This question is solved using the conditional probability concept.
Using this concept, we find that:
a) P(AIB)= 5.3%b) P(A'|B') = 99.9%First, the concept is presented.
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(A|B) = \frac{P(A \cap B)}{P(B)}[/tex]
In which
P(A|B) is the probability of event A happening, given that B happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(B) is the probability of B happening.
----------------------------------------------------
Question a:
For relation with the formula presented above, I will change events A and B.
Event A: Person is infected.
Event B: Positive test.
Probability of a positive test:
85% = 0.85 out of 1/300 (person has the virus).5% = 0.05 out of 299/300(person does not have the virus)Thus:
[tex]P(B) = 0.85\frac{1}{300} + 0.05\frac{299}{300} = \frac{0.85\times1 + 0.05\times299}{300} = 0.0527[/tex]
Probability of a positive test and the person is infected.
85% = 0.85 out of 1/300. Thus:
[tex]P(A \cap B) = \frac{0.85}{300} = 0.0028[/tex]
Desired probability:
[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.0028}{0.0527} = 0.053[/tex]
0.053*100% = 5.3%, thus:
P(AIB)= 5.3%
---------------------
Question b:
Event A: Does not have the virus
Event B: Test negative.
Probability of a negative test:
100% - 85% = 15% = 0.15 out of 1/300 (person has the virus).100% - 5% = 95% = 0.95 out of 299/300(person does not have the virus)Thus:
[tex]P(B) = 0.15\frac{1}{300} + 0.95\frac{299}{300} = \frac{0.15\times1 + 0.95\times299}{300} = 0.9473[/tex]
Probability of a negative test and the person is not infected.
0.95 out of 299/300
Thus:
[tex]P(A \cap B) = \frac{0.95\times299}{300} = 0.9468[/tex]
Desired probability:
[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.9468}{0.9473} = 0.999[/tex]
0.999*100% = 99.9%, so:
P(A'|B') = 99.9%
A similar question can be found at https://brainly.com/question/24275491
1/1*2 +1/2*3+...+1/n(n+1)= n/n+1 proof by mathematical induction
I need this asap!!
Base case (n = 1):
• On the left side: 1/(1×2) = 1/2
• On the right side: 1/(1 + 1) = 1/2
Induction hypothesis: Assume the statement is true for n = k ; that is,
1/(1×2) + 1/(2×3) + … + 1/(k × (k + 1))) = k/(k + 1)
Inductive step (n = k + 1):
1/(1×2) + 1/(2×3) + … + 1/(k × (k + 1))) + 1/((k + 1) × (k + 2)))
= k/(k + 1) + 1/((k + 1) × (k + 2))
= (k × (k + 2) + 1) / ((k + 1) × (k + 2))
= (k ² + 2k + 1) / ((k + 1) × (k + 2))
= (k + 1)² / ((k + 1) × (k + 2))
= (k + 1) / (k + 2)
and this is what we wanted to show.
Based on corresponding angles and vertical angles, which angles must always be congruent to the angles given? Complete the table.
Answer:
A and B must always be congruent
B and D
E and G
F and H
Step-by-step explanation:
I have to be honest. from the picture I cannot see the vertical angles. All I see is a straight blue line and red letters. But based on the vertical theorem
A and B must always be congruent
B and D
E and G
F and H
also if you want to make sure it's right try to include another picture.
Answer:
Step-by-step explanation:
edmentum :)
Which equation can be used to find the length of Line segment A C?
Answer:
I don't see the problem.
Step-by-step explanation:
8 rational numbers between 3 and 4
Answer:
31/10,32/10,33/10,34/10,35/10
Step-by-step explanation:
a rational number is formed when any two integers p and q are expressed in the form of p/q
to find two two sets of rational numbers BETWEEN any two numbers
a and b we need to express a and b and rational numbers....let us express 3and4 as rational numbers 3=30/10 4=40/10
the list of rational numbers between 3and4,that is, 30/10,31/10,32/10,33/10,34/10,35/10,36/10,37/10,38/10,39/10,40/10.
therefore the five rational numbers between 3 and 4 are (31/10,32/10,33/10,34/10,35/10...
