By standard deviation, 3.4 defects per million that a six sigma program has. Whereas the remaining ones are not appropriate in this context.
What does standard deviation mean ?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.
Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
Describe standard deviation using an example?
The dispersion of the data around the mean value is measured by the standard deviation. It might be helpful when comparing data sets that may have the same mean but a different range.
The means of the two numbers 15, 15, 15, 14, 16, and 2, 7, 14, 22, 30 are the same, for instance. The second is, however, obviously more dispersed.
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) let x be an exponential random variable. then, its mean and its standard deviation are equal. true or false?
False. The mean and the standard deviation of an exponential random variable are not equal.
An exponential random variable has a probability density function given by:
[tex]$f(x) = \lambda e^{-\lambda x}$ for $x > 0$[/tex]
where[tex]$\lambda > 0$ i[/tex]s the rate parameter.
Mean for exponential random variable:
[tex]$\frac{1}{\lambda}$[/tex]
Standard deviation for exponential random variable:
[tex]$\frac{1}{\lambda}$[/tex]
Thus, the mean and the standard deviation of an exponential random variable are not equal, and they have different values depending on the value of [tex]$\lambda$[/tex]
It is important to note that exponential random variables have a memoryless property, which means that the future behavior of an exponential random variable is independent of its past values. This property makes exponential random variables useful for modeling various real-world phenomena such as the time between failures in reliability engineering or the time between events in a Poisson process.
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A savings account gathers compound interest at a rate of 7% per annum. The amount of money in the account over the first two years is shown below. Copy and complete the expression below for the amount of money in the account after n years
The equation that gives the balance of the account after n years is given as follows:
[tex]A(t) = P(1.07)^t[/tex]
In which P is the initial amount in the account.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for the function in thisp roblem are given as follows:
r = 0.07, n = 1.
Hence the function is given as follows:
[tex]A(t) = P(1.07)^t[/tex]
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Manjit bought a house. The value of her house went up by 5% in the first year. In the second year, the value went up by 2%. At the end of the two years her house was worth £171360.
What was the total percentage increase?
Work out the amount Manjit paid for her house
Answer:
The percentage increase is 7%.
She paid £160150 for her house.
Step-by-step explanation:
first year : increase 5%
second year : increase 2%
after 2 years : £171360
100%+5%+2%= 107%
107%= £171360
1%= £171360÷107
= £1601.5 (to 5 s.f.)
100%= £1601.5×100
= £160150
identify the circumstances in which the median rather than the mean is the preferred measure of central tendency. check all that apply.
The circumstances in which the median rather than the mean is the preferred measure of central tendency is when there is a skewed distribution (a few extreme scores), an open-ended distribution or undetermined scores.
What is central tendency?Central tendency is defined as the summative measure that tries to describe the entire set of data with a single value representing the mean or center of the distribution.
A skewed distribution occurs when one tail is longer than the other.
Therefore, in this type of distribution, the median should be chosen as the preferred measure of central tendency.
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how many integers are between the square root of 7 and square root of 200
Answer:
12
Step-by-step explanation:
√7 =2.65
√200 = 14.14
so 3,4,5,6,7,8,9,10,11,12,13,14
a survey of 25 grocery stores revealed that the average price of a gallon of milk was $2.98, with a standard error of $0.10. what is the 98% confidence interval to estimate the true cost of a gallon of milk? $2.85 to $3.11 $2.73 to $3.23 $2.95 to $3.01 $2.94 to $3.02
The 98% confidence interval to estimate the true cost of a gallon of milk is $2.73 to $3.23.
What do you mean by standard error?The standard error is a measure of the variability or spread of a set of sample values. In statistics, the standard error is used to quantify the precision of an estimate of a population parameter, such as the mean or standard deviation. It is calculated as the standard deviation of the sampling distribution of a statistic, usually the mean. The standard error is a useful measure because it provides a way to compare different estimates of a population parameter, and it can be used to construct confidence intervals, which provide a range of values within which the true population parameter is likely to lie with a specified degree of confidence.
