Define a useful quantity for our expectation about the amount of a time an
in-control process will remain ostensibly in-control, the average run length (ARL), to be the number of samples that will be observed, on average, before a point falls outside control limits. If p is the probability that any given point falls outside the control limits, then:
ARL = 1/p
(Estimating the true ARL may be useful for detecting an out-of-control process, but not
necessarily doing so quickly.) A process is Gaussian with mean 8 and standard deviation 2. The process is monitored by taking samples of size 4 at regular intervals. The process is declared to be out of control if a point plots outside the 3σ control limits on an X-chart. If the process mean shifts to 9, what is the average number of samples that will be drawn before the shift is detected on an X-chart?

Answer:

5x+5

______

x^2-2x this the correct one

To multiply a decimal number by 10^2, you need to move the decimal point two places to the right. This is because multiplying by 10^2 is equivalent to multiplying by 100, which means shifting the decimal point two places to the right.

For example, let's say you have the decimal number 3.14 and you want to multiply it by 10^2. To do this, you move the decimal point two places to the right:

3.14 * 10^2 = 314.00

As you can see, the decimal point has been shifted two places to the right, resulting in the product of 314.00.

Similarly, if you have a decimal number with fewer digits, such as 0.25, and you want to multiply it by 10^2, you would still move the decimal point two places to the right:

0.25 * 10^2 = 25.00

Again, the decimal point has been shifted two places to the right, resulting in the product of 25.00.

Therefore, to multiply a decimal number by 10^2, you move the decimal point two places to the right.

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Answer:

V = πr²(h/3)

Step-by-step explanation:

83.74 = πr²(5/3)

R = 4.00 in

Diamater = 2r = 2 x 4.00 = 8 inches

The numerical expression, -200 121 3 (4.5), represents the depth of the diver. The expression is to be simplified using the order of operations.

According to the given expression, the diver begins at sea level and dives down 200 feet. Then he ascends at a steady rate of 121/3 feet per minute for 4.5 minutes. The depth is represented by the numerical expression: -200 121/3 (4.5). Here, the expression has to be simplified using the order of operations as follows:

First, we need to simplify 121/3 * 4.5 which is equal to 363/2. Next, we have to multiply -200 with 363/2 to get -72600/2. Finally, -72600/2 can be simplified to -36300. Now, it is evident that the result of the simplified expression in feet is -36300/12 which is equal to -3025/4 or -7550/8 or -1895/2 or -947.5. Therefore, the diver's depth is -255.5 feet.

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None of the wind gusts (17, 22, 8, 13, 19, 36, and 14) fall below -0.5 or above 35.5, there are no outliers in this data set. Therefore, the correct answer is D) none.

To identify any outliers in the data set, we can use a common method called the 1.5 interquartile range (IQR) rule.

The IQR is a measure of statistical dispersion and represents the range between the first quartile (Q1) and the third quartile (Q3) of a dataset. According to the 1.5 IQR rule, any value below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR can be considered an outlier.

To determine if there are any outliers in the given data set of wind gusts (17, 22, 8, 13, 19, 36, and 14), let's follow these steps:

Sort the data set in ascending order: 8, 13, 14, 17, 19, 22, 36.

Calculate the first quartile (Q1) and the third quartile (Q3).

Q1: The median of the lower half of the data set (8, 13, 14) is 13.

Q3: The median of the upper half of the data set (19, 22, 36) is 22.

Calculate the interquartile range (IQR).

IQR = Q3 - Q1 = 22 - 13 = 9.

Step 4: Identify any outliers using the 1.5 IQR rule.

Values below Q1 - 1.5 × IQR = 13 - 1.5 × 9 = 13 - 13.5 = -0.5.

Values above Q3 + 1.5 × IQR = 22 + 1.5 × 9 = 22 + 13.5 = 35.5.

Since none of the wind gusts (17, 22, 8, 13, 19, 36, and 14) fall below -0.5 or above 35.5, there are no outliers in this data set.

Therefore, the correct answer is D) none.

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Answer:

a = 2

Step-by-step explanation:

The subtraction of Matrix B from Matrix A is represented as:

\(\[A - B = \begin{bmatrix}0 & -4 \\7 & -4 \\1 & 1\end{bmatrix}\]\)

Given Matrix:

\(\[ A = \begin{bmatrix}3 & -1 \\2 & 0 \\-3 & 3\end{bmatrix} \]\)  and  \(\[ B = \begin{bmatrix}3 & 3 \\-5 & 4 \\-4 & 2\end{bmatrix} \]\)

To find the result of subtracting Matrix B from Matrix A,

subtract the corresponding elements of the matrices.

