No triangle can form with the given measurements.
What is a triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
The given angles are 53° and 27°.
By using angle sum of property of a triangle, we get
53°+27°+x=180°
x=100°
It is not possible to draw a unique triangle with any 3 possible measurements of angles.
Therefore, no triangle can form with given measurements.
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what is accounting and how to maintain our business accounting?
Answer:
accounting is a systematic and detailed recording of all the financial transactions that further help owners, investors, suppliers, etc. in making the right business decision.
Step-by-step explanation:
What is 4/16 in simplest form
Assume Marleen adds security Y to her portfolio that is less than perfectly positively correlated with the portfolio. Security Y has the same standard deviation as the portfolio. What will happen to the standard deviation of the portfolio after she adds security Y?
Select one:
It will remain the same
It will decrease
It will increase
It may increase or decrease, depending on the weightings of the portfolio holdings
The standard deviation of the portfolio may increase or decrease, depending on the weightings of the portfolio holdings. after she adds security Y
The portfolio standard deviation as a result of revealing how reliable an investment's earnings are, mean serves as a risk indicator. Because it reveals that the earnings are extremely unstable and fluctuating, a high standard deviation in a portfolio denotes significant risk.
The statistical measure of market volatility used to determine how widely prices deviate from the average price is called standard deviation. The standard deviation will show a low number, which denotes little volatility if prices move within a small range of prices.
The term "standard deviation" (or " σ") refers to a measurement of the data's dispersion from the mean.
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find the supplement of each of the following angles measured in radians. 2.68 is supplementary to 2.79 is supplementary to 1.79 is supplementary to 2.04 is supplementary to 0.34 is
The supplement of angles 2.68, 2.79, 1.79, 2.04, 0.34 are 1.32, 1.21, 1.21, 1.96, 2.66 radians respectively.
The supplement of an angle is defined as the difference between π radians (180 degrees) and the given angle. If the measure of an angle is "x" radians, then its supplement is calculated as π - x radians.
The supplement of an angle represents the smallest angle that when added to the original angle.
Supplement of 2.68 radians: π - 2.68 = 1.32 radians
Supplement of 2.79 radians: π - 2.79 = 1.21 radians
Supplement of 1.79 radians: π - 1.79 = 1.21 radians
Supplement of 2.04 radians: π - 2.04 = 1.96 radians
Supplement of 0.34 radians: π - 0.34 = 2.66 radians
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___________The given question is incomplete, the complete question is given below:
find the supplement of each of the following angles measured in radians: 2.68 is supplementary to_____, 2.79 is supplementary to_____, 1.79 is supplementary to_______, 2.04 is supplementary to______, 0.34 is supplementary to_______.
A consumer interest group is comparing two brands of vitamin C. One group advertises that its tablets contain 500 mg of vitamin C. The other advertises that its tablets contain 250 mg of vitamin C. Tablets for each group were selected randomly. The table below shows the results.Vitamin C Content (mg) Brand A (500 mg) x = 250s = 500Brand B (250 mg) x = 500s = 10a) Calculate the coefficient of variation (CV) for Brand A (1point) b) Calculate the coefficient of variation (CV) for Brand B (1 point) c) Which brand more consistently produces tablets as advertised? (2 points) d) Explain your answer to c) above. (1 point)
a) The coefficient of variation (CV) for Brand A, is equals to the 2.8%.
b) The coefficient of variation (CV) for Brand B, is equals to the 2.0%.
c) Brand B, is more consistently produces tablets as advertised.
We have comparing data of consumer groups of vitamin C tablets of two brands. Tablets for each group were selected randomly. Data from above table, For brand A :
Tablets contains the quantity of vitamin C = 500 mg
Sample mean = 250
Standard deviation = 7
For brand B :
Tablets contains the quantity of vitamin C = 250 mg
Sample mean = 500
Standard deviations = 10
Cofficient of variation, CV is statistical parameter and it is the ratio of the standard deviation to the mean. Formula is, Coefficient of Variation (CV)
= (Standard Deviation/Mean) × 100.
a) To calculate the coefficient of variation (CV) for Brand A = (7/250 )×100
= 2.8%
b) To calculate the coefficient of variation (CV) for Brand B = (10/500 )×100
= 2.0%
c) As we see, Cofficient of variation of advertising for brand B is less than brand A. So, Brand B more consistently produces tablets as advertised.