The 98% confidence interval to estimate the true cost of a gallon of milk can be calculated using the following formula:
CI = (sample mean) ± (critical value) * (standard error)
Where critical value can be obtained from a standard normal distribution table, corresponding to a given level of confidence.
For 98% confidence, the critical value is 2.33.
CI = $2.98 ± 2.33 * $0.10 = $2.98 ± $0.23 = $2.73 to $3.23
Therefore, the 98% confidence interval to estimate the true cost of a gallon of milk is $2.73 to $3.23
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you deposit 35000 in an account that pays 2.3% annual interest. find the balance after 6 years compounded quarterly
The value of balance after 6 years compounded quarterly is , $44,450
What is Simple interest?A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that;
You deposit 35000 in an account that pays 2.3% annual interest.
We know that;
Amount = P (1 + r/4)⁴ⁿ
Where, P is the starting amount, r is interest rate and n is time.
Substitute all the value we get;
Amount = P (1 + r/4)⁴ⁿ
Amount = 35000 (1 + 0.023/4)²⁴
Amount = 35000 (4.023/4)²⁴
Amount = 35000 × 1.01²⁴
Amount = 35000 × 1.27
Amount = $44,450
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who is correct in each question and fix their statement
In triangle XYZ The image will be in the second quadrant hence Joseph is correct
In the rectangle, the image of A' will be in the quadrant III hence Chad is correct
What is rotation in transformation?Rotation in transformation refers to the process of rotating an object around a fixed point by a certain angle, changing its orientation.
The fixed point is known as the center of rotation, and the angle of rotation determines the extent to which the object is rotated.
In 2D graphics, rotation can be represented by a matrix multiplication,
Inn the triangle rotation, the transformation rule is for 90° clockwise rotation
In the rectangle rotation, this is equivalent to reflection over the line y = x
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ion know how to do this and im tired i need help please
To solve this, you can use the geometric mean theorem. The leg of a right triangle is the geometric mean between the hypotenuse and the portion of the hypotenuse adjacent to the leg.
So that means that 28/y = y/12. You can then use means and extremes of proportions to simplify, and you get y^2 = 336, a.k.a y = 4 root 21.
Then you do the same thing but with x.
28/x = x/16
x^2 = 448
x = 8 root 7
Answer:
B. x = 8√7, y = 4√21
Step-by-step explanation:
Look at the largest right triangle so the hypotenuse equals 12 + 16 = 28
According to the Pythagorean Theorem: y^2 + x^2 = 28^2
Then for the 2 smaller right triangles, they all the the same side, just called it z
so y^2 = 12^2 + z^2 => z^2 = y^2 - 12^2
and x^2 = 16^2 + z^2 => z^2 = x^2 - 16^2
then y^2 - 12^2 = x^2 - 16^2
y^2 - 144 = x^2 - 256
y^2 = x^2 - 112
Using the first equation
y^2 + x^2 = 28^2 => x^2 = 784 - y^2
So we have y^2 = x^2 - 112
and x^2 = 784 - y^2
then y^2 = (784 - y^2) - 112
y^2 + y^2 = 784 - 112
2y^2 = 672
y^2 = 336
y = 4√21
x^2 = 784 - y^2 = 784 - 336 = 448
x = 8√7
use the four-step method in problem solving to solve the problem. city a has an elevation of 13,764 feet above sea level while city b has an elevation of 19,343 feet below sea level. how much higher is city a than city b?
The difference between city a and city b is 33,107 feet, with city a being 33,107 feet higher than city b.
Step 1: Identify the problem.
How much higher is city a than city b?
Step 2: Gather information.
City a has an elevation of 13,764 feet above sea level while city b has an elevation of 19,343 feet below sea level.
Step 3: Analyze the information.
City a is 13,764 feet above sea level, and city b is 19,343 feet below sea level. To find the difference, we need to subtract 19,343 from 13,764.
Step 4: Formulate a solution.
The difference between the two cities is 33,107 feet. City a is 33,107 feet higher than city b.
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Helen and Reid are walking to their classes at Cedarburg College. Helen comes from her dorm room, walking at a speed of 4 miles per hour down a straight path. Reid comes from the gymnasium on the other end of campus, moving up the same path at 3 miles per hour. If they start out 3 miles apart, how long will it be before they meet?
