Find the following limit or state that it does not exist. 2 X -5x + 6 lim X-3 X-3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 2 x? - 5x + 6 O A. lim X +3 X-3 (Type an exact answer.) OB. The limit does not exist.

the amount of juice left in Luna's glass is 1/2.

We have been given that Luna mixes 3/4 cup of orange juice with 3/8 cup of cranberry juice.

First of all, let us find the total amount of juice Luna had by adding the amount of orange juice to amount of cranberry juice.

Total amount of juice Luna had = 3/4 + 3/8

                                                 = 9/8

Since Luna gave 5/8 cup of juice to Mags, so let us subtract amount of juice given to Mags from the total amount of juice to find the amount of juice left in Luna's glass.

Hence, Amount of juice left in Luma glass is,

= 9/8 - 5/8

= 4/8

= 1/2

Therefore, the amount of juice left in Luna's glass is 1/2.

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The value of x is  10.05 meters .

To find the value of x, we need to consider that the rectangular piece of land has been subdivided into small squares. We can use the given dimensions of the rectangle to determine the number of small squares that will fit along each dimension.

The number of squares along the 9.8km side will be:

Number of squares = length of side / length of each square

Number of squares = 9.8km / x

Similarly, the number of squares along the 7.2km side will be:

Number of squares = width of side / length of each square

Number of squares = 7.2km / x

Since the rectangular piece of land has been subdivided into small squares, the total number of squares can also be calculated as the product of the number of squares along each dimension:

Total number of squares = (9.8km / x) * (7.2km / x)

We can simplify this expression by multiplying the terms in the brackets and simplifying:

Total number of squares = 70.56 / [tex]x^2[/tex]

We know that the total number of squares is equal to the number of squares that fit in the rectangular piece of land, which is given by:

Total number of squares = (9.8km * 7.2km) / [tex]x^2[/tex]

We can equate the two expressions for the total number of squares and solve for x:

70.56 / [tex]x^2[/tex] = (9.8km * 7.2km) / [tex]x^2[/tex]

[tex]x^2[/tex] = (9.8km * 7.2km) / 70.56

[tex]x^2[/tex]= 101.04

x = 10.05 m (rounded to two decimal places)

Therefore, each small square has a side length of approximately 10.05 meters

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Angle 4 is congruent to Angle 2

Angle 4 and 3 are Linear pair

Angle 1 and 3 are Vertical angles

Angle 1 is  congruent to Angle 3

There are no alternate angles in the image above

A linear pair is a pair of adjacent angles that are formed when two lines intersect. In a linear pair  the angles share a common vertex and a common side

Linear pairs are Supplementary angles hence we can say that angle 4 and 3 are supplementary angles. Angles 1 and 2 have similar feature

The vertical angle theorem also have it that vertical angles are congruent and in the figure

Angle 4 and Angle 2 are vertical angles, and so is Angle 1 and  Angle 3

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[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ \left( x^{\frac{8}{15}} \right)^3\implies \left( x^{\frac{8}{15}\cdot 3} \right)\implies x^{\frac{8}{5}}\implies x^{1+\frac{3}{5}}\implies x\cdot x^{\frac{3}{5}}\implies x\sqrt[5]{x^3}[/tex]

The geometric transformation is shown in the line of music is a (b) glide reflection

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

The line of music

In the line of music, we have the following transfromations

When the two transformations i.e. reflection and translation are combined, the result is a glide reflection

This means that the geometric transformation is shown in the line of music is a glide reflection

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We can say with 95% confidence that the true proportion of adults who have read a book in either print or digital format in the preceding 12 months lies between 0.

to calculate the confidence interval for the population proportion of adults who have read a book in either print or digital format in the preceding 12 months, we need to know the sample proportion, sample size, and confidence level. let's assume that a random sample of n adults was selected and p is the sample proportion of adults who have read a book in either print or digital format in the preceding 12 months. we will use the formula:

