2. question 2 a data analyst is creating a chart for a presentation. the data they will display shows a correlation between variables. why should they be careful when presenting their chart to an audience? 1 point correlation can only be represented in bar charts. correlation can be misunderstood as causation. correlation should be avoided in charts. correlation causes accessibility issues.

This matrix has exactly one (real) eigenvalue of 2, and the 2-eigenspace is the line spanned by the vector [1, 0, 0].

To find a 3x3 matrix with exactly one (real) eigenvalue 2, such that the 2-eigenspace is a line, we can start by constructing a diagonal matrix with a 2 in the top left corner, a 1 in the middle, and a 0 in the bottom right corner. This matrix would have a single eigenvalue of 2, since the other two entries do not affect the determinant.

Next, we can choose a non-zero vector v that lies in the 2-eigenspace. Since the eigenspace is a line, any non-zero vector in that line will suffice. Let's choose v = [1, 0, 0] for simplicity.

Finally, we can construct our desired matrix A by using the formula A = PDP^-1, where P is the matrix whose columns are the eigenvectors of A, and D is the diagonal matrix of eigenvalues. Since we only have one eigenvalue of 2, D will be [2 0 0]. We already have one eigenvector v = [1, 0, 0] in the 2-eigenspace, so we need two more linearly independent eigenvectors to complete P.

One option is to choose any two linearly independent vectors that are orthogonal to v. Let's choose u = [0, 1, 0] and w = [0, 0, 1]. These vectors are clearly orthogonal to v and to each other.

We can then construct the matrix P by placing the eigenvectors v, u, and w as the columns of P:

P = [1 0 0; 0 1 0; 0 0 1]

Finally, we can compute the inverse of P by swapping the rows and columns:

P^-1 = [1 0 0; 0 1 0; 0 0 1]

Putting it all together, we have:

A = PDP^-1 = [1 0 0; 0 1 0; 0 0 1][2 0 0; 0 1 0; 0 0 0][1 0 0; 0 1 0; 0 0 1]

A = [2 0 0; 0 1 0; 0 0 0]

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Answer:

14 glasses

Step-by-step explanation:

Total volume of the mix = 64 + 48 = 112 ounces

Each glass can hold 8 ounces

Number of glasses needed = 112/8 = 14

Answer:

14 glasses

Step-by-step explanation:

64 + 48 = 112

112 ÷ 8 = 14

14 glasses of juice mixture

There are no missing length to complete in the set of triangles

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

The triangles

As a general rule, a triangle has three sides

Using the above as a guide, we have the following:

The side lengths of the four triangles are complete i.e. no missing length

This implies that there is no missing length in the triangles

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Answer:the mode is 2 1/2 because it repeats twice

Step-by-step explanation:repeats twice

Problem

The difference of a number and 72 is 12. Find the number.​

Solution

Let x the number of intertest and we can write this:

x-72=12

And solving for x we got:

x= 72+12= 84

Answer:

A

Step-by-step explanation:

Answer:

-3/7m=12

-3m/7=12 multiplying by 12 on both sides

-3m=12x7

-3m=84

divide by -3

-3m/-3= 84/-3

m= -28

Ans is A

Answer: C is the domain of the function

Step-by-step explanation:

y=f(x) and x in y=f(x) is domain.

The power series solution of the differential equation about x0 = 1 has a radius of convergence of 1.

To find the minimum radius of convergence R of power series solutions about the ordinary point x0 = 1 for the given differential equation, we need to use the Cauchy-Hadamard formula. The formula states that the radius of convergence R is given by:

R = 1/lim sup(|an|)^(1/n)

where an is the nth coefficient of the power series solution.

First, we need to find the power series solution of the differential equation about x0 = 1. We can assume that the solution is in the form of a power series:

y(x) = ∑ an (x-1)^n

We can differentiate this power series to find the derivatives needed to substitute into the differential equation. After substituting and simplifying, we get:

∑ (n+2)(n+1)an (x-1)^n + ∑ (n+1)an (x-1)^n + 4∑ an (x-1)^n = 0

Next, we need to find the coefficients an. We can do this by equating the coefficients of each power of (x-1) to zero. The first few coefficients are:

a0 = y(1)

a1 = y'(1)

a2 = y''(1)/2!