Here is the subtraction result

\(\[A - B = \begin{bmatrix}3 - 3 & (-1) - 3 \\2 - (-5) & 0 - 4 \\(-3) - (-4) & 3 - 2\end{bmatrix} = \begin{bmatrix}0 & -4 \\7 & -4 \\1 & 1\end{bmatrix}\]\)

Therefore, the subtraction of matrices is:

\(\[A - B = \begin{bmatrix}0 & -4 \\7 & -4 \\1 & 1\end{bmatrix}\]\)

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Area of the 8 Triangular windows is 8 * 84 = 672 sq.ft ,  Option C is the correct answer.

A triangle is a polygon with three sides , angles and vertices

It is given that

There are 8 triangular windows

The base of the triangle is 12 inches

The height of the window is 14 inches

Area of the triangle is (1/2) * base * height

Area of the triangle = (1/2) * 12 * 14

Area of the triangular window is 84 sq. inches

Area of the 8 Triangular windows is 8 * 84 = 672 sq.ft

Therefore Option C is the correct answer.

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Answer:

b.

Step-by-step explanation:

The correct function of the graph is,

⇒( f(x) = (x-a)²(x-b)⁴

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Now, Clearly from the graph of the function we could see that zero is not a root of the polynomial function

Hence, option (a) and (c) are discarded.

Now, we will check for option (b) and option (d)

As the graph touches the x-axis at two point i.e. a and b that means that both the roots of the polynomial equation are of even degree.

Hence, the correct option is:

⇒ f(x) = (x-a)²(x-b)⁴

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Answer:

r, a, t, i, o

Step-by-step explanation:

Looking back at the question before this, Among these points, circle the points where x<y (the first coordinate, x, is smaller than the second coordinate, y.) the points were a, t, o, i, r. Those are the circled numbers.

Looking at this problem now, we will count those letters up from the y axis, in an increasing order. (also it spells out ratio)

A dance portfolio for precaliberence in dance should feature a comprehensive resume, videos of performances, photographs, and any relevant awards or certifications. This combination of elements provides a well-rounded representation of a dancer's skills, accomplishments, and potential.

A dance portfolio is a collection of works that showcases an individual's skills, creativity, and versatility in the field of dance. It is a comprehensive representation of their training, experiences, and accomplishments. As a dancer, my portfolio would include various elements that highlight my precaliberence in dance.

Firstly, I would include a detailed resume outlining my dance education, including the styles I have studied, the instructors I have trained under, and any notable performances or competitions I have participated in. This provides a snapshot of my training and experience.

Next, I would include a compilation of videos showcasing my dance performances. These videos would demonstrate my technical proficiency, artistry, and ability to interpret different styles of dance. They may include solo performances, duets, or group routines, allowing the viewer to witness my versatility and adaptability as a dancer.

Additionally, I would include high-quality photographs capturing dynamic moments from my performances. These images would convey the emotions and expressions that I bring to my dance, as well as demonstrate my stage presence and physicality.

Lastly, I would incorporate any awards, scholarships, or certifications I have received throughout my dance journey. These achievements serve as evidence of my dedication, commitment, and recognition within the dance community.

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the probability that it will take at most 7 minutes to serve the 4 customers is approximately 0.9861.

(a) To find the probability that the wait time for the next customer served will exceed one minute, we need to use the exponential distribution with a rate parameter of λ = 0.5 (since the average time between customers is 2 minutes, the rate parameter is 1/2). Let X be the time between customer arrivals. Then, we need to find P(X > 1).

Using the exponential distribution, we have:

\(P(X > 1) = e^(-lamda * 1) = e^(-0.5)\)≈ 0.6065

Therefore, the probability that the wait time for the next customer served will exceed one minute is approximately 0.6065.

(b) Given that the customer has already been waiting for 1 minute, we can model the remaining waiting time as an exponential distribution with a rate parameter of λ = 0.5. Let Y be the remaining time until the next customer is served. Then, we need to find P(Y > 2 | Y > 1).

Using conditional probability, we have:

P(Y > 2 | Y > 1) = P(Y > 2 and Y > 1) / P(Y > 1)

Simplifying the numerator, we have:

P(Y > 2 and Y > 1) = P(Y > 2)

Using the exponential distribution, we have:

\(P(Y > 2) = e^(-λ * 2) = e^(-1)\)

Similarly, we have:

\(P(Y > 1) = e^(-λ * 1) = e^(-0.5)\) ≈ 0.6065

Substituting into the conditional probability formula, we have:

P(Y > 2 | Y > 1) = P(Y > 2) / P(Y > 1) ≈ 0.6065

Therefore, the probability that the wait time for the next customer served will exceed three minutes, given that they have been waiting for 1 minute already, is approximately 0.6065.

(c) Let Z be the total time it takes to serve the 4 customers. Then, Z follows the gamma distribution with shape parameter k = 4 and rate parameter λ = 0.5. We need to find P(Z ≤ 7).

Using the gamma distribution, we have:

P(Z ≤ 7) = F(k, λ, 7)

where F is the cumulative distribution function of the gamma distribution. We can use a calculator or software to find this probability, or we can use the incomplete gamma function as follows:

P(Z ≤ 7) = 1 - Γ(k, λ * 7)

where Γ is the incomplete gamma function. Using a calculator or software, we have:

P(Z ≤ 7) ≈ 0.9861

Therefore, the probability that it will take at most 7 minutes to serve the 4 customers is approximately 0.9861.

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It occurs on day 7 when the population is 1,280,000.

Solving an equation involves finding the values of the variables that make the equation true. This can often involve manipulating the equation using mathematical operations such as addition, subtraction, multiplication, or division. Equations are used in a wide range of mathematical and scientific fields, as well as in everyday life. For example, equations are used to model the behavior of physical systems, to calculate interest on loans, to determine the speed and trajectory of moving objects, and to solve many other types of problems.

Here,

a. To complete the table, we can use the information given that the bacteria population doubles each day. Starting with an initial population of 10,000, we can find the population for each day by multiplying the previous day's population by 2.

d, time(days) p, population

0 10,000

1 20,000

2 40,000

3 80,000

4 160,000

5 320,000

6 640,000

7 1,280,000

8 2,560,000

9 5,120,000

10 10,240,000

b. To find the first day that the bacteria population is more than 1,000,000, we can look at the table and see that it occurs on day 7 when the population is 1,280,000.

c. We can write an equation relating the bacteria population (p) to the number of days since it was first measured (d) using the formula for exponential growth.

p = 10,000 x 2ᵇ

This equation states that the population (p) is equal to the initial population of 10,000 multiplied by 2 raised to the power of the number of days since it was first measured (d).

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An equation she can use to find Plant A's height in centimeters is a = b - 4

What is an equation?

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

Here, we have

Given: Miram is studying a type of plant that grows at a constant rate. Every month, she visits two of these plants and measures their heights.

Let's use the table to think about the difference between Plant A's height and Plant B's height. That will help us write an equation we can use to find Plant A's height from Plant B's height.

plant  A's height is always 4 cm less the plant B's so we can write an equation to find plant A's height in terms of plant B's.

Hence, An equation she can use to find Plant A's height in centimeters is a = b - 4

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Step-by-step explanation:

Since you added 12 to the x coordinate and subtracted 7 from the y coordinate, to undo that translation, you need to subtract 12 from the x coordinate of the image and add 7 to the y coordinate of the image.

This gives you that C=(-2-12, 1+7)=(-14, 8)

Paired sample data may include one or more​ influential points, which are points that strongly affect the graph of the regression line.

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Answer: B. statistic

Step-by-step explanation: A characteristic, usually a numerical value, which describes a sample, is called a statistic.

The data distribution is skewed to the right. This is because the bars are clustered towards the left side of the histogram and taper off towards the right side.

The histogram of distances students live from school provided in the question shows that the majority of students in Tuan's homeroom live within a short distance of the school, with only a few students living farther away. The distribution is skewed to the right because the bars are clustered towards the left side of the histogram and taper off towards the right side. This indicates that there are fewer students who live farther away from school. A skewed distribution means that the data is not evenly distributed and tends to cluster towards one end. In this case, the distribution is skewed to the right because there are fewer students living farther away from school.

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Complete question is in the image attached below

Answer:

B. skewed.

Step-by-step explanation:

and then the next part is

1

hope this helps :)

The equation of line is y = 35x + 10 and Juan followed the instructions

The solution is Option A. Yes, his free throws can be represented by

y = 35x + 10

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 1 , 45 )

Let the second point be Q ( 2 , 80 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 80 - 45 ) / 2 - 1

Slope m = 35

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 45 = 35 ( x - 1 )

On simplifying the equation , we get

y - 45 = 35x - 35

Adding 45 on both sides of the equation , we get

y = 35x + 10

Hence , the equation of line is y = 35x + 10

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The complete question is :

Juan recorded the total number of free throws he attempted during practices. His results are shown in the table.

