Which statement about the points (5, 7) and (10, 12) is true? CLEAR CHECK There is not enough information to determine if the points show direct variation. They show direct variation because y = x + 2 and 10 – 5 = 12 – 7. The line they are on does not show direct variation. They show direct variation because the line they are on has a positive slope.

Since the form a linear pair, it means that we can add them to make the complete angle.

However, as we can see, the two angles to gether make a straight line, so the angles ABD and CBD are supplementary, that is, their sum is 180°:

Matrix A is diagonalizable

Yes, it is possible to test a matrix \( A \in M_{n \times n}(R) \) for diagonalizability. If \( A \) is diagonalizable, then there exists an invertible matrix \( Q \) and a diagonal matrix \( D \) such that \( A = Q D Q^{-1}\). To find these matrices, we can use the following steps:

1. Find the characteristic polynomial \( p(\lambda) \) of \( A \).
2. Find the eigenvalues of \( A \) by solving \( p(\lambda) = 0 \).
3. Find the corresponding eigenvectors for each eigenvalue of \( A \).
4. Construct the matrix \( Q \) as a matrix whose columns are composed of the eigenvectors of \( A \).
5. Construct the diagonal matrix \( D \) by placing the eigenvalues of \( A \) along the diagonal entries.
6. Check that \( A = Q D Q^{-1} \).

If these steps all check out, then \( A \) is diagonalizable.

Learn more about diagonalizability

brainly.com/question/28119462

#SPJ11

Answer:

17°

Step-by-step explanation:

m∠1 = m∠2.

Set the expressions for 1 and 2 equal to each other.

6x + 5 = 9x - 46

Separate x's on one side.

3x = 51

x = 17

The expected number of balls in the first bin would be (1/n)^n

It is given that,

The number of balls and bins is same

If so, then there should always be one ball in each container. The likelihood that every ball will land in the first bin is (1/n)^n.

For example -

Let there be three balls and three bins. Put an A, B, and C next to each ball. The bins are marked 1, 2, and 3. Ball A is likely to land in bin 1 with a 1/3 chance. However, there is a 1/3 chance that ball B will land in bin 1, and there is a 1/3 chance that ball C will land in bin 1. As a result, bin 1 should have a value of 1/3 + 1/3 + 1/3 = 1. The expected values of bins 2 and 3 follow a similar rationale.

By the same reasoning, bins 2 and 3 should likewise have anticipated values of 1.

How likely is it that all three balls will fall into bin one?

1/3 x 1/3 x 1/3 = 1/27, or in the general situation, (1/n)^n, which equals (1/3)^3.

Hence, the expected number of balls in the first bin would be (1/n)^n

To learn more about, expected number of balls here

https://brainly.com/question/20262586

#SPJ4

Answer:

the value of x is 8

Step-by-step explanation:

the catheters were equal to each other

Answer:

7r is the correct answer

Step-by-step explanation:

7 x 8 = 56

Using Green's theorem, the counterclockwise circulation is 3/2, and the counterclockwise outward flux is 5/6.

Green's theorem relates the circulation of a vector field around a closed curve to the outward flux of the curl of the vector field over the region bounded by that curve. In this case, we are given the vector field F(x, y) = (x + y)i + (x^2 + y^2)j and the triangle bounded by x = 1, y = 0, and y = x.

To calculate the counterclockwise circulation, we integrate the dot product of F and the tangent vector along the boundary of the triangle. The circulation can be written as ∮C F · dr, where C represents the curve bounding the triangle. Parameterizing the curve C, we have r(t) = (t, t) for 0 ≤ t ≤ 1. The tangent vector dr/dt is (1, 1).

Evaluating the circulation, we have ∮C F · dr = ∫₀¹ (t + t)(1) + (t^2 + t^2)(1) dt = ∫₀¹ (2t + 2t^2) dt = [t^2 + (2/3)t^3]₀¹ = 1 + (2/3) = 3/2.

Next, we need to find the counterclockwise outward flux. The outward flux can be calculated by integrating the curl of F over the region bounded by the triangle. The curl of F is given by ∂Q/∂x - ∂P/∂y, where P = x + y and Q = x^2 + y^2.

To find the flux, we integrate the curl over the region R enclosed by the triangle. We can rewrite the triangle as R: 0 ≤ y ≤ x, 1 ≤ x ≤ 1. Parameterizing the region R, we have r(x, y) = (x, y) for 1 ≤ x ≤ 1 and 0 ≤ y ≤ x. The normal vector pointing outward is (-∂y/∂x, ∂x/∂x) = (-1, 1).