The time it will take for Helen and Reid to meet is given as follows:
3/7 of an hour = 26 minutes.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:
v = d/t.
The parameters for this problem are given as follows:
Distance of 3 miles.Relative velocity of 7 miles, as they are moving in opposite directions, and 4 + 3 = 7.Hence the time is obtained as follows:
7 = 3/t
7t = 3
t = 3/7 of an hour = 26 minutes.
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santa clara county, ca, has approximately 27,873 japanese-americans. what percentage of the community is under age 35?
The percentage of Japanese-Americans under 35 in Santa Clara County, CA is approximately 11.3%.
Santa Clara County, CA is home to approximately 27,873 Japanese-Americans. To determine what percentage of this population is under age 35, it is necessary to first calculate the total number of Japanese-Americans under 35. To do this, we can subtract the estimated number of Japanese-Americans over age 35 from the total population of Japanese-Americans. We can then divide this number by the total population of Japanese-Americans to find the percentage of Japanese-Americans under age 35. In Santa Clara County, CA, the estimated number of Japanese-Americans over age 35 is 24,672, and the total population of Japanese-Americans is 27,873. Subtracting 24,672 from 27,873 yields 3,201 Japanese-Americans under age 35. We can then divide 3,201 by 27,873 to get a percentage of 11.3%. Therefore, approximately 11.3% of the Japanese-American population in Santa Clara County, CA is under age 35.
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Find the coordinate of the point P that divides each directed line segment in the given ratio. Round the
coordinate to the nearest tenth if necessary.
from K to L; 1 to 5
The coordinate of point P is
The direction of point P is (2.5, 3.3). In this way, the point P that separates the line fragment from K to L with a 1 to 5 proportion has the coordinate (2.5, 3.3).
Given a line segment from K to L, and the proportion of the division as 1 to 5, we can find the direction of point P that separates the line section into the predetermined proportion.
The direction of point P can be tracked down utilizing the accompanying recipe:
P = (1 - t) K + t L
where t is the relative separation from direct K toward point P. To fulfill the 1 to 5 proportion, we can set t = 1/6.
Subbing the qualities into the equation, we get:
P = (1 - 1/6) K + 1/6 L
= 5/6 K + 1/6 L
To find the genuine direction of point P, we want to substitute the directions of K and L into the equation. For instance, if K = (3, 4) and L = (7, 8), the direction of point P can be determined as:
P = (5/6)(3, 4) + (1/6)(7, 8)
= (15/6, 20/6)
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Ty has a 50% chance of answering a trivia question correctly. He wants to know the probability that he will answer 3 of 4 trivia questions correctly. He flips a coin to conduct the simulation shown below.
HHTH HHIT THHT HHHH THỊT
THHT THHT HITH THIT HHHH
THTT THTT HTHT HHTT THTT
TTHT HHTH THHT HHIT THTH
H represents a correct answer, and T
represents an incorrect answer. Based on this simulation, what is the probability that he answers at least 3 trivia questions correctly?
Answer:
Step-by-step explanation:
Triangle ABC with points A (9,1) B (2,7) C(-2,-5) was translated 3 units left, 2 units down and then was reflected across the line y = x. What is the image point of C?
The point of C is, (- 7, - 5).
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Triangle ABC with points A (9,1) B (2,7) C(-2,-5) was translated 3 units left, 2 units down and then was reflected across the line y = x.
Now, Triangle ABC with points A (9,1) B (2,7) C(-2,-5) was translated 3 units left, 2 units down.
Hence, The point of C is,
⇒ C = (- 2, -5) + (- 3, - 2)
⇒ C = (- 5, - 7)
Since, It was reflected across the line y = x.
Hence, The point of C is,
⇒ C = (- 7, - 5)
Thus, The point of C is, (- 7, - 5).
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Lucy made 247 for 13 hours of work. At the same rate, how much would she make for 9 hours of work?
Answer: $171
Step-by-step explanation:
$247 divided by 13 hrs = $19/hr
$19/hr times 9 hrs = $171
a mountain is 6,874 feet above sea level whereas a nearby valley is 280 feet below sea level. determine the elevation difference between the height of the mountain and the height of the valley. the difference between the two heights is feet.
