company a is developing a new pregnancy test. based on their experiments, the test gives the correct result about 82% of the time, meaning the test result is positive when the person is pregnant, it is negative when the person is not pregnant. suppose that 55.00000000000001% of women who take the test are pregnant. if the test result is positive, what is the probability that the person is actually not pregnant? you can express your answer as a fraction, decimal, or a percentage. if you asnwer in decimal, include at least 3 digits after the decimal point. if you answer is a percentage, make sure to include a % sign in your answer.
Answers
The probability that the person is actually not pregnant given a positive test result is 0.127, which can be expressed as a fraction of 127/1000 or as a percentage of 12.7%.
To solve this problem, we can use Bayes' theorem, which states that the probability of an event given some evidence is proportional to the probability of the evidence given the event and the prior probability of the event. In this case, we want to find the probability that the person is not pregnant given a positive test result:
P(not pregnant | positive test) = P(positive test | not pregnant) * P(not pregnant) / P(positive test)
We know that P(positive test | not pregnant) is the probability of a false positive, which is 1 - 0.82 = 0.18. We also know that P(not pregnant) is 1 - 0.55 = 0.45. To find P(positive test), we can use the law of total probability:
P(positive test) = P(positive test | pregnant) * P(pregnant) + P(positive test | not pregnant) * P(not pregnant)
= 0.82 * 0.55 + 0.18 * 0.45
= 0.637
Now we can plug these values into Bayes' theorem:
P(not pregnant | positive test) = 0.18 * 0.45 / 0.637
= 0.127
Therefore, the probability that the person is actually not pregnant given a positive test result is 0.127, which can be expressed as a fraction of 127/1000 or as a percentage of 12.7%.
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Related Questions
David is tracking the amount of water he drinks each day.
On Thursday, he drinks 15 cups of water.
On Friday, he drinks 12 cups of water.
What is the percent change in his water intake?
Answers
Answer:
The original amount of water is 15 cups.
The change in David's water intake is 3 cups.
The percent change is 20 %. This is a percent decrease .
Step-by-step explanation:
It was correct
The percentage change in the amount of water David drank from Thursday to Friday is -20%.
On Thursday, David drank 15 cups of water and then on Friday drank 12 cups.
The first thing to do is find the difference:
= Friday water - Thursday
= 12 - 15
= -3 cups
The percentage change is:
= Change / Number of cups on Thursday x 100%
= -3 / 15 x 100%
= -20%
In conclusion, the percentage change was -20%
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a. If Mei has earned 30 points, write and solve a multiplication equation to find how many books she needs to read.
Answers
If Mei has earned 30 points, the multiplication equation to find how many books she needs to read is 30=5x.
How to find the number of books she needs to read?Let x represent the number of books she needs to read.
So,
The equation to find the number of books she need to read is:
30=5x
Let solve for x
30 =5x
Divide both side by 5x
x = 30/5
x = 6 books
Therefore the number of books is 6 books.
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Help me please! I really need it
Answers
Answer:
264 remainder 19
Step-by-step explanation:
-
7.5 ft
Find the perimeter of the semicircular region
Answers
Circle w has a radius of 20 in and central right angle. VWX find the length of VX. Leave answer in terms of pi
Answers
The arc length is 10 Pi
(I don't know for sure, but its what I got)
Hello!
Solve this Quadratic Equation: \(x^2 + 4x + 3 = 0\)
Use factoring to solve, then double-check using the Quadratic Formula.
Include all steps and show your work in detail. The best answer gets Brainliest.
Answers
Answer:
\(x = -1, -3\)
Solve by FactoringTo solve by factoring, we will split up the equation using our factoring rules.
In this particular instance, we will factor out common variables.
We need to ensure that we get two numbers that add to equal 4 and two numbers that multiply to equal 3.
\(x^2 + 4x + 3 = 0\)
\((x+3)(x+1)=0\)
Set each factor equal to zero and solve.
