Three pairs of fractions that have a sum of 5/6 are;
1/3 + 2/3 = 5/6
1/4 + 3/4 = 5/6
2/6 + 3/6 = 5/6
How to calculate this?1/3 + 2/3 = 5/6: The fractions have a common bottom number of 3 because they both have the same bottom number.
Adding the top numbers: 1 plus 2 equals 3.
The total is three divided by three, which can also be written as one.
However, we need to show the total with a bottom number of 6 to match the original part. So, we make the top and bottom numbers twice as big to get 2/6. Hence , 1/3 + 2/3 = 2/6.
1/4 + 3/4 = 5/6:The fractions have the same bottom number, so their common denominator is 4.
When you add 1 and 3 together, you get 4.
The sum is four over four, and when simplified, it equals one.
Once again, we have to find a way to write the sum with a bottom number of 6 so that it is the same as the first number in the fraction. So, we take the top number and the bottom number and multiply them both by 3 to get the fraction 3/6. Hence, 1/4 + 3/4 = 3/6.
2/6 + 3/6 = 5/6:In this situation, the fractions already have the same bottom number which is 6.
Adding the top numbers together: 2 + 3 = 5.
The answer is 5/6, which is what we wanted to get.
Therefore each pair shows a different way to add numbers together, either by finding a number that both denominators can divide evenly into or by using numbers that already work well together.
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A submarine dives 20 m each minute for 15 minutes. What is the total change in depth after 15 minutes?
Answer:
Step-by-step explanation:300 mStep-by-step explanation:20 meters per minute. 15 minutes it dives. 20x15 is 300
which statement describes whether marjan’s graphs are correct
Yes, g(x) is a 3 unit translation down after a reflection of f(x) over the x-axis.
What is meant by graphs?The set of ordered pairs with the f(x) = y is the graph of a function f in mathematics. These pairs, which are Cartesian coordinates of points in two-dimensional space and thus constitute a subset of this plane in the typical case where x and f(x) are real numbers, are examples of real numbers.
Pie charts, line graphs, bar graphs and histograms, and Cartesian graphs are likely the four most popular types. They are typically utilized for, and are most effective for, very different purposes. You'd employ: Bar graphs are used to display numbers that are unrelated to one another.
Use line/area charts if your data is continuous, or bar charts or histograms if your data is nominal. Use a scatter plot, bubble chart, or line chart to illustrate how the values in your dataset relate to one another.
y = −f(x) Reflects it about x-axis
y = f(x) + C C < 0 moves it down
The complete question is:
Consider the function f(x) = x3 + 0.5x – 1. Marjan needs to graph f(x) and g(x) = –f(x) – 3. His graphs are shown below. Which statement describes whether Marjan’s graphs are correct? No, the reflection should be over the x-axis, not the y-axis. No, the reflection should be over the y-axis, not the x-axis. Yes, g(x) is a reflection of f(x) over the y-axis followed by a translation of 3 units down. Yes, g(x) is a reflection of f(x) over the x-axis followed by a translation of 3 units down.
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using a survey, we have obtained a large dataset of how many close friends people have. its mean is 6 and its median is 4. the variance is 64. we calculate the standard scores. what is the value of the median of the standardized dataset?
The standard median value of the data set is -0.25.
The standard value of any data is the converted value of the variable, such that the mean of the data set is 0 and the standard deviation is 1.
To convert any data set to its standard form we use the equation
(X - μ)/σ
where,
μ = mean
σ = standard deviation
here,
μ = 6
σ = √64 = 8
Now median is that value which gives the midpoint of the frequencies.
Hence the standard median should be the standard value of the median obtained from the data set which is 4
Hence standard median
= (4 - 6)/8
= -2/8
= -0.25
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What is the value of x?
The value of x in the diagram is 9
What is an equilateral triangle?equilateral triangle is a triangle that has all its sides equal in length. Since the three sides are equal therefore the three angles, opposite to the equal sides, are equal in measure. Therefore, it is also called an equiangular triangle, where each angle measure 60 degrees. Just like other types of triangles, an equilateral triangle also has its area, perimeter and height formula
From the diagram all the sides are equal which means it is an equilateral triangle in which each angle is equal to 60°
To find x,
7x -3 = 60
7x = 60 + 3
7x = 63
x = 63/7
x = 9
In conclusion the value of x is 9
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Sport Hours
Soccer 5
jogging 20 what percentage of total hours was spent skiing
walking 10
skiing 5
football 10
total 50
The percentage of total hours was spent skiing is 10%
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Here, total number of hours =5+20+10+5+10 =50
Number of spent on skiing is 5
Now, percentage is 5/50 ×100
=10%
Therefore, percentage of hours spent on skiing is 10%
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"Your question is incomplete, probably the complete question/missing part is:"
What percentage of total hours were spent skiing?