The difference in elevation between the height of mountain and height of valley measuring from sea level is equal to 6594 feet.
Since it is given that the height of mountain from the sea level is 6874 feet and the height of valley is 280 feet. Therefore to calculate the difference in elevation, the heights will be subtracted from one another to get a value which will show the elevation. Since both the heights are measured from the sea level which is taken as constant, so no extra calculations will be needed.
Elevation difference = Height of mountain - height of valley
Elevation difference = 6874 - 280 = 6594 feet
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Your family drives 126 miles from Key West to the Florida mainland about 15% of this distance is spent on bridges how many miles of the bridges do you come travel over
Answer:
Step-by-step explanation:
The 15% of 126 is 18.96 thus, my family travels 18.96 miles over the bridge.
What is the percentage?
The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
As per the given,
Total travel = 126
Percentage travel over the bridges = 15% of 126
15% of 126 = (15/100)126 = 18.96 miles
Hence "The 15% of 126 is 18.96 thus, my family travels 18.96 miles over the bridge".
a quiz consists of 10 multiple-choice questions, each with 6 possible answers. for someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 50 %.
The probability of passing a 10-question multiple-choice quiz by random guessing is about 2.4%.
How to find the probabilityA quiz consists of 10 multiple-choice questions, each with 6 possible answers. for someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 50 %.
The probability of a random guess being correct for a single multiple-choice question with 6 options is 1/6, or approximately 0.17.
To find the probability of passing the quiz with a minimum passing grade of 50%, we need to calculate the probability of getting 5 or more correct answers out of 10.
This can be calculated as the sum of the probabilities of getting exactly 5, 6, 7, 8, 9, or 10 correct answers:
P(pass) = P(5) + P(6) + P(7) + P(8) + P(9) + P(10)
where P(x) is the probability of getting exactly x correct answers.
This can be calculated using the binomial distribution and its cumulative distribution function (CDF). The result is approximately 0.024, or 2.4%.
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Find the midpoint between (9, -1) and (1, 15).
The midpoint between the endpoints (9, -1) and (1, 15) is equal to (5, 7).
How to determine the midpoint of a line segment?In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Substituting the given parameters into the midpoint of a line segment formula, we have the following;
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Midpoint = [(9 + 1)/2, ((-1) + 15)/2]
Midpoint = [(10)/2, (14)/2]
Midpoint = (5, 7).
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Aabbccc
I have to rewrite that using exponents
The expressions aaaaaaa, aabbbb, aabbccc, and 3xxyyyz will be a⁷, a²b⁴, a²b²c³, and 3x²y³z.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We know that if x is multiplied by n time of x, then we can be written as xⁿ.
1. aaaaaaa = a⁷
2. aabbbb = a²b⁴
3. aabbccc = a²b²c³
4. 3xxyyyz = 3x²y³z
The expressions aaaaaaa, aabbbb, aabbccc, and 3xxyyyz will be a⁷, a²b⁴, a²b²c³, and 3x²y³z.
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Translate the following phrases into expressions. Algebraic word problems
60 kilometres per x litres
60 kilometres per x litres can be expressed algebraically as 60/x km/L.
What is algebra?Algebra is a branch of mathematics that is used to manipulate symbols and equation in order to solve the problems algebra help to solve problems involving unknown quantities into the block relationship between different variable it is a powerful tool that can be used to solve the and analyze a variety of mathematical problem and equation.
This can be used to represent the relationship between the number of kilometres travelled and the number of litres of fuel that was used. For example, if a car travelled 240 kilometres using 4 litres of fuel, the expression would be 60/4 km/L, which would equal 15 km/L.
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A truck that can carry no more than 7100 lb is being used to transport refrigerators and upright pianos. Each refrigerator weighs 250 lb and each piano weighs 425 lb. Write and graph an inequality to show how many refrigerators and how many pianos the truck could carry. Will 12 refrigerators and 11 pianos overload the truck? Explain
Yes, 12 refrigerators and 11 pianos overload the truck, because 12 refrigerators and 11 pianos weighs more than 7100 lb.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that, a truck that can carry no more than 7100 lb is being used to transport refrigerators and upright pianos
Let the number of refrigerators be x and the number of pianos be y.