Hence, required brand is brand B.
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Complete question:
consumer interest group is comparing two brands of vitamin C. One group advertises that its tablets contain 500 mg of vitamin C. The other advertises that its tablets contain 250 mg of vitamin C. Tablets for each group were selected randomly. The table above shows the results.Vitamin C Content (mg) Brand A (500 mg) x = 250s = 500Brand B (250 mg) x = 500s = 10
a) Calculate the coefficient of variation (CV) for Brand A (1point)
b) Calculate the coefficient of variation (CV) for Brand B (1 point)
c) Which brand more consistently produces tablets as advertised? (2 points) d) Explain your answer to c) above. (1 point)
Consider a bowler in a league who keeps track of individual games, as well as average scores for three games played each time the league meets
Donald has a higher three-game series score.
What is Z-score?In statistics, the standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores.
here, we have,
Given that :
BRUCE :
score (x) = 500
League average (m) = 620
Standard deviation (σ) = 20
DONALD:
score (x) = 520
League average (m) = 625
Standard deviation (σ) = 25
Take standardized score of both Bruce and Donald
BRUCE:
Zscore = (x - m) / σ
Zscore = (500 - 620) / 20
Zscore = - 120 / 20
Zscore = - 6
DONALD:
Zscore = (x - m) / σ
Zscore = (520 - 625) / 25
Zscore = - 105 / 25
Zscore = - 4.2
Bruce's standardized score is lesser Than Donald's.
Hence, Donald has a higher three-game series score.
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The pH level, P, of a liquid can be determined from the hydronium ion (H3O+) concentration, c, using the equation P = –log(c). If the pH level of orange juice is 3.5, what is the hydronium ion concentration? (2 points) 1.25 x 105 3.16 x 103 5.44 x 10–1 3.16 x 10–4
The hydronium ion concentration in orange juice with pH 3.5 is 3.16 × 10⁻⁴
What is hydronium ion concentration?The hydronium ion is an important factor when dealing with chemical reactions that occur in aqueous solutions. Its concentration relative to hydroxide is a direct measure of the pH of a solution. It can be formed when an acid is present in water or simply in pure water.
Given that, the pH level, P, of a liquid can be determined from the hydronium ion (H3O+) concentration, c, using the equation P = –log(c). we need to determine the hydronium ion concentration in orange juice with pH level of 3.5
Therefore,
P = -log(c)
P = 3.5
Therefore,
3.5 = -log(c)
log(c) = -3.5
(10)⁻³⁵/₁₀ = c
c = 0.000316227766
c = 3.16 × 10⁻⁴
Hence, the hydronium ion concentration in orange juice with pH 3.5 is 3.16 × 10⁻⁴
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Use a technique of integration or a substitution to find an explicit solution of the given differential equation. (squareroot x + x) dy/dx = squareroot y + y y =
The explicit solution of the given differential equation is [tex]& y=[c(1+\sqrt{x})-1]^2[/tex]
Solution of the Differential Equation :
Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation (i.e., independent variable)
[tex]\frac{dy}{dx} =f(x)[/tex]Here, the independent variable "x" and the dependent variable "y" are both present.We employ the approach of variable separation to discover the answer to the differential equation. By splitting the equation into two halves, we can find a solution. We integrate both sides after moving all of the equations involving the y variable to one side and all of the equations involving the x variable to the other side.
∫P(y)dy=∫Q(x)dx⇒[tex](\sqrt{x}+x) \frac{d y}{d x} & =(\sqrt{y}+y) \\[/tex]
⇒[tex]\frac{d y}{\sqrt{y}(1+\sqrt{y})} & =\frac{d x}{\sqrt{x}(1+\sqrt{x})}[/tex]
Put [tex]$\sqrt{y}=u \quad \sqrt{x}=v$[/tex]
⇒[tex]& \frac{1}{2 \sqrt{y}} d y=d u \frac{1}{2 \sqrt{x}} d x=d v \\[/tex]
⇒[tex]& \frac{d y}{\sqrt{y}}=2 d u \frac{d x}{\sqrt{x}}=2 d v[/tex]
By substituting,
⇒[tex]& \int \frac{7 d u}{1+u}=\int \frac{2 d v}{1+v} \\[/tex]
⇒[tex]& \ln (1+u)=\ln (1+v)+\ln c \\[/tex]
⇒[tex]& \ln (1+u)=\ln [c(1+v)] \\[/tex]
⇒[tex]& (1+u)=c(1+v) \\[/tex]
⇒[tex]& (1+\sqrt{y})=c(1+\sqrt{x}) \\[/tex]
⇒[tex]& \sqrt{y}=c(1+\sqrt{x})-1 \\[/tex]
⇒[tex]& y=[c(1+\sqrt{x})-1]^2[/tex]
Therefore, the explicit solution of the given differential equation is [tex]& y=[c(1+\sqrt{x})-1]^2[/tex]
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Which of the following is true for all rectangles?
