correctly.
T = person tests positive for Lupus
~T = person tests negative for Lupus
P(T given L) = 0.98
The complement of this is
P(~T given L) = 1 - 0.98 = 0.02 = false negative rate
On the other hand, if a person does not have Lupus, then the test will return negative correctly 74% of the time.
P(~T given ~L) = 0.74
Its complement is
P(T given ~L) = 1 - 0.74 = 0.26 = false positive rate
------------------
Dr House saying "It's never Lupus" can be translated to "If the test is positive, then P(L) = 0"
Phrased another way symbolically:
P(L given T) = 0
-------------------
We'll use Bayes Theorem to determine the value of P(L given T)
In general, Bayes Theorem is
P(A given B) = P(B given A)*P(A)/P(B)
So for this problem, we'll have
P(L given T) = P(T given L)*P(L)/P(T)
We almost have everything needed but we're missing P(T)
So we'll need to use the law of total probability to break that up like so
P(T) = P(T and L) + P(T and ~L)
P(T) = P(T given L)*P(L) + P(T given ~L)*P(~L)
P(T) = 0.98*0.02 + 0.26*0.98
P(T) = 0.2744
-------------------
To recap, we have:
P(T given L) = 0.98P(L) = 0.02P(T) = 0.2744We finally have all the info needed to get the probability we're after.
P(L given T) = P(T given L)*P(L)/P(T)
P(L given T) = 0.98*0.02/0.2744
P(L given T) = 0.07142857142858 approximately
What does this tell us? It says that if a patient gets a positive test for lupus, then there's roughly a 7% chance the test is correct, and the person actually has lupus.
So it's likely Dr House is onto something. The reason why the small result is because a small percentage of the population has the disease.
Also, notice how the false positive rate P(T given ~L) = 0.26 = 26% is fairly high. This also provides more evidence to Dr House's claim.
To be entirely technically accurate, he shouldn't have used "never" because the result of P(L given T) is not zero. But I think a bit of wiggle room can be had for the interpretation of his words.
PLS ANSWER THE FOLLOWING QUESTION AS QUICKLY AS POSSIBLE
PLSSSSSSSSSSSSSSSSSSSS
Answer:
120
Step-by-step explanation:
25 + 35 = 60
60 + 60 = 120
pls explain why no pls and thank u
Answer:
Step-by-step explanation:
So we have : c + 2.5 < 4.3
And it's asking whether c = 1.8 is a solution.
Substitue c = 1.8 in, we get :
1.8 + 2.5 < 4.3
4.3 < 4.3 (not true)
So, c = 1.8 is NOT a solution.
Answer:
No, because c = 1.8 would be wrong and the real answer would be c < 1.8
Step-by-step explanation:
If two angles are supplementary and one of the angles measures 38, what is the measure of the larger angle?
Answer:
142°
Step-by-step explanation:
Angles are supplementary when they total 180°. If one of them is 38°, then the measure of the other angle is ...
180° -38° = 142°
The larger angle is 142°.
Marquis used the steps below to find the solution to the inequality Negative 5. 6 greater-than-or-equal-to x 3. 6. Step 1 Subtract 3. 6 from both sides of the inequality. Negative 5. 6 greater-than-or-equal-to x 3. 6. Negative 5. 6 minus 3. 6 greater-than-or-equal-to x 3. 6 minus 3. 6. Negative 9. 2 greater-than-or-equal-to x. Step 2 Interpret the results. X greater-than-or-equal-to negative 9. 2 x is greater than or equal to –9. 2. Step 3 Draw a number line. A number line going from negative 9. 5 to negative 8. 8. A closed circle is at negative 9. 2. Everything to the left of the circle is shaded. Which describes the first step in which Marquis made an error? In Step 1, Marquis should have added 3. 6 to each side of the inequality. In Step 2, Marquis should have interpreted the results as x less-than-or-equal-to negative 9. 2, which means that x is less than or equal to –9. 2. Marquis should have used an open circle at –9. 2 in Step 3. Marquis should have shaded the number line to the right of –9. 2 in Step 3.
Marquis solutions are;
The value of x is less than or equal to -9.2.Negative 9.2 is greater than or equal to x.The closed circle is at -9.6 that is everything to the left of the circle is shaded.What is inequality?Inequality is simply a type of equation that does not have an equal sign in it. Inequality is defined as a statement about the relative size as we will as is used to compare two statements.