Root 1
\(x+3=0\)
\(x=-3\)
Root 2
\(x+1=0\)
\(x=-1\)
The final answer is \(\boxed{x = -1, -3}\).
As requested in the question, we must now check with the quadratic formula.
What is the quadratic formula?To solve this quadratic equation, we will utilize the quadratic formula:
\(\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
The parent formula for a quadratic equation is \(ax^2+bx+c=0\).
We will define our variables:
a: 1b: 4c: 3Now, we will plug these into the equation and solve the equation.
Solve\(\displaystyle x=\frac{-4\pm\sqrt{4^2-4(1)(3)}}{2(1)}\)
\(\displaystyle x=\frac{-4\pm\sqrt{16-12}}{2}\)
\(\displaystyle x=\frac{-4\pm\sqrt{4}}{2}\)
\(\displaystyle x=\frac{-4\pm2}{2}\)
Root 1
\(\displaystyle x=\frac{-4+2}{2}\)
\(\displaystyle x=\frac{-2}{2}\)
\(\boxed{x=-1}\)
Root 2
\(\displaystyle x=\frac{-4-2}{2}\)
\(\displaystyle x=\frac{-6}{2}\)
\(\boxed{x=-3}\)
Final AnswerThe final answer is \(\boxed{x = -1, -3}\).
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Given the equation, we can start by rewriting:
x^2 + 4x + 3 = 0
Now, let’s write in factored form:
(x + 1) (x + 3) = 0
since x is the only variable and there are 2 numbers, we can make 2 equations:
x + 1 = 0
x + 3 = 0
This forms:
(X + 1) (x + 3) = 0
Now, we can solve:
? + 1 = 0
? + 3 = 0
-1 + 1 = 0 and -3 + 3 = 0
x = -1 AND -3
A factory uses 3/8 of a barrel of pecans in each batch of cookies. Yesterday, the factory used 3/4 of a barrel of pecans. How many batches of cookies did the factory make yesterday
Answers
Answer:
3/4
Step-by-step explanation:
1 batch of cookies is equal to 0.375. 3/4 a barrel of cookies is equal to 0.75. 0.75/0.375 is equal to 2. So 3/4 a barrel is 2 batches of cookies.
help me with this question please
Answers
Answer:
N+1
Step-by-step explanation:
It begins with = 2
then n+1=3
then n+2=4 and so on it is n+1
1)4/9 ÷ 2/3
2) 5/13 ÷ 7/6
3)13/15 ÷ 9/10
4) 5.2 x 8.5
5) 12.5 x 7.9
6) 0.3 x 11.2
7) 9 ÷ 4.5
8) 5.9 ÷ 0.54
9) 12.9 ÷ 46.5
Solve these question while showing your work.
Answers
2. 30/91. Flip 7/6 to 6/7 and then multiply. You cannot simplify the fraction.
3. 26/27. Flip 9/10 to 10/9 and then multiply. You cannot simplify the fraction.
4. 44.2. Multiply it as if there was no decimal. Then count the number of digits after the decimal in each factor. Then put the same number of digits behind the decimal in the product.
5. 98.75. Multiply it as if there was no decimal. Then count the number of digits after the decimal in each factor. Then put the same number of digits behind the decimal in the product.
6. 3.36. Multiply it as if there was no decimal. Then count the number of digits after the decimal in each factor. Then put the same number of digits behind the decimal in the product.
7. 2. Multiply the divisor by as many 10’s as necessary until you get a whole number. Remember to multiply the dividend by the same number of 10’s. Then divide it normally.
8. 10.93 (rounded). Multiply the divisor by as many 10’s as necessary until you get a whole number. Remember to multiply the dividend by the same number of 10’s. Then divide it normally. I rounded it to the hundredth.
