in how many ways can four people line up in a straight line if the youngest person cannot be first in line?

Based on the given data, the process is out of control.

To determine if the process is still in control, we need to compare the new sample measurements to the control limits established in the X-bar and R control charts.

For the X-bar chart:

The UCL (Upper Control Limit) is calculated as the grand average (X-Double Bar) plus A2 times R-Bar:

UCL = 25 + (0.483 * 5) = 27.415

The LCL (Lower Control Limit) is calculated as the grand average (X-Double Bar) minus A2 times R-Bar:

LCL = 25 - (0.483 * 5) = 22.585

For the R chart:

The UCL (Upper Control Limit) for the R chart is calculated as D4 times R-Bar:

UCL = 2.004 * 5 = 10.020

The LCL (Lower Control Limit) for the R chart is 0.

Given the new sample measurements: 33, 37, 25, 35, 34, and 32, we can determine if any of the measurements fall outside the control limits. If any data point falls outside the control limits, it indicates that the process is out of control.

Upon comparing the new sample measurements to the control limits, we find that the measurement 37 exceeds the UCL of the X-bar chart. Therefore, the process is considered out of control.

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a) Probability of getting a sum less than 9 is 5/18

b) Probability of getting a sum greater than or equal to 10 is 1/6

c) Probability of getting a 3 on one die or on both dice is 2/9.

a) Sum less than 9: Out of 36 possible outcomes, the following combinations are included in a sum less than 9: (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1).

There are a total of 10 successful outcomes.

Therefore, the probability of getting a sum less than 9 is: P(A) = 10/36 = 5/18b) Sum greater than or equal to 10: Out of 36 possible outcomes, the following combinations are included in a sum greater than or equal to 10: (4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6).

There are a total of 6 successful outcomes.

Therefore, the probability of getting a sum greater than or equal to 10 is: P(B) = 6/36 = 1/6c) A 3 on one die or on both dice:

The combinations that include a 3 on one die or both are: (1, 3), (2, 3), (3, 1), (3, 2), (3, 3), (4, 3), (5, 3), and (6, 3).

There are 8 successful outcomes. Therefore, the probability of getting a 3 on one die or on both dice is: P(C) = 8/36 = 2/9

Therefore, the simple answer to the following questions are:

a) Probability of getting a sum less than 9 is 5/18

b) Probability of getting a sum greater than or equal to 10 is 1/6

c) Probability of getting a 3 on one die or on both dice is 2/9.

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Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

In the equation y=mx+b the m will equal the rate of change and the b will represent the initial value.

The equation which correctly models the situation in discuss is; P = 2.5(1.012)^y.

If follows from the task content that the situation given is that The number of people in the world was 2.5 billion in 1950.

Afterwards, The population has grown by 1.2% each year since then. Hence it follows that the function is an exponential one whose factor is; (100+1.2)%= 1.012.

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The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.

First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.

Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.

We can continue this process for all the intervals in the sequence, until we reach In. So we have:

a1 ≤ a2 ≤ ... ≤ an-1 ≤ an

and

b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn

This shows that the endpoints of the intervals are ordered in the same way.

Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:

Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .

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Answer:

150

Step-by-step explanation:

150

To show the formation of a sulfide ion from a neutral sulfur atom, we need to add two electrons to the sulfur atom, as sulfide ion has a charge of -2. Therefore, the equation for this process is: S + 2e- → S2-

In this equation, S represents the neutral sulfur atom, while S2- represents the sulfide ion that is formed after the addition of two electrons. This reaction is a reduction reaction, as sulfur is gaining two electrons to form a negatively charged ion.
In summary, the equation S + 2e- → S2- shows the formation of the sulfide ion from a neutral sulfur atom by adding two electrons to it. This equation highlights the importance of electron transfer in chemical reactions and how it can lead to the formation of new compounds.

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Answer:

(-40 -2i)

Step-by-step explanation:

-10i + -40 + 8i

Combine like terms

-40 + -10i + 8i

-40 -2i

Answer:

Nickel is not a layer of earth. It is a white metal that belongs to the group of transition metals and is said to be present in the core of the Earth. Sial- refers to the upper layer of the Earth's crust. This layer has an abundance of minerals having aluminum and silicates.

Answer:

I dont see the following but these are the layers of the Earth

Step-by-step explanation:

Answer:

28.875 or 28 7/8

Step-by-step explanation:

pls mark brainliest!

steps:

(23+1/2) + (15+1/8) - (9+3/4) then solve

46+1 over 2 + 120+1 over 8 - 36+3 over 4

solve

47/2 + 121/8 - 39/4

solve

188+121-78 over 8 = 231/8

convert 231/8= 28 7/8

a. No, the selection of the adults is not a binomial experiment.

