Five children divide 4/5 of a cake equally. Which fraction represents the part of the whole cake each child recives

The cumulative distribution function (CDF) for a normal distribution: b. tells us how much of a normal distribution is to the left of any given point. The CDF represents the probability that a random variable will take a value less than or equal to a given value.

In the case of a normal distribution, the CDF gives the area under the curve to the left of a specific point, indicating the probability of the random variable being less than or equal to that point. The correct answer is b. The cumulative distribution function (CDF) tells us how much of a normal distribution is to the left of any given point. It is a function that maps the possible values of a random variable to their respective probabilities. The CDF is a cumulative function, meaning that it accumulates the probabilities as we move along the distribution. The shape of the CDF is the same as the normal distribution, but it ranges from 0 to 1, with wider tails.

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About 3.25 seconds have gone by when the rocket is at its highest point.

The height of the rocket at any time t can be calculated using the equation h = -16t² + 104t.

The vertex of the parabolic function will give the value of the highest point of the rocket. The x-coordinate of the vertex gives us the time at which the rocket reaches its maximum height.

The x-coordinate of the vertex can be found using the formula: x = -b / 2a, the coefficient of the t² term is a and coefficient of the t term is b.

In this case, a = -16 and b = 104, so the x-coordinate of the vertex is,

x = -b / 2a

= -104 / (2*(-16))

= 3.25

Therefore, the rocket is at its highest point 3.25 seconds after launch.

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CI = 6.76 ± 1.96 × (2.67/√50)
CI = 6.76 ± 0.96
Therefore, the 95% confidence interval for the population means rating for Miami is: (5.80, 7.72)

We can be 95% confident that the true mean rating for Miami International Airport falls within this interval.
To develop a 95% confidence interval for the population means rating for Miami International Airport, we need to follow these steps:

1. Calculate the sample mean (x) by adding up all the ratings and dividing by the sample size (n=50).
2. Calculate the sample standard deviation (s).
3. Use a t-distribution to find the t-score for a 95% confidence interval with (n-1) degrees of freedom.
4. Calculate the margin of error (ME) using the t-score, standard deviation, and sample size.
5. Add and subtract the margin of error from the sample mean to find the lower and upper limits of the confidence interval.

To calculate the 95% confidence interval, we need to use the formula:
CI = x ± Z' (s/√n)
Where:
x = sample mean
Z' = z-score for the desired confidence level (in this case, 95%, so

Z' = 1.96)
s = sample standard deviation
n = sample size

Step 1: Calculate the sample mean (x)
Sum of ratings = 346
Sample size (n) = 50
x = 346/50 = 6.92

Step 2: Calculate the sample standard deviation (s)
Variance = [(Sum of (rating - x)^2) / (n-1)] = 88.48
Standard deviation (s) = √(88.48) = 9.41

Step 3: Find the t-score
For a 95% confidence interval with 49 (n-1) degrees of freedom, the t-score is approximately 2.01.

Step 4: Calculate the margin of error (ME)
ME = t-score × (s / √n) = 2.01 × (9.41 / √50) = 2.01 × 1.33 = 2.67

Step 5: Find the confidence interval
Lower limit: x - ME = 6.92 - 2.67 = 5.80
Upper limit: x + ME = 6.92 + 2.67 = 7.72

Thus, the 95% confidence interval for the population mean rating for Miami International Airport is approximately

(5.80, 7.72)

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Using DeMorgan's Law, an expression for the complement of F if F(x,y,z) = (x′ + y)(x + z)(y′ + z)′ is F'(x,y,z) = x'y'z' + xy'z' + x'y'z + xyz' + xyz.

To find the complement of F, we first need to apply DeMorgan's Law, which states that the complement of a product is the sum of the complements of the terms. So, we can rewrite F(x,y,z) as:
F(x,y,z) = (x' + y)(x + z)(y' + z)'
Using DeMorgan's Law, we can take the complement of each term inside the parentheses, and then switch the operation from multiplication to addition:
F'(x,y,z) = (x' * y')(x' * z') + (x * y')(x' * z') + (x' * y)(y' * z') + (x * y)(y' * z') + (x * z)(y' * z')
Simplifying this expression, we get:
F'(x,y,z) = x'y'z' + xy'z' + x'y'z + xyz' + xyz
Therefore, the complement of F(x,y,z) is F'(x,y,z) = x'y'z' + xy'z' + x'y'z + xyz' + xyz.