I hope that helps
find all the missing measurement
Answer:
Hello,
|FD|=15
Step-by-step explanation:
Since the triangles are similar, the bissects are also.
k*35=21 ==> k=21/35
k*25=|FD|
|FD|=(21/35)*25=15
How many times will the digit "3" appear if we write all whole numbers from 1-9999?
Answer:
4000
Step-by-step explanation:
from 1 - 1000 = 300
1's = 100
10's = 100
100's = 100
1000's = 0
300 * 10 = 3000
then add in all the 3000's (ie 3001,3002, etc ) that adds one more thousand
3000 + 1000 = 4000
Answer:
3000?
Step-by-step explanation:
Knowing that AQPT = AARZ, a congruent side pair is:
Answer:
A. QT ≅ AZ
Step-by-step explanation:
When writing a congruence statement of two triangles, the order of arrangement of the letters used in naming the triangles are carefully considered. Corresponding sides and angles of both triangles are arranged accordingly in the order they appear.
Given that ∆QPT ≅ ∆ARZ, we have the following sides that correspond and are congruent to each other:
QP ≅ AR
PT ≅ RZ
QT ≅ AZ
The only correct one given in the options given above is QT ≅ AZ
In the figure, m<1= m<2 = 22 and m<3 = m<4 = 123. Find m
Answer:
35
Step-by-step explanation:
35 because the two angles are added 22 and 123 = 145. 145-180=35
Given a mean score of 1150, standard deviation of 90, and 500 participants, solve the following problem. Using this data and the z-score distribution provided in class. Be sure to give your answer in the units requested. Only place your answer in the box.
1. What is the score for someone in the 15th percentile?
2. What is the percentile rank of someone with a score of 1100?
3. How many students have scores of 1060 or greater?
4. How many students scored between 1200 and 1250?
Answer:
1. 1056.67
2. 29th percentile.
3. 79
4. 77
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean score of 1150, standard deviation of 90
This means that [tex]\mu = 1150, \sigma = 90[/tex]
1. What is the score for someone in the 15th percentile?
This is X when Z has a p-value of 0.15, so X when Z = -1.037.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.037 = \frac{X - 1150}{90}[/tex]
[tex]X - 1150 = -1.037*90[/tex]
[tex]X = 1056.67[/tex]
2. What is the percentile rank of someone with a score of 1100?
This is the p-value of Z when X = 1100. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1100 - 1150}{90}[/tex]
[tex]Z = -0.555[/tex]
[tex]Z = -0.555[/tex] has a p-value of 0.29, so 29th percentile.
3. How many students have scores of 1060 or greater?
The proportion is 1 subtracted by the p-value of Z when X = 1060. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1060 - 1150}{90}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587.
Out of 500:
0.1587*500 = 79
79 is the answer.
4. How many students scored between 1200 and 1250?
The proportion is the p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1200. So
X = 1250
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1250 - 1150}{90}[/tex]
[tex]Z = 1.1[/tex]
[tex]Z = 1.1[/tex] has a p-value of 0.8643.
X = 1200
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1200 - 1150}{90}[/tex]
[tex]Z = 0.555[/tex]
[tex]Z = 0.555[/tex] has a p-value of 0.7106
0.8643 - 0.7106 = 0.1537
Out of 500:
0.1537*500 = 77
77 is the answer.
Logan has $1.95 in dimes and quarters in his pocket. He has 2 more dimes than quarters. (Keep in mind that dimes are worth 10c and quarters 25c.)
1. Write an equation that will help you determine the number of quarters.
2. Solve the equation showing all your steps.
3. Tell how many quarters and dimes he has.
Answer:
17 dimes 1 quarter
Step-by-step explanation:
logan has 1.95
step by step explanation:
a dime can not be more than 10 c
and less than 10c
a quarter can not be more than 25c
and less than 25 c
so logan must have 17 dimes and 1 quarter
key = 1 dime = 10c, 1 quarter = 25c
$1.70 + 25c = $1.95
hope this helps!!