Substituting these coefficients into the formula for R, we get:

R = 1/lim sup(|(n+2)(n+1)/2!|^(1/n) + |(n+1)/1!|^(1/n) + |4/0!|^(1/n))

Taking the limit as n approaches infinity, we get:

lim sup(|(n+2)(n+1)/2!|^(1/n) + |(n+1)/1!|^(1/n) + |4/0!|^(1/n)) = 1

Therefore, the minimum radius of convergence R is:

R = 1/1 = 1

So the power series solution of the differential equation about x0 = 1 has a radius of convergence of 1.

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Answer:

c

Step-by-step explanation:

10^2 - 9^2 = 100 - 81 = 19

The length in centimeters of side OP is 8.

A triangle is a plane figure which is bounded by three straight sides, and has a sum of its internal angle to be 180^o.

Two or more triangles can be referred to as similar if the corresponding sides and measure of corresponding internal angles have some common properties on comparison.

Thus on comparing the corresponding sides of the two given similar triangles, we have;

JK/ ON = KL/ OP

2/ 4 = 4/ OP

2OP = 4*4

       = 16

OP = 16/ 2

     = 8

OP = 8 cm

Therefore, the length of side OP is 8 cm.

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The average angular velocity during the dive is option b, 3 π/ √2=rad/s.

The height of the platform, h = 10 m

The number of revolutions made by the diver = 2.5 revolutions = 5π radThe initial velocity of the diver = 0

The final velocity of the diver:

We know,

The formula for final velocity in terms of initial velocity, acceleration, and distance is given as;

v² = u² + 2

Here, Initial velocity, u = 0

Final velocity, v =

Acceleration due to gravity, a = 9.8 m/s²

Distance, s = h = 10 m

Therefore, v² = 0 + 2 × 9.8 × 10v²

   = 196v = √196v = 14.00 m/s

We know, the formula for average angular velocity is given as;

ω = θ/t

Here, angular displacement, θ = 5π rad

Time taken, t

We know, the formula for time taken is given as;

t = √2h/g

Here, height of the platform, h = 10 m

Acceleration due to gravity, g = 9.8 m/s²

Therefore,t = √2 × 10/9.8t = 1.427 s

Substituting the values of θ and t in the formula for average angular velocity, we get;

ω = θ/tω = 5π/1.427ω = 3.5 π/ √2rad/s

Therefore, the average angular velocity during the dive is option b, 3 π/ √2=rad/s.

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The components of the vector with initial point (7,−6) and a terminal point at (6,−3) are:

The components of a vector are the vectors that makes up the resultant as described in the problem to have starting point (7,−6) and terminal point (6,−3).

This can be gotten by plotting these points and getting the coordinates of the points that makes the initial point and the terminal point the hypotenuse of the triangle

From the graph, the coordinates are:

component 1: (6, -6) to (3, -6)

component 2: (7, -6) to (6, -6)

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Note that this is undefined because the square root of a negative number is not a real number. So, f'(x) is also undefined.

If f(x) = sin z, find f'(x)Finding f'(x)Given that f(x) = sin z, differentiate both sides w.r.t x f'(x) = d/dx(sin z)\

Differentiating sin(z) w.r.t z we get,d/dz(sin z) = cos z

Therefore,f'(x) = d/dz(sin z) * dz/dx = cos(z) * dz/dx

Note that we do not know what z equals, and we are given no information that allows us to determine the value of z. Thus, we must leave the derivative of f in terms of z rather than x.

However, we can still evaluate the value of f'(3) at a particular value of z.

So the answer for this part isf'(x) = cos z * dz/dx

Finding f'(3)Now we can plug in the value z = 3 to find the value of f'(3).f'(3) = cos(3) * dz/dx = cos(3) * 0 = 0

Hence, f'(3) = 0.Question 16Given, y = e²²-7Taking the derivative of y with respect to a, we get dy/da.The derivative of e²²-7 with respect to a is 0 because e²²-7 is a constant.

Therefore,dy/da = 0.Question 17If f(x) = 5 sin-¹ (25), then f'(x) =Finding f'(x)Given that f(x) = 5 sin-¹ (25), differentiate both sides w.r.t x. We get, f'(x) = d/dx(5 sin-¹ (25))Now let u = 25 and y = sin-¹u.