O The diagonals bisect the angles.
O The consecutive sides are congruent.
O The consecutive sides are perpendicular.
O The diagonals are perpendicular.
A big tank had 890/ of water. A small tank had 170/ of water. When an equal amount of water was added to both tanks, the big tank had 3 times as much water as the small tank. How much water was added to each tank?
The plant manager of a company that makes pillows claims that only 8 percent of the pillows made have a stitching defect. The quality control director thought that the percent might be different from 8 percent and selected a random sample of pillows to test. The director tested the hypotheses H : p=0.08 versus Hp +0.08 at the significance level of a = 0.05. The p- value of the test was 0.03. Assuming all conditions for inference were met, which of the following is the correct conclusion? The p-value is less than a, and the null hypothesis is rejected. There is convincing evidence to suggest the true proportion of stitching defects is less than 0.08. Subm B The p-value is less than a, and the null hypothesis is rejected. There is convincing evidence to suggest the true proportion of stitching defects is not 0.08. The p-value is less than o, and the null hypothesis is rejected. There is convincing evidence to suggest the true proportion of stitching defects is greater than 0.08 The p-value is less than , and the null hypothesis is not rejected. There is convincing evidence to suggest the true proportion of stitching defects is not 008 The p-value is less than a, and the null hypothesis is not rejected. There is not convincing evidence to suggest the true proportion of stitching defects is not 0.08
The correct statement regarding the test of the hypothesis is given as follows:
B. The p-value is less than the significance level, and the null hypothesis is rejected. There is convincing evidence to suggest the true proportion of stitching defects is not 0.08.
What is the relation between the p-value and the conclusion of the test hypothesis?Depends on if the p-value is less or more than the significance level:
If it is more, the null hypothesis is not rejected, meaning that the research study is not statistically significant.If it is less, it is rejected, meaning that the research study is statistically significant.
The parameters for this problem are given as follows:
Hence the null hypothesis is rejected, as 0.03 < 0.05, and the conclusion is that the proportion is different of 0.08, which is the test made for this problem.
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Mrs. Goldstein baked 24 cookies. 2 thirds of the cookies were oatmeal. How many oatmeal cookies did Mrs. Goldstein bake?
16 cookies were oatmeal
Oatmeal cookies' shelf lifeHow long do cookies with oats last? The cookies can last up to two weeks when kept in an airtight container. The cookies may be frozen and kept for two months. But, these cookies taste best when they are still warm from the oven!
Where do you keep cookies with oatmeal?Keep crisp cakes in a jar with such a loose-fitting cover for cookies which will be consumed within a day or two; keep soft sweets in a jar with a close cover. Wax paper should be placed between the layers of cookies that are exceptionally soft, delicate, iced, or adorned. Many cookies may be frozen.
To find the number of oatmeal cookies, take the total number of cookies and multiply by the fraction that were oatmeal
24 * 2/3 = 48/3 = 16
16 cookies were oatmeal
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Given ab 12 ac 6 prove c is the midpoint
Answer:
yes
Step-by-step explanation:
Given ab 12 ac 6 prove c is the midpoint is true because the midpoint of 12 is 6.
One option in a roulette game is to bet $15 on red. (There are 18 red compartments, 18 black compartments, and two compartments that are neither red nor black.) If the ball lands on red, you get to keep the $15 you paid to play the game and you are awarded $15. If the ball lands elsewhere, you are awarded nothing and the $15 that you bet is collected. What is the expected value for playing roulette if you bet $15 on red?
The expected value for playing roulette if you bet $15 on red is $6.32
What is probability?Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.
The expected value for playing roulette if you bet $15 on red can be calculated as follows:
There are 18 red compartments out of a total of 38 compartments (18 red + 18 black + 2 neither red nor black).
Therefore, the probability of the ball landing on red is 18/38 or 9/19.