Marquis used the steps below to find the solution to the inequality Negative 5.6 greater than or equal to x + 3.6 that can be written as
[tex]\rm -5.6 \geq x + 3.6[/tex]
A. Then the value of x will be
- 5.6 ≥ x + 3.6
-5.6 - 3.6 ≥ x
-9.2 ≥ x
B. Negative 9.2 is greater than or equal to x.
C. The number line is shown. The closed circle is at -9.6 that is everything to the left of the circle is shaded.
More about the inequality link is given below.
https://brainly.com/question/19491153
Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
3, 5, 7, ...
Answer:
Step-by-step explanation:
This is an arithmetic series.
3 , 5 , 7 ,......
Common difference = second term - first term
= 5 - 3
= 2
Whats the variable for 4/2 = 3/x
Answer: 3/2
Step-by-step explanation:
We can cross multiply.
4x = 6.
Divide both sides by 4.
x = 6/4 which simplifies to 3/2
Charlotte made a bracelet using red, gray, and white beads.
Five-ninths of the bracelet is white.
The rest of the bracelet has an equal amount of red and gray.
How much of Charlotte's bracelet is gray?
Answer:
2/9
Step-by-step explanation:
5/9 is white,we have 4/9 left. 4/9 ÷ 2 is 2/9
Hope this helps
Vicki would like to estimate the probability of tails coming up fewer than 2 times in 3 coin flips. To do this, she has a computer randomly select 0 or 1 three times, with 0 representing heads and 1 representing tails. The results of 15 trials are shown in the table. 110 111 000 011 000 010 101 100 000 000 111 101 110 101 111 What is Vicki's estimated probability, based on this simulation? Enter your answer as a fraction, in simplified form, in the box.
Probability helps us to know the chances of an event occurring. Vicki's estimated probability, based on this simulation is 0.4167.
What is Probability?
The probability helps us to know the chances of an event occurring.
[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
As it is given that if the output of the computer is 1, then it represents tails, while the 0 represents the head. Also, the results of 12 trials are 111, 011, 000, 010, 100, 111, 010, 111, 111, 101, 000, 111.
Now, in the set of results, we need to calculate the number of results in which the outcome of tails comes up fewer than 2 times, therefore, we need the output that has 2 or more zeroes in it.
Results with 2 or more zeroes are 000, 010, 100, 010, 000
The number of results with 2 or more zeroes is 5.
The total number of possible results is 12.
The probability That Vicki will get 2 or more heads can be written as,
[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
[tex]\rm Probability(2\ or\ more\ zeroes)=\dfrac{\text{Number of results with 2 or more zeroes}}{\text{Total number of possible results}}[/tex]
[tex]\rm Probability(2\ or\ more\ zeroes)=\dfrac{5}{12} = 0.4167[/tex]
Hence, Vicki's estimated probability, based on this simulation is 0.4167.
Learn more about Probability:
https://brainly.com/question/795909
From the observation deck of a skyscraper, Madison measures a 67^{\circ} ∘ angle of depression to a ship in the harbor below. If the observation deck is 1143 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.
The horizontal distance from the base of the skyscraper out to the ship is 485.2 feet.
What is trigonometric ratio?Trigonometric ratio is used to show the relationship between the sides and angles of right angled triangle.
Let d represent the horizontal distance from the base of the skyscraper out to the ship. Since the angle of depression is 67°, hence:
Angle = 90 - 67 = 23°
Using trig ratio:
tan(23) = d/1143
d = 485.2 feet
The horizontal distance from the base of the skyscraper out to the ship is 485.2 feet.
Find out more on trigonometric ratio at: https://brainly.com/question/24349828
Answer:
Step-by-step explanation:
The horizontal distance from the base of the skyscraper out to the ship is 485.2 feet.
What is trigonometric ratio?
Trigonometric ratio is used to show the relationship between the sides and angles of right angled triangle.
Let d represent the horizontal distance from the base of the skyscraper out to the ship. Since the angle of depression is 67°, hence:
Angle = 90 - 67 = 23°
Using trig ratio:
tan(23) = d/1143
d = 485.2 feet
The horizontal distance from the base of the skyscraper out to the ship is 485.2 feet.