Hope this helps!
can someone solve these
1. a number times 4 minus 3 is 5
2. 11 is a number divided by 2 plus 1
Answers
Answer:
1. a number is 2
2. a number is 20
Step-by-step explanation:
Answer:
1: 2×4-3=5 (2) is your answer for the first one
50 Points!!! Is there a difference between the Additive Inverse and Additive Identity? If so, explain.
Answers
Answer:
There is a difference between additive inverse and additive identity.
Step-by-step explanation:
Additive inverse is the number added to get the result as zero. Additive identity is the value that is added to get the original number, which is zero.
Additive Inverse ~
ex. a+1=0
(additive inverse = a)
Additive inverse can be any number as long as the sum of the additive inverse and the other addend is 0.
Additive Identity
ex. 5+b=5
(additive identity = b)
The additive identity will always have to be 0.
Additive inverse: add the inverse aka opposite (basically add a negative so if its negative it becomes positive and if positive it becomes negative) it will always equal zero.
a+(-a)=0
.
Additive identity: add zero to the number to get itself.
.
a+0=a
given any set of seven integers, must there be at least two that have the same remainder when divided by 6?
Answers
Given any set of seven numbers that should be at least 2 that must have the same remainder when divided by 6
What are the factors?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product since the product is divisible by them.
How do you find factors?Step 1: factor the provided number into primes, or describe it as the product of primes.
Step 2: Write the prime factorization in exponent form in step three.
Step 3: Increase each exponent by one.
Step 4: Multiply each of the results.
There can only be a maximum of six different remainders when dividing by six: 0, 1, 2, 3, 4, and 5.
In any set of seven integers, two must have the same remainder when divided by seven according to the pigeon hole principle.
b) Consider set of integers 0, 1 ,2, 3, 4, 5 and 66. All these have different remainders upon division by 8 and hence the answer is no.
The interpretation is yes
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Rubber balls with a radius of 15 millimeters are stored in a 60,000 cubic millimeter box. What is the maximum number of rubber balls that will fit in the box?
A maximum of Select Choice rubber balls will fit in the box.
Answers
A 60,000 cubic millimeter box contains rubber balls with a radius of 15 millimeters. A maximum of 4 balls will fit in rubber box.
For finding the maximum number of rubber balls, firstly we will need the volume of the box. We have been given that the volume of the box is 60,000 mm³.
Now, we will find the volume of the rubber balls which have to be fit in the box. We know that the radius of one ball is 15 mm.
Volume of ball = 4/3 πr³
= 4/3 × 22/7 × 15³
= 4/3 × 22/7 × 3375
= 99,000/7
To find the maximum number of balls, we will divide the volume of box by volume of sphere.
Maximum number of balls = volume of box / volume of balls
= 60,000 / (99,000 / 7)
= (60,000 × 7) / 99,000
= 420 / 99
= 4.24
So, rounding up maximum 4 balls can be fit into the box.
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Correct question:
Rubber balls with a radius of 15 millimeters are stored in a 60,000 cubic millimeter box. What is the maximum number of rubber balls that will fit in the box?
the picture uploaded
Answers
Answer:
If the sequence is arithmetic:
\(\boxed{\sf a_n=168n-328}\)
\(\sf a_9=1184\)
If the sequence is geometric:
\(\boxed{ \sf a_n=2(4)^{n-1}}\)
\(\sf a_9=131072\)
Step-by-step explanation:
An explicit formula allows you to find the nth term of a sequence.
As the question has not specified if the given terms are from an arithmetic or geometric sequence, I will provide answers for both.
-------------------------------------------------------------------
Explicit formula: Arithmetic sequence
\(\sf a_n=a+(n-1)d\)
where:
\(\sf a_n\) is the nth term.a is the first term.n is the number of the term.d is the common difference.Given:
\(\sf a_2=8\)\(\sf a_5=512\)Substitute the values into the formula to create two equations:
\(\begin{aligned}\sf a_2 & =\sf 8\\\sf a+(2-1)d&=\sf 8\\\sf a+d&=\sf 8\end{aligned}\)
\(\begin{aligned}\sf a_5 & =\sf 512\\\sf a+(5-1)d&=\sf 512\\\sf a+4d&=\sf 512\end{aligned}\)
Subtract the first equation from the second to eliminate a, and solve for d:
\(\begin{aligned}\implies \sf (a+4d)-(a+d) & = \sf 512-8\\\sf 3d & = \sf 504\\\sf d & = \sf 168\end{aligned}\)
Substitute the found value of d into one of the equations and solve for a:
\(\begin{aligned}\sf a+d & = \sf 8\\\implies \sf a+168 & = \sf 8\\\sf a & = \sf -160\end{aligned}\)
Substitute the found values of a and d into the formula to create an explicit formula:
\(\implies \sf a_n=-160+(n-1)168\)
\(\implies \sf a_n=-160+168n-168\)
\(\implies \sf a_n=168n-328\)
To find a₉, substitute n = 9 into the found explicit formula:
\(\implies \sf a_9=168(9)-328\)
\(\implies \sf a_9=1512-328\)
\(\implies \sf a_9=1184\)
-------------------------------------------------------------------
Explicit formula: Geometric sequence
\(\sf a_n=ar^{n-1}\)
where:
\(\sf a_n\) is the nth term.a is the first term.n is the number of the term.r is the common ratio.Given:
\(\sf a_2=8\)\(\sf a_5=512\)Substitute the values into the formula to create two equations:
\(\begin{aligned}\sf a_2 & =\sf 8\\\sf ar^{2-1}&=\sf 8\\\sf ar&=\sf 8\end{aligned}\)
\(\begin{aligned}\sf a_5 & =\sf 512\\\sf ar^{5-1}&=\sf 512\\\sf ar^4&=\sf 512\end{aligned}\)
Divide the second equation by the first to eliminate a, and solve for r:
\(\begin{aligned}\implies \sf \dfrac{ar^4}{ar} & = \sf \dfrac{512}{8}\\\sf r^{4-1} & = \sf 64\\ \sf r^3 & = \sf 64\\ \sf r & = \sf \sqrt[\sf 3]{\sf 64} \\ \sf r & = \sf 4\end{aligned}\)
Substitute the found value of r into one of the equations and solve for a:
\(\begin{aligned}\sf ar & = \sf 8\\\implies \sf 4a & = \sf 8\\\sf a & = \sf 2\end{aligned}\)
Substitute the found values of a and r into the formula to create an explicit formula:
\(\implies \sf a_n=2(4)^{n-1}\)
To find a₉, substitute n = 9 into the found explicit formula:
\(\implies \sf a_9=2(4)^{9-1}\)
\(\implies \sf a_9=2(4)^8\)
\(\implies \sf a_9=131072\)
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In the picture below, what is the value of x?
с
D
Х
9
E
10
115
А
В
8
10
ОООО
с
14
d
5
Answers
Answer: 9
Step-by-step explanation:Because you have to loom at the answer
Which of the following uses the distributive property correctly?
3(x+5)=3-x+5
3(x+5)=3-x-3-5
3(x+5)=3+3.5
3(x+5)=3-x+3.5
Answers
Answer:
None of them, 3x + 15 is correct.
Step-by-step explanation:
In order to apply the distributive properly correctively, we need to multiply everything in the parentheses. For an example, lets look at the given expression:
\(3(x+5)\)
We multiply everything in the parentheses by 3
\(3x+15\)
Looking at out choices, none of them uses the distributive property correctly.
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
20y - 16x = 120
Answer:
15
2
Submit Answer
PLS HEP ASAP
Answers
alright I can help!!
so slope intercept form is y= mx +b
20y=16x+120
y=(16x+120)/20
final answer: y=(4/5)x +6
Given a confidence interval for a certain confidence level and sample size determine the mean of the sample and the margin of error:
Answers
Answer: 94, 9
Explanation:
The formula for calculating the margin of error is expressed as
margin of error = (upper value - lower value)/2
From the information given,
upper value = 103
lower value = 85
margin of error = (103 - 85)/2
margin of error = 9
To find the sample mean, we would apply the formula below;
sample mean = upper value - margin of error
sample mean = 103 - 9
sample mean = 94
Which of the following equations will yield the surface area of cylinder?
Answers
Answer: \(A=2\pi rh+2\pi r^2\)
The guy on the top is rite. ☻♥
HELP PLEASE!!!!
Which of the following is the correct factorization of the trinomial below?
-7x^2 - 4x + 20
A. (-7x + 10)(x - 2)
B. -1(7x - 10)(x + 2)
C. -7(x - 5)(x + 2)
D. 7(x + 10)(-x + 2)
Answers
A line has slope
13/4
and passes through the point (-1, -1).
By substituting into the equation y = mx + b, find the value of b for this line.
Answers
-1 = 13/4 (-1) +b
-4/4 + 13/4 = b
9/4 = b
24 PTS. LIMITED TIME!
YOUR AWARD: BRAINLIEST, A BIG THANKS, 24 PTS.
Answers
Answer:$3.00
Step-by-step explanation:
How do I Simplify V5(8+3V6) ???
Answers
Answer:
\(8\sqrt{5}+3\sqrt{30}\)
Step-by-step explanation:
When we have any quantity being multiplied to an expression, we can use the distributive property. The distributive property says that \(a(b+c)=ab+ac\). In other words, we can distribute the outer number inside the parentheses.
Using the distributive property, we can then simplify the given equation as follows:
\(\sqrt{5}(8+3\sqrt{6})=8\sqrt{5}+3\sqrt{6}\sqrt{5}\)
Finally, you should recall that when multiplying square roots, you can simply bring all the numbers inside of one root. For instance, \(\sqrt{2}*\sqrt{3}=\sqrt{2*3}=\sqrt{6}\) (note, this does not work for addition or subtraction, only multiplication or division). Therefore, we can simplify \(\sqrt{6}\sqrt{5}=\sqrt{6*5}=\sqrt{30}\).
Finally, we can combine our answer into \(\sqrt{5}(8+3\sqrt{6})=8\sqrt{5}+3\sqrt{6}\sqrt{5}=8\sqrt{5}+3\sqrt{30}\)
The human resource department at a certain company wants to conduct a survey regarding worker benefits. The department has an alphabetical list of all 4247 employees at the company and wants to conduct a systematic sample of size 40.a. What is k? b. Determine the individuals who will be administered the survey.
Answers
a) k = 11360.7
b) The individuals who will be administered the survey can be selected by picking every 107th person on the list.
What is Systematic Sample?
Systematic sampling is a form of probability sampling approach in which sample members from a larger population are chosen at random and at regular intervals. The sampling interval is determined by dividing the population size by the desired sample size.
a) k = 107 (4247/40)
k = 11360.7
b) The individuals who will be administered the survey can be selected by picking every 107th person on the list, starting from a randomly selected employee.
For example, if the first selected employee is "Anderson", then the next selected employees would be "Baker", "Chung", and so on, until 40 employees have been selected.
Thus, The Value of k would be 11360.7 and The individuals who will be administered the survey can be selected by picking every 107th person on the list.
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3 3/8 - 2 1/4 ÷ 1 1/2 - in the simplest form of a fraction
Answers
Answer:
1 7/8
Step-by-step explanation:
First convert mixed fraction to improper fraction. Then do division using KCF method. Then do subtraction.KCF method.
Keep the first fractionChange division to multiplicationFlip the second fraction\(\sf 3 \dfrac{3}{8}-2\dfrac{1}{4} \div 1\dfrac{1}{2}= \dfrac{27}{8}-\dfrac{9}{4}\div\dfrac{3}{2} \\\\\)
\(\sf = \dfrac{27}{8}-\dfrac{9}{4}*\dfrac{2}{3}\\\\=\dfrac{27}{8}-\dfrac{3}{2}\\\\=\dfrac{27}{8}-\dfrac{3*4}{2*4} \ [\text{LCM of 2 and 8 is 8}]\\\\=\dfrac{27}{8}-\dfrac{12}{8}\\\\=\dfrac{27-12}{8}\\\\=\dfrac{15}{8}\\\\=1\dfrac{7}{8}\)
Ryan and Cody are selling cookie dough for a school fundraiser. Customers can buy packages of white chocolate chip cookie dough and packages of double chocolate cookie dough. Ryan sold 6 packages of white chocolate chip cookie dough and 12 packages of double chocolate cookie dough for a total of $204. Cody sold 7 packages of white chocolate chip cookie dough and 7 packages of double chocolate cookie dough for a total of $147. What is the cost each of one package of white chocolate chip cookie dough and one package of double chocolate cookie dough?
Answers
9514 1404 393
Answer:
white: $8double: $13Step-by-step explanation:
Let w and d represent the costs of white chocolate chip cookie dough and double chocolate chip cookie dough, respectively.
6w +12d = 204 . . . . . . Ryan's sale
7w +7d = 147 . . . . . . . . Cody's sale
We can divide out the common factor to put these equations into standard form:
w +2d = 34
w +d = 21
Subtracting the second of these equations from the first, we get ...
(w +2d) -(w +d) = (34) -(21)
d = 13
Using the second equation, we can find w:
w = 21 -d = 21 -13 = 8
The costs of the chocolate chip cookie dough packages are ...
white: $8
double: $13
the correlation between variables x and y is .50. You compute a least squares regression line wit this bivariata data. Which of the following is true?
a. the r^2 is greater than .50
b. the regression constant is positive
c. the regression coefficient is positive
d. the slope of the regression line is negative
e. all of the above
Answers
The correlation between variables x and y is 0.50 . The true option is option (c) .
that's the regression coefficient is positive for given bivariata.
Correlation: Correlation is a statistical measure of how linearly two variables are related (meaning they change together at a constant rate). The
sample correlation coefficient r quantifies the strength of the relationship.
Correlation Coefficient: The Correlation Coefficient formula is used to examine the strength of the relationship between data. The formula returns a value between -1 and 1.
Here:
1 indicates a strong positive relationship.-1 indicates a strong negative relationship.A result of zero indicates no relationship at allPearson's correlation coefficient is denoted by "r" and is
r = (n∑xy - ∑x∑y )/√( n ∑x² - (∑x )² ) ( √ n∑y² - (∑y)²)
We have given that correlation between x and y is 0.50.
cor(x,y) = √r^2 => √r^2 = 0.50 => r ^2 = (0.50)^2
=> r^2 = 0.25 > 0 but less than 0.50 ---( 1)
Regression coefficient is the constant "b" in the regression equation that gives the change in the value of the dependent variable equal to the unit change in the independent variable.
Symbolically it can be expressed as:
bₓᵧ= r σ ₓ /σ ᵧ
where x and y are correlated
σ ₓ --> standard deviation of X
σᵧ ---> standard deviation of y
We know that standard deviations is square root value of variance of observations. we also know square root any quantity is always positive or zero.
Using the above fact about standard deviations and correlation coefficient (r) is also positive we see that bₓᵧ is postive.
Hence, Regression cofficient is positive.
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(8.11×107)–(4.3×107)
Answers
Answer: 407.67
Explanation:
(8.11×107)–(4.3×107) =
(8.11)(107)−(4.3)(107) =
407.67
PLZ HELP ME WITH THIS!!!!!
Answers
First, divide to find the unit price.
14.25 / 3 = $4.75 per bag
Second, multiply by how much he wants to buy.
4.75 * 6 = $28.50 for 6 bags of dog food.
Best of Luck!
What is the surface area of the right square pyramid?A. 48 in2
B. 64 in?
C. 96 in
D. 112 in2
Answers
48x2 is 96