Then we can write f(x) = 5y.

Using the chain rule, we have:d/dx(5 sin-¹ (25)) = d/dx(5y) = 5 dy/dxSo we need to find dy/dx.

Let's differentiate y = sin-¹u with respect to u:dy/du = 1/√(1-u²)

Now, substitute u = 25:dy/du = 1/√(1-(25)²) = 1/√(1-625) = 1/√(-624)

Note that this is undefined because the square root of a negative number is not a real number. So, f'(x) is also undefined.

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Answer:

xy=15

Step-by-step explanation:

The interpretation of R-square in this simple regression model is that 87% of the variation in the dollar price of unleaded gas can be explained by the variation in the dollar price of crude oil, which is option A.

R-square is a measure of how much of the variability in the dependent variable (dollar price of unleaded gas) is explained by the independent variable (dollar price of crude oil).

An R-square of 0.87 means that 87% of the variation in the dependent variable can be explained by the independent variable. Therefore, option A correctly interprets the meaning of R-square in this regression model.

Option B is incorrect as it suggests the opposite relationship, and option C is incorrect as it refers to the sum of squared errors, not the R-square. Option D is also incorrect as R-square does not measure the accuracy of the forecasting model.

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--The given question is incomplete, the complete question is given

" Consider the following results of a simple regression model of dollar price of unleaded gas (dependent variable) and dollar price of crude oil independent variable): If the Table Does not display, this is the data: Coefficient T Stats Intercept Crude Oil 0.56 0.0457 28.27 73.34 Icoefficient Ilt-statistics Intercept 10.56 28.27 Crude Oil 0.0457 73.34 R-square - 0.87 What is the interpretation of R-square? O a. 87% of the movement in crude oil price can be explained by the changes in unleaded gas price. 6.87% of the movement in unleaded gas price can be explained by the changes in crude oil price O c. the sum of squared errors is close to 8796. O d.87% of the time this forecasting model will correctly predict the price of unleaded gas."--

Answer: 5:12

Step-by-step explanation:

25:60

But we can simplify this down too.

25:60

5:12

Answer:

0.4 is the whole number 5/12 is the fraction

Step-by-step explanation:

Answer:

the answer is 64

Step-by-step explanation:

becasue 4 time 4 is 16 and 16 times 4 is 64. You have to multiply 4 against itself 3 times.

Answer:

64

Step-by-step explanation:

4³ = 4 · 4 · 4 = 64

the slope is 1 cos its goin ovr one, up one

y-int is (0,3) or jus strait up 3 cos thts where it crosses the y

iiiif you write it using y=mx+b,, m is the slope n b is the y int so itd jus be: y=x+3

The standard deviation of the sampling distribution of sample means, based on samples of the amounts of weight lost by 72 people on this diet, is approximately 0.695 pounds.

To calculate the standard deviation of the sampling distribution of sample means, we need to use the formula for the standard deviation of a sample mean. This formula states that the standard deviation of the sampling distribution (σ) is equal to the standard deviation of the population (σ) divided by the square root of the sample size (n).

Given that the population standard deviation (σ) is 5.9 pounds and the sample size (n) is 72, we can plug these values into the formula:

Standard Deviation of the Sampling Distribution (σ) = σ / √n

σ = 5.9 pounds

n = 72

Substituting these values, we get:

Standard Deviation of the Sampling Distribution (σ) = 5.9 / √72

To find the standard deviation of the sampling distribution, we need to evaluate the square root of 72. Using a calculator or mathematical software, we find that √72 is approximately 8.49.

Now, let's calculate the standard deviation of the sampling distribution:

Standard Deviation of the Sampling Distribution (σ) = 5.9 / 8.49 ≈ 0.695 pounds (rounded to two decimal places)

Therefore, the standard deviation of the sampling distribution of sample means, based on samples of the amounts of weight lost by 72 people on this diet, is approximately 0.695 pounds.

This value represents the average amount of variation or dispersion in the means of different samples taken from the population. It indicates how much the sample means are likely to deviate from the population mean.

