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How much a statistic varies from one sample to another is known as the sampling variability of a statistic.

Testing variability arises due to the reality that exceptional samples of the same size can produce special values of a statistic, although the samples are described from the same populace. the quantum of slice variability depends on the scale of the sample, the variety of the populace, and the unique statistic being calculated.

The end of statistical conclusion is to apply the data attained from a sample to make consequences about the population, while counting for the slice variability of the statistic. ways similar as thesis checking out and tone belief intervals do not forget the sampling variability of a statistic to make redundant accurate consequences about the populace.

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Answer:

A. 2:1

Step-by-step explanation:

pretty sure larger numbers go first

Answer:

D)  1:2

Step-by-step explanation:

The coordinates of the point that divides the line segment from (6, 2) to (8, -10) into a ratio of 1 to 3 are (7, -1).

To find the coordinates of the point on the directed line segment that partitions it into a ratio of 1 to 3, we can use the concept of section formula.

The section formula states that if we have two points A(x₁, y₁) and B(x₂, y₂) dividing a line segment in the ratio of m₁ : m₂, then the coordinates of the dividing point P are given by:

Px = (m₁ * x₂ + m₂ * x₁) / (m₁ + m₂)

Py = (m₁ * y₂ + m₂ * y₁) / (m₁ + m₂)

In this case, the ratio is 1:3, which means m₁ = 1 and m₂ = 3. The given points are A(6, 2) and B(8, -10). Substituting these values into the formula, we can calculate the coordinates of the dividing point P:

Px = (1 * 8 + 3 * 6) / (1 + 3) = 7

Py = (1 * -10 + 3 * 2) / (1 + 3) = -2/2 = -1

Therefore, the coordinates of the point that divides the line segment from (6, 2) to (8, -10) into a ratio of 1 to 3 are (7, -1).

To find the coordinates of the point that divides the line segment between (6, 2) and (8, -10) in a 1:3 ratio, we can use the section formula. Applying the formula, where m₁ is 1 and m₂ is 3, the point P(x, y) can be determined.

By substituting the values into the formula, the x-coordinate is calculated as (1 * 8 + 3 * 6) / (1 + 3) = 7, and the y-coordinate is (1 * -10 + 3 * 2) / (1 + 3) = -1. Thus, the coordinates of the point that partitions the line segment into a ratio of 1 to 3 are (7, -1).

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Answer:

91. The probability that Caroline will be ready before Andrew is 0.25 (Option B). Since the service times are exponentially distributed with a mean 15 minutes, the remaining service time for Andrew when Caroline arrives is also exponentially distributed with the mean 15 minutes. The service time for Caroline is also exponentially distributed with mean 15 minutes. The probability that Caroline’s service time is less than Andrew’s remaining service time is given by the formula P(X < Y) = 1 / (1 + λY / λX), where λX and λY are the rates of the exponential distributions for X and Y respectively. Since both service times have the same rate (λ = 1/15), the formula simplifies to P(X < Y) = 1 / (1 + 1) = 0.5. Therefore, the probability that Caroline will be ready before Andrew is 0.25.

92. The probability that Caroline will be ready before Bob is 0.35 (Option A). Since Bob arrived 10 minutes after Andrew, his remaining service time when Caroline arrives is exponentially distributed with mean 15 minutes. Using the same formula as above, we get P(X < Y) = 1 / (1 + λY / λX) = 1 / (1 + 1) = 0.5. Therefore, the probability that Caroline will be ready before Bob is 0.35.

Answer:

C) 240ma

Step-by-step explanation:

Therefore, the area of the trapezoid is 1338 3/4 square units.

A quadrilateral with at least one set of parallel sides is known in geometry as a trapezium, or trapezium in British and other versions of English. In Euclidean geometry, a trapezium is invariably a convex quadrilateral. The trapezoid's parallel sides are referred to as its bases.

To find the area of a trapezoid, we use the formula:

Area = (1/2) × (sum of parallel sides) × (height)

In this case, we have the following information:

The two parallel sides are 12 1/4 and 24 1/4.

The height is 73 1/2.

First, we need to add the two parallel sides to find the sum:

12 1/4 + 24 1/4 = 36 1/2

Next, we can plug these values into the formula:

Area = (1/2) × 36 1/2 × 73 1/2

Area = 1338.75

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Correct Question:

Given sides are 12(1/4), 24 (1/4), 73 (1/2) and 134(1/2), then What is the area of this trapezoid?

The mean of x₂ is α(α+1)β² and the variance-covariance matrix of the random vector x is:

[αβ²    0]
[  0     α(α+1)(α+2)β³]

The random vector x can be represented as x = (x₁, x₂), where x₁ and x₂ are independent random variables.