I need help please! 6 1/2 x 2 6/13
Answer:
16
Step-by-step explanation:
6x2+1/2=13/2
2x13+6=32/13
13/2x32/13=416/26
416/26=16
Help please Im giving brianless and 100 points to the person who answer and show their work thank you very much
Answer:
8.5 ft (nearest tenth)
Step-by-step explanation:
To find the depth of the pool at the deep end, we need to find the height of the right triangle with angle 16.5° and add it to 4.5 ft
Base of the triangle = 35 - 9 - 12.5 = 13.5 ft
Use the tan trig ratio:
[tex]\tan(x)=\dfrac{O}{A}[/tex]
where x is the angle, O is the side opposite and angle and A is the side adjacent to the angle in a right triangle.
Given:
x = 16.5°O = h (height)A = 13.5 ft[tex]\implies\tan(16.5)=\dfrac{h}{13.5}\\\\\implies h= 13.5\tan(16.5)\\\\\implies h = 4.0 \textsf{ ft (nearest tenth)}[/tex]
Therefore, the depth of the pool at the deepest end = 4 + 4.5 = 8.5 ft (nearest tenth)
Now
[tex]\\ \rm\Rrightarrow tan\theta=\dfrac{P}{B}[/tex]
[tex]\\ \rm\Rrightarrow tan16.5=\dfrac{P}{13.5}[/tex]
[tex]\\ \rm\Rrightarrow P=13.5tan16.5[/tex]
[tex]\\ \rm\Rrightarrow P=13.5(0.3)[/tex]
[tex]\\ \rm\Rrightarrow P\approx 4ft[/tex]
Andre is designing a website that will display reviews of school lunches. Each item on the menu is rated from 0 to 5 stars. The main display can only show 6 reviews, so Andre needs to decide how to choose which reviews to show at the top.
1. If each rating also has a sentence or two explaining the rating, what are some good reasons to keep this sample displayed first? What are some good reasons to change the sample that is displayed first?
2. Is the sample representative of the population? Representative Not representative
Answer:
1. some good reasons are that put the most reviewed lunch at the top and good reasons to change it is that if you change it you could get more reviewers 2. yes it is representative of the population
Step-by-step explanation:
I hope it helps :-)
Reasons to maintain the sample at the top of the display:
The sample offers users a comprehensive perspective of the school lunch alternatives by representing a wide range of menu items and ratings.A variety of favorable and negative assessments are present in the sample, offering a well-rounded viewpoint.The most recent reviews are included in the sample, guaranteeing that the data is accurate.The sample has reviews from a range of students or sources, giving it a more varied viewpoint.What is Sampling?Sampling is the process of choosing a portion of a broader group of people or things for research or analysis. Since it is frequently difficult or impossible to test or examine every member of a group, conclusions about the population are instead drawn from a representative sample.
The information provided makes it unclear whether the sample is representative of the population. The sample is more probable to be representative if it was drawn using a random sampling technique and includes a variety of menu items and ratings. However, if the sample wasn't chosen at random or was biased, or if it just included a small portion of the available menu items and ratings, it might not be accurate.
Therefore, reasons to maintain the sample at the top of the display:
The sample offers users a comprehensive perspective of the school lunch alternatives by representing a wide range of menu items and ratings.Learn more about Sampling, here:
brainly.com/question/29852583
#SPJ2
Please answer with steps
|-10k+7|
-------------
3 =4
Can someone help with this rq?
Please help me, I will give brainliest
Julia has a farm on a rectangular piece of land that is 150 meters long. This area is divided into two parts: A square area where she lives (whose side is the same as the width of the farm), and the remaining area where she grows artichokes. Every week, Julia spends $8 per square meter on the area where she lives and earns $4 per square meter from the area where she grows artichokes. This way, she manages to save some money every week. Write an inequality that models the situation. Use w to represent the width of Julia's farm.
Answer:
8w² < 4w(150-w)
Step-by-step explanation:
Square area of living : w · w = w²
Money spent : 8 · w²
Square area of artichokes : (150 - w) · w
Money earned : 4 · w · (150 - w)
Julia manages to save some money every week. That means that the money earned is bigger than the money spent ( the money spent is less than the money earned)
8 · w² < 4 · w · (150 - w)
Which of the following is NOT true about parallelograms?
options:
a parallelogram is a rectangle
a parallelogram is a quadrilateral
a parallelogram has no lines of symmetry
a parallelogram has 2 sets of parallel lines
"a parallelogram is a rectangle" is the correct answer.
