Answer:
There is approximately 17% chance of a person not having a disease if he or she has tested positive.
Step-by-step explanation:
Denote the events as follows:
D = a person has contracted the disease.
+ = a person tests positive
- = a person tests negative
The information provided is:
[tex]P(D^{c})=0.95\\P(+|D) = 0.98\\P(+|D^{c})=0.01[/tex]
Compute the missing probabilities as follows:
[tex]P(D) = 1- P(D^{c})=1-0.95=0.05\\\\P(-|D)=1-P(+|D)=1-0.98=0.02\\\\P(-|D^{c})=1-P(+|D^{c})=1-0.01=0.99[/tex]
The Bayes' theorem states that the conditional probability of an event, say A provided that another event B has already occurred is:
[tex]P(A|B)=\frac{P(B|A)P(A)}{P(B|A)P(A)+P(B|A^{c})P(A^{c})}[/tex]
Compute the probability that a random selected person does not have the infection if he or she has tested positive as follows:
[tex]P(D^{c}|+)=\frac{P(+|D^{c})P(D^{c})}{P(+|D^{c})P(D^{c})+P(+|D)P(D)}[/tex]
[tex]=\frac{(0.01\times 0.95)}{(0.01\times 0.95)+(0.98\times 0.05)}\\\\=\frac{0.0095}{0.0095+0.0475}\\\\=0.1666667\\\\\approx 0.1667[/tex]
So, there is approximately 17% chance of a person not having a disease if he or she has tested positive.
As the false negative rate of the test is 1%, this probability is not unusual considering the huge number of test done.
h(x)=x^2-4x-12 in factored form?
k(x)=x^2-4x+8 in factored form?
Answer:
h(x) = (x-6)(x+2)
k(x) is not further factorable
Step-by-step explanation:
h(x) = x²-4x-12
= (x-6)(x+2)
k(x) = x²-4x+8
not further factorable
Astronomers treat the number of stars X in a given volume of space as Poisson random variable. The density of stars in the Milky Way Galaxy in the vicinity of our solar system is one star per 16 cubic light-years, on average. NOTE: Light-years is a distance measure. 7. What is the probability of exactly two stars in 16 cubic light-years? 8. What is the probability of three or more stars in 16 cubic light-years? 9. How many stars would be expected in 4 cubic light years? 10. How many stars would be expected in t cubic light years? 11. How many cubic light-years of space must be studied so that the probability of one or more stars exceeds 0.95? HINT: let `t' represent the unknown region of space, then nd the `t' that gives you the relevant probability.
Answer:
Explained below.
Step-by-step explanation:
The random variable X is defined as the number of stars in a given volume of space.
[tex]X\sim \text{Poisson}\ (\lambda=1)[/tex]
The probability mass function of X is:
[tex]p_{X}(x)=\frac{e^{-\lambda}\lambda^{x}}{x!}[/tex]
(7)
Compute the probability of exactly two stars in 16 cubic light-years as follows:
[tex]P(X=2)=\frac{e^{-1}\times 1^{2}}{2!}=\frac{e^{-1}}{2}=\frac{0.36788}{2}=0.18394\approx 0.184[/tex]
(8)
Compute the probability of three or more stars in 16 cubic light-years as follows:
[tex]P(X\geq 3)=1-P(X<3)\\\\=1-P(X=0)-P(X=1)-P(X=2)\\\\=1-\sum\limits^{2}_{x=0}[\frac{e^{-1}\times 1^{x}}{x!}]\\\\=1-0.36788-0.36788-0.18394\\\\=0.0803[/tex]
(9)
In 16 cubic light years there is only 1 star.
Then in 1 cubic light years there will be, (1/16) stars.
Then in 4 cubic light years there will be, 4 × (1/16) = (1/4) stars.
(10)
In 16 cubic light years there is only 1 star.
Then in 1 cubic light years there will be, (1/16) stars.
Then in t cubic light years there will be, [t × (1/16)] stars.