Find the equation for the line that passes through the points ( - 1, - 10) and ( - 6,9). Give your
answer in point-slope form. You do not need to simplify.
Answer:
The point slope form of the equation is,
[tex]y + 10 = - \frac{19(x + 6)}{5} [/tex]
m = (y2-y1)/(x2-x1) = (9-(-10))/((-6)-(-1)) = -19/5
b = y1-mx1 = -69/5
Answered by GAUTHMATH
Im new to this app!
And im looking for help!!
Please help ASAP!!!
Please!!!!
y=x²-10x-7
a>0 so we will be looking for minimum
x=-b/2a=10/2=5
y=25-50-7=-32
Answer: (5;32)
How is the graph of y=(x-1)2-3 transformed to produce the graph of y-3(x+4)??
The graph is translated left 5 units, compressed vertically by a factor of 2, and translated up 3 units.
The graph is stretched vertically by a factor of Ź, translated left 5 units, and translated up 3 units.
O The graph is translated left 5 units, compressed horizontally by a factor of 3, and translated down 3 units.
O The graph is stretched horizontally by a factor of Ž, translated left 5 units, and translated down 3 units.
Step-by-step explanation:
How is the graph of y=(x-1)2-3 transformed to produce the graph of y-3(x+4)??
The graph is translated left 5 units, compressed vertically by a factor of 2, and translated up 3 units.
The graph is stretched vertically by a factor of Ź, translated left 5 units, and translated up 3 units.
O The graph is translated left 5 units, compressed horizontally by a factor of 3, and translated down 3 units.
O The graph is stretched horizontally by a factor of Ž, translated left 5 units, and translated down 3 units.
Answer:
B. The graph is stretched vertically by a factor of One-half, translated left 5 units, and translated up 3 units.
Step-by-step explanation:
just did the test
tìm tích phân tổng quát
xy'lny/x=x+ylny/x
Answer:
rhe
ehd
end
Step-by-step explanation:
jsu
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dj
dje
ej
e
What is the completely factored form of this polynomial? x3 + 3x2 - 6x – 18
A. (x - 2)(x - 3)(x + 3)
B. (x2 - 6)(x + 3)
C. (x2 + 3)(x-6)
D. (x + 6)(x - 1)(x + 3)
Answer:
(x+3) ( x^2 -6)
Step-by-step explanation:
x^3 + 3x^2 - 6x – 18
Factor by grouping
x^3 + 3x^2 - 6x – 18
Factor x^2 out of the first group and -6 out of the second group
x^2( x+3) -6(x+3)
Factor out x+3
(x+3) ( x^2 -6)
Simplify the following expression by using these values:
m = −6; n = 2; p = 4
[tex]-3m^{2}[/tex]+4n-p
Hi there!
Given the expression below:-
[tex] \large{ - 3 {m}^{2} + 4n - p}[/tex]
We are also given these three values below:
m = -6n = 2p = 4Simply substitute these values in:-
[tex] \large{ - 3 {( - 6)}^{2} + 4(2) - 4}[/tex]
Any negative numbers squared would result in positive.
[tex] \large{ - 3(36) + 8 - 4} \\ \large{ - 108 + 4} \\ \large \boxed{ - 104}[/tex]
Hence, the answer is -104 when substituting values in the expression.
Let me know if you have any questions!