A binomial experiment is a statistical experiment that has a fixed number of trials and two possible outcomes, often referred to as a "success" and a "failure". In this case, the sample of adults surveyed is not a fixed number of trials, and there is no set number of successes or failures.

Rather, the survey is attempting to measure the percentage of adults who save nothing for retirement. Therefore, the selection of the adults is not a binomial experiment.

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Terry's starting elevation is 3000 feet, and it is decreasing at a rate of 90 feet per second.

The given function e(t) = 3000 - 90t describes Terry's elevation, in feet, as a function of time, in seconds.

The function has a slope of -90, which represents the rate of change of elevation with respect to time. This means that Terry's elevation is decreasing at a constant rate of 90 feet per second.

The initial elevation, or starting point, is given by the y-intercept of the function, which is 3000 feet. This means that Terry began skiing from an elevation of 3000 feet.

As time passes, Terry's elevation decreases linearly, with a constant rate of 90 feet per second. This linear relationship between time and elevation can be used to predict Terry's elevation at any given time during the descent.

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Answer:

The value of x = 0    

Step-by-step explanation:

Given

To determine

The value of x = ?

If we closely observe the value of the y-coordinate of the image B'(x, 20), we can see that the y-coordinate of the image B' is 4 times the y-coordinate of the original point (0, 5).

i.e. y → 5×4 =20

It means the coordinates of the image B'(x, 20) can be determined by dilating the original point (0, 5) by a scale factor of 4.

Thus, the x-coordinate of B'(x, 20) can also be obtained by multiplying the x-coordinate of B(0, 5) by 4.

i.e. x → 4×0 = 0

Thus, the rule of dilation is:

P(x, y) = P'(4x, 4y)

Hence,

B(0, 5) → B'(4(0), 4(5)) → B'(0, 20)

Thus,

The value of x = 0           ∵ 0×4 = 0

Dispersion is a measure of how spread out a set of data values is. For the given data, I'll calculate three common measures of dispersion: range, variance, and standard deviation.

Sorted data: 0, 0, 1, 1, 3, 5, 6, 6, 7, 8, 9, 10, 11, 12, 12, 12, 12, 13, 14, 14, 15, 17, 18, 19, 20

1. Range: The range is the difference between the highest and lowest values in the dataset. In this case, the range is 20 (highest value) - 0 (lowest value) = 20.

2. Variance: Variance is the average of the squared differences between each data point and the mean of the dataset. First, calculate the mean (sum of values / number of values) which is 233/25 = 9.32. Next, find the squared differences between each data point and the mean, and then average these squared differences. The variance for this dataset is approximately 34.93.

3. Standard Deviation: The standard deviation is the square root of the variance. In this case, the standard deviation is approximately √34.93 ≈ 5.91.

In summary, the range for the given data is 20, the variance is approximately 34.93, and the standard deviation is approximately 5.91. These measures of dispersion provide insights into the variability of the data.

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The magnitude of the x-component of this vector is 9.05m.

The angle of inclination of the vector is calculated as;

θ = 90 ⁰ - 48.4 ⁰

θ = 41.6 ⁰

The magnitude of the x-component of the vector is calculated as;

Vx = 12.1 m x cos ( 41.6 )

Vx = 9.05 m

A vector can be represented by an ordered set of numbers, called components, that indicate the magnitude and direction of the vector in a particular coordinate system. The components of a vector can be added or subtracted using vector addition and subtraction, and multiplied by a scalar (a real number) using scalar multiplication.

Vectors can be visualized as arrows in a two- or three-dimensional space, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. Vectors can also be represented as matrices, which can be used to perform various operations on vectors, such as dot product and cross product.

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Complete Question:-

The factored form of the expression \(x^2 - 9\) is \((x+3)(x-3)\)

The expression x^2 + 9 has no real roots hence cannot be factored

Quadratic equations are equations with a degree of 2.

Given the quadratic function \(x^2-9 \ and \ x^2+9\)

For the function \(x^2 - 9\)

\(=x^2-9\\=x^2-3^2\)

Using the difference of two squares:

\(a^2-b^2=(a-b)(a+b)\\x^2-3^2=(x-3)(x+3)\)

For the expression x^2 + 9

The expression x^2 + 9 has no real roots hence cannot be factored

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\( \sf2x + 3y = - 6 \\ \sf2x + 3 \times 0 = - 6 \\ \sf2x = - 6 \\ \boxed{ \tt x = - 3}\)

Answer:

rise/run= -20/5= -4/1=-4 slope

or you sound use the slope formula (y2-y1)/(x2-x1)

(-9-11)/(1+4)

-20/5

-4

Step-by-step explanation:

Answer:

2nd option below

Step-by-step explanation:

the rectangle with size 12ft×8ft is similar to the rectangle with size 3ft×2ft.

because they have the same ratio of the length and the width.