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Answer:

800/920

400/460

40/46

20/23

Answer:

9

Step-by-step explanation

First you multiply 3 five times, then you multiply 3 seven times and you divide the results of each multiplication

Answer:

0.111111111111111

Step-by-step explanation:

=> 3⁵÷3⁷

Note 3⁵ means multiplying 3 five times

And 3⁷ means multiplying 3 7 times

=> 3×3×3×3×3÷3×3×3×3×3×3×3

multiply the values and then divide

=> 243÷2,187

divide 243 by 2187

=> 0.111111111111111

Answer:a

Step-by-step explanation:slope=4  y-int=-9

Answer:

A: Slope is 4

    Y intercept (0,-9)

Step-by-step explanation:

slope intercept form is y=Mx+b

m= slope

b= y intercept

y=4x-9

here the m or slope is 4

And b or y intercept is -9

So a is the correct answer

Hopes this helps please mark brainliest

Answer: To determine the break-even quantity, we need to find the point where the revenue equals the cost. In other words, we need to solve the equation R(x) = C(x).

Given:

Setting R(x) = C(x), we have:

Subtracting 135x from both sides of the equation:

Simplifying the left side:

Dividing both sides by 45:

The break-even quantity is 1,236 units.

Since the break-even quantity (1,236 units) is less than the maximum number of units that can be sold (2,097 units), the firm can produce the product because it would make money.

To determine the break-even quantity and decide whether to proceed with the production of the new product, we need to analyze the cost and revenue data provided.

The cost function is given as C(x) = 135x + 55,620, where x represents the quantity of units produced. The revenue function is given as R(x) = 180x. To break even, the total cost and total revenue should be equal. We can set up an equation based on this condition: C(x) = R(x). Substituting the given cost and revenue functions: 135x + 55,620 = 180x

To solve for x, we can subtract 135x from both sides: 55,620 = 45x. Now, divide both sides by 45: x = 1,236. The break-even quantity is 1,236 units.

Since the number of units that can be sold is no more than 2,097 units, which is greater than the break-even quantity of 1,236 units, the firm can produce the product. The break-even point indicates the minimum number of units that need to be sold to cover the costs, and since the firm can sell more than the break-even quantity, it has the potential to make a profit. However, further analysis of other factors such as market demand, competition, and potential profitability should also be considered before making a final decision.

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The most appropriate choice for percentage will be given by

Cost of fencing 1.1 foot = $5.995

Cost of sodding 1.1 sq. foot = $0.715

Total cost of fencing and sodding = $6.71

What is percentage?

Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

For example- 2% means \(\frac{2}{100}\)

Here,

Cost of fencing 1 foot = $5.45

10% of 1 foot = \(\frac{10}{100}\times 1\)

                     = 0.1 foot

1 foot + 10% of 1 foot = 1 + 0.1 = 1.1 feet

cost of fencing 1.1 foot = $5.45 \(\times\) 1.1 = $5.995

Cost of sodding 1 sq foot = $0.65

Cost of sodding 1.1 sq foot = $0.65 \(\times\) 1.1 = $0.715

Total cost of fencing and sodding = $(5.995 + 0.715)

                                                         = $6.71

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Question 1: MetaSpace is unlikely to succeed in a legal battle against Marcus Superberg under the Australian Consumer Law.

Question 2: Ingrid may be entitled to workers compensation as an employee of RoadRunners.

Question 1:

Issue: Can MetaSpace succeed in a legal battle against Marcus Superberg under the Australian Consumer Law?

Rule: Under the Australian Consumer Law, businesses are prohibited from engaging in misleading or deceptive conduct in trade or commerce. To establish a claim, MetaSpace needs to show that Marcus Superberg made false representations about the security and privacy of DeltaVerse, which misled or deceived the general public.

Application: Marcus Superberg claims that DeltaVerse complies with privacy and cybersecurity legislation worldwide, and personal data cannot be accessed, stolen, or sold. He further claims to have an unbreakable unique algorithm protecting user data. Will Bates, the founder of MetaSpace, argues that such claims are impossible and accuses Marcus Superberg of misleading the public.

To assess MetaSpace's likelihood of success, it is important to determine if MetaSpace falls within the scope of consumers under the Australian Consumer Law. While MetaSpace is a competitor, it is possible for businesses to be considered consumers if they acquire goods or services for personal, domestic, or household use. If MetaSpace can establish that it falls within the definition of a consumer, it may have standing to bring an action against Marcus Superberg.