I can't find the answer
Answer: what grade is this
Step-by-step explanation:
Adding/Subtracting Rational Expressions
9514 1404 393
Answer:
(4x^2 +21x +18)/(3x^2 +34x -24)
Step-by-step explanation:
I find it helpful to keep in mind the form ...
a/b + c/d = (ad +bc)/(bd)
When we apply that to this case, we get ...
[tex]\dfrac{x+3}{x+12}+\dfrac{x+2}{3x-2}=\dfrac{(x+3)(3x-2)+(x+12)(x+2)}{(x+12)(3x-2)}\\\\=\dfrac{(3x^2+7x-6)+(x^2+14x+24)}{(x+12)(3x-2)}=\boxed{\dfrac{4x^2+21x+18}{3x^2+34x-24}}[/tex]
7.5 more than the quotient of h and 3 is w
Answer: h/3 + 7.5 = w
A farmer wanted to distribute 36 mangoes in paper bags, how many ways he can contribute the mangoes equally in paper bags?? Solve this using Factoring, Finding multiples and Divisibility Rules.
Answer:
36 = 2 x 2 x 3 x 3
Step-by-step explanation:
Given:
Number of mangoes = 36
Computation:
Factor of 36
36 = 2 x 2 x 3 x 3
Number of packing = 2 and number of mangoes in each = 18
Number of packing = 4 and number of mangoes in each = 9
Number of packing = 12 and number of mangoes in each = 3
Number of packing = 6 and number of mangoes in each = 6
Number of packing = 36 and number of mangoes in each = 1
Let p = log10 x, q = log10 y, and r = log10 z. (The 10s are base numbers.)
Write the expression log10 (x / y^2 √z) in terms of p, q, and r.
Please show work! I have the answer ( p- (2q + 1/2 r) ), but I need to show my work.
Answer:
(p / q^2 √r)
Just make x, y, z into p, q, r.
Very simple!
I need these graphed, they’re easy but I don’t have time to do them since it’s late. Excuse the bad handwriting
Answer:
For #5 all you have to do is set down to points in order for it to count. The answer is: (0,2) and (3,6)
Step-by-step explanation:
In order to find where exactly you must plot the points, we plug in what we know. In our equation, the 2 is our y intercept, this means that the point is (0,2) (Side Note: here's another example, (0,6) the 6 would be our y intercept)
From the point (0,2) we use the other value given. The other value given in this case, is our slope. When dealing with slope, we use Rise over Run or Rise/Run. This means that from the 2 on the graph, you rise 3 which would be 5 and you run to the right for 4. This now gets you the points (3,6)
Hope this helps with plotting the other questions! :)
(SIDE NOTE: IF THEY GIVE THE VALUE WITH X AS JUST A NUMBER, YOU CAN PLACE A 1 UNDER IT TO TURN IT INTO A FRACTION. FOR EXAMPLE 3X CAN BE TURNED INTO 3/1 WHICH WOULD THEN BE RISE 3 AND RUN 1.
(sooory about the caps, it's just to get your attention.)
3. f(x) = x2 + 4x - 2
Answer:
f(x)= -(x-2)^2+2
Step-by-step explanation:
the same valuve needs the be added to both sides
f(x)+?= -x^2+4x+?-2
to complete the square -x^2+4x-4= -(x-2)^2 add the -4 to the expression
f(x)+?= -x^2+4x-4-2
since -4 was added to the right side, also add -4 the the left side
f(x)-4= -x^2+4x+?-2
now factor out the negative sign from the expression
f(x)-4= -(x^2-4x+4)-2
using a^2-ab+b^2=(a-b)^2
f(x)-4= -(x-2)^2-2
move the constant the the right side and change its sign
f(x)= -(x-2)^2-2+4
now calculate the sum
f(x)= -(x-2)^2+2
What is five times the difference of a number and three?
Btw I need answer immediately
Answer:
t=x+3
y = (x+3)^2 + 5
y = x^2+6x + 9 + 5
y= x^2 + 6x + 14
Answer:
5 times x-3?
Step-by-step explanation:
Sorry if its wrong i didn't really understand what you wanted.
I need help with 35-38 please!!!