If the ball lands on red, you win $15 in addition to keeping your original $15 bet. So your total payout is $30.
If the ball does not land on red, you lose your $15 bet.
Using the formula for expected value, we can calculate the expected value of betting $15 on red as:
Expected value = (probability of winning * payout for winning) - (probability of losing * amount lost)
Expected value = (9/19 * $30) - (10/19 * $15)
Expected value = $270/19 - $150/19
Expected value = $120/19
Therefore, the expected value for playing roulette if you bet $15 on red is $6.32
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6x^2 + x − 1
quadratic monomial
quadratic trinomial
cubic trinomial
quadratic binomial
Answer:
The expression 6x^2 + x − 1 is a quadratic trinomial.
Step-by-step explanation:
HI can u please help me
Solution in da attachment!! :)
The ages of people visiting a senior center one afternoon are recorded in the line plot.
A line plot titled Ages At Senior Center. The horizontal line is numbered in units of 5 from 60 to 115. There is one dot above 80 and 100. There are two dots above 70 and 85. There are three dots above 75.
Does the data contain an outlier? If so, explain its meaning in this situation.
No, there is no outlier. This means that the people were all the same age.
No, there is no outlier. This means that the people are all around the mean age.
Yes, there is an outlier at 100. This means that one person's age was 100, which is 15 years older than the next closest age.
Yes, there is an outlier of 100. This means that the average person at the center is 100 years old.
Hurrrry up
No, there is no outlier. this means that the people are all the same age
No, there isn't an outlier. This indicates that everyone is roughly the same age.
What is an Outlier?
An outlier in a data graph or dataset you're dealing with is a data point that is disproportionately high or low compared to the closest data point and the rest of the nearby coexisting values.
Extreme values that significantly deviate from the dataset for graph's normal distribution are known as outliers.
How to Spot the Outlier?
Data points in a dataset must be fewer than Q1 - 1.5xIQR in order to qualify as low outliers.
As a result, a data point cannot be regarded as a low outlier unless it falls below the first quartile by more than 1.5 times the interquartile range.
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Bridge A surveyor needs to find the distance
BC across a lake as part of a project to build a
bridge. The distance from point A to point B
is 325 feet. The measurement of angle A is 42°
and the measurement of angle B is 110°.
What is the distance BC across the lake to the
nearest foot?
The value of the distance BC across the lake to the nearest foot is 463 ft.
What are triangles?In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle. All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Unless when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean plane.
Extend the segment AB and draw a perpendicular line from B to C.
From the figure we see that:
tan (42) = y / 325 + x
y = tan (42) (325 + x)
Also, tan (70) = y / x
y = tan(70) x
Equating the values of y together we have:
tan (42) (325 + x) = tan(70) x
x = 158.430
Now,
cos (70) = 158.430/h
h = 463.2 ft
Hence, the value of the distance BC across the lake to the nearest foot is 463 ft.
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calculating area and circumference or perimeter of a 2d shape. use your measurements to calculate the area and circumference of the circle and to calculate the area and perimeter of the rectangle.
The area and perimeter of 2D shape of Rectangle is 6.8448cm and 11.04cm repectively. The area and perimeter of 2D shape of circle is 5.0761cm and 8.0028cm respectively.
2D shape of Rectangle with dimensions of Length is3.72 cm and Width is 1.84 cm. we can find the area of rectangle with formula Area = length x width and the formula of perimeter is Perimeter = 2(length + width).
Area = length x width = 3.72 cm x 1.84 cm = 6.8448 square cm (rounded to four decimal places)
Perimeter = 2(length + width) = 2(3.72 cm + 1.84 cm) = 11.04 cm
2D shape of Circle with dimension of diameter of 2.54 cm. we can find the area with formula Area = πr^2 and circumference with formula Circumference = 2πr
Radius = diameter / 2 = 2.54 cm / 2 = 1.27 cm
Area = πr^2 = π(1.27 cm)^2 = 5.0761 square cm (rounded to four decimal places)
Circumference = 2πr = 2π(1.27 cm) = 8.0028 cm (rounded to four decimal places)
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____The given question is incomplete, the complete question is given below:
Calculating area and circumference or perimeter of a 2D shape. Use your measurements to calculate the area and circumference of the circle and to calculate the area and perimeter of the rectangle. Rectangle Length: 3.72 cm Width: 1.84 cm Circle : 2.54 cm Diameter of circle
Juan earned 166 points on a school assignment. Because the assignment was turned in late, the score was reduced to 163 points. What was the percentage decrease in the score? Round your answer
to the nearest tenth.
The percentage decrease in the score is 1.8%
How to calculate the percentage decrease in the score?
Juan earned 166 points on a school assignment
The assignment was turned in late which made the score to be reduced to 163 point
The first step is to calculate the decrease
= 166-163
= 3
The percentage decrease is
3/166 × 100
= 0.0180 × 100
= 1.8
Hence the percentage decrease in the score is 1.8%
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Solve the system it’s 9th grade work and you have to put one solution no solution or infinite many
The system of equations has only one solution and is the point (1, 1)
How to solve the system of equations?Here we have the graph of a system of equations, where we can see that both of them are linear equations.
Whenw e have a graph of a system, the solutions are all the points where the graphs of the equations intercept.
On the given graph, we can see that the two lines intersept at the point (1, 1)
So we have only one solution and is the point (1, 1)
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Find the values at the 25th and 75th percentiles for the data set
22 20 3 20 16 10 20 5 7 11 11 8 17 12 4 18 5 16 6 16
The solution is, the value at the 75th percentiles for the data set is 17.
What is percentile?In statistics, a k-th percentile is a score below which a given percentage k of scores in its frequency distribution falls or a score at or below which a given percentage falls.
here, we have,
The 75th percentile of the data is the value which is greater than 75% of the data. Arranging the values first in ascending order:
given that,
3 4 5 5 6 7 8 10 11 11 12 16 16 16 17 18 20 20 20 22
The data has 20 elements, so 75% of the data consists of .75(20) = 15.
The 75th percentile must be the 15th element.
Therefore, 17.
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Solve for t.
1/3 • t = 3
t =
Write your answer as a fraction or as a whole or mixed number.
Submit
Answer:
t = 9
Step-by-step explanation:
We know that 1/3 of t is 3, so to find t, we have to multiply 3 x 3 because we want to find 3/3 or 1 of t. When we multiply 3 x 3, we get t = 9
OR
We could also solve it like this-
1/3 × t = 3
1/3 goes to the other side so it becomes: [tex]t = \frac{3}{1/3} \\[/tex]
Then, it become multiplication so: [tex]t = 3 * 3/1[/tex]
So t is 9
Hope this helps!
What is the area of this figure?
9 km
7 km
3 km
5 km
4 km
2 km
13 km
3 km
The area of the composite figure is 203 square km
How to determine the area of the figureThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Area of the figure = Sum of the areas of the individual shapes
Using the above as a guide, we have the following:
Area of the figure = 3 * 4 + 12 * 6 + 17 * 7
Evaluate the expression
Area of the figure = 203
Hence, the area is 203 square km
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Color in 6/6 and 3/3 to make both equivalent
We have to multiply numerator and denominator to 3/3 to make 6/6.
What is Fraction?A fraction represents a part of a whole.
We have to convert the fraction three by three to six by six.
The given fraction is 3/3
Three by three
3 is the numerator and 3 in the denominator.
We have to make it 6/6.
To do this we have to multiply numerator and denominator by 2
3/3×2/2
Three by three times of two by two.
We get six divide by six
6/6
We know that the value of 3/3 is equal to one and the value of 6/6 is one.
So the fraction 3/3 and 6/6 are equivalent fractions.
Hence, we have to multiply numerator and denominator to 3/3 to make 6/6.
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Complete question
How to make 3/3 to 6/6 ratio?
Find three consecutive integers such that the sum of the first and the third is 8 more than the second number.
Answer: Let's call the first integer "x". Then, the second integer would be x + 1, and the third integer would be x + 2.
According to the problem, the sum of the first and the third integer is 8 more than the second integer:
x + (x + 2) = (x + 1) + 8
Simplifying the left side of the equation:
2x + 2 = x + 9
Subtracting x from both sides:
x + 2 = 9
Subtracting 2 from both sides:
x = 7
So the first integer is 7, the second integer is 8, and the third integer is 9. These are three consecutive integers that satisfy the condition in the problem.
Step-by-step explanation:
What is the error of improved Euler's method?
The error of Improved Euler's Method is that it underestimates the true solution of the differential equation, leading to an inaccurate result.