Given that y follows a gamma distribution with parameters α and β, we can express y as y = αz + β, where z follows a standard gamma distribution with shape parameter 1 and scale parameter 1.

To find the mean and variance-covariance matrix of the random vector \(x^T\) = \((x_1, x_2)^T\), where        x₁ = y and x₂ = y², we need to calculate the mean and variance of each component separately.

1. Mean:
The mean of x₁ (y) can be found using the mean of the gamma distribution. The mean of a gamma distribution with shape parameter α and scale parameter β is given by αβ. Therefore, the mean of x₁ is αβ.

The mean of x₂ (y²) can be calculated using the moment generating function (MGF) of the gamma distribution. The MGF of a gamma distribution with shape parameter α and scale parameter β is\(\left(1-\beta t\right)^{-\alpha}\). By differentiating the MGF twice and setting t = 0, we can find the second moment of the gamma distribution. The second moment is given by α(α+1)β². Therefore, the mean of x₂ is α(α+1)β².

2. Variance-Covariance Matrix:
The variance of x₁ (y) can be found using the variance of the gamma distribution. The variance of a gamma distribution with shape parameter α and scale parameter β is given by αβ². Therefore, the variance of x₁ is αβ².

The variance of  x₂ (y²) can also be calculated using the MGF of the gamma distribution. By differentiating the MGF thrice and setting t = 0, we can find the third moment of the gamma distribution. The third moment is given by α(α+1)(α+2)β³. Therefore, the variance of x₂ is α(α+1)(α+2)β³.

Since x₁ and x₂ are independent, the covariance between x₁ andx₂ is 0. Therefore, the variance-covariance matrix of the random vector x is:

   [αβ²    0]
   [  0     α(α+1)(α+2)β³]

In summary, the mean of x is (αβ, α(α+1)β²), and the variance-covariance matrix of x is given by the matrix above.

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Answer:

So basically if there's 6 numbers on each dice, that means that there's a 5/6 chance of not getting a 3. So multiply that and you get 5/6*5/6. That is equal to 25/36 change.

Answer:

x=.3 or 3/10

Step-by-step explanation:

to solve for x, we need to separate it

so, we add 13 to the left side

40-11x=x

then add 11x to the right side so we have different coefficients on each side to solve for x

40=12x

then we divide 40/12 to get what x equals

we get

x= 0.3 or 3/10

hope this helped!

Answer:

x=10/3

Step-by-step explanation:

27 - 11x = x - 13

27+13=x+11x

40=12x

x=40/12

x=10/3

The answers that  best explains how we check to make sure that this condition is met is: c. Make sure there is similar spread around the sample mean of y.

The equal spread condition states that the residuals (differences between the actual and predicted values of y) should have roughly equal variance at each value of x.

To check if this condition is met, we examine the residual plot, which is a scatterplot of the residuals versus the independent variable x. If the spread of residuals around the mean is roughly equal for all x, then the equal spread condition is satisfied.

Therefore the correct option is C.

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Answer:

x = 13

Step-by-step explanation:

10x - 6 = - 136

10x = - 136 + 6

10x = 130

x = 130/10

x = 13

Answer:

x = (-13)

Step-by-step explanation:

\(10x - 6 = - 136 \\ 10x = - 136 + 6 \\ 10x = - 130 \\ x = \frac{ - 130}{10} \\ x = ( - 13) \\ \)

The sum of the given series ∑ \((cos(n) / 2^n)\)  from n=1 to infinity converges absolutely.

To determine whether the series converges absolutely, conditionally, or not at all, we will analyze the given series:
∑ \((cos(n) / 2^n)\) from n=1 to infinity.

Step 1: Test for absolute convergence: We can test for absolute convergence by applying the Ratio Test to the absolute value of the terms in the series. We first consider the series: ∑ \(|cos(n) / 2^n|\) from n=1 to infinity.

Step 2: Apply the Ratio Test: For the Ratio Test, we compute the limit as n approaches infinity of the ratio of consecutive absolute terms: lim (n→∞) \((|cos(n+1) / 2^(n+1)|) / (|cos(n) / 2^n|)\)
= lim (n→∞) \((|cos(n+1)| / |cos(n)|) * (2^n / 2^(n+1))\) = lim (n→∞) \((|cos(n+1)| / |cos(n)|) * (1/2)\)

Since the cosine function has values between -1 and 1, the limit of the ratio of consecutive cosine terms exists but does not have a specific value. However, since we're multiplying the limit by 1/2, which is less than 1, the Ratio Test concludes that the series converges absolutely.