Answer:
-3
Step-by-step explanation:
A gardener has 27 pansies and 36 daisies. He planted an equal number of each type of flower in each row. What is the greatest possible number of pansies in each row? I need the answer quick
Answer:
There will be 3 rows of pansies
Step-by-step explanation:
g(x) = 30x + 5
h(x) = 10x – 15
Find h(–3) + g(–5)
Answer:
The answer is: -190
Step-by-step explanation:
First, you need to input the -3 into the h(x) equation as follows:
h(-3) = 10(-3) - 15, then solve.
h(-3) = -30 - 15
h(-3) = -45.
Then you do the same for g(-5).
So, g(-5) = 30(-5) + 5
g(-5) = -150 + 5
g(-5) = -145.
Now you add the -45 and -145.
h(-3) + g(-5) = -45 - 145
h(-3) + g(-5) = -190.
Please help!!!! I'll give you 15 points!!
Step-by-step explanation:
the answer is C
2/5(2x+3)
I hope it helps
Solve for x:3(x+1)=-6
Answer:
x=-3
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
3(x +1) =-6
3x +3 =-6
3x =-6 - 3
3x=-9
x=-9:3
x=-3
factorise x squared - 42 squared
Answer:
42 squared is 1764
Step-by-step explanation:
Answer: (x + 42)(x - 42)
Step-by-step explanation:
factorise: x^2 - 42^2
. x^2 - 42^2 have ^2 in common (so you can ignore that).
. put in brackets (x - 42)(x + 42)
. +/- any order really doesn't matter :D
Mary has 96 muffins which she needs to box up, 5 of which are blueberry, into dozens. How many boxes dose he need
Answer:
8
Step-by-step explanation:
Mary needs 8 boxes to put 96 muffins in dozens so 96÷12 gives you 8
8
Write the equation of the line through the
points (-8, -2) and (-4,-3) in POINT-SLOPE
FORM
Answer:
Y=-1/4x-4
Step-by-step explanation:
To find the slope, you would need to use the equation y2-y1/x2-x1 by the coordinates. You would get -3-(-2)/-4-(-8). This would result in -1/4. Now that you have your slope, you plug in one of the coordinates. If you used (-8,-2), you would get -2=-8(-1/4)+b. Simplify the equation to get -2=2+b, which simplifies to -4=b, and b is the y intercept.
Reese wants to organize a party and decides to save money for it.He calculates that he needs $420 in 9 weeks.He already has $60
Rick invest $5,830 into a retirement saving account. The account compounds at 3.2% monthly for. How much money will Rick have in 4 years? Show work. Use comma and dollar signs in the final answer.
Answer:
$746.24
Step-by-step explanation:
3.2/100 = 0.032
5,830 X 4 = 23,320
23,320 X 0.032 = 746.24
According to Boyle's Law, if the temperature of a confined gas is held fixed, then the product of the pressure P and the volume V is a constant, suppose that, for a certain gas, PV=800 where P is measured in pounds per square inch and V is measured in cubic inches. Answer the following: (this is calculus)
A) Find the average rate of change of P as V increases from 200in^3 to 250in^3.
B) Express V as a function of P and show that the instantaneous rate of change of V with respect to P is inversely proportional to the square of P.
If PV = 800, then P can be written as a function of V,
P(V) = 800 / V
(a) The average rate of change of P as V increases from 200 to 250 in³ is then
(P (250) - P (200)) / (250 in³ - 200 in³) = (3.2 lb/in² - 4lb/in²) / (50 in³)
... = -0.016 (lb/in²)/in³
(Or -0.016 lb/in⁵, but I figure writing the rate as (units of pressure) per (unit volume) makes more sense.)
(b) We can also write V as a function of P :
V(P) = 800 / P
Take the derivative:
V'(P) = - 800 / P²
which immediately demonstrates that V'(P) ∝ 1 / P², as required. (The fish-looking symbol, ∝, means "is proportional to".)