Soccer 5
Jogging 20
walking 10
skiing 5
football 10
suppose that the number of miles that a car can run before its battery wears out is exponentially distributed with an average value of 11k miles. (a) what is the probability that the battery lasts between 12k and 14k miles?
The probability that the battery lasts between 12,000 and 14,000 miles is approximately 0.084.
The number of miles that a car can run before its battery wears out follows an exponential distribution with an average value of 11,000 miles. The probability that the battery lasts between 12,000 and 14,000 miles can be calculated as follows:
P(12,000 < x < 14,000) = P(x < 14,000) - P(x < 12,000)
To calculate the probabilities on the right-hand side of the equation, we can use the formula for the cumulative distribution function (CDF) of an exponential distribution:
F(x) = 1 - e^(-x/λ)
where λ is the mean value of the distribution. In this case, λ = 11,000 miles.
Plugging in the values and solving, we get:
P(12,000 < x < 14,000) = F(14,000) - F(12,000)
= (1 - e^(-14,000/11,000)) - (1 - e^(-12,000/11,000))
= e^(-12,000/11,000) - e^(-14,000/11,000)
≈ 0.242 - 0.158
≈ 0.084
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Solve pls brainliest
Answer:
d = 9.43398113206
Step-by-step explanation:
d=√((x2 – x1)² + (y2 – y1)²)
d = √((-4-1)² + (5+3)²)
d = √((-5)² + (8)²)
d = √(25 + 64)
d = √89
d = 9.43398113206
What are two points that represent Justine‘s function for the yards left to hike in terms of the hours she spent hiking?
The two points that represent Justine‘s function for the yards left to hike in terms of the hours she spent hiking are; (0, 320) and (4, 0)
How to find the correct coordinates?
From the table in the attached file, we see that;
Justine started when Michael was 320 yards from the top.
This coordinate is expressed as (0,320)
where;
0 represents the time Justine started
320 represents the number of yards left.
Now, it is clear that every minute, Justine covers 80 yards.
Thus;
After 1 minute, Justine will have:
(320 - 80) yards left
After 2 minutes, Justine will have:
(320 - 80 - 80) yards left
After 3 minutes, Justine will have:
(320 - 80 - 80 - 80) yards left
After n minutes, Justine will have;
(320 - 80n) yards left
Thus, the possible coordinates are:
(0, 320), (1, 240), (2, 160), (3, 80), (4, 0)
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Write the equation of a line with an undefined slope through the point (-4, 2)
Answer:
x = - 4
Step-by-step explanation:
A line with an undefined slope is a vertical line parallel to the y- axis with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (- 4, 2 ) with x- coordinate - 4 , then
x = - 4 ← equation of line
when will the height be 37 feet?
As the tree grows 1& 3/4 feet per year, it will take 9 years to reach a height of 37 feet.
What is division?Division is a basic procedure in which an integer is divided. It's best to imagine of it as a number of things being distributed among a particular number of persons, such as in the previous example. In mathematics, division is the process of dividing a number into equal parts and determining how many equal parts can be made. For instance, dividing 15 by 3 implies dividing 15 into three equal groups of five. Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers. The dividend is the number that is being divided in this case. The divisor is the number, which divides the number (dividend) into equal parts.
Here,
37 - 21 and 1/4 = 36 and 4/4 - 21 and 1/4 = 15 and 3/4 = 63/4
63/4 divided by 1 and 3/4 = 63/4 divided by 7/4 = 63/4 * 4/7 = 9 years
It will take 9 years to reach at the height of 37 feet as the tree grow 1& 3/4 feet per year.
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Complete question:
A tree grow 1& 3/4 feet per year. How long will it take the tree to grow from a height of 21 & 1/4 feet to a height of 37 feet?
A given measures 30 degrees, and the measure of its vertical angle, is expressed as (5x+5) degrees. Solve for x
After solving the equation, the value obtained for x will be equal to 5.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.
A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the given expression in the question,
5x + 5 = 30
5x = 30 - 5
5x = 25
x = 25/5
x = 5
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Need help on tis promblommm
Answer:
C,D
Step-by-step explanation:
C and D are multiplying 250 by a number greater than one so the result will be greater than 250
The first two are multiplying 250 by a frction less than one....the result will be less than 250
What is the center and radius of the circle defined by the equation x² y² 49?
