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.
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
Yolanda has quarters, Q, and dimes, D, in her coin jar. She has a total of 31 coins.
The total amount of money in the jar is $4.75\$4.75$4.75 . Write two equations that could be used to find the number of quarters and the number of dimes in the jar.
Solve the equations to find out how many quarters and
how many dimes Yolanda has in her jar.
Answer:
11 Quarters 20 Dimes
Step-by-step explanation:
Q+D=31
25Q +10D = 475 (miltiplied all by 100 to avoid decimals)
Multiply the first by -10(to eliminate D)
-10Q - 10D = - 310
25Q+10D = 475
ADD BOTH( D will cancel)
15Q = 165
Q= 11
31-11 =20 (dimes =20)
11x0.25 = 2.75
20x0.10=2
2.75+2 = $4.75
The line that passes through the points (-6, p) and (-10, 2) has a slope of -1/6. What is the value of p?
Work Shown:
Slope = rise/run
Slope = (change in y)/(change in x)
Slope = (2-p)/(-10-(-6))
Slope = (2-p)/(-10+6)
Slope = (2-p)/(-4)
Set this equal to the stated slope -1/6 and solve for p
(2-p)/(-4) = -1/6
6(2-p) = -4(-1)
12-6p = 4
-6p = 4-12
-6p = -8
p = -8/(-6)
p = 4/3
Please help!
x and y are 2 complementary angles such that Y is 8 degrees larger then X.
Find the value of X
Answer: x = 41
Step-by-step explanation:
Since x and y are complementary angles, that means x + y = 90 degrees.
We are given that y = x + 8
We can substitue y as x + 8 in the complementary angle equation.
Therefore, we get x + x + 8 = 90
2x = 82
x = 41
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.
Writing If the measures of two angles of a triangle are 86 and 12°, what is the measure of the third angle? Use pencil and paper. Explain how a straight angle is
related to the angles of a triangle.
The measure of the third angle is
Answer: 82 degrees
Step-by-step explanation:
The sum of the angles in a triangle is 180 degrees which is a straight angle.
Let the unknown third angle be x.
Therefore, 86 + 12 + x = 180
98 + x = 180
x = 82
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.
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
Enlarge the rectangle.
When a figure is enlarged, the scale factor must be
.
Reduce the rectangle.
When a figure is reduced, the scale factor must be
.
Answer:
1: greater than 1
2:between 0 and 1
Step-by-step explanation:
I think
Please mark me Brainlest
Answer:
When a figure is enlarged, the scale factor must be: Greater than one
Reduce the rectangle.
When a figure is reduced, the scale factor must be: Between 0 and 1
5. The area of a rectangle is 4 1/5
inches. If the length is 2 inches,
what is the length.
Answer:
If you mean width then...
Step-by-step explanation:
4.2=4 1/5
4.2/2=2.1
Answer: w=2.1
check:
l*w=A, 2*2.1=4.2
Pls help asap I’ll give brainliest
Answer:
100 (I believe)
Step-by-step explanation:
The length would be 20
20 x 2 (because we have two sides) is 40
the width would have to be 5 then
5x2 (because we have to sides) is 10
5x4 is 20 (Showing that the length is 4 times the width)
40 + 10 = 50 (Which is the perimeter)
Since we know the length is 20 and the width is 5
we just do
20 * 5 = 100
Answer:
L = 20
Width = 5
Step-by-step explanation:
"The perimeter of the rectangle is equal to 2 times length + 2 times width:
P = 2L + 2W
We know that length is 4 times the width, so L = 4 W
We can now replace l by 4W in the equation of the perimeter:
P = 2L + 2W = 50
P = 2(4W) + 2W = 50
P = 8W + 2W = 50
P = 10W =50
So W = 50 /10
W = 5
And L = 4W
L= 4 (5)
L = 20"
2O × 5 = 100
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
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]
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.
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 :)
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)
1 point
James carries a balance on his credit card each month. Today is the first
day of the new, 30-day billing cycle. The current balance is $x and the APR
is 30%. James is buying his father a gift that costs $1,500 that he plans to
put on his credit card. This will be his only purchase this month, and he will
be making this purchase on the first day of the billing cycle. If his finance
charge will be $60, what is the current balance on his credit card *
James's current balance on his credit card is $900.
This amount represents the card's balance before the current charge of $1,500 and the finance charge of $60.
What is a credit card balance?A credit card balance is the amount of the charges made on a credit card, including the finance charges, and therefore, owed to a credit card company.
Data and Calculations:Current current balance = $x
APR (Annual Percentage Rate) of interest = 30%
Monthly APR = 2.5% (30%/12)
Current purchase for the month = $1,500
Finance charge for the month = $60
Finance charge for the current purchase = $37.50 ($1,500 x 2.5%)
Finance charge for the current balance = $22.50 ($60 - $37.50)
The current balance that attracts the finance charge of $22.50 will be $900 ($22.50/2.5%).
Alternatively:
Since the monthly APR is 2.5% and the finance charge is $60 for the month, the balance at the end of the month is $2,400 ($60/2.5%).
Thus, the current balance on James' credit card is $900 ($2,400 - $1,500) while the end-of-the-month balance is $2,460 ($900 + $1,500 + $60).
Learn more about credit card balance at https://brainly.com/question/6872962
A high school has 60 senior girls and 5 are selected to be on Snowcoming court. How
any different Snowcoming courts could be chosen?
Answer:
12
Step-by-step explanation:
There are 60 girls in total, and 5 got picked. So if you divide 60 by 5, you get the answer 12.
Ya'll FR get 25 points if you answer this question.
_________________________________________________________
Knowing that correlation coefficients have values between -1 and 1 and that the closer the value is to -1 or 1, the stronger the correlation -- which of the following correlation coefficients would represent the strongest correlation?
0.02
0.87
-0.5
-0.97
Yes we need that value which is equidistant from -1 and 1 both.
It simply means we need the average or mean.So the answer is -1/2=-0.5
Determine the correct set up for: log x + log (x-9) = 18
Answer:
log ( x(x-9)) = 18
Step-by-step explanation:
We know that log a + log b = log ( a* b)
log x + log (x-9) = 18
log ( x* (x-9)) = 18
log ( x(x-9)) = 18
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
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
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
The height of a hill, h(x), in a painting can be written as
a function of x, the distance from the left side of the
painting. Both h(x) and x are measured in inches.
What is the height of the hill in the painting 3 inches
from the left side of the picture?
06 inches
n(x) = -
-- }(x)/x = 13)
O 13 inches
O 30 inches
O 150 inches
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:
Can someone help with this rq?
Not sure how to do this
PLS ANSWER THE FOLLOWING QUESTION AS QUICKLY AS POSSIBLE
PLSSSSSSSSSSSSSSSSSSSS
Answer:
120
Step-by-step explanation:
25 + 35 = 60
60 + 60 = 120
anyone?? pls help.........
Answer
C
Area of a circle is pi r to the power of 2.
so the radius is 6
so pi(6)^2= 36pi