=> 12 : 3 <=> 8 : 2

Answer:

64

Step-by-step explanation:

i calculated using https://www.calculator.net/triangle-calculator.html :/

Answer:

\(m=64\)

Step-by-step explanation:

\(m^2=n^2+0^2-2n~0~ co~12\)

\(= 78^2+14^2-2*78*14~co ~12\)

m= \(\sqrt{78^2+14^2-28*78 ~co~12}\)

\(m=64\)

---------------------------

hope it helps....

have a great day!!

The given expression : 2x + 3 = 5

Absolute of (2x + 3 = 5)

Apply the absolue bar:

|2x+3|=5

For negtaive part:

-( 2x + 3) = 5

For positive part:

2x + 3 = 5

Solve the negative part:

-( 2x + 3 ) = 5

-2x - 3 = 5

-2x = 5 + 3

-2x = 8

x = (-4)

Solve the positive part:

(2x + 3) = 5

2x + 3 = 5

2x = 5 - 3

2x = 2

x = 1

So, the two possible values of x are x = (-4), 1

Answer : x = (-4), x = 1

The true statements are:

Logarithms may be used to linearize data.

Powers may be used to linearize data. Roots may be used to linearize data.

If a data set is linearized by taking the common logarithm (log) or natural logarithm (ln) of the y-values, then the data follows a power model.

Another format for writing exponents is in logarithms.

The use of a logarithm can be utilized to solve issues that cannot be resolved using the concept of exponents alone. A logarithm is simply another way to describe exponents. Exponent and logarithm are inverse forms of one another. A logarithm is defined using an exponent.

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Answer:

A.Logarithms may be used to linearize data.

B.Powers may be used to linearize data.

C.Roots may be used to linearize data.

E.If a data set is linearized by taking the pth root of the y-values, then the data follows a power model.

Step-by-step explanation:

Yes

Answer:

29 degrees

Step-by-step explanation:

Given

<D = 2x+8

<A = 122

The sum of the adjacent angle of the trapezoid is 180 degrees

<D + <A = 180

2x + 122 = 180

2x = 180-122

2x = 58

x = 58/2

x = 29 degrees

Hence the value of x is 29 degrees

To determine the set of reflections that would carry hexagon ABCDEF onto itself, we need to identify the lines of reflection that preserve the hexagon's symmetry.

A hexagon has six sides and six vertices. The lines of reflection that can carry the hexagon onto itself are those passing through the midpoints of opposite sides or through the midpoints of opposite vertices.

In this case, there are three possible lines of reflection that would preserve the hexagon's symmetry:

1. The line passing through the midpoints of AB and CD.

2. The line passing through the midpoints of BC and DE.

3. The line passing through the midpoints of CD and EF.

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Partial initialization allows us to initialize only some elements of an array, leaving the rest with default values.

The statement you provided, `int num]= (88, 92, 75, 95, 82)`, contains syntax errors and is not a valid example of partial initialization of an array in C or C++.

To understand partial initialization of an array, let's consider a correct example. Suppose we have an integer array named `num` with a size of 10. We want to initialize the first five elements of the array with specific values, and the remaining elements should be set to 0. Here's how partial initialization would look like:

int num[10] = {88, 92, 75, 95, 82};

In this example, we declare an integer array `num` with a size of 10. We provide an initializer list inside curly braces `{}` to initialize the elements of the array. The first five elements are explicitly initialized with values `88`, `92`, `75`, `95`, and `82`. The remaining elements are automatically set to 0 because we haven't provided explicit values for them.

Partial initialization allows us to initialize only some elements of an array, leaving the rest with default values. It's particularly useful when we want to set certain values while keeping others as defaults, such as zero in the case of integers.

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Rounding to the nearest whole number, she will have run a total distance of 13 kilometers after 16 days.

To find out how far she will have run in total after 16 days, we can use the formula for calculating compound interest:

A = P(1 + r/100)^n

Where:

A = Total distance run after n days

P = Initial distance (4.8 kilometers)

r = Rate of increase per day (6.9%)

n = Number of days (16)

Plugging in the given values, we can calculate the total distance:

A = 4.8(1 + 6.9/100)^16

Using a calculator or performing the calculations step by step, we get:

A ≈ 4.8(1.069)^16 ≈ 4.8(2.092473)^16 ≈ 4.8(2.628)

A ≈ 12.6144

Rounding to the nearest whole number, she will have run a total distance of 13 kilometers after 16 days.

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Answer:

a^2b^7

Step-by-step explanation:

dividing exponents is basically subtracting the top exponent by the bottom. So, 3 - 1 = 2, thus giving you a^2, and 9 - 2 = 7, giving you b^7