Evaluating the flux, we have ∬R (∂Q/∂x - ∂P/∂y) dA = ∫₁¹ ∫₀ˣ (2y - 1 - 1) dy dx = ∫₁¹ (y^2 - y)₀ˣ dx = ∫₁¹ (x^2 - x - (0 - 0)) dx = ∫₁¹ (x^2 - x) dx = [(1/3)x^3 - (1/2)x^2]₁¹ = (1/3) - (1/2) = 5/6.

Therefore, the counterclockwise circulation is 3/2, and the counterclockwise outward flux is 5/6.

To learn more about integrate click here, brainly.com/question/31744185

#SPJ11

A graph to represent this scenario is number line with open circle on the number 89 and line shaded to the right

In Mathematics, the following rules are generally used for writing and interpreting an inequality on a number line:

Let the age of the grandparents be x. Therefore, an inequality which represents the situation described above is given by:

x > 89

Read more on number line here: https://brainly.com/question/29046211

#SPJ1

Answer:

x ≈ 68.8°

Step-by-step explanation:

The length of the arc of a sector is calculated as

arc = circumference × fraction of circle , that is

6 = 2πr × \(\frac{x}{360}\) = 2π × 5 × \(\frac{x}{360}\)  = 10π × \(\frac{x}{360}\) ( multiply both sides by 360 )

2160 = 10πx ( divide both sides by 10π )

68.7549... = x , that is

x ≈ 68.8° ( to 1 dec. place )

Answer:

The percentage increase is 78.72%

Step-by-step explanation:

Here, we want to calculate a percentage increase

We proceed to use the mathematical relation as follows;

Percentage increase = (new value - old value)/old value * 100%

new value is value in 2011 = 252

old value is value in 2006 = 141

Substituting these values, we have;

(252-141)/141 * 100%

= 111/141 * 100%

= 78.72%

From the histogram, we can say that the observations were selected from a normal distribution. We are 95% confident that the population mean ACT score for students taking freshman calculus is between 24.208 and 26.582. The calculus students have a higher average score of 25.395. we are 99% confident that the population standard deviation is between 8.246 and 23.639.

To check whether the observations were selected from a normal distribution, we can create a histogram or a normal probability plot.

From the histogram, it seems plausible that the observations were selected from a normal distribution, as the data appears to be roughly symmetric.

Using the given data, we can calculate a 95% confidence interval for the population mean using the formula

confidence interval = sample mean ± (critical value)(standard error)

The critical value for a 95% confidence interval with 19 degrees of freedom (n - 1) is 2.093.

The sample mean is 25.395, and the standard error can be calculated as the sample standard deviation divided by the square root of the sample size

standard error = 2.630 / sqrt(20) = 0.588

Therefore, the 95% confidence interval is

25.395 ± (2.093)(0.588)

= [24.208, 26.582]

We are 95% confident that students taking freshman calculus is between 24.208 and 26.582.

The university ACT average for entire freshmen that year was about 21. The calculus students have a higher average score of 25.395. Therefore, we can say that the calculus students performed better on the ACT than the average freshman.

To calculate a 99% confidence interval for the population standard deviation, we can use the chi-square distribution. The formula for the confidence interval is

confidence interval = [(n - 1)s^2 / χ^2_(α/2), (n - 1)s^2 / χ^2_(1-α/2)]

where n is the sample size, s is the sample standard deviation, and χ^2_(α/2) and χ^2_(1-α/2) are the chi-square values with α/2 and 1-α/2 degrees of freedom, respectively.

For a 99% confidence interval with 19 degrees of freedom, the chi-square values are 8.906 and 32.852.

Plugging in the values from the sample, we get

confidence interval = [(19)(6.615^2) / 32.852, (19)(6.615^2) / 8.906]

= [8.246, 23.639]

Therefore, we are 99% confident  that the population standard deviation is between 8.246 and 23.639. This interval assumes that the population is normally distributed. If the population is not normally distributed, the interval may not be valid.

To know more about confidence interval:

https://brainly.com/question/29680703

#SPJ4

The correct statement is: provided that the sample size is reasonably large (for any population).

The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

These conditions include a random sample from the population and a sufficiently large sample size (typically, n > 30 is considered large enough).

Therefore, the Central Limit Theorem is important because it allows us to make inferences about the population mean using the normal distribution, even if we do not know the population distribution.

This is useful in many applications of statistics, including hypothesis testing, confidence intervals, and estimating population parameters

Learn more about Central Limit Theorem

brainly.com/question/18403552

#SPJ11

The length of the diameter of circle is 12 feet .

Given equation of circle,

(x - 13)² + (y + 20)² = 36

Now let us see the standard form of equation of circle,

Since, the equation of a circle is,

\({(x-h)^2} + (y - h)^2 = r^2\)

Where,

(h, k) is the center of the circle,

r = radius of the circle,

Comparing it with the standard form  the values of h, k , r are:

Here,

(h, k) = (13, -20)

r²  = 36

r = 6 units,

Now,

Diameter is double than that of radius.