The equation x² + y² = 49 can be written in standard form as (x-0)² + (y-0)² = 49, which is the equation for a circle with a center at (0, 0) and a radius of 7.
The equation for a circle is (x-h)² + (y-k)² = r², where (h, k) represents the center of the circle and r represents the radius.
In order to find the center (h, k) and radius (r) of the circle, we need to rearrange the equation to put it in the standard form. To do this, we subtract 49 from each side of the equation, which will give us x² + y² - 49 = 0. Then, we can factor the equation to get (x² + y²) - 7(7) = 0. This can be further simplified to (x + 7)(x - 7) + (y + 7)(y - 7) = 0.
Since there are no solutions for (x + 7) or (x - 7) when set equal to 0, we can conclude that the equation for the circle is (x-0)² + (y-0)² = 49, which is the equation for a circle with a center at (0, 0) and a radius of 7.
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Graph f(x) = √√x+2 over the domain -2 ≤x≤7.
The graph of the function square root of the square root of x + 2 in the given domain is given by the image shown at the end of the answer.
How to graph the function?The function for this problem is defined as follows:
f(x) = √√x+2
The double square root means that in reality, we have the fourth root of the function, hence the function is then defined as follows:
f(x) = fourth root(x + 2).
The fourth root function is defined for values of x for which the inner term is zero and greater, hence:
x + 2 >= 0
x >= -2.
Then the graph is made over a domain that goes until x = 7, and is given by the image presented at the end of the answer.
(the domain is chosen because it is the domain given by the problem).
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question which system of equations models the following problem if x represents the number of angelfish yves bought and y represents the number of parrotfish he bought? yves bought 420 tropical fish for a museum display. he bought 6 times as many parrotfish as angelfish. how many of each type of fish did he buy?
Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."
Calculation:x + y = 420; y = 6x
Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."
How well-versed are you in fish size?The smallest and largest fish range in size from 1 cm to 18 m. 18 m then equals 18 x 100 or 1800 cm. ∴ The length of large fish exceeds that of little fish by 1800 times.
How many parrotfish purchased by Carlos?The number of parrotfish Carlos purchased is represented by the variable y, whereas the number of angelfish Carlos purchased is represented by the variable x.
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a popular magazine tests cars and trucks for mileage on the road and around the city. the magazine reports that 50% of the cars tested had mileages below 24.7 mpg on the road, and the other 50% of the cars tested had mileages above 24.7 mpg. which statistic does this 24.7 represent?
The decimal number 24.7 represents the average mileage of the vehicle.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or discipline to collect and summarise the data.
A famous magazine tests vehicles and trucks for mileage out and about and around the city. the magazine reports that half of the vehicles tried had mileages beneath 24.7 mpg out and about, and the other half of the vehicles tried had mileages above 24.7 mpg.
The decimal number 24.7 means the vehicle can cover 24.7 miles with each gallon of gas.
The decimal number 24.7 represents the average mileage of the vehicle.
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Popular wisdom is that eating presweetened cereal tends to increase the number of dental caries (cavities) in children A sample of children was (with parental consent) entered into a study and followed for several years. Each child was classified as a sweetened-cereal lover or a unsweetened cereal lover. At the end of the study, the amount of tooth damage was measured. Here are the summary data: 10 15 Mean 6.41 5.20 Std Dev 5.0 15.0 225 Sweetened Unsweetened Assuming the necessary conditions for inference are met, which of the following an approximate 95% confidence interval for the difference in the mean tooth damage?
O (6.41 -5.20) + 2.145 3+
O (6.41 - 6:20) +1.96 Vi+
O (6.41 -- 5.20) +1,96/13 + 38
O (6.41 -5.20) +2.202/33+
O (6.41 - 5:20): 2.2821+13 228 X
An approximate 95% confidence interval for the difference in the mean tooth damage is (6.41 - 5.20) ± 2.26[tex]\sqrt{\frac{25}{10}+\frac{225}{15} }[/tex]
For sweetened samples
The value of n = 10
The mean of the samples = 6.14
The standard deviation of the sample = 5.0
For unsweetened samples
The value of n = 15
The mean of the sample = 5.20
The standard deviation of the sample = 15.0
We have to assume that necessary conditions for inference are met
The confidence interval = 95%
The equation will be
(6.41 - 5.20) ± 2.26[tex]\sqrt{\frac{25}{10}+\frac{225}{15} }[/tex]
Therefore, the difference in the mean tooth damage is (6.41 - 5.20) ± 2.26[tex]\sqrt{\frac{25}{10}+\frac{225}{15} }[/tex]
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Find the value of x. Round to the nearest tenth: 29,26, and 50
The value of x is 23.22°. By using the Cosine rule
Cosine RuleThe Cosine Rule of trigonometry states that the square of any side of a given triangle is equal to the sum of the squares of the other sides minus twice the product of the other two sides multiplied by the cosine of the angle included between them. The Law of cosines and Cosine Formula are other names for the cosine rule.
