Answer:
0.009804
Step-by-step explanation:
We are given;
probability of testing positive given that you have the disease is 0.99
Also, probability of not testing positive and not having the disease is 0.99
We are also told that it is a rare disease and so strikes only 1 in 1000 people = 0.0001
Let's denote positive test by T+, negative test by T¯, having the disease by D+, not having the disease by D¯.
So, we can now denote all the values in probability we have written earlier.
Thus:
P(T+ | D+) = 0.99
P(T¯ | D¯) = 0.99
P(D+) = 0.0001
Thus, P(D¯) = 1 - P(D+) = 1 - 0.0001 = 0.9999
Now, let's find probability of testing positive;
P(T+) = (P(T+ | D+) × P(D+)) + (P(T+ | D¯) × P(D¯))
Now, (P(T+ | D¯) is not given but by inspection, we can infer from the values given that it is 0.01
Thus;
P(T+) = (0.99 × 0.0001) + (0.01 × 0.9999)
P(T+) = 0.010098
Chances that one has the disease would be gotten from Baye's theorem;
P(D+ | T+) = (P(T+ | D+) × P(D+))/P(T+) = (0.99 × 0.0001)/0.010098 = 0.009804
for each equation below, find y if x=3
what is the domain and range of f(x)=2x+3
Answer:
D:{x∈R}
R:{y∈R}
Step-by-step explanation:
This is just a linear function. I know this because the degree of the x-variable is 1.
Domain and range are sets of possible values the function can have - though not necessarily at the same time.
Thus, there are no restrictions to the domain and range unless context is given.
Therefore, the domain and range is:
D:{x∈R}
R:{y∈R}
Write an equation in slope-intercept form (y = mx + b).
A vertical line passing through (1, -4).
Answer:
x=1
Step-by-step explanation:
Anytime there is a vertical line, the y value becomes infinite as the line goes on forever. The only restriction on the line is on the x value of your coordinate. The same goes for a horizontal line, only the x value would become infinite and the y value would be constant.
Vertical Line: (x,∞)
Horizontal Line: (∞,y)
The average spending at Neco's salad bar is $8.73 with a standard deviation of $3.41. The distribution follows t-distribution. The management is interested in the middle 90% of the customers (spending wise) as it believes that they represent their true customer base. What will be the difference between the upper and lower spending cut-offs which define the middle 90% of the customers if the sample contains 41 customers
Answer:
Difference between upper and lower limits is : 1,816
Step-by-step explanation:
A CI (confidence interval ) for t student distribution is:
( μ₀ - t(α/2)* s/√n ; μ₀ + t(α/2)* s/√n )
Where:
μ₀ is the mean and s the standard deviation of the dstribution
n size of the sample
CI = 90 % means α = 10 % α = 0,1 α/2 = 0,05
and degree of freedom df = n - 1 df = 40
From t student table we get:
tα/2 = 1,6839
Then:
t(α/2)* s/√n = 1,6839* 3,41/√40
t(α/2)* s/√n = 0,908
8,73 - 0,908 = 7,822
8,73 + 0,908 = 9,638
CI (90%) = ( 7,822 ; 9,638 )
Difference between upper and lower cut-offs points is:
Δ = 1,816
-1/2(-6x -5/2) +1= 9x
Answer:
x=3/8
Step-by-step explanation:
Multiplique dentro del paréntesis por -1/2.Después de haber multiplicado le ecuación le quedará así 3x + 5/4 +1 = 9x.Ahora vamos a calcular la suma de la ecuación y quedará a 3x + 9/4 =9x.Después vamos a multiplicar ambos lados de la ecuación por 4 y quedará a 12x + 9= 36x.Luego vamos a mover la constante ( que es 9) al lado derecho y cambié su signo y quedará a 12x = 36x - 9.Después vamos agrupar los términos semejantes ( en este caso x) y quedará a -24x = -9.Finalmente vamos a dividir ambos lados de la ecuación entre -24 y la respuesta nos quedará a x = 3/8.Angles 1 and 2 form a right angle. 2 lines form a right angle. Another line extends between the 2 lines to form 2 angles. The top angle is labeled 1, and the bottom angle is labeled 2. Which word describes their measures? linear congruent complementary supplementary
Answer:
complementary
Step-by-step explanation:
yes
The word that describes their measures of ∠1 and ∠2 is: complementary.