If differentiating is supposed to be more involved, you can use the limit definition:
[tex]V'(P)=\displaystyle\lim_{h\to0}\frac{V(P+h)-V(P)}h[/tex]
[tex]V'(P)=\displaystyle\lim_{h\to0}\frac{\frac{800}{P+h}-\frac{800}P}h[/tex]
[tex]V'(P)=\displaystyle\lim_{h\to0}\frac{\frac{800P-800(P+h)}{P(P+h)}}h[/tex]
[tex]V'(P)=\displaystyle800\lim_{h\to0}\frac{-\frac h{P(P+h)}}h[/tex]
[tex]V'(P)=\displaystyle-800\lim_{h\to0}\frac1{P(P+h)}=-\dfrac{800}{P^2}[/tex]
Part(a): The average rate of change of [tex]\frac{dP}{dV}[/tex] is [tex]-0.0164 lb/in^{2}[/tex]
Part(b): The required answer is [tex]\frac{dV}{dP} \infty \frac{1}{P^{2}}[/tex]
Part(a):
Given,
[tex]PV=800[/tex]
Differentiating the above equation with respect to [tex]V[/tex].
[tex]\frac{dP}{dV}=-\frac{P}{V}[/tex]
Now, at [tex]V=200 in^{3}[/tex] and [tex]P=4 lb/in^2[/tex]
At [tex]V=250 in^3[/tex] and [tex]P=\frac{80}{25} lb/in^2[/tex]
Hence, we can write,
[tex]\frac{dP}{dV}[/tex] at [tex]V=200[/tex] we get,
[tex]\frac{-1}{200}=\frac{-1}{50}[/tex]
Again [tex]\frac{dP}{dV}[/tex] at [tex]V=250[/tex] we get,
[tex]\frac{-80}{25\times 250}[/tex]
So, the average rate of change of [tex]\frac{dP}{dV}[/tex] is,
[tex]\frac{-\frac{1}{50}- \frac{8}{25\times25} }2\\=-\frac{1}{100}-\frac{1}{625}\\=-0.0164 lb/in^2[/tex]
Part(b):
Given,[tex]PV=800[/tex] then,
[tex]V=\frac{800}{P}[/tex]
Now,[tex]\frac{dV}{dP} =-\frac{800}{P^2}[/tex]
Then the above implies,
[tex]\frac{dV}{dP} \infty \frac{1}{P^{2}}[/tex]
Learn more:https://brainly.com/question/12817429
Is Triangle B a rotation of Triangle A?
Explain How u know
Answer:
No, triangle B is a reflection of triangle A.
Step-by-step explanation:
The points of triangle A are reflected across the dotted line. So as a result triangle B is a reflection of triangle A.
Answer:
No
Step-by-step explanation:
Its a reflection because even if you did rotate it it would never be in that orientation.
The graph of y = -3x + 4 is:
Answer:
(0,4)
Step-by-step explanation:
Referring to the methods for calculating average atomic mass, which one is 'incorrect' ?
Mary
Jack
Alan
Alan's method is correct coz to find we add all the given value and divide by the numbers present
2. Find the distance between (-2,1) and (3,4).
how many decimal places would the answer have when you find the product of 43.09281×5.092?
Answer:
219.42858852
Step-by-step explanation:
I WILL GIVE EXTRA POINTS!!! HELPPPPP PLEASE!!!! SHOW ALL WORK!!!
Answer: 2x+52=2(x+26)
3x-35=-105
Step-by-step explanation:
3x - 15 = 7 - 8x how do you solve this
Answer:
X=2
Step-by-step explanation:
3x-15=7-8x
3x+8x=7+15
11x=22
x=[tex]\frac{22}{11}[/tex]
x=2
Answer:
324
Step-by-step explanation:
3x3 = 9
9-15 = -6
8x8=64
7-64=-54
-54 x -6 = 324
Solve.
2x + 4 3
B) x < 3
B) x 1/3
D) x < 1/3
Answer:
c
Step-by-step explanation:
what is the product of (2/5x-3/4y^2) and (2/5x+3/4y^2)?
Answer:
[tex]\frac{2x}{5}- \frac{3y^{2} }{4}[/tex]
Step-by-step explanation:
(2/5x-3/4y^2) & (2/5x+3/4y^2) is [tex]\frac{2x}{5}- \frac{3y^{2} }{4}\\[/tex]