Each refrigerator weighs 250 lb and each piano weighs 425 lb.
Here, 250x+425y≤7100
Will 12 refrigerators and 11 pianos overload the truck
Now, put x=12 and y=11 in the inequality 250x+425y≤7100, we get
250×12+425×11≤7100
7675≤7100 not true
Therefore, the inequality represent the given scenario is 250x+425y≤7100.
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Solve for x. Enter the solutions from least to greatest.
3x²+36x + 81 = 0
lesser x =
greater x =
Answer:
Step-by-step explanation:
Simplify.
x^2 + 12x + 27
Factor.
(x + 9)(x + 3)
Solutions.
x = -9
x=-3
Answer:
x=-3 or x=-9
Step-by-step explanation:
No need to explain
Create a system of linear and exponential functions that pass through the point 1,12
The system of linear and exponential functions passing through (1,12) is given as follows:
Linear: y = 2x + 10.Exponential: y = 6(2)^x.What is the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For the function to pass through point (1,12), we have that when x = 1, y = 12, hence one example of a linear function is given as follows:
y = 2x + 10.
What is the exponential function?An exponential function is defined as follows:
y = a(b)^x.
When x = 1, y = 12, hence one example is given as follows:
y = 6(2)^x.
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There are 50 marbles in a bag. 35 of the marbles are brown. Otti takes at random a marble from the bag. He records the colour of the marble and puts the marble back in the bag. He does this 300 times. Work out an estimate for the number of brown marbles he takes.
If there are 50 marbles in a bag and 35 of them are brown, and Otti takes one marble and put it back afterwards and does it 300 times, then the estimated number of brown marbles Otti takes is around 105.
The expected number of brown marbles Otti takes can be estimated by multiplying the probability of drawing a brown marble (35/50) by the number of times he draws (300).
(35/50) × 300 = 105
This gives an estimated result of 105 brown marbles. It's important to note that this is just an estimate and the actual number could be different. The variation in the actual number of brown marbles Otti takes can be attributed to the randomness of the process.
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I need help with this problem
Answer: 33
Step-by-step explanation:
There are lots of things you have to remember in parallel lines with transversal lines (the lines that cut through the parallel lines). In this picture, the angles shown are co-interior angles. Co-interior angles add up to 180°.
Given this, we can make and solve the following equation:
[tex](x + 20) + (4x-5) = 180\\x + 20 + 4x - 5 = 180\\5x + 15 = 180\\5x = 165\\x = 33[/tex]
If there are any steps you don't understand, I can go through it again, so please tell me :)
find the number of ways the digits 0,1,2 and 3 can be permuted to give rise to a number greater than 2000
The number of ways the digits 0,1,2 and 3 can be permuted to give rise to a number greater than 2000 is 9.
What is permutation?A permutation is a word that describes the number of ways things can be ordered or arranged.
Given are numbers, 0,1, 2, 3
We asked for numbers greater than 2000, so those numbers will start either from 2 or 3.
2 _ _ _ = 3! = 6
3 _ _ _ = 3!/2! = 3
Hence, total possible ways are 6+3 = 9
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5i + 4 = 14 + 4i thanks yall
Answer:
The solution to the equation 5i + 4 = 14 + 4i is i = 10.
Step-by-step explanation:
To solve for i in this equation, isolate the variable (i) on one side of the equation. To do this, we'll subtract 4 from both sides:
5i + 4 - 4 = 14 + 4i - 4
This leaves us with:
5i = 10 + 4i
Next, we'll subtract 4i from both sides:
5i - 4i = 10 + 4i - 4i
This leaves us with:
i = 10.
So the solution to the equation 5i + 4 = 14 + 4i is i = 10.
Please help me, thank you
Answer:
548km^2
Explanation:
if the surface area is 137 km, and then it has a dialation of 4, then all you need to do is multiply by 137 by 4, which equals 548. That means the surface area of cylinder B is 548 km^2. Hope that helps.