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Answer:

x=92°

Step-by-step explanation:

x+21+66+59+x+30=360

2x+176=360

2x=184

x=92°

In order to determine the sample size needed to achieve a desired margin of error for the population proportion, you will need to use a formula that takes into account the confidence level, the margin of error, and an estimate of the population proportion (p*).

However, since you do not have a reliable estimate of p*, you can use a conservative estimate of 0.5 to calculate the sample size. This will ensure that you have a large enough sample size to capture any changes in the population proportion, while still maintaining a reasonable level of precision in your estimate. Once you have collected your data, you can use the sample proportion as an estimate of the population proportion in any subsequent analyses.

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The test strategy involves collecting data on the number of complaints (response variable) that employees submit for each OS. The CTO aims to gather 19 observations for each operating system, which will help her analyze the data and make a decision based on the performance and satisfaction of the employees.

The CTO of the company is planning to use a comparative test strategy to decide which operating system (OS) to use as the standard for the company. The OS types being compared are Apple, Linux, and Windows. To gather data, the CTO plans to look at the number of complaints submitted by employees for each OS, which will be the response variable. The CTO has set a goal of having 19 observations for each OS.

The experimental data will have a general structure where the number of complaints will be recorded for each OS. This data will be analyzed to determine which OS has the least amount of complaints and is therefore the most suitable for use as the standard in the company. It is important for the CTO to ensure that the testing process is fair and unbiased so that accurate conclusions can be drawn from the data.

To help the CTO make an informed decision on which operating system (OS) to use as standard in the company, she plans to compare Apple, Linux, and Windows OS types. The test strategy involves collecting data on the number of complaints (response variable) that employees submit for each OS. The CTO aims to gather 19 observations for each operating system, which will help her analyze the data and make a decision based on the performance and satisfaction of the employees.

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From the given distances and time it is clear that Mrs.Peter arrive before Mr Peter by 5 minute.

Mrs. Peter arrives 5 minutes before Mr. Peter

To find who arrives first we first need to find the speed and time they require to arrive.

Given : From Boston to Worcester

Mr. Peter takes 30 minutes time and speed=60 miles per hour

Mrs. Peter travels with speed 90 miles per hour

We will now calculate Mr.Peters speed

60 miles/h × h/60 = miles/min

We know that, Distance = Speed /Time

Mr.Peters speed is 60 miles per hour

Distance=Miles÷Min /30 minutes

Distance = 30 miles

Similarly, we will now calculate Mrs.Peters speed

90 miles/h h/60 = 1.5 miles per min

Here, Time = 30 / 1.5

= 20 minutes

Here, we know that Mrs.Peter leaves from Boston to Worcester 5 minutes after Mr.Peter so we will add 5 minutes to Mrs. Peters time.

Time = 20+5 =15 minutes

Therefore,

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The water level will rise by V2/ (length x width) = (cm^3)/ (cm x cm) = cm.

Let's call the dimensions of the base of the aquarium "length," "width," and "height," and represent them by the variables L, W, and H, respectively. Similarly, let's call the dimensions of the base of the brick "length," "width," and "height," and represent them by the variables l, w, and h, respectively. Finally, let's call the height by which the water level rises "x."

Since the aquarium is rectangular, its volume can be calculated as V_aquarium = L * W * H. Similarly, the volume of the brick can be calculated as V_brick = l * w * h.

When the brick is placed in the aquarium, it displaces an amount of water equal to its own volume, so the water level rises by an amount equal to the volume of the brick divided by the area of the base of the aquarium:

x = V_brick / (L * W)

Substituting the given values, we get:

x = (cm * cm * cm) / (cm * cm) = cm

Therefore, the water level in the aquarium rises by cm when the brick is placed in it.

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178 square meters is the area of the complex figure.

To find the area of this composite figure, we need to find the areas of the individual shapes and add them up.