(lower bound, upper bound) = (p - z*sqrt((p*(1-p))/n), p + z*sqrt((p*(1-p))/n))

where z is the z-score corresponding to the desired confidence level. for example, if we want a 95% confidence interval, z = 1.96. if we want a 99% confidence interval, z = 2.58.

let's assume that a sample of 500 adults was selected and 300 of them reported having read a book in either print or digital format in the preceding 12 months. then the sample proportion is:

p = 300/500 = 0.6

if we want a 95% confidence interval, the z-score is 1.96. substituting these values into the formula, we get:

(lower bound, upper bound) = (0.6 - 1.96*sqrt((0.6*(1-0.6))/500), 0.6 + 1.96*sqrt((0.6*(1-0.6))/500))

simplifying this expression, we get:

(lower bound, upper bound) = (0.5516, 0.6484) 5516 and 0.6484.

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The value of sin(A+B) is 32/25. We can use the trigonometric identities to find the value of sin(A+B). First, we need to determine the value of cos(B) using the given information about sin(B) and the quadrant of angle B.

Since sin(B) is negative and B is in Quadrant III, we can deduce that cos(B) must be positive. Using the Pythagorean identity sin^2(B) + cos^2(B) = 1, we can find cos(B) as follows:

sin^2(B) + cos^2(B) = 1

(-24/25)^2 + cos^2(B) = 1

576/625 + cos^2(B) = 1

cos^2(B) = 1 - 576/625

cos^2(B) = 49/625

cos(B) = √(49/625) = 7/25

Next, we can use the sum-to-product identity for sine:

sin(A + B) = sin(A) * cos(B) + cos(A) * sin(B)

Substituting the given values:

sin(A + B) = (−4/5) * (7/25) + (−24/25) * (−4/5)

sin(A + B) = −28/125 + 96/125

sin(A + B) = 68/125

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The first derivative of f(x) = (3x⁴ - 5)⁵ is f'(x) = 60x³(3x⁴ - 5)⁴.the limit of the following rational functions: lim 4+x x--2-x+2 2.

to find the limit of the rational function, we can substitute the given value of x into the function and evaluate it. let's compute the limit step by step:

lim(x→2) (4 + x) / (x - 2 - x + 2)

first, simplify the expression in the denominator:

lim(x→2) (4 + x) / 0

since the denominator is 0, we need to apply a different approach to find the limit. we can try factoring the numerator:

lim(x→2) x + 4 / 0

now, we can observe that the numerator is nonzero, and the denominator is zero. this indicates that the limit of the function does not exist as x approaches 2.

moving on to the second part of your question, we need to compute the first derivative of the function f(x) = (3x⁴ - 5)⁵.

to find the derivative, we can use the chain rule. let's differentiate the function step by step:

f(x) = (3x⁴ - 5)⁵

applying the chain rule:

f'(x) = 5(3x⁴ - 5)⁴ * d/dx(3x⁴ - 5)

differentiating the inner function:

f'(x) = 5(3x⁴ - 5)⁴ * (12x³)

simplifying further:

f'(x) = 60x³(3x⁴ - 5)⁴

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The expected value or the average number of times a customer visits the store, given the probability distribution of X, is 1.4.

To find the expected value of X, we need to multiply each possible value of X by its corresponding probability and then sum up the products. In this case, we have:

E(X) = (0 x 0.1) + (1 x 0.4) + (2 x 0.4) + (3 x 0.1)

= 0 + 0.4 + 0.8 + 0.3

= 1.4

Therefore, the expected value or the average number of times a customer visits the store in a one week period is 1.4. This means that if we were to observe a large number of customers over a long period of time, we would expect the average number of visits per customer to be approximately 1.4.

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The value of GR(x) is 4.

A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication operations.

We have,

GR(y) = 12

We have given the polynomial as, P(x, y) = 9 x⁵y ⁷ᵃ⁻² - 7xᵃ⁺² y⁵

Now, we have to compare the power of y which contain the variable.

From the given polynomial we have the expression a-2 to compare.

So, using GR(y) = 12

7a-2= 12

7a = 14

a = 2

We get the value a = 2 then we substitute the value of a in the expression a +2 as

So, a+ 2 = 4

So, the value of GR(x) is 4.

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The function is​ linear and, the equation of the function is f(x) = 7 + 22x

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

x       y

0      7

1      29

2     51

3     73

4    95

Calculate the first difference

x       y     First

0      7

1      29       22  

2     51         22

3     73       22

4    95       22

Because the first difference are equal

Then, the function is​ linear

Also, the equation of the function is

f(x) = 7 + 22x

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The function is​ linear and, the equation of the function is f(x) = 7 + 22x

Determining whether the function is​ linear, quadratic, or exponential

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

x       y

0      7

1      29

2     51

3     73

4    95

Calculate the first difference

x       y     First

0      7

1      29       22  

2     51         22

3     73       22

4    95       22

Because the first difference are equal

Then, the function is​ linear

Also, the equation of the function is

f(x) = 7 + 22x

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The correct answer is c. Use case oval. Use case ovals are part of use case diagrams, not activity diagrams. Activity diagrams primarily consist of activity ovals, actor names, and relationship lines.

The activity diagram is a type of UML diagram that is widely used to visualize the flow of activities and actions in a system. It is an important tool for modeling the behavior of a system and its components. The activity diagram consists of various constructs that are used to represent the different elements of a system. These constructs include activity ovals, actor names, use case ovals, and relationship lines.

A relationship line is used in other types of UML diagrams, such as class diagrams or sequence diagrams, to represent the relationships between objects or classes.

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The solution set is {(-5 + 3√5)/2, (-5 - 3√5)/2}. These are exact, irrational solutions.

Using the product rule of logarithms, we can combine the two logarithms into a single logarithm:

log3[(x + 4)(x + 1)] = 2

Now, we can rewrite this equation without logarithms:

3^2 = (x + 4)(x + 1)

Expanding the right side:

9 = x^2 + 5x + 4

Bringing everything to one side:

x^2 + 5x - 5 = 0

Using the quadratic formula:

x = (-5 ± √(5^2 - 4(1)(-5))) / (2(1))

x = (-5 ± √45) / 2

Simplifying the radical:

x = (-5 ± 3√5) / 2

So, the solution set is {(-5 + 3√5)/2, (-5 - 3√5)/2}. These are exact, irrational solutions.

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Answer:

x =416

Step-by-step explanation:

8365 = 20x +45

8320=20x

x =416

Answer:

416 tokens, Brainliest please! or not whatever you do, enjoy the rest of your day :D!

Step-by-step explanation:

Camilla collected 405 tokens. We can use the formula p = 20x + 45 to solve for x. Substituting p = 8365, we get:

8365 = 20x + 45 8320 = 20x x = 416

So, Camilla collected 416 tokens.

The length of the radius r is given by the following option:

B. 8.4.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

For this problem, we have that:

Hence the radius r is obtained as follows:

r² + 9² = 12.3²

[tex]r = \sqrt{12.3^2 - 9^2}[/tex]

r = 8.4.

The diagram is given by the image presented at the end of the answer.

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The curl of the vector field F = (3x sin(y), 2y cos(x)) is curl F = (2cos(x) - 3sin(y), -2sin(x)).

To find the curl of a vector field, we can use the following formula:

curl F = (∂Fz/∂y - ∂Fy/∂z, ∂Fx/∂z - ∂Fz/∂x, ∂Fy/∂x - ∂Fx/∂y)

Given the vector field F = (3x sin(y), 2y cos(x)), we can calculate its curl as follows:

∂Fz/∂y = ∂(2y cos(x))/∂y = 2cos(x)

∂Fy/∂z = ∂(3x sin(y))/∂z = 0

∂Fx/∂z = ∂(3x sin(y))/∂z = 0

∂Fz/∂x = ∂(2y cos(x))/∂x = -2y sin(x)

∂Fy/∂x = ∂(3x sin(y))/∂x = 3sin(y)

∂Fx/∂y = ∂(3x sin(y))/∂y = 3x cos(y)

Putting all the partial derivatives together, we have:

curl F = (2cos(x) - 3sin(y), -2y sin(x), 3x cos(y))

Simplifying the expression, we get:

curl F = (2cos(x) - 3sin(y), -2sin(x))

Therefore, the curl of the vector field F is curl F = (2cos(x) - 3sin(y), -2sin(x)).