Hope this helps :0
Answer:
a parallelogram has no lines of symmetry
PLEASE HELP WITH THIS ASAP
⚠️Whoever solves this gets marked as Brainleist⚠️
a)
The dark rectangle : 6x (square units)
The light rectangle : 5 x 6 = 30 (square units)
b) 2 ways to show the area of the entire figure :
6x + 30 square units (sum of 2 area)
6 x (x+5) (length x width, where the width is 6, and length is x + 5)
Hope it helps :)
Pablo took his $50 gift card to the
toy store. He bought a game for
$24.99. How much money does he have left on his gift card?
Answer:
$25.01
Step-by-step explanation:
I used simple subtraction:
50 - 24.99 = 25.01
Hope this helps!! :)
Find the formula for an arithmetic sequence problems.
Answer:
The arithmetic sequence formula to find the sum of n terms is given as follows: Sn = n/2 (a1 + an) Where Sn is the sum of n terms of an arithmetic sequence.
sam and jennna decide to purchase a tv on black friday. the sale price is $499. if jenna pays $123 more than sam, how much did sam pay?
Answer:
Sam would pay $188 and jenna would pay $311.
Step-by-step explanation:
You leave a 20% tip of $4.50. How much was the bill?
Answer:
Rm5.40
Step-by-step explanation:
First, 20/100 × Rm4.50 = Rm0.90. Second, Rm4.50 + Rm 0.90 = Rm5.40
Please give me brainliest hehe.
Answer: 0.90 BUT IF YOU ROUND UP TO HOLE DOLLARS THEN YOUR TIP WOULD BE 1 DOLLAR
Step-by-step explanation: THAT IS YOUR ANSWER HOPE I HELPED :D
3. A wire of length 90 cm is cut into three pieces. The lengths of the pieces are in the ratio 3:5:7. Calculate the length of (a) the longest piece. (b) the difference between the longest and the shortest piece. 3:5:1 Wire length: 90 cm
the difference between the longest and the shortest piece
Answer:
Step-by-step explanation:
First, simplify into the parts given by sum of ratio values.
90cm / 15 = 6 cm
(a) longest piece
= 7 x 6 = 42 cm
(b) difference between longest and shortest
shortest = 3 x 6 = 18 cm
Difference = 42 - 18 = 24 cm
Not sure how to do this
The sum of two numbers is 32. Their difference is 30. What are the two numbers? Show all work
Answer:
a=30 , b = 0
Step-by-step explanation:
let the two numbers be represented as a and b
a + b = 30... eqn 1
a - b = 30 ...... eqn 2
we then add the two equations to get values for a and b
a + b + a - b = 30 + 30
a + b + a -b = 60
2a = 60 ( diivide both sides by 2)
a = 30
we then put value for a = 30 into any of the equations to get b
a + b = 30, 30 + b= 30
b = 30 -30 , b = 0
to confirm if the answers are correct, we insert the values for a and b in the two equations.
a + b = 30..... eqn 1, 30 + 0 = 30
a - b = 30 ...... eqn 2 , 30 - 0 = 30
this is a problem i need help with
Answer:
He sold 12 phones and 20 watches.
Step-by-step explanation:
X × 10 = 120. Y × 2 = 40
12 × 10 = 120. 20 × 2 = 40
120 + 40 = $160
Answer:
10 times 3= 30 3 times 10=30 so total is 60 3mphones sold 10 watches sold
Step-by-step explanation:
Help me please, I really don't want to fail
Which system of equations has no solution?
Answer: Top left i'm pretty sure
Step-by-step explanation: Because there isn't a blue line and you need a blue line for it to be an equation
Answer:
Parallel line
Step-by-step explanation:
The parallel line doesn't connect so it a infinite therefore it means its a no solution line
Find the length of AB.
please help!!
Answer:
8.6 is the answer
Step-by-step explanation:
A = (3,9)
B = (8,2)
d² = (8-3)² + (2-9)²
or, d² = 5² + (-7)²
or, d² = 25 + 49
or, d² = 74
d = 8.6
Talia wants to find the amount of sugar that will fit in a box that is 4 inches long, 2 inches wide, and 6 inches high. What measurement does she need to calculate?
Answer:
Volume She needs to calcite the volume of the box
Answer:
48
Step-by-step explanation:
If y=6 when x=15 then which of thr following is the value of x when y=20
Answer:
if you meant x times y...
15 x 20 is 300.
if you meant x + y...
15 + 20 is 35.
if you meant anything else, please let me know
the way it was written confused me but I tried.