So, the given series ∑ \((cos(n) / 2^n)\) from n=1 to infinity converges absolutely.

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Hello there!

x+5x-6<12

Combine like terms:

6x-6<12

Move all the numbers (constants) to the right side:

6x<12+6

6x<18

Divide both sides by 6 in order to isolate x:

x<3

Hope this helps you!

~Just a joyful teen

\(SilentNature\)

The area of the polygon is 37.81 units and the perimeter is 33.02 units.

The given points are in order, we have:

a(-3, 2)

f(2, -3)

b(0, 5)

c(3, 2)

d(5, 4)

e(7, 2)

g(0, -1)

Using the distance formula, we can find the lengths of the sides of the polygon. Then, we can add up the lengths of all the sides to find the perimeter of the polygon.

As per the shown figure,

Length of side fa = 7.07 units

Length of side ef = 7.07 units

Length of side de = 7.6 units

Length of side cd = 2.8 units

Length of side bc = 4.24 units

Length of side ab = 4.24 units

The perimeter of the polygon is:

= fa + ef + de + cd + bc + ab

= 7.07 + 7.07 + 7.6 + 2.8 + 4.24 + 4.24

= 33.02 units

The area of the polygon is:

= area of rectangle (1) + area of sqare (2)

= 7.07 × 4.24 + 2.8 × 2.8

= 37.81 units

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Answer:

Step-by-step explanation:

True

Step-by-step explanation:

explanation is written inside the attachment

Answer:

\(d=4\)

Step-by-step explanation:

Distance Formula: \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Simply plug in the 2 coordinates into the distance formula to find distance d:

\(d=\sqrt{(-5-(-5))^2+(6-2)^2}\)

\(d=\sqrt{(-5+5)^2+(4)^2}\)

\(d=\sqrt{(0)^2+16}\)

\(d=\sqrt{0+16}\)

\(d=\sqrt{16}\)

\(d=4\)

The answers are:

Q1 = x < -1

Q2 = x ≤ 2

Q3 = x > -2

Q4 = x > 0

Code = 4776

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Solve for x.

3 < -5x + 2x

3 < -3x

Divide both sides by 3.

1 < -x

Change sign.

x < -1

18 ≥ 5x  + 4x

18 ≥ 9x

Divide both sides by 9.

2 ≥ x

-6x - 16 < 2x

Add 16 on both sides.

-6x < 2x + 16
Subtract 2x on both sides.

-6x - 2x < 16

-8x < 16

Divide both sides by 8.

-x < 2

Change sign.

x > -2

(1/2)x - 4 > -4

1/2x > -4 + 4

1/2x > 0

x > 0

Code = 4776

Thus,

The answers are:

Q1 = x < -1

Q2 = x ≤ 2

Q3 = x > -2

Q4 = x > 0

Code = 4776

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Answer:

x=-9

Step-by-step explanation:

3 x=-27

x = -9

Answer:

-9

Step-by-step explanation:

x3 = -27 OR 3x = -27

3x/3 = -27/3

x = - 9

Answer:

D

Step-by-step explanation:

in order to get the process of solving the equation, we need to solve it.

our goal to solve the equation 6x-19=77 is to isolate the variable onto one side, and have the numbers (value of x) on the other

we have the equation:

6x-19=77

first, we can get rid of -19 on the left side and leave 6x on that side by adding 19 to both sides (-19+19=0).

The reason why we're adding 19 to both sides is because if we do something to one side, we have to do it to the other side to make sure the value of the equation stays the same.

6x-19= 77

   +19  +19

_________

6x=96

now, we do have the variables on one side and the numbers on another side, but we aren't done yet, as we want the value of x by itself

divide by 6 on both sides

x=16 (because 6x/6=1x, or x. 96/6=16).

the option of D shows the same method I did and has the correct answer as well.

This is what was given for D:

6x-19=77

6x-19+19=77+19

6x=96

6x/6=96/6

x=16

(same thing I did)

So D is the correct answer.

Hope this helps!

The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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The value of the expression "true && !false" can be determined by evaluating each part separately and then combining the results.

1. The "!" symbol represents the logical NOT operator, which negates the value of the following expression. In this case, "false" is negated to "true".

2. The "&&" symbol represents the logical AND operator, which returns true only if both operands are true. Since the first operand is "true" and the second operand is "true" (as a result of the negation), the overall expression evaluates to "true".

Therefore, the value of the expression "true && !false" is "true".

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Answer:

It's a positive correlation.

Step-by-step explanation:

It's gradually going up, even if there's a few points that are a bit uncorrelated.

Answer:

The answer is 1.2 or 5

Step-by-step explanation:

Answer:

B,D,E

Step-by-step explanation: