Classify each error as a sampling error or a non-sampling error. Sampling error Non-sampling error A mistake is made while copying down the responses. A specific group was accidentally excluded from the sample. The person distributing the medicine subconsciously made a face when handing out the placebo pill. The way questions were worded influenced the responses. The proportion in the sample is not equal to the proportion in the population. Some people refused to answer certain questions, and these people are likely to have different opinions from those who did answer those questions.

The diameter of the circle is 26 in

To find the diameter of circle Q, we used the concept that the diameter of a circle is twice the radius.

We were given the area of the circle, and we used the formula for the area of a circle, A = πr², to find the value of the radius.

Once we found the value of the radius, find the diameter by finding twice the radius.

Here we have

Area of the Circle Q, A = 169π in²  

Let r be the radius of the circle

Using the formula,

Area of the circle A = πr²

=> πr² =  169π

=>  r² = 169

=>  r = 13

Hence radius of the circle = 13

So diameter of the circle, d = 2r = 2(13) = 26 in

Therefore,

The diameter of the circle is 26 in.

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The diameter of the circle is 8 cm, and its area is approximately 50.27 cm².

Tito draws a square with side lengths of 8 cm.

He inscribes a circle inside the square so that it touches all four sides.

Diameter and area of the circle:
The diameter of the circle is equal to the side length of the square, since the circle touches all four sides of the square.
Diameter = 8 cm
Calculate the radius of the circle by dividing the diameter by 2.
Radius = Diameter ÷ 2 = 8 cm ÷ 2 = 4 cm
Calculate the area of the circle using the formula:

Area = π × (Radius)².
Area = π × (4 cm)² = π × 16 cm² ≈ 50.27 cm².

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Question: The largest square that can be drawn in a circle has a side whose length is 0.707 times the diameter of the circle. By this rule, find the length of the side of such a square when the diameter of the circle is(a) 14.35 cm (b) 8.63 cm

The action you are referring to is known as "refutation" or "disproving."

This process involves presenting evidence or logical reasoning that contradicts a statement or theory, ultimately demonstrating its falsehood or inaccuracy.

The key terms to remember when discussing refutation include:
Statement or theory: The initial claim that is being challenged.
Evidence: The facts or data used to support or refute the statement or theory.

Logical reasoning: The use of well-structured arguments to systematically evaluate the statement or theory.

Contradiction: The act of presenting information that is in direct opposition to the statement or theory.

Falsehood or inaccuracy: The final conclusion drawn when a statement or theory is successfully refuted or disproven.
In summary, refutation is the process of using evidence and logical reasoning to contradict a statement or theory, ultimately proving it to be wrong or false.

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To find the number of students with red hair, we need to calculate 5% of 800, Therefore, there are approximately 40 middle-school students with red hair.

A circle graph, also called a pie chart, is a circular illustration of data that shows the percentage or proportion of each category in the data set through slices.

Each slice is proportional to the value or frequency that it represents in terms of size.

According to the circle graph, the red section represents 5% of the total. We must calculate 5% of 800 in order to determine the number of students with red hair.(the total number of students surveyed).

5% of 800 can be calculated as:

(5/100) x 800 = 40

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The Turing machine scans the input string from left to right, marking each symbol with a dot, until it reaches the end.

For the language that consists of all strings of a's and b's, we can construct a Turing machine as follows:

Start at the beginning of the input string.

If the input symbol is an a or a b, mark it with a dot and move right.

If the input symbol is already marked with a dot, move right without marking it.

If the input symbol is blank (the end of the input), move left to the previous symbol.

If the previous symbol is marked with a dot, move left until an unmarked symbol is found.

If the previous symbol is unmarked, mark it with a dot and move right.

If the previous symbol is blank, the machine accepts the input if all symbols are marked with a dot (which means the input had even length), and rejects the input otherwise.

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The domain of the function (fog)(x) is -∞<x<∞  or  (-∞,∞).

What is function?

In mathematics, function is an expression, rule, or law which defines a relationship between one variable which is the independent variable and another variable which is called the dependent variable.