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{-3m}\mathsf{^2}\large\textsf{ + 4n - p}\\\large\textsf{= -3(-6)}\mathsf{^2}\large\textsf{ + 4(2) - 4}\\\\\large\textsf{(-6)}^2\\\large\textsf{= (-6)(-6)}\\\large\textsf{= \bf 36}\\\\\large\textsf{= -3(36) + 4(2) - 4}\\\\\large\text{-3(36)}\\\large\textsf{= \bf -108}\\\\\large\textsf{= -108 + 4(2) - 4}\\\\\large\textsf{4(2)}\\\large\textsf{= \bf 8}\\\\\large\textsf{= -108 + 8 - 4}\\\\\large\textsf{-108 + 8}\\\large\textsf{= \bf -100}\\\\\large\textsf{-100 - 4}\\\large\text{ = \bf -104}[/tex]
[tex]\boxed{\boxed{\huge\text{Therefore, your answer is: \boxed{\bf -104}}}}\huge\checkmark[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Write an equation and solve it to answer each question. A pile of 55 coins consisting of nickels and dimes is worth $3.90. Find the number of each. I only need the equation plz. WILL MARK BRAINLIEST.
Answer:
0.05x + 0.1(55 - x) = 3.9
Step-by-step explanation:
There are 55 coins.
Let x = number of nickels.
The number of dimes is 55 - x.
The value of a nickel is $0.05, and the value of a dime is $0.10.
The value of x nickels is 0.05x
The value of 55 - x dimes is 0.1(55 - x)
The total value of the coins is 0.05x + 0.1(55 - x)
The total value of the coins is $3.90
0.05x + 0.1(55 - x) = 3.9
of its employees based on the number of sales per hour. One employee had the following sales for the last 20 hours 3 4 5 5 6 7 What is the median for the distribution of number of sales per hour? ____________ Express as a number
What is 8% of 1125?
Answer:
90
Step-by-step explanation:
1125/100=11.25
11.25x8=90
Im new, and i hope someone tells me the right answers!
A factor is a natural number that can be multiplied by another natural number to get a value. The greatest common factor refers to when one compares the factors of two numbers, the largest natural number that both numbers have in common is the number's greatest common factor.
In the case of ([tex]m^2[/tex]) and ([tex]m^4[/tex]), the greatest common factor is ([tex]m^2[/tex]) because there are no factors of ([tex]m^2[/tex]) that are larger than it. No number can have a factor larger than itself. Since ([tex]m^2[/tex]) is also a factor of ([tex]m^4[/tex]) it is the greatest common factor of the two numbers.
What information is NOT necessary to find the area of a circle?
a.
pi
c.
diameter
b.
radius
d.
height
Answer:
D. Height
General Formulas and Concepts:
Geometry
Area of a Circle: A = πr²
r is radiusStep-by-step explanation:
In order to find the area of a circle, we must follow the formula. Out of all the options given, height is not incorporated into the formula.
It wouldn't make sense to use height anyways since it would be 3-dimenional and we're talking 2-dimensional.
∴ our answer is D.
Twelve different video games showing drug use were observed. The duration times of drug use were recorded, with the times (seconds) listed below. Assume that these sample data are used with a 0.05 significance level in a test of the claim that the population mean is greater than 85 sec. If we want to construct a confidence interval to be used for testing that claim, what confidence level should be used for a confidence interval? If the confidence interval is found to be −1.8 sec<μ<213.5 sec, what should we conclude about the claim? The given confidence interval ▼ does not contain contains the value of 85 sec, so there ▼ is is not sufficient evidence to support the claim that the mean is greater than 85 sec
Answer:
95% confidence level should be used for a confidence interval.
The given confidence interval contains the value of 85 sec, so there is not sufficient evidence to support the claim that the mean is greater than 85 sec.
Step-by-step explanation:
0.05 significance level
1 - 0.05 = 0.95
0.95*100% = 95%
This means that a 95% confidence level should be used for a confidence interval.
Confidence interval is found to be −1.8 sec<μ<213.5 sec, what should we conclude about the claim?
Contains the value of 85 sec, thus there is not sufficient evidence to support the claim that the mean is greater than 85 sec.
"The fitted regression line will always run through the mean of the observed data. In other words, the point (x with bar on top, y with bar on top) will always lie on the estimated (fitted) regression line. Is it true or false?"
the formula for finding the circumference of a circle with radius,r, is circumference= 2πr. What is the formula for the circumference of a circle with a radius r/2?