Number of practices = { 1 , 2 , 3 , 4 }

Number of throws attempted = { 45 , 80 , 115 , 150 }

Juan's coach told him to attempt 10 free throws before the first practice and then 35 free throws each practice. Did Juan follow his coach's instructions?

A) Yes, his free throws can be represented by y = 35x + 10.

B) Yes, his free throws can be represented by y = 45x.

C) No, his free throws can be represented by y = 35x.

D) No. his free throws can be represented by y = 45x.

Answer:Older workers are staying in the workforce longer.

Step-by-step explanation: I had the same question as you it should be right.

Answer:

\(x = 25\)

Step-by-step explanation:

The angles are vertical since they form from two lines crossing at a point and they share a same vertex.

Vertical angles are equal so

\(4x - 25 = 75\)

\(4x = 100\)

\(x = 25\)

Answer:

B.97

Step-by-step explanation:

Heyy so angle ADC and DAB are supp to one another, thus

83 + DAB = 180 --> subtracting

DAB =97. B

Hope that made sense :)

Answer:

im sorry about that i couldn't figure this out try useing a calculator

Answer:

2 + x

2 + (x)

x + (2)

Step-by-step explanation:

Switch them around.

Answer:

D this is a quadratic equation and if we draw it's graph it will represent a parabola. this means that the equation is a function. It also represents a relation ,if the gradient is negative it will face downwards and if it's positive it will face upwards.

the probability that it will rain on the day of Marie's wedding, given that the weatherman predicts rain, is approximately 0.0122 or 1.22%.

To calculate the probability that it will rain on the day of Marie's wedding, we can use Bayes' rule.

P(A) = 5/365 (probability of rain on any given day)

P(B|A) = 0.9 (probability of the weatherman predicting rain given that it actually rains)

P(B|¬A) = 0.1 (probability of the weatherman predicting rain given that it doesn't rain)

find P(A|B), the probability of rain given that the weatherman predicts rain.

Using Bayes' rule,

P(A|B) = (P(B|A) * P(A)) / P(B)

To calculate P(B), the probability that the weatherman predicts rain,  use the law of total probability:

P(B) = P(B|A) * P(A) + P(B|¬A) * P(¬A)

P(¬A) is the complement of event A, i.e., the probability that it doesn't rain.

Therefore, P(¬A) = 1 - P(A) = 1 - 5/365 = 360/365.

Substituting these values into the equation,

P(B) = (0.9 * 5/365) + (0.1 * 360/365)

Now calculate P(A|B):

P(A|B) = (0.9 * 5/365) / [(0.9 * 5/365) + (0.1 * 360/365)]

Calculating this expression:

P(A|B) ≈ 0.0122

Therefore, the probability that it will rain on the day of Marie's wedding, given that the weatherman predicts rain, is approximately 0.0122 or 1.22%.

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Answer:

8: $732.03

9: $629.52

10: $1281.52

11: $731.52

12: $653.52

13: $1090.52

14: $851.52

Step-by-step explanation:

The Amount of Trans shows us that we subtract those numbers from the balance and the Amount of Deposit shows us that we add those numbers to the balance.

In a baseball league of 7 teams, then 231 games are needed to complete the schedule if each team plays 11 games with each other

In the given question

In a baseball league of 7 teams.

We have to find  how many games are needed to complete the schedule if each team plays 11 games with each other team

Think about it for every team playing every other team once.

You would have \(^{7}C_{2}\) =7!/2!(7-2)!

\(^{7}C_{2}\) = 7×6×5!/2×1×5!

\(^{7}C_{2}\) = 7×3

\(^{7}C_{2}\) = 21

Now, this is done 11 times,

So 11 × 21 is 231 games.

Hence, the games are needed to complete the schedule are 231 games with each other.

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The right question is:

In a baseball league of 7 teams, how many games are needed to complete the schedule if each team plays 11 games with each other?

Answer:

8 pizzas

Step-by-step explanation:

If 1/5 was remaining, the hoard consumed 4/5 of all the pizza.

(4/5)*(10 pizzas) = 8 pizzas

Answer:

2 pizzas

Step-by-step explanation:

\(\frac{10}{1}\)*\(\frac{1}{5}\)=\(\frac{10}{5}\)

then divided 5 by 10 and it equals 2 pizzas.