Improved Euler's Method is used to approximate the solution to a differential equation. The method begins by using the initial value of the function, as well as its derivative at that point. The derivative is then multiplied by a step size, h, and added to the initial value to obtain an estimate of the function at the next point. This estimate is used to calculate the derivative at the new point, which is then multiplied by the same step size and added to the initial value to obtain the next estimate. This process is repeated until the desired solution is obtained. The error of Improved Euler's Method is that it underestimates the true solution of the differential equation, leading to an inaccurate result.
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sample of size n will be selected from population with population proportion p. Which of the following must be true for the sampling distribution of the sample proportion to be approximately normal? a. Both np and n(1 P) are at least 10.b. n is greater than 30 c. p is greater than 0.5. d. The mean is equal to np e. the variance is equal to np(1-p)
True sampling distribution sample which is proportion to be approximately normal is "Both np and n(1 P) are at least 10".
For the sampling distribution of the sample proportion to be approximately normal, the sample size must be sufficiently large, and the sample proportion must be neither too small nor too large.
Specifically, the sample size multiplied by the sample proportion (np) and the sample size multiplied by one minus the sample proportion (n(1-P)) must both be at least 10. This is known as the "success-failure" condition.
Option b is not entirely accurate, as a sample size greater than 30 is a rule of thumb for the Central Limit Theorem to apply, but it is not a strict requirement for normality.
Option c is incorrect as a sample proportion greater than 0.5 means the distribution is skewed towards one end and not normal.
Option d and e are the mean and variance of the binomial distribution and are not directly related to normality.
The correct answer is option a. Both np and n(1-P) are at least 10.
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Please help me with all asap I’ll mark brainly
The number of solution of each of the equations -2x + 4 = 4 - 2x, 5 - 3x = -5 - 3x and 2 + 3x = 2 + 2x are infinite solution, no solution and one solution respectively.
What is the number of solutions of each equation?Given the equations in the question;
a) -2x + 4 = 4 - 2x
b) 5 - 3x = -5 - 3x
c) 2 + 3x = 2 + 2x
To determine the number of solutions of each equation, solve for x.
a)
-2x + 4 = 4 - 2x
Solve for x
-2x + 2x + 4 - 4 = 4 - 4 - 2x + 2x
-2x + 2x = 4 - 4
0 = 0
Hence, the equation has infinite solutions.
b)
5 - 3x = -5 - 3x
Solve for x
5 - 5 - 3x + 3x = -5 - 5 - 3x + 3x
- 3x + 3x = -5 - 5
0 = -10
Hence, the equation has no solution.
c)
2 + 3x = 2 + 2x
Solve for x
2 - 2 + 3x - 2x = 2 - 2 + 2x - 2x
3x - 2x = 2 - 2
x = 0
Hence, the equation has one solution.
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benedictine brewery (mount angel abbey, oregon) has two bottling machines. machine a fills 75% of the bottles. given that the bottles are filled by machine a, 10% are defective. given that the bottles are not filled by machine a (that is, machine ac), 5% are defective. using the theorem of bayes, determine the probability that a randomly sampled bottle was filled by machine a, given that it is defective.
The probability that Machine A filled a randomly selected bottle, given that it is defective, is 2/3 or approximately 0.67.
Let's define the subsequent events:
A: Machine A filled the bottle.
A': The bottle wasn't mechanically filled A (i.e. filled by machine AC).
D: the bottle is defective.
The chance that a randomly selected bottle was filled by machine A, assuming that it is broken, is known as P(A|D). The Bayes theorem provides us with:
P(A|D) = P(D|A)P(A) / P(D)
The following three terms on the right-hand side must be calculated:
P(D|A): the probability that a bottle is flawed given that machine A filled it. 10% of the bottles filled by machine A are reported to be faulty. so P(D|A) = 0.1.
P(A): the previous probability that machine A filled a bottle. There are just two machines, both of which fill bottles., P(A) = P(A') = 0.5.
P(D): the slight possibility that a bottle is flawed. The law of total probability can be used to calculate this:
P(D) = P(D|A)P(A) + P(D|A')P(A') = 0.1 x 0.5 + 0.05 x 0.5 = 0.075
Now we can plug in the values:
P(A|D) = 0.1 x 0.5 / 0.075 = 2/3
Therefore, the probability that Machine A filled a randomly selected bottle, given that it is defective, is 2/3 or approximately 0.67.
To learn more about Bayes theorem, visit the link below:
https://brainly.com/question/17010130
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