Answer:
πr
Step-by-step explanation:
radius = r/2
so circumference = 2π(r/2)
= 2πr/2
= πr
Answer:
The answer is B which is C=2πr
Step-by-step explanation:
i just did it
i need help with this question asapppppp
9514 1404 393
Answer:
$11,680.58
Step-by-step explanation:
Usually, I would say copy the example, using 70,000 instead of 55,000. However, the example you show has a couple of errors in it. You need to do what it says, not follow what it did.
__
The first 48,535 is taxed at 15%, so the tax is 0.15×48535 = 7280.25.
The next (70,000 -48,535) = 21,465 is taxed at 20.5%, so the tax is ...
0.205×21,465 = 4400.325 ≈ 4400.33
The the total tax due on $70,000 is ...
$7280.25 +4400.33 = $11,680.58 . . . . tax due on $70,000
_____
Additional comments
The example shown has a couple of errors. The tax on the excess amount is figured at 2.05%, not 20.5%, and the 132.53 value from that is shown as 132.23.
__
Any tax table like this one can be reduced to a set of simpler formulas. Here are the formulas for the brackets shown in your tax table.
≤ 48535 -- income × 0.15
≤ 97069 -- income × 0.205 -2669.425
≤ 150,473 -- income × 0.26 -8008.22
≤ 214,368 -- income × 0.29 -12,522.41
> 214,368 -- income × 0.33 -21,097.13
In this case, the second row of this simpler table would give the tax on $70,000 as ...
tax = 70,000 × 0.205 -2669.425
tax = 14350 -2669.425 = 11680.575 ≈ 11,680.58 . . . same as above
define ascending and descending order by your and give one example
Answer:
ascending order} an order of numbers from least to greatest like 1 2 3 4
descending order} an order of numbers from greatest to least like 4 3 2 1
Please help 20 points
What is the best point estimate for the population's standard deviation if the sample standard deviation is 37.3
Answer:
The best point estimate for the population's standard deviation is 37.3.
Step-by-step explanation:
Best point estimate:
The best point estimate for the population mean is the sample mean.
The best point estimate for the population standard deviation is the sample standard deviation.
In this question:
Sample standard deviation of 37.3, and thus, the best point estimate for the population's standard deviation is 37.3.
Which expression is equivalent to
R^9/r^3?
Answer:
r^9/r^3 = r^9-3 = r^6
Step-by-step explanation:
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]r^6[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Simplifying...}}\\\\\frac{r^9}{r^3} \\--------------\\\\\text{Recall the quotient rule:}} \frac{a^x}{a^y}=a^{x-y}\\\\\rightarrow \frac{r^9}{r^3}\\\\\rightarrow r^{9-3}\\\\\rightarrow \boxed{r^6}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
2√3x+1 - √4x+5 =3
show your steps please
Answer:
x = 5
Step-by-step explanation:
I'm assuming that 3x +1 & 4x + 5 are all underneath the square root
2 √3x + 1 - √4x + 5 = 3
2 √3x + 1 = 3 + √4x + 5
4 (3x+1) = 9 + 6 √4x + 5 + 4x + 5
12x + 4 = 14 + 6√4x + 5 + 4x
-6 √4x + 5 = 14 + 4x - 12x - 4
-6 √4x + 5 = 10 - 8x
3 √4x + 5 = -5 + 4x (divided both sides by - 2)
9 (4x +5) = 16x^2 - 40x + 25
36x + 45 = 16x^2 - 40x + 25
36x + 45 - 16x^2 + 40x - 25 = 0
76x + 20 - 16x^2 = 0
-16x^2 + 76x + 20 = 0
4x^2 - 19x -5 = 0 (dividied by -4)
4x^2 + x - 20x -5 = 0
x (4x + 1) -5 (4x +1) = 0
(4x +1) (x-5) = 0
Possible answers:
4x + 1 = 0
x - 5 = 0
x = -1/4
x =5
Now we will check which one satisfies the equation
2√3x+1 - √4x+5
Substitue 5 for x and we get 3
Thus we know that 5 is the correct answer
Answered by Gauthmath