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The radius of convergence (R) is infinite, indicating that the series converges for all values of x. Therefore, the interval of convergence is (-∞, +∞).

To estimate the value of the expression (2n + 1)^-6, we can substitute the given value n = 1 into the expression and evaluate it. (2n + 1)^-6 = (2(1) + 1)^-6 = (2 + 1)^-6 = 3^-6. Calculating the value: 3^-6 = 1/(3^6) = 1/729. So, the expression (2n + 1)^-6, when n = 1, is approximately equal to 0.001371742112.

Regarding the series (-1)^(8n)/(8n)!, let's analyze its convergence properties. The radius of convergence (R) of a power series is determined by the formula: 1/R = Lim (n -> ∞) |a(n+1)/a(n)|. In this case, a(n) is the term (-1)^(8n)/(8n)!. To simplify the analysis, let's consider the absolute value of a(n): |a(n)| = |(-1)^(8n)/(8n)!| = 1/(8n)!

Now, let's calculate the ratio |a(n+1)/a(n)|: |a(n+1)/a(n)| = |(-1)^(8(n+1))/(8(n+1))!| / |(-1)^(8n)/(8n)!| = |(-1)^8(n+1)/(8(n+1))!| * |(8n)!/(-1)^(8n)| = 1/(8(n+1)). Taking the limit as n approaches infinity: Lim (n -> ∞) |a(n+1)/a(n)| = Lim (n -> ∞) (1/(8(n+1))) = 0. Since the limit is 0, the radius of convergence (R) is infinite, indicating that the series converges for all values of x. Therefore, the interval of convergence is (-∞, +∞).

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Answer:

The HCF would be 8 (1,2,4,8).                                        

The value of the integral over region R is 16(√2 - 1).

To evaluate the given integral over the region R, we first need to determine the limits of integration. The region R is defined by the inequalities 16 ≤ x² + y² ≤ 36 and x ≤ 0.

This region can be visualized as a semicircle with radius 4 centered at the origin, with the left half of the circle included (since x ≤ 0). Therefore, we can express the integral as follows:

∫∫R 2(x + y) dA = ∫π/2₀ ∫₀⁴ 2(r cosθ + r sinθ) r dr dθ

where r is the radial coordinate and θ is the angular coordinate.

Evaluating this integral gives:

∫π/2₀ ∫₀⁴ 2(r cosθ + r sinθ) r dr dθ = ∫π/2₀ [r² cosθ + r² sinθ] from r=0 to r=4 dθ

= ∫π/2₀ (16 cosθ + 16 sinθ) - (0 cosθ + 0 sinθ) dθ

= ∫π/2₀ 16(cosθ + sinθ) dθ

= 16[-cos(π/4) + sin(π/4)]

= 16(√2 - 1)

Therefore, the value of the integral over region R is 16(√2 - 1).

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Answer:

24°

Step-by-step explanation:

π radians = 180°

180°/(π radians) = 1

2π/15 radians × 180°/(π radians) = 24°

The vectors of the translation vectors are written as follows

a {6, 3]

b [-6, 3]

A translation vector is a vector that describes the displacement of a point or object from its original position to its new position after a translation or movement occurs.

In other words it specifies how much and in what direction a point or object is moved.

In the translation vector given, e represents the x direction and movements from left to right. While f represents the y direction and movements from up to down

For 6 square to the right and 3 squares up, we have  {6, 3] all positive

6 squares to the left and 3 squares up is written as {-6, 3].

To the left is written in negative for x direction. While for y direction, when the translation is down, we use negative.

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The given statement "2 6e6x 3e3x еx e3x" is false because the correct particular solution is [tex]\(y_p(x) = 6e^{6x}\tan(9x)e^{3x} + 3e^{3x}xe^{3x}\)[/tex].