The expression for representing cosine rule is expressed as:
c² = a² + b² - 2ab cos C
Given,
a = 26
b = 50
c = 29
Substituting the value to the equation:
c² = a² + b² - 2ab cos C
29² = 26² + 50² - 2(26)(50) cos C
841 = 676 + 2500 - 2600cosC
2335 =2600cos C
cos C = [tex]\frac{2335}{2660}[/tex]
C = 23.22°
The value of x is 23.22°
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Answer: 23.2 rounded to nearest tenth
Step-by-step explanation:
invert a multiply to evaluate the division expression 3/4 ÷ 1/3 help
To multiply the division expression 3/4 ÷ 1/3 is 9/4. Division expressions are mathematical expressions using division
What is meant by mathematical expression ? When numbers and variables are properly combined using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions, a set of mathematical symbols known as an expression is produced. For instance, "4 added to 2" will have the mathematical formula 2+4. Addition, subtraction, multiplication, and division are all considered operations. There are a lot more operations that can be employed in a mathematical equation. You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6.3/4 : 1/3
= 3/4 · 3/1
= 3·3/4.1
= 9/4
Hence this proved.
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f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].
[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]f(x)= 2x^2 + 12x +16 \qquad \begin{cases} x_1=-3\\ x_2=-2 \end{cases}\implies \cfrac{f(-2)-f(-3)}{-2 -( -3)} \\\\\\ \cfrac{[2(-2)^2 + 12(-2) + 16]~~ - ~~[2(-3)^2 + 12(-3) + 16]}{-2+3} \\\\\\ \cfrac{[8-24+16]~~ - ~~[18-36+16]}{1}\implies 0-(-2)\implies \text{\LARGE 2}[/tex]
what expression is equivalent to 3/4a + 2/3 - 1/2a - 1/3 + 1/2a
Answer:
(3/4)a + 1/3
Step-by-step explanation:
3/4a + 2/3 - 1/2a - 1/3 + 1/2a
(3/4)a + (2/3) - (1/2)a - (1/3) + (1/2)a [added () to clarify. Is "3/4a" (3/4)a or 3/(4a)?
(3/4)a + (2/3) - (1/2)a - (1/3) + (1/2)a
(3/4)a - (1/2)a - (1/3) + (1/2)a + (2/3)
(3/4)a - (1/2)a + (1/2)a - (1/3) + (2/3) [Rearrange: like terms together]
a[(3/4) - (1/2) + (1/2)] - (1/3) + (2/3) [bring out the "a"]
a[(3/4)] + (1/3) [simplify]
(3/4)a + 1/3
decide whether enough information is given to prove that $\triangle abc\cong\triangle dbe$ using the sss congruence theorem. explain. two triangles, triangle a c b and triangle d e b that share a common vertex b. point b is on the segment a d. in triangle a c b, side a c is marked with single tick, side b c is marked with double ticks and side a b is marked with three ticks. in triangle d e b, side d e is marked with single tick, side b e is marked with double ticks and side b d is marked with three ticks.put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse.you are given that $\overline{ab}\cong$ response area, $\overline{bc}\cong$ response area, and $\overline{ac}\cong$ response area. so, the triangles response area be proven congruent using the sss congruence theorem.
No, enough information is not given to prove that triangles are congruent using the SSS congruence theorem.
The SSS congruence theorem expresses that assuming in two triangles, three sides of one are consistent to three sides of the other, then, at that point, the two triangles are said to be congruent.
Now, we are given that triangle ACB and triangle DEB that share a common vertex b. So, both triangles share a common side. So, one side is same for both of triangles.
From the diagram, we can see that both triangles opposite side are equal. So, second side is equal for both of triangles.
Now, from the diagram, we can see that both triangles vertically opposite angles are equal. So, we have two sides equal and one angle is equal.
So, given triangle is proved to congruent by SAS congruency not by SSS congruency.
Hence, enough information is not given.
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The values of f(x) and g(x) are shown for selected values of x in the table below. x f(x) g(x) 0 0 1 1 3 2 2 6 4 3 9 8 4 12 16 Of these two functions, one is exponential and the other is linear. Determine which of the functions is linear, and explain why this must be the case.
The linear function is f(x) and the exponential function is g(x).
What is an exponential function?The exponential function is a mathematical function that is represented by e^x. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.
Linear functions have a straight line as their graph. The following is the form of a linear function. y = f(x) + a+bx There is one independent variable and one dependent variable in a linear function.
In this case, the function for g(x) is 2^x.
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Suppose that the average cost, in dollars, of producing a shipment of a certain product is C = 5,000x + 20,000/x, x > 0 where x is the number of machines used in the production process. (a) Find the critical values of this function. (Assume 0 < x < [infinity]. Enter your answers as a comma-separated list.) x = Incorrect: Your answer is incorrect. (b) Over what interval does the average cost decrease? (Enter your answer using interval notation.) (c) Over what interval does the average cost increase? (Enter your answer using interval notation.)
The average cost function is C(x) = 5000x + 20,000/x, where x is the number of machines used in the production. The critical value is C(x) = 20,000 and it happens when x = 2.
If we have a function f(x), the critical point happens when its first derivative is equal to zero.
f '(x) = 0
In the given problem, the function is:
C(x) = 5000x + 20,000/x
Take the derivative:
C '(x) = 5000 - 20,000/x² = 0
5000 x² = 20,000
x² = 4
x = ±2
Since x is within the interval: 0<x<∞, the solution is x = 2
Substitute x = 2 into the function:
C(2) = 5000 (2) + 20000/2
C(2) = 10000 + 10000 = 20,000
Hence, the critical value is C(x) = 20,000 and it happens when x = 2.
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quota sampling occurs when available or accessible people or materials are selected, and the sample is weighted so that certain predetermined characteristics are represented. group of answer choices true false
Following the Sampling Theorem of statistics, the answer is True.
What are statistics?The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data.
What is Sampling Theorem?Each member of the group or community has an equal chance of being chosen when using probability sampling. According to probability-based statistical theory, this indicates that the sample is more likely to match the larger population, allowing for the drawing of more precise conclusions about the latter.
Yes, the quota sampling process occurs when the available or accessible people or material are selected. Due to large population size, Sampling process is preferred.
Since, Statistics convey characteristics of data to us. So yes, The sample is weighted so that predetermined characteristics are represented.
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How many inches is there in 1/8th of a yard?
Answer:
4.5
Step-by-step explanation:
You calculate it. look 1 yard is 36 inches. so 1/8 of a yard is 36 divided by 8. 4.5!
The width of a rectangle is the length minus 3 units. The area of the rectangle is 28
units. What is the length, in units, of the rectangle?
PLEASE HELP ME WITH THESE 2 QUESTIONS
Answer:
Question 1: Calculate the coordinates of 2 points. You know that the value of the Y coordinate in a point is 4 times the value of the x in the same point. Once you figure out the points, put them on the graph and draw a straight line through them with a ruler.
Question 2: What number do you multiply 5 by to get 12? You multiply that same number by the 375 to get the value in the corresponding row. That's called proportion.
Question 3: You can find the proportion between the two values (distance and energy). Its how many times bigger (or smaller) the values are in relation to each other. You can use this proportion for the scale of the graph so that the location of points are easier understood in relation to each other and discernable all by your eye.
with one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. the abc electronics company has just manufactured 1200 write-rewrite cds, and 150 are defective. if 3 of these cds are randomly selected for testing, what is the probability that the entire batch will be accepted?
The probability that the entire batch will be accepted.
What is Acceptance Sampling?
Acceptance sampling is a statistical measure used in quality control. It allows a company to determine the quality of a batch of products by selecting a specified number for testing.
abc Electronics Company manufactured 1200 write-rewrite cds, and 150 are defective. Since 150 are defective, the number of write-rewrite cds that would be accepted is (1200 - 150 = 1050).
Since the items at selected without replacement, the number of write-rewrite cds will continue to decrease anytime a write-rewrite cds is taken out. For example if they are 1050 accepted write-rewrite cds if one is taken out they would then be 1049 accepted write-rewrite cds, and if another one is taken out they would be 1049 accepted write-rewrite cds and so on.
If 3 of these cds are randomly selected for testing without replacement,
The probability that the entire batch will be accepted
= (1050/1200) × (1049/1200) × (1048/1200) × (1047/1200)
= 0.8750 × 0.8742 × 0.8733 × 0.8725
=0.5828
The probability that the entire batch will be accepted is 0.5828 .
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HELP MEEEEEEEEEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!