Recall:
Angles that are complementary are angles whose sum equals 90 degrees.A right angle equals 90 degrees.From the information given, we know that:
m∠1 and m∠2 forms a right angle.
Since a right angle = 90 degrees, therefore:
m∠1 + m∠2 = 90° (complementary)
Therefore, the word that describes their measures of ∠1 and ∠2 is: complementary.
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What is the fractional equivalent of the repeating decimal 0.2 ?
Answer:
1/5
Step-by-step explanation:
I put it in a graphing calculator and converted it into a fraction
You invest $2000 in a bank account. Find the amount of simple interest you earn in two years for an annual interest rate of 5.5%. Use the formula for simple interest I = p · r · t, where I is the interest, p is the principal, r is the annual interest rate, and t is the time in years.
Answer:
$220 is the amount of simple interest you will earn
Step-by-step explanation:
I = p * r * t
Principle = $2000
Rate = 5.5% (you need to change this to a decimal by dividing by 100) or
0.055
Time = 2 years
I = 2000 * 0.055 * 2
I = $220
help me asap i don't know this
Answer:
y = 3
Step-by-step explanation:
Step 1: Write equation
-2(7 - y) + 4 = -4
Step 2: Subtract 4 on both sides
-2(7 - y) = -8
Step 3: Distribute
-14 + 2y = -8
Step 4: Add 14 to both sides
2y = 6
Step 5: Divide both sides by 2
y = 3
Evaluate x^2 + 2x + 3
for x = 4
Steps to solve:
x^2 + 2x + 3 when x = 4
~Substitute
4^2 + 2(4) + 3
~Simplify
16 + 8 + 3
~Add
24 + 3
~Add
27
Best of Luck!
In a particularclass of 22 students, 10 are men. What fraction of the students in the class are
women?
Answer: 6/11
Work Shown:
22 people total, 10 men, so 22-10 = 12 women are in the class.
12/22 = (2*6)/(2*11) = 6/11 is the fraction of women in the class
Answer:
I'm pretty sure the answer they want is 12/22 or 6/11 students are women although some people are not men or women which technically makes the question impossible to solve.
.At a certain animal shelter, the ratio of puppies to adult dogs is 7 to 4. This week there are a total of55 dogs in the shelter. How many puppies are in the shelter this week? How many adult dogs are in the shelter this week
Answer:
There are 35 adult dogs and 20 puppies
Step-by-step explanation:
Represent the puppies with P and the Adult dogs with A
Given
[tex]A : P = 7 : 4[/tex]
Dogs = 55
Required
Determine A and P
First, we need to sum the ratios;
[tex]Total = A + P[/tex]
[tex]Total = 7 + 4[/tex]
[tex]Total = 11[/tex]
Adult Dogs is then calculated as follows;
[tex]A = \frac{A\ Ratio}{Total} * Dogs[/tex]
[tex]A = \frac{7}{11} * 55[/tex]
[tex]A = \frac{385}{11}[/tex]
[tex]A = 35[/tex]
Puppies is calculated by subtracting the number of adult dogs from the total
[tex]P = Dogs - Adult\ Dogs[/tex]
[tex]P = 55 - 35[/tex]
[tex]P = 20[/tex]
Hence;
There are 35 adult dogs and 20 puppies
Solve the equation -4 = 5 -x.
Answer:
when x goes opposite side of equals to sign of x changes and same goes with 4 then x=5+4 then the answer will be 9
If x=.5, what is the numerical value of 20x ?
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How much discount is received on an item with a marked price of Rs 500 if the discount rate is 3%? * Rs 50 Rs 15 Rs 25 Rs 5
Answer:
Rs.15
Step-by-step explanation:
3% = 3/100 × 500 = 15
Question 1 (1 point)
When simplified [9(7 – 3) + 13] - [11 - (6 + 9)] equals:
53
39
43
None of these
Answer:45
Step-by-step explanation:
[9(7-3)+13]-[11-(6+9)]
[9(4)+13]-[11-(15)]
[36+13]-[4]
49-4
45
Answer: The answer is 53
on Tuesday, the Soto salad restaurant served 6 1/2 cups of Italian salad dressing. if the restaurant serves 1/2 cups of dressing with each salad, how many salads where ordered?