To find a particular solution of the nonhomogeneous differential equation (DE) 2y'' - 18y' + 36y = tan(9x) using the variation of parameters method, we assume a particular solution of the form [tex]\(y_p(x) = u_1(x)y_1(x) + u_2(x)y_2(x)\)[/tex], where [tex]\(y_1(x)\)[/tex] and [tex]\(y_2(x)\)[/tex] are the solutions of the associated homogeneous DE, and [tex]\(u_1(x)\)[/tex] and [tex]\(u_2(x)\)[/tex] are functions to be determined.

The solutions of the associated homogeneous DE 2y'' - 18y' + 36y = 0 can be found by solving the characteristic equation:

[tex]\(2r^2 - 18r + 36 = 0\)[/tex],

which gives us the repeated root r = 3.

Hence, the homogeneous solutions are [tex]\(y_1(x) = e^{3x}\)[/tex] and [tex]\(y_2(x) = xe^{3x}\)[/tex].

To find [tex]\(u_1(x)\)[/tex] and [tex]\(u_2(x)\)[/tex], we use the formulas:

[tex]\(u_1(x) = -\frac{{y_2(x) \int y_1(x)f(x)dx}}{{W(y_1, y_2)}}\)[/tex]

and

[tex]\(u_2(x) = \frac{{y_1(x) \int y_2(x)f(x)dx}}{{W(y_1, y_2)}}\)[/tex],

where [tex]\(W(y_1, y_2)\)[/tex] is the Wronskian of [tex]\(y_1(x)\)[/tex] and [tex]\(y_2(x)\)[/tex].

Evaluating the integrals and simplifying the expressions, we obtain:

[tex]\(u_1(x) = 6e^{6x} \tan(9x)\) and \(u_2(x) = 3e^{3x}\)[/tex].

Therefore, the particular solution of the nonhomogeneous DE is:

[tex]\(y_p(x) = u_1(x)y_1(x) + u_2(x)y_2(x) = 6e^{6x}\tan(9x)e^{3x} + 3e^{3x}xe^{3x}\)[/tex].

So, the given statement is false.

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This equation shows that y is Inversely proportional to the square of x. As x increases, y decreases rapidly. Conversely, as x decreases, y increases rapidly.

We know that y is directly proportional to W^2, so we can write:

y = kW^2

where k is the constant of proportionality. We can find k using the given values when W = 10 and y = 5:

5 = k(10)^2

5 = 100k

k = 5/100

k = 0.05

Therefore, the equation for y in terms of W is:

y = 0.05W^2

We also know that x is inversely proportional to W, so we can write:

x = k/W where k is the constant of proportionality. We can find k using the given values when W = 10 and x = 0.4:

0.4 = k/10

4 = k

Therefore, the equation for x in terms of W is:

x = 4/W

Now we need to express y in terms of x. We can substitute the expression for W in terms of x into the equation for y:y = 0.05W^2

y = 0.05(4/x)^2

y = 0.05(16/x^2)

y = 0.8/x^2

Therefore, the equation for y in terms of x is:

y = 0.8/x^2

This equation shows that y is inversely proportional to the square of x. As x increases, y decreases rapidly. Conversely, as x decreases, y increases rapidly.

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The index "i" is an integer, then the "pth" percentile is simply the data value in position "i".

The answer depends on the specific definition used for computing percentiles. However, the most common convention is to use linear interpolation, in which the "pth" percentile is the weighted average of the data values in positions "i" and "i+1", where "i" is the integer part of the index of the "pth" percentile, with weights given by the fractional part of the index. In other words, if "d(i)" and "d(i+1)" are the data values in positions "i" and "i+1", respectively, and "f" is the fractional part of the index, then the "pth" percentile is given by:

(1-f) * d(i) + f * d(i+1)

If the index "i" is an integer, then the "pth" percentile is simply the data value in position "i".

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The approximate solution of the exponential equation 19e¹, rounded to 4 decimal places, is: x ≈ -1.5299.

To find the solution of the exponential equation 19e^x = 5, we need to first isolate x. Here's the step-by-step explanation:
1. Divide both sides by 19: e^x = 5/19
2. Take the natural logarithm (ln) of both sides: ln(e^x) = ln(5/19)
3. Use the logarithm property ln(a^b) = b*ln(a): x * ln(e) = ln(5/19)
4. Since ln(e) = 1, we get x = ln(5/19)
The exact solution using natural logarithms is: x = ln(5/19)
To find the approximate solution, use a calculator to evaluate the natural logarithm:
x ≈ ln(5/19) ≈ -1.5299
Therefore, the approximate solution, rounded to 4 decimal places, is: x ≈ -1.5299

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The equation of the tangent line to the curve at the point (2, 0) is :

y = (-3/7)(x - 2)

To find the equation of the tangent line to the curve at the point (2, 0), we need to determine the slope of the tangent line at that point.

Given the parametric equations:

x = t^3 - 5t

y = 12 - 3t - 10

We can find the derivative dy/dx by taking the derivative of y with respect to t and dividing it by the derivative of x with respect to t:

dy/dx = (dy/dt)/(dx/dt)

Let's find dx/dt first:

dx/dt = d/dt(t^3 - 5t)

= 3t^2 - 5

Now, let's find dy/dt:

dy/dt = d/dt(12 - 3t - 10)

= -3

Next, we calculate dy/dx:

dy/dx = (dy/dt)/(dx/dt)

= (-3)/(3t^2 - 5)

To find the slope of the tangent line at the point (2, 0), substitute t = 2 into dy/dx:

dy/dx = (-3)/(3(2)^2 - 5)

= (-3)/(12 - 5)

= (-3)/7

Therefore, the slope of the tangent line at the point (2, 0) is -3/7.

Now, we can use the point-slope form of a linear equation to find the equation of the tangent line:

y - y₁ = m(x - x₁)

Substituting the point (2, 0) and the slope m = -3/7 into the equation:

y - 0 = (-3/7)(x - 2)

Simplifying the equation:

y = (-3/7)(x - 2)

This is the equation of the tangent line to the curve at the point (2, 0).

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If a simple Pearson correlation value = .685, the percentage of variance accounted for by the correlation is 47%.

To determine the percentage of variance accounted for by a Pearson correlation coefficient, we need to square the correlation coefficient and multiply it by 100.

In this case, the given correlation coefficient is 0.685. Squaring this value gives us 0.469225. Multiplying this by 100, we find that the percentage of variance accounted for by the correlation is approximately 46.92%.

Therefore, the correct answer is c. 47%.

The squared correlation coefficient, also known as the coefficient of determination ([tex]r^2[/tex]), represents the proportion of the variance in one variable that can be explained or accounted for by the linear relationship with the other variable. It indicates the strength and extent to which the two variables are related.

In this case, the [tex]r^2[/tex] value of approximately 0.469225 means that approximately 46.92% of the variance in the dependent variable can be explained by the linear relationship with the independent variable. The remaining 53.08% of the variance is attributed to other factors or sources of variation that are not accounted for by the correlation.

Understanding the percentage of variance accounted for by a correlation is valuable in assessing the strength and meaningfulness of the relationship between variables. A higher [tex]r^2[/tex] value indicates a greater proportion of variance explained, indicating a stronger and more predictive relationship between the variables.

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The distance between the two actors in this problem is given as follows:

9 feet.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates given as [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The positions for each actor are given as follows:

Hence the distance is given as follows:

[tex]D = \sqrt{(6 - (-3))^2+(-2-(-2))^2}[/tex]

D = 9 units.

As each square represents one foot, the distance is:

9 x 1 = 9 feet.

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Answer:

[tex] {(x - 6)}^{2} + {(y - 3)}^{2} = {4}^{2} [/tex]

[tex] {(x - 6)}^{2} + {(y - 3)}^{2} = {16} [/tex]

Answer:

V = π(6^2)(8) = 288π cu. in.

= 904.78 cu. in.