Conclusion: Based on the information provided, it is unclear whether MetaSpace can succeed in a legal battle against Marcus Superberg under the Australian Consumer Law. MetaSpace's ability to establish its consumer status and prove that Marcus Superberg engaged in misleading or deceptive conduct would be crucial factors in determining the outcome.

Question 2:

Issue: Is Ingrid entitled to workers compensation?

Rule: The entitlement to workers compensation depends on the classification of Ingrid's working relationship with RoadRunners. If she is considered an employee, she may be eligible for workers compensation benefits. However, if she is classified as an independent contractor, she may not have the same entitlements.

Application: Ingrid works for RoadRunners as a delivery courier, using her bicycle to deliver packages. She receives a fixed rate for each delivery, works at her own discretion, and follows RoadRunners' guidelines. She also faces penalties for exceeding the 15-minute delivery guarantee. Ingrid has been injured while performing her delivery duties.

To determine Ingrid's employment status, it is necessary to consider various factors, including the level of control exercised by RoadRunners over Ingrid's work, the degree of independence she has, the provision of equipment, and the nature of the work relationship. The fact that Ingrid uses the RoadRunners application and follows their guidelines suggests a degree of control indicative of an employment relationship.

If Ingrid is found to be an employee, she may be entitled to workers compensation benefits, including medical expenses and income replacement during her recovery period. However, if she is classified as an independent contractor, she may need to seek compensation through other avenues, such as a personal injury claim.

Conclusion: Based on the information provided, Ingrid may be entitled to workers compensation if she is classified as an employee of RoadRunners. The determination of her employment status will depend on a thorough assessment of the specific circumstances of her working relationship with RoadRunners, considering factors such as control, independence, and the nature of her work. Ingrid should seek legal advice to fully evaluate her entitlement to workers compensation benefits.

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Answer:

Step-by-step explanation:

The equation would be: y-4>5

Hope this helps...

El área de papel utilizada para cada CD es aproximadamente 20.41 cm².

How much paper area is used for each CD?

Para calcular el área de papel utilizado para cada CD, necesitamos determinar el área de la región entre dos círculos concéntricos.

El área de un círculo se calcula utilizando la fórmula A = πr², donde r es el radio. En este caso, tenemos dos círculos con radios diferentes: el radio mayor de 5.8 cm y el radio menor de 0.7 cm.

El área del papel utilizado será la diferencia de áreas entre los dos círculos. Entonces, podemos calcularlo de la siguiente manera:

Área utilizada = Área del círculo mayor - Área del círculo menor

= π(5.8²) - π(0.7²)

= π(33.64) - π(0.49)

≈ 105.72 - 1.54

≈ 104.18 cm²

Por lo tanto, aproximadamente se utilizan 104.18 cm² de papel para cada CD.

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Dialyzer re-use efficiency is largely determined by the fiber bundle volume (FBV).

This estimation is performed after the dialyzer has been pressure cleaned and may underrate the level of coagulated strands a patient really experiences while on dialysis.

The package's dimensions:

length = 32 in

width = level = 16 in

Volume of bundle = 8192 in³

The square-shaped package is depicted in the attached image.

Expect that the length is y in and that width = level = x in (since the base is a square)

This implies that the circumference is 4*x = 4x in

We are given that the greatest amount of length and circumference is 96.

This indicates:

This can be rewritten as: y + 4x = 96

The volume of the package can be calculated as follows: y = 96 - 4x..............> I

Volume is equal to the following: length * width * height * y * x * x = x2y in3 Substitute equation I for the following volume equation:

Volume = x2 (96-4x) = 96x2 - 4x3 in3 to achieve maximum volume:

dV/dx = 0 indicates that:

2(96) x - 4(3) x2 = 0 192x - 12x2 = 0 x (192-12x) = 0

either x = 0.......> This is rejected because the side cannot be zero or 192 - 12x = 0...............> 192 = 12x...............> x = 16 in.......> accepted

In Part (b), y = 96 - 4x = 96 - 4(16) = 96 - 64 = 32: obtaining a volume:

The volume of the package is equal to 32 x 16 x 16 x 8192 in3.

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