Two functions are given by:

f(x)= x+7 and g(x)= -2x-15

(fog)(x)= f(g(x))

           = f(-2x-15)

            putting -2x-15 in the place of x in f(x) we get,

(fog)(x)= -2x-15+7

            = -2x - 8

so (fog)(x)= -2x-8

The domain of a function means the set of all possible values or inputs of the function.

Here x takes all the values from -∞ to +∞

Hence, the domain of the function (fog)(x)= -∞<x<∞

or it can be written as (-∞,∞).

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log_b(3 square root of ab) = (1/3)*log_b(3) + 3 = 1/3 + 3 = 10/3. Therefore, log_b(3 square root of ab) = 10/3.

We can use the properties of logarithms to simplify the expression log_b(3sqrt(ab)). Using the product rule, we have:

log_b(3sqrt(ab)) = log_b(3) + log_b(sqrt(ab))

Using the power rule, we can simplify the second term:

log_b(sqrt(ab)) = 1/2 log_b(ab)

Using the product rule again, we have:

1/2 log_b(ab) = 1/2 (log_b(a) + log_b(b))

We are given that log_b(a) = 5 and log_b(b) = -2, so we can substitute these values in to get:

1/2 (log_b(a) + log_b(b)) = 1/2 (5 - 2) = 3/2

Substituting this result into our original equation, we have:

log_b(3sqrt(ab)) = log_b(3) + log_b(sqrt(ab))

= log_b(3) + 1/2 log_b(ab)

= log_b(3) + 3/4

Therefore, log_b(3sqrt(ab)) = log_b(3) + 3/4.

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To find the interval of convergence of the power series ∑n=1∞ (2x+5)^n/n3^n, we will use the ratio test:
lim┬(n→∞)⁡|(2x+5)^(n+1)/(n+1)3^(n+1)|/|(2x+5)^n/n3^n)|
= lim┬(n→∞)⁡|(2x+5)/(n+1)(3/2)| = 0
Thus, the interval of convergence for the given power series is (-3, -2).

Since the limit is less than 1 for all values of x, the series converges for all x. Therefore, the interval of convergence is (-∞, ∞).
The interval of convergence for the given power series ∑(2x+5)^n/(n*3^n) can be found using the Ratio Test.

First, we'll find the limit as n approaches infinity:
L = lim (n → ∞) |((2x+5)^(n+1))/((n+1)*3^(n+1)) * (n*3^n)/((2x+5)^n)|

This simplifies to:
L = lim (n → ∞) |(2x+5)(n*3^n)/(n+1)*3^(n+1)|

Cancel the common terms:
L = lim (n → ∞) |(2x+5)n/(n+1)|

For the series to converge, we need L < 1:
|(2x+5)n/(n+1)| < 1

Since we're interested in the interval of convergence, we can ignore the n term:
|2x+5| < 1

Now solve for x:
-1 < 2x+5 < 1
-6 < 2x < -4
-3 < x < -2

Thus, the interval of convergence for the given power series is (-3, -2).

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The age of the bone is an illustration of exponential function

The bone is 1354.3 years old

What is the purpose of carbon 14?

In situations involving unidentified human remains, measuring the carbon-14 levels in human tissue may be able to aid forensic experts identify the age and year of death. Carbon-14 dating, usually referred to as radiocarbon dating, has been used by archaeologists for a long time to determine the age of various artefacts.

How to determine the age of the bone

From the complete question, the function is represented as:

[tex]y = ae^{0.00012t}[/tex]

The proportion of the bone is 85% or 0.85

So, we have:

  [tex]0.85a = ae^{-0.00012t}[/tex]

Divide through by a

   [tex]0.85 = e^{-0.00012t}[/tex]

Take the natural logarithm of both sides

  -0.16252 = -0.00012t

Divide through by -0.00012

      t = 1354.3

Hence, the bone is 1354.3 years old.

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The converse of Euclid's fifth postulate states that if two lines don't intersect and there exists a line that intersects both lines on the same side of a point, then the sum of the interior angles on that side of the lines must be less than 180 degrees, and this can be proven using neutral geometry.

The converse of Euclid's fifth postulate states that if two lines intersect at a point and the two interior angles on one side of the lines add up to less than 180 degrees, then there exists a line that intersects both of those lines on that side of the point.

In other words, if two lines don't intersect and there exists a line that intersects both lines on the same side of a point, then the sum of the interior angles on that side of the lines must be less than 180 degrees.

The proof of the converse of Euclid's fifth postulate can be done using neutral geometry, which is a type of geometry where the parallel postulate is replaced with another axiom. The proof involves constructing a line that intersects the two lines on the same side of the point and then showing that the sum of the interior angles on that side of the lines is less than 180 degrees.

This can be done using the other axioms of neutral geometry, such as the angle sum of a triangle, the exterior angle theorem, and the parallel postulate alternative.

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The given question is incomplete, the complete question is:

Euclid's fifth postulate: If two lines are intersected by a transversal in s ich a way that the sum of the degree measures of the two interior ances on one side of the transversal is less than 180°, then the two lines meet on that side of the transversal. State the converse to Euclid V (Euclid's fifth postulate). Prove this converse as a proposition in neutral geometry

The effect of increasing the random sample size of Canadian voters in the Gallup poll from 1,500 to 4,000 people is to reduce the margin of error and increase the accuracy of the poll results.

By increasing the sample size, the Gallup poll is able to gather more data points from a diverse group of voters, which improves the representativeness of the sample.

This helps to minimize biases and better capture the opinions of the population as a whole. In turn, the increased sample size leads to a lower margin of error, meaning that the poll results are more likely to accurately represent the true opinions of Canadian voters.

This is particularly important right before an election, as accurate poll results can inform strategies for political parties and provide insights for voters. Ultimately, increasing the sample size of the random sample in the Gallup poll enhances its reliability and validity, making it a more valuable tool in understanding voter sentiment.

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a. The mean distance between schools is 8 miles.

b. The new mean distance between schools is 7 miles.

Explain mean

The mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by adding up all the values in the set and dividing by the total number of values. The mean is commonly used to describe the typical value in a data set and is an important concept in data analysis and probability theory.

According to the given information

a. To find the mean, we add up all the distances and divide by the number of schools:

Mean = (8 + 9 + 5 + 11 + 7 + 8) / 6 = 8

Therefore, the mean distance between schools is 8 miles.

b.To find the new mean, we add up all the distances (including the new one) and divide by the new total number of schools:

New mean = (8 + 9 + 5 + 11 + 7 + 8 + 1) / 7 = 7

Therefore, the new mean distance between schools is 7 miles.

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Row operations involve manipulating the rows of a matrix in a specific way to simplify the system of equations. The three main row operations are:

1. Swapping two rows
2. Multiplying a row by a nonzero constant
3. Adding a multiple of one row to another row

By performing these operations on the augmented matrix (the matrix formed by adding the constants to the coefficient matrix), we can transform it into an equivalent matrix that is easier to solve.

The final matrix should be in reduced row echelon form, which means that each leading coefficient (the first nonzero number in each row) is a 1, and all other entries in the same column are 0. This makes it easy to read off the solution to the system of equations.

If there are any free variables (variables that do not have a leading coefficient in their corresponding row), we can introduce arbitrary parameters to represent them. These parameters can take on any value, and we can use them to express the solution to the system of equations in terms of a formula.

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a) We should invest $4,636.36 in the Moderate Allocations fund, $3,636.36 in the Equity 500 Index fund, and $1,727.27 in the Barclays U.S. Aggregate Bond Index fund to achieve an average return of 9%.

b) We should invest $5,176.47 in the Moderate Allocations fund, $3,529.41 in the Equity 500 Index fund, and $1,294.12 in the Barclays U.S. Aggregate Bond Index fund to achieve an average return

a. To find how much should be invested in each fund if you want an average return of 9%, we will set up the following system of equations:

0.0885x + 0.16y + 0.0421z = 0.09(10000)

x - y = 200

x + y + z = 10000

To solve this system of equations using matrices, we will first create a matrix of the coefficients:

| 0.0885 | 0.16 | 0.0421 |

| 1 | -1 | 0 |

| 1 | 1 | 1 |

We will then create a matrix of the constants:

| 900 |

| 200 |

| 10000 |

To solve for x, y, and z, we will use the formula:

| x |

| y |

| z | = Coefficients⁻¹ x Constants

where Coefficients⁻¹ is the inverse of the coefficients matrix. In Excel, we can find the inverse of a matrix by using the MINVERSE function.

Using this formula, we get:

| x |

| y |

| z | = MINVERSE(Coefficients) * Constants

Plugging in the values, we get:

| x |

| y |

| z | = MINVERSE({0.0885,0.16,0.0421;1,-1,0;1,1,1}) * {900;200;10000}

This gives us the solution:

| x |

| y |

| z | = {4,636.36; 3,636.36; 1,727.27}

b. To find how much should be invested in each fund if you want an average return of 10%, we will set up the following system of equations:

0.0885x + 0.16y + 0.0421z = 0.1(10000)

x - y = 200

x + y + z = 10000

We can solve this system of equations using the same method as in part (a), and we get the solution:

| x |

| y |

| z | = {5,176.47; 3,529.41; 1,294.12}

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For y-fx)=xex-5, when x= 5 and dx=0.1 : dy Hence the linear approximation using dy is f(5.1)-f(5)+dy)= 0%:  the linear approximation using dy is f(5.1)-f(5)+dy)= 0% (rounded to the nearest percent).

The problem is asking for the linear approximation of the function f(x) = xex-5 at x=5 using dy, when dx=0.1.

To begin, we need to find dy. We can do this by taking the derivative of f(x) with respect to x and then plugging in x=5 and dx=0.1:

f'(x) = ex + xex-5
f'(5) = e^5 + 5e^0 = e^5 + 5

dy = f'(5) dx = (e^5 + 5)(0.1) = e^5/10 + 0.5

Now we can use the linear approximation formula:

f(x+dx) ≈ f(x) + f'(x) dx

Plugging in x=5, dx=0.1, and dy=e^5/10 + 0.5:

f(5.1) ≈ f(5) + f'(5) (0.1) + dy
f(5.1) ≈ (5e^0) + ((e^5 + 5)(0.1)) + (e^5/10 + 0.5)
f(5.1) ≈ 5.7e^0 + 1.05e^5 + 1

Finally, we can check the accuracy of this linear approximation by calculating the percentage error:

(f(5.1) - f(5) - dy) / f(5.1) x 100%

= [(5.7e^0 + 1.05e^5 + 1) - (5e^0 + e^5 - 5) - (e^5/10 + 0.5)] / (5.7e^0 + 1.05e^5 + 1) x 100%

= -0.0005%

Therefore, the linear approximation using dy is f(5.1)-f(5)+dy)= 0% (rounded to the nearest percent).

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(a) The general solution of the differential equation y'' + 7y' + 12y = sin(2x) using the method of undetermined coefficients is y = A sin(2x) + B cos(2x) - (1/10) sin(x) - (3/10) cos(x).

(b) The general solution of the differential equation y'' + 4y' + 4y = e^(-2x) using the method of undetermined coefficients is y = (A + Bx) e^(-2x).

(c) The general solution of the differential equation y'' - y' - 2y = xe^(-x) using the method of undetermined coefficients is y = (Ax + B) e^(-x) + (C/2) x e^(-x).

(a) To find the general solution, we first find the complementary solution by solving the characteristic equation r^2 + 7r + 12 = 0, which gives us r = -3 or -4. Therefore, the complementary solution is y_c = c_1 e^(-3x) + c_2 e^(-4x).

Next, we need to find the particular solution. Since sin(2x) is not a solution of the homogeneous equation, we assume the particular solution to be of the form y_p = A sin(2x) + B cos(2x). Taking the first and second derivatives of y_p, we get y_p' = 2A cos(2x) - 2B sin(2x) and y_p'' = -4A sin(2x) - 4B cos(2x).

Substituting these values in the original differential equation, we get -4A sin(2x) - 4B cos(2x) + 14A cos(2x) - 14B sin(2x) + 12A sin(2x) + 12B cos(2x) = sin(2x).

Equating the coefficients of sin(2x) and cos(2x), we get A = -1/10 and B = -3/10.

Therefore, the general solution is y = y_c + y_p = c_1 e^(-3x) + c_2 e^(-4x) - (1/10) sin(2x) - (3/10) cos(2x).

(b) Again, we first find the complementary solution by solving the characteristic equation r^2 + 4r + 4 = 0, which gives us r = -2. Therefore, the complementary solution is y_c = c_1 e^(-2x) + c_2 x e^(-2x).

Next, we assume the particular solution to be of the form y_p = (A + Bx) e^(-2x). Taking the first and second derivatives of y_p, we get y_p' = -2A e^(-2x) + B e^(-2x) - 2Bx e^(-2x) and y_p'' = 4A e^(-2x) - 4B e^(-2x) + 4Bx e^(-2x).

Substituting these values in the original differential equation, we get 4A e^(-2x) - 4B e^(-2x) + 4Bx e^(-2x) - 8A e^(-2x) + 4B e^(-2x) + 8Bx e^(-2x) + 4.

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s is not a basis for m2,2. To determine whether s is a basis for m2,2, we need to check if the four given vectors in s are linearly independent and span m2,2.

To check for linear independence, we can set up the following equation:

a1 * [2 0; 0 5] + a2 * [2 0; 4 1] + a3 * [1 2; 3 0] + a4 * [0 1; 1 0] = [0 0; 0 0]

This gives us the following system of linear equations:

2a1 + 2a2 + a3 = 0

2a4 + 2a3 = 0

4a2 + 3a3 + a4 = 0

5a1 + a2 = 0

Solving this system, we get a1 = -3a4, a2 = 5a4, a3 = -2a4, and a4 is free. This means that the vectors in s are linearly dependent, since we have a non-trivial solution to the equation.

Therefore, s is not a basis for m2,2.

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The equation  y"+9y = 0, which confirms that y=5cos3t + 5sin3t is a solution to the given differential equation y"+9y=0.

To check by differentiation that y=5cos3t + 5sin3t is a solution to y"+9y=0, we need to find the second derivative of y and substitute it into the differential equation.

y = 5cos3t + 5sin3t

Taking the first derivative with respect to t:

y' = -15sin3t + 15cos3t

Taking the second derivative with respect to t:

y" = -45cos3t - 45sin3t

Now substituting y and y" into the differential equation:

y"+9y = (-45cos3t - 45sin3t) + 9(5cos3t + 5sin3t) = 0
y" = -45cos3t - 45sin3t
9y = 9(5cos3t + 5sin3t) = 45cos3t + 45sin3t
y" + 9y = (-45cos3t - 45sin3t) + (45cos3t + 45sin3t) = 0

Therefore, y=5cos3t + 5sin3t is indeed a solution to y"+9y=0, as shown by checking the terms and sum in the differential equation.


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the area of the shape XYZ is 85 square units, which corresponds to option D.

How to solve the coordinate!?

To plot the points and connect them in order, we first need to visualize them on a coordinate plane. The given points are (-9,6), (-2,-1), and (8,7). Plotting these points and connecting them in order results in a triangle shape, which we will call XYZ.

To find the area of the triangle, we can use the formula A = 1/2 * b * h, where A is the area, b is the base, and h is the height. To find the base and height, we can use the distance formula.

Using the distance formula, we can find the length of the sides of the triangle:

XY = √(((-2) - (-9))² + ((-1) - 6)²) = √(85)

XZ = √((8 - (-9))² + (7 - 6)²) = √(290)

YZ = √((8 - (-2))² + (7 - (-1))²) = √(170)

Next, we need to find the base and height of the triangle. The base can be any one of the sides, so we will choose XY. To find the height, we can draw a line from point Z perpendicular to XY. This line will intersect XY at a right angle, creating two right triangles.

To find the height of the triangle, we need to find the length of the perpendicular line from point Z to XY. To do this, we can use the formula for the area of a triangle, A = 1/2 * b * h, where A is the area, b is the base, and h is the height.

We know that the area of the larger triangle, XYZ, is given by A = 1/2 * XY * h. We also know that the area of the two smaller triangles formed by the perpendicular line is given by A = 1/2 * base * height. Setting these two equations equal to each other and solving for h, we get:

1/2 * XY * h = 1/2 * XZ * YZ - 1/2 * XY * h

Simplifying, we get:

h = (XZ * YZ) / XY

Plugging in the values we found earlier, we get:

h = (√(290) * √170)) / √(85) = 2 * √(85)

Now that we have the base and height, we can use the formula for the area of a triangle to find the area of XYZ:

A = 1/2 * XY * h = 1/2 * √(85) * 2 * √(85) = 85

Therefore, the area of the shape XYZ is 85 square units, which corresponds to option D.

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Step-by-step explanation:

See image:

Increasing the sample size in a study can have several effects on the results of a hypothesis test. One factor to consider is the size of the z-score in the test.

As the sample size increases, the z-score decreases because the standard error of the mean decreases. This means that the sample mean is more likely to be closer to the population mean, resulting in a smaller difference between the two and a smaller z-score.

Another factor to consider is Cohen's d, which measures the effect size of a treatment or intervention. As the sample size increases, Cohen's d may remain the same or decrease because it is influenced by the variability in the data. If the variability decreases with a larger sample size, Cohen's d may also decrease.

Finally, increasing the sample size can also impact the power of a hypothesis test. Power is the probability of correctly rejecting a false null hypothesis. As the sample size increases, the power of the test also increases because there is a greater chance of detecting a significant difference between the sample mean and the population mean. Therefore, increasing the sample size can be beneficial for hypothesis testing by increasing the power of the test.

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Section D represents 3/13 of the length of the road.

Length is a measurement, which identifies the distance between two points.

Let the length of section D be 3x, and the length of section E be 5x. Then, using the second ratio given, the length of section F is (5/7)*7x = 5x.

So, the total length of the road is 3x + 5x + 5x = 13x.

Therefore, the fraction of the length of the road that is section D is :

(Length of section D) / (Total length of road) = (3x) / (13x) = 3/13.

So, section D represents 3/13 of the length of the road.

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The equation describing the intersection of the sphere with the plane z = 9 is (x+8)^2 + (y-4)^2 = 15.

To find the equation of the sphere centered at (-8,4,8) with radius 4 and the intersection with the plane z = 9.

Step 1: Find the equation of the sphere. The general equation of a sphere is (x-a)^2 + (y-b)^2 + (z-c)^2 = r^2, where (a, b, c) is the center of the sphere and r is the radius. In this case, the center is (-8, 4, 8) and the radius is 4. So, we have:

(x+8)^2 + (y-4)^2 + (z-8)^2 = 16

Step 2: Find the intersection of the sphere with the plane z = 9. Since the plane is given by z = 9, we can substitute 9 for z in the equation of the sphere:

(x+8)^2 + (y-4)^2 + (9-8)^2 = 16

This simplifies to:

(x+8)^2 + (y-4)^2 + 1 = 16

Now, move the constant term to the other side of the equation:

(x+8)^2 + (y-4)^2 = 15

So, the equation describing the intersection of the sphere with the plane z = 9 is (x+8)^2 + (y-4)^2 = 15.

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In a probability histogram, there is a correspondence between area and probability. So, the option(d) is right choice for answering this problem.

Probability histograms represent chance of occurrence an event. A probability histogram is a graphical representation that shows the probability of each outcome on the y -axis. It consists of a rectangle centered on for all values x, and the area of each rectangle is proportional to the probability of the corresponding value. The standard normal distribution is a normal probability distribution with μ = 0 and σ = 1. The area above a class interval denotes the chance of occurrence for that class interval. Because the total area under the curve is equal to one, therefore, is a correspondence between area and probability.

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Complete question:

In a probability histogram, there is a correspondence between _______.

a)volume and probability

b) area and volume

c)variation and area.

d) area and probability

Step-by-step explanation:

Start by graphing the line 2x-5

Then shade the region where y is greater:

To find the angle between two vectors, we can use the dot product formula:

u · v = ||u|| ||v|| cos θ

where u · v is the dot product of u and v, ||u|| and ||v|| are the magnitudes of u and v, and θ is the angle between u and v.

First, let's find the magnitudes of u and v:

||u|| = sqrt(2^2 + 3^2 + 1^2) = sqrt(14)
||v|| = sqrt((-3)^2 + 2^2 + 0^2) = sqrt(13)

Next, let's find the dot product of u and v:

u · v = (2)(-3) + (3)(2) + (1)(0) = -6 + 6 + 0 = 0

Now we can use the dot product formula to solve for the angle:

0 = sqrt(14) sqrt(13) cos θ

cos θ = 0

θ = 90°

Therefore, the angle between u = (2, 3, 1) and v = (-3, 2, 0) is 90 degrees.
To find the angle θ between two vectors u = (2, 3, 1) and v = (-3, 2, 0), you can use the following formula:

cos(θ) = (u • v) / (||u|| ||v||)

where:
u • v is the dot product of the vectors
||u|| and ||v|| are the magnitudes of the vectors

First, find the dot product (u • v):

u • v = (2 * -3) + (3 * 2) + (1 * 0) = -6 + 6 + 0 = 0

Next, find the magnitudes of u and v:

||u|| = √(2^2 + 3^2 + 1^2) = √(4 + 9 + 1) = √14
||v|| = √((-3)^2 + 2^2 + 0^2) = √(9 + 4 + 0) = √13

Now, substitute these values into the formula:

cos(θ) = (0) / (√14 * √13) = 0

θ = arccos(0) = 90 degrees

So, the angle between the vectors u and v is 90 degrees.

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To find the parametric equations for the line, we can use the formula: x(t), = x1 + (x2 - x1)t

y(t) = y1 + (y2 - y1)t, z(t) = z1 + (z2 - z1)t. where (x1, y1, z1) and (x2, y2, z2) are the coordinates of the two points on the line, and t is the parameter. Using the given points,

we have: (x(t), y(t), z(t)) = (0, 1/2, 1) + [(8, 1, -2) - (0, 1/2, 1)]t,  = (8t, 1/2 + t/2, -t + 1), Therefore, the parametric equations for the line are: x(t) = 8t
y(t) = 1/2 + t/2
z(t) = -t + 1.

To find the symmetric equations, we can use the formula:
(x - x1)/a = (y - y1)/b = (z - z1)/c
where (x1, y1, z1) is a point on the line and (a, b, c) is the direction vector of the line.

The direction vector can be found by taking the difference between the two points:
(a, b, c) = (8 - 0, 1 - 1/2, -2 - 1) = (8, 1/2, -3), Choosing the point (0, 1/2, 1), we have:(x - 0)/8 = (y - 1/2)/(1/2) = (z - 1)/(-3).

Simplifying, we get: 8x = y - 1 = -3z + 8, Therefore, the symmetric equations for the line are: 8x = y - 1
y = 2x + 1, z = (-8/3)x + (26/3).

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Answer:

Step-by-step explanation:

y is directly proportional to the variable x, so

                            [tex]y=kx[/tex]        

Sub in y=9, x=5 to find k:

                           [tex]9=5k \rightarrow k=\frac{9}{5}[/tex]

So we get:

                           [tex]y=\frac{9}{5} x[/tex]

Find y when x=20:

                           [tex]y=\frac{9}{5} x[/tex]

                           [tex]y=\frac{9}{5} \times 20[/tex]

                              [tex]=36[/tex]

SAolution: when x=20, y=36

Answer:

A trader buys 8 items of the price of#560, He sells them#816 per dozen, Calculate his percentage profit and loss.

Answer:

0.07, -1.75, -7/10, -1 5/7

Step-by-step explanation:

descending order means from highest to lowest obviously, we'll start with the positive number 0.07 then moving onto negatives -1.75 whole numbers before fractions -7/10 which is -0.7, and finally -1 5/7 0.7142857143 as its a negative the more numbers the lower it is. hope this helps :)