Answer:
11
Step-by-step explanation:
PLZ HELP ASPPP PLZ WILL GIVE YOU BRAINLIST
Answer:
x=(-9)
PQ=2
PR=3
Step-by-step explanation:
y=1/4x + 6
that passes through the point (-4, 3) in slope-intercept form.
Answer:
The answer is
[tex]y = \frac{1}{4} x + 4[/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line.
The equation is
y = 1/4x + 6
Comparing with the general equation above
Slope = 1/4
Since the lines are parallel their slope are also the same
That's
Slope of parallel line = 1/4
So the equation of the parallel line using point (-4 , 3) and slope 1/4 is
[tex]y - 3 = \frac{1}{4} (x + 4) \\ y - 3 = \frac{1}{4} x + 1 \\ y = \frac{1}{4} x + 1 + 3[/tex]We have the final answer as
[tex]y = \frac{1}{4} x + 4[/tex]Hope this helps you
I have 4 questions
1. Suppose point T is between points R and V on a line. If RT = 63 units and RV = 131 units,
then what is TV?
131
194
68
80
2.Given point P is between M and N. If MN = 26, MP = x + 4, and PN = 2x + 1, what is the value of x?
x = 3
x = 7
x = 12.5
x = 22
3.Given M is the midpoint of HJ, HM = 4x - 12, and MJ = 3x + 9. What is the value of x?
4.If D is the midpoint of CE, DE = 2x + 4, and CE = 6x + 2, then what is CD?
There are 18 men on 2 baseball teams. 2/3 of them brought their sons to watch them play. How many brought their son?
Consider the graphs of f (x) = x cubed and of g (x) = StartFraction 1 Over x cubed EndFraction. Are the composite functions commutative? Why or why not?
Answer:
c
Step-by-step explanation:
They are not commutative because the domains of f(x) and g(x) are different.
The functions [tex]f(x) = x^{3}[/tex] and [tex]g(x) = \frac{1}{x^{3} }[/tex] are not commutative because domains of f(x) and g (x) are different.
Here,
The functions are [tex]f(x) = x^{3}[/tex] and [tex]g(x) = \frac{1}{x^{3} }[/tex] and graph of the function are shown in figure.
We have to check the function are composite or not.
What is Domain of function?
The domain of a function is the set of all possible inputs for the function.
Now,
Domain of function [tex]f(x) = x^{3}[/tex] is ( -∞, ∞).
And, Domain of function [tex]g(x) = \frac{1}{x^{3} }[/tex] is ( -∞,0 ) U ( 0, ∞).
Hence, the domain of the functions are different so they are not commutative.
So, The functions [tex]f(x) = x^{3}[/tex] and [tex]g(x) = \frac{1}{x^{3} }[/tex] are not commutative because domains of f(x) and g (x) are different.
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If KL = x + 4, LM = 2, and KM = 5x − 3, what is KL?
Step-by-step explanation:
then put x valule into KL equation
I
rep
What is the solution of 4(2y + 1) = 2(y - 13)
What is the answer
Answer:
- 5
Step-by-step explanation:
Step 1:
4 ( 2y + 1 ) = 2 ( y - 13 )
Step 2:
8y + 4 = 2y - 26
Step 3:
6y + 4 = - 26
Step 4:
6y = - 30
Answer:
y = - 5
Hope This Helps :)
What number line correctly shows one way to find 2-6 ?
Jack is packing snacks for him and his three brothers. He bought 10 1/2 ounces of pretzels. He wants to put the pretzels into bags so that he and his three brothers have the same of pretzels in their bags. How many ounces of pretzels should he put into each bag?
Answer:
3.5
Step-by-step explanation:
total pretzel=10 1/2 or10.5
no. of brother = 3
now,
10.5 pretzel for each borther= 10.5/3
=3.5 ans
List several figures other than rectangles that tessellate the plane using translations
Answer:
A
Step-by-step explanation:
an airplane is traveling at 400 miles per hour. which equation can be used to find the total distance the plane will travel in h hours.
Answer:
y=400h
Where y is distance and h is time.
The velocity of an object is given by the following function defined on a specified interval. Approximate the displacement of the object on this interval by subdividing the interval into the indicated number of subintervals. Use the left endpoint of each subinterval to compute the height of the rectangles. v = 1/(2t + 4) (m/s) for for 0 ≤ t ≤ 88; n = 22
Answer:
The displacement of the object on this intervals is 1.33 m.
Step-by-step explanation:
Given that,
The function of velocity is
[tex]v=\dfrac{1}{2t+4}\ m/s[/tex]
For 0 ≤ t ≤8 , n = 2
We need to calculate the intervals
Using formula for intervals
For, n = 1
[tex]\Delta x=\dfrac{t_{f}-t_{i}}{n}[/tex]
[tex]\Delta x=\dfrac{8-0}{2}[/tex]
[tex]\Delta x=4[/tex]
So, The intervals are (0,4), (4,8)
We need to calculate the velocity
Using given function
[tex]v=\dfrac{1}{2t+4}[/tex]
For first interval (0,4),
Put the value into the formula
[tex]v_{0}=\dfrac{1}{2\times0+4}[/tex]
[tex]v_{0}=\dfrac{1}{4}[/tex]
For first interval (4,8),
Put the value into the formula
[tex]v_{4}=\dfrac{1}{2\times4+4}[/tex]
[tex]v_{4}=\dfrac{1}{12}[/tex]
We need to calculate the total displacement
Using formula of displacement
[tex]D=(v_{0}+v_{4})\times(\Delta x)[/tex]
Put the value into the formula
[tex]D=(\dfrac{1}{4}+\dfrac{1}{12})\times4[/tex]
[tex]D=1.33\ m[/tex]
Hence, The displacement of the object on this intervals is 1.33 m.
The displacement of the object whose velocity function is given is 1.33 m
The given parameters are:
[tex]\mathbf{v = \frac{1}{2t + 4},\ 0 \le t \le 8; n =2}[/tex]
The end point of intervals is calculated as:
[tex]\mathbf{\triangle t = \frac{b - a}{n}}[/tex]
So, we have:
[tex]\mathbf{\triangle t= \frac{8 - 0}{2}}[/tex]
[tex]\mathbf{\triangle t = \frac{8}{2}}[/tex]
[tex]\mathbf{\triangle t= 4}[/tex]
So, the intervals are (0,4) and (4,8)
Calculate the velocity at the beginning of each interval
[tex]\mathbf{v_0 = \frac{1}{2(0) + 4} = \frac 14}[/tex]
[tex]\mathbf{v_4 = \frac{1}{2(4) + 4} = \frac 1{12}}[/tex]
Calculate the displacement (S) using:
[tex]\mathbf{S = (v_0 + v_4) \times \triangle t}[/tex]
So, we have:
[tex]\mathbf{S = (1/4 + 1/12) \times 4}[/tex]
Expand
[tex]\mathbf{S = 1 + 1/3}[/tex]
Add
[tex]\mathbf{S = 1 \frac 13}[/tex]
Express as decimals to 2 decimal places
[tex]\mathbf{S = 1.33}[/tex]
Hence, the displacement is 1.33 m
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G(x) = 2x^2 and h(x) = √x^2+1 .What is (goh)^-1 and is it a function?
Answer:
Step-by-step explanation:
Hello,
[tex](goh)(x)=g(h(x))=2\left( \sqrt{x^2+1}\right)^2=2(x^2+1)\\\\x=(goh)((goh)^{-1}(x))=2((goh)^{-1}(x)^2+1)\\ \\\left((goh)^{-1}(x)\right)^2=\dfrac{x}{2}-1=\dfrac{x-2}{2}\\ \\(goh)^{-1}(x)=\sqrt{\dfrac{x-2}{2}}[/tex]
And this is a function defined for x-2 [tex]\geq[/tex] 0, meaning x [tex]\geq[/tex] 2
Thanks