The area of the first rectangle is:

16 m x 8 m = 128 m²

The area of the triangle is:

1/2 x base x height = 1/2 x 5 m x 8 m = 20 m²

The area of the second rectangle is:

6 m x 5 m = 30 m²

To find the total area, we add the areas of the three shapes:

128 m² + 20 m² + 30 m² = 178 m²

Therefore, the area of this complex figure is 178 square meters.

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The 99% confidence interval estimating the proportion of all Ford Fusion drivers who are women is (0.40685, 0.67007). The closest option to this interval is option 2) (0.40385, 0.67307).

The answer is option 1) (0.41689, 0.66003). To design a new advertising campaign, Ford Motor Company conducted a sample survey of 91 Fusion owners and found that 49 of them were women. To estimate the proportion of all drivers who are women, a confidence interval is calculated. The formula for calculating the confidence interval is:

sample proportion ± z*(standard error)

where z is the critical value for the desired confidence level and the standard error is calculated as:

sqrt((sample proportion*(1 - sample proportion))/sample size)

For a 99% confidence interval, the critical value is 2.576. Plugging in the values from the sample, we get:

sample proportion = 49/91 = 0.5385
sample size = 91

Using the formula above, we can calculate the standard error as:

sqrt((0.5385*(1 - 0.5385))/91) = 0.0625

Finally, we can plug in the values into the confidence interval formula:

0.5385 ± 2.576*0.0625

which gives us the interval (0.41689, 0.66003). Therefore, option 1) is the correct answer.

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The measure of the vertical angle 3 is equal to be 98°

When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, alternate angles, complementary and supplementary angles.

The angle (5x + 198)° and (3x + 158) are alternate arrangements, hence they are equal so;

5x + 198° = 3x + 158 {alternate angles}

5x - 3x = 158 - 198

2x = -40

x = -20

5x + 198° = 5(-20) + 198°

5x + 198° = -100 + 198°

5x + 198 = 98°

The angle (5x + 198)° and angle 3 are vertical angles and are equal so;

angle 3 = 98°.

Therefore, the measure of the vertical angle 3 is equal to be 98°.

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The volume of the solid generated [tex]\pi \int\limits^4_0 {(6 - x^2 + 3x)^2 - (6 - x)^2} \, dx[/tex] dx.

The correct option is B.

We have y = x² - 3x and y = x about the horizontal line y = 6.

Now, the integral expression for the volume of the solid formed by revolving is

[tex]\pi \int\limits^4_0 {(6 - x^2 + 3x)^2 - (6 - x)^2} \, dx[/tex]

Each term in above expression represent:

By evaluating this integral,  find the volume of the solid formed by revolving the given region about the horizontal line y = 6.

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The question attached here seems to be incomplete the complete question here:

What is the integral expression for the volume of the solid formed by revolving the region bounded by the graphs of y = x ^ 2 - 3x and y = x about the horizontal line y = 6'

[tex]\pi \int\limits^3_0 {(6 - x^2 + 3x)^2 - (6 - x)^2} \, dx[/tex]

[tex]\pi \int\limits^4_0 {(6 - x^2 + 3x)^2 - (6 - x)^2} \, dx[/tex]

[tex]\pi \int\limits^3_0 { (6 - x)^2 - (6 - x^2 + 3x)^2} \, dx[/tex]

[tex]\pi \int\limits^4_0 { (6 - x)^2 - (6 - x^2 + 3x)^2} \, dx[/tex]

The probabilities of the independent events are as given as follows:

Since all the events are independent events, the probabilities are calculated as follows:

P (B) = 3/10, P (A and B) = 27/200; find P (A)

P (A) =  P (A and B) / P (B)

P (A) = (27/200) / (3/10)

P (A) = 9/20

2. P (A)= 2/5, P (A and B)= 3/10, find P (B)

P (B) = (3/10) / (2/5)

P (B) = 3/4

3. P (B) = 0.25, P (A and B) = 0.1, find P (A)

P (A) = 0.1/0.25

P (A) = 0.4

4. P (A) = 0.3, P (A and B) = 0.075, find P (B)

P (B) = 0.075/0.3

P (B) = 0.25

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Answer:

The Correct answer is C

10<_y>_14

Answer:  A

Step-by-step explanation:

The question is asking for the range, which means for the whole function where do you have y values.

you have y values from 0 to 14

I sometimes use a horizontal line.   If the function is touching the horizontal line than that is where you have a y value.

A total of 5 cars would be needed for both families to ride the bumper cars.

To find the number of cars needed for the two families, we can use the following set of equations:

Let x be the number of cars needed for the family of 6.
Let y be the number of cars needed for the family of 4.

We know that each car holds 2 people, so:

2x = 6  (each car holds 2 people in the family of 6)
2y = 4  (each car holds 2 people in the family of 4)

Solving for x and y, we get:

x = 3  (the family of 6 needs 3 cars)
y = 2  (the family of 4 needs 2 cars)

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We have L < 0 and L > 0, which is a contradiction. Therefore, (zn) does not converge

To prove that xn ≤ zn ≤ yn for all n ∈ N, we just need to compare the values of xn, yn, and zn for any given n. We have xn = -1, yn = 1, and zn = (-1)^n+1, so we need to show that -1 ≤ (-1)^n+1 ≤ 1.

For n even, we have (-1)^n+1 = -1, so -1 ≤ (-1)^n+1 ≤ 1 holds.

For n odd, we have (-1)^n+1 = 1, so -1 ≤ (-1)^n+1 ≤ 1 holds.

Therefore, we have xn ≤ zn ≤ yn for all n ∈ N.

Next, we will prove that (xn) converges to -1 and (yn) converges to 1.

Since xn = -1 for all n ∈ N, (xn) is a constant sequence and converges to -1. Similarly, since yn = 1 for all n ∈ N, (yn) is also a constant sequence and converges to 1.

Finally, we will prove that (zn) does not converge.

Suppose (zn) converges to some limit L. Then, for any ε > 0, there exists N ∈ N such that |zn - L| < ε for all n > N.

Let ε = 1. Then, there exists N such that |zn - L| < 1 for all n > N.

Consider the cases when n is even and odd separately.

When n is even, we have zn = -1. So, we have |-1 - L| < 1, which implies L - 1 < -1 and L < 0.

When n is odd, we have zn = 1. So, we have |1 - L| < 1, which implies L - 1 < 1 and L > 0.

Thus, we have L < 0 and L > 0, which is a contradiction. Therefore, (zn) does not converge.

Complete question:  If [tex]$x_n=-1, y_n=1$[/tex], and [tex]$z_n=(-1)^{n+1}$[/tex], then [tex]$x_n \leq z_n \leq y_n$[/tex] for all [tex]$n \in \mathbb{N}$[/tex], the sequence [tex]$\left(x_n\right)$[/tex] converges to -1 and [tex]$\left(y_n\right)$[/tex] converges 1 , but [tex]$\left(z_n\right)$[/tex]does not converge.

As once consequence, we show that we can take absolute values inside limits.

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The Laplace transform of f(t) cosh kt cos kt is:

L[f(t) cosh kt cos kt] = F(s) [4k^4 + 4ks(s^2 + k^2) + s^4]/s^2(s^2 + k^2)^2

The Translation (Shifting) Theorem states that if F(s) is the Laplace transform of f(t), then the Laplace transform of e^(at)f(t) is F(s - a).

Using this theorem, we can find the Laplace transform of f(t) cosh ktcoskt as follows:

Let g(t) = cosh kt cos kt. Then, using the identity cosh x = (e^x + e^-x)/2 and the linearity of the Laplace transform, we have:

L[f(t) cosh kt cos kt] = L[f(t) g(t)]

= L[e^(0t)f(t)g(t)]

= L[e^(kt) (e^-kt f(t)) g(t)]

= L[e^(kt) F(s - (-k)) g(t)]

where we used the Translation (Shifting) Theorem with a = -k and F(s) = L[f(t)].

Now, using the fact that g(t) = cosh kt cos kt = (e^kt + e^-kt)/2 * cos kt, we can write:

L[f(t) cosh kt cos kt] = L[e^(kt) F(s + k) (e^kt + e^-kt)/2 * cos kt]

= 1/2 L[e^(2kt) F(s + k) cos kt] + 1/2 L[F(s + k) cos kt]

Using the Laplace transform of cos kt (which can be found in a Laplace transform table or by integrating by parts), we get:

L[f(t) cosh kt cos kt] = 1/2 [(s + k)/(s^2 + k^2)^2 - 2k/(s^2 + k^2)] F(s + k) + 1/2 (s/(s^2 + k^2)^2 - 1/(s^2 + k^2)) F(s)

Simplifying this expression, we get:

L[f(t) cosh kt cos kt] = [s^2 - k^2 + 2ks + 4k^2/s^2(s^2 + k^2)^2] F(s)

which is algebraically equivalent to F(s) [4k^4 + 4ks(s^2 + k^2) + s^4]/s^2(s^2 + k^2)^2.

Therefore, the Laplace transform of f(t) cosh kt cos kt is:

L[f(t) cosh kt cos kt] = F(s) [4k^4 + 4ks(s^2 + k^2) + s^4]/s^2(s^2 + k^2)^2

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The margin of error for the 99% confidence interval for the population mean of grass seed germination periods is approximately 3.374 days.

To find the margin of error for the confidence interval for the population mean with a 99% confidence level for germination periods of grass seed, follow these steps:

1. Identify the given information:
- Sample size (n) = 21
- Sample mean (x) = 34 days
- Population standard deviation (σ) = 6 days
- Confidence level = 99%

2. Determine the appropriate z-score for the 99% confidence level:
- Since the confidence level is 99%, we need to look for the z-value that corresponds to 0.005 in the z-table (because 1 - 0.99 = 0.01, and 0.01/2 = 0.005).
- z0.005 = 2.576

3. Calculate the standard error of the mean (SEM):
- SEM = σ/√n = 6/√21 = 1.31

4. Calculate the margin of error (ME):
- ME = z * SEM = 2.576 * 1.31 = 3.374

5. Round the answer to three decimal places:
- ME = 3.374

Your answer: The margin of error for the 99% confidence interval for the population mean of grass seed germination periods is approximately 3.374 days.

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The mean pollution intake among all school buses used in the Southern California Air Basin that travel the route investigated in the study, with the outliers removed, is 0.365 grams per person per million grams emitted. The 90% confidence interval is(0.308, 0.389).grams per person per million grams emitted.

To find the 90% confidence interval with outliers removed (1.15 and 1.35) for the mean pollution intake among all school buses used in the Southern California Air Basin traveling the specific route, follow these steps:

1. Remove the outliers: 0.33, 0.40, 0.33, 0.38, 0.25, 0.40, 0.35
2. Calculate the mean (average) of the remaining values: (0.33+0.40+0.33+0.38+0.25+0.40+0.35)/7 = 2.44/7 = 0.3486
3. Calculate the standard deviation (SD) of the remaining values. The SD is approximately 0.056.
4. Determine the t-value for the 90% confidence interval for 6 degrees of freedom (n-1, where n is the number of samples): t = 1.943
5. Calculate the margin of error (ME) using the t-value, SD, and the number of samples: ME = t*(SD/sqrt(n)) = 1.943*(0.056/sqrt(7)) = 0.0407
6. Calculate the confidence interval bounds by adding and subtracting the ME from the mean:
  Lower bound: 0.3486 - 0.0407 = 0.3079
  Upper bound: 0.3486 + 0.0407 = 0.3893

The 90% confidence interval with outliers removed for the mean pollution intake among all school buses used in the Southern California Air Basin traveling the route investigated in the study is (0.308, 0.389).

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TRUE. The design matrix for linear regression is a matrix that contains the predictor variables for each observation. In this case, the predictor variables are Li, Yi, zi, and zxy, and there are n observations. Therefore, the design matrix would be a n x 4 matrix.

True. If you want to fit data (Li, Yi, Zi) ∈ R³ to a model z = B₀ + B₁x + B₂y + B₃xy, and you have n data points, then the design matrix for linear regression will be an n x 4 matrix.

Here's why:
- Each row of the matrix represents one data point.
- Each column of the matrix corresponds to the coefficients B₀, B₁, B₂, and B₃ in the model.

For n data points, the design matrix will look like this:

| 1  x₁  y₁  x₁y₁ |
| 1  x₂  y₂  x₂y₂ |
| 1  x₃  y₃  x₃y₃ |
| ...             |
| 1  xₙ  yₙ  xₙyₙ |

Thus, it is an n x 4 matrix.

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Answer:

123.5

Step-by-step explanation:

Number of acres in the forest = 93 hectares * 2.47 acres/hectare = 229.71 acres

Number of trees in the forest = 229.71 acres * 50 trees/acre = 11485.5 trees

Next, we can find the density of this species in trees per hectare:

Density of trees per hectare = Number of trees in the forest / Area of the forest in hectares

Density of trees per hectare = 11485.5 trees / 93 hectares

Density of trees per hectare ≈ 123.5 trees/hectare

Therefore, the approximate density of this species in trees per hectare is 123.5 trees/hectare.

The approximate density of this species in trees per hectare is 123.5 trees/hectare.

Density refers to the measurement of the amount of mass of a substance per unit of volume. This measurement of a pure substance has the same value as its mass concentration.

Given that, the tree density for this species in this forest is about 50 trees per acre and forest is 93 hectares in area,

Number of acres in the forest = 93 hectares × 2.47 acres/hectare

= 229.71 acres.

Number of trees in the forest = 229.71 acres × 50 trees/acre

= 11485.5 trees.

Density of this species in trees per hectare:

Density of trees per hectare = Number of trees in the forest / Area of the forest in hectares.

Density of trees per hectare = 11485.5 trees / 93 hectares

≈ 123.5 trees/hectare

Hence, the approximate density of this species in trees per hectare is 123.5 trees/hectare.

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Answer:

the last 5 means 500

Step-by-step explanation:

the seconed 5 means 50

Therefore, the 90% lognormal prediction interval for the price of the stock after 6 months is (71.25, 87.95). The closest answer option is D) (61.91, 110.74), but it is not an exact match.

To determine the 90% lognormal prediction interval for the price of the stock after 6 months, we can use the following formula:
ln(S) = ln(S₀) + (r - σ²/2)t + σ√tZ
Where:
- ln(S) is the natural logarithm of the stock price after 6 months
- ln(S₀) is the natural logarithm of the initial stock price ($80)
- r is the expected continuously compounded rate of return (10%)
- σ is the volatility (25%)
- t is the time in years (0.5)
- Z is the standard normal distribution value for the desired confidence level (90% corresponds to Z = 1.645)
Substituting the values, we get:
ln(S) = ln(80) + (0.1 - 0.25²/2) x 0.5 + 0.25√0.5 x 1.645
ln(S) = 4.382 + 0.089
ln(S) = 4.471
To convert back to the stock price, we take the exponential of both sides:
S = e⁴.⁴⁷¹
S ≈ 87.95
The lower bound of the prediction interval is obtained by using Z = -1.645:
ln(S) = ln(80) + (0.1 - 0.25²/2) x 0.5 - 0.25√0.5 x 1.645
ln(S) = 4.382 - 0.108
ln(S) = 4.274
S = e⁴.²⁷⁴
S ≈ 71.25

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Answer: she would have ran 4,000 yards

Step-by-step explanation: 1 foot is equal to 3 yards so you multiply that and you will get your answer.

The given example involves data extraction, manipulation, and loading, which falls under the category of ETL (Extract, Transform, Load) in the spectrum of solutions for large analytical data repositories.

ETL is a process used to integrate data from various sources and make it available for querying and analysis. In this example, data is extracted from 10 different sources, transformed by removing duplicates and combining two sources, and then loaded into the target repository. Therefore, the given example is an example of ETL in the spectrum of solutions for large analytical data repositories.

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The data values differ from the mean by an average of 4

From the question, we have the following parameters that can be used in our computation:

8,12,4,3,14,1,9,13

The mean of the above data is

x = (8 + 12 + 4 + 3 + 14 + 1 + 9 + 13)/8

Evaluate

x = 8

The mean absolute deviation is calculated as

M = 1/n * sum of |data points - mean|

So, we have

M = (|8 - 8| + |12 - 8| + |4 - 8| + |3 - 8| + |14 - 8| + |1 - 8| + |9 - 8| + |13 - 8|)/8

Evaluate the absolute differences

M = (0 + 4 + 4 + 5 + 6 + 7 + 1  + 5)/8

So, we have

M = 4

Hence, the mean absolute deviation is 4

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