So,

d = 2r

d = 12 feet

Know more about Circles,

brainly.com/question/29266465

#SPJ1

Answer:

£54 and 168.75 mins

Step-by-step explanation:

Answer:

Technically there's an infinite number of equivalent fractions for 2/3 but to list a few 4/6, 6/9, 8/12, 12/18, 18/27.

Step-by-step explanation:

Hope this helps!

-MoCKEry

Answer:

The answer is D) x+7

Step-by-step explanation:

First you have to find multiples of 84 and see if they add up to equal 19.

Evidence against OLS assumption #1, which states that the conditional distribution of the error term has a mean of zero, can be found in options C and D.

These options indicate that the covariance or correlation between intelligence and education is not zero, suggesting a potential violation of the assumption.

OLS assumption #1 states that the conditional distribution of the error term (u) given the explanatory variable (Education) has a mean of zero. In other words, it assumes that there is no systematic relationship between the unobserved factors affecting wage (captured by the error term) and the explanatory variable after accounting for the observed variable (Education).

Option C provides evidence against OLS assumption #1 by stating that the covariance between intelligence and education is not equal to zero. This suggests that there is a systematic relationship between unobserved intelligence and observed education, potentially violating the assumption.

Option D also provides evidence against OLS assumption #1 by stating that the correlation between intelligence and education is not equal to zero. A non-zero correlation implies a systematic relationship between the two variables, indicating a potential violation of the assumption.

On the other hand, options A and B do not provide evidence against OLS assumption #1. A zero correlation (option A) or equal expected values of intelligence and education (option B) do not necessarily contradict the assumption that the conditional distribution of the error term has a mean of zero.

In conclusion, options C and D provide evidence against OLS assumption #1, indicating a potential violation of the assumption based on the covariance or correlation between intelligence and education.

Learn more about covariance  here:

https://brainly.com/question/28135424

#SPJ11

When working together, it will take Angela and Brandon about 3 hours and 12 minutes to paint the school rock.

The answer is 3

Let's first assume that Angela can paint the school rock in x hours, then Brandon would be able to paint the school rock in y hours.Angela’s work rate: \frac{1}{x} of the rock per hour .

So, Angela’s work rate = \($\frac{1}{5.5}$\)and Brandon’s work rate = \frac{1}{7} Working together, Angela and Brandon’s work rate will be: \frac{1}{5.5} + \frac{1}{7} of the rock per hour \($\frac{1}{5.5} + \frac{1}{7}$ = $\frac{0.1818 + 0.1429}{1}$ = $\frac{0.3247}{1}$\) Working together, they will paint the rock in \frac{1}{0.3247} hours = 3.08 hours. Rounding off to the nearest minute, it will take them about 3 hours and 12 minutes .

To know more about work rate visit :-

https://brainly.com/question/14305692

#SPJ11

Answer:

+2 ، +3 ، - 2 ، - 3

Step-by-step explanation:

-12.2÷-6.1=+2

(3(3/7))÷((1(1/7))=+3

16/-8=-2

(-2(2/5))÷(4/5)=-3

Answer:

3 --> 3 3/7 ÷  1 1/7

-2 --> 16 ÷ (-8)

-3 --> -2 2/5 ÷ 4/5

2 -->  -12.2 ÷ (-6.1)

Solution:

Simply plug these numbers into the calculator and receive your answer.

Answer:

Potential

Step-by-step explanation:

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Read more about area here:https://brainly.com/question/27440983

#SPJ1

The relative frequency is solved and the table of values is plotted

Given data ,

The lunch order is given by the 2 sets of dishes as

A = { Sandwich , Pastas }

Now , the sports activities are given by 2 sets as

B = { Volleyball , Swimming }

From the table of values , we get

The relative frequency is solved as

Relative Frequency = Subgroup frequency / Total frequency

The percentage of Swimming ( sandwich ) = 26/36

Swimming ( sandwich ) = 72 %

And , the percentage of Swimming ( pasta ) = 10/36

Swimming ( pasta ) = 28 %

Now , the percentage of total sandwich = 45/70 = 64 %

And , the percentage of total pasta = 25/70 = 36 %

Hence , the relative frequency is solved

To learn more about relative frequency click :

https://brainly.com/question/29739263

#SPJ1

The decimal number that is equivalent to fifty-six hundredths is 0.56.

Therefore, the answer is option b) 0.56.

What's meant by decimal numbers?

Numbers are the figures, which correspond of two corridor videlicet, a whole number part and a fractional part separated by a decimal point. For illustration,12.5 is a decimal number.

What are the different types of decimal numbers?

The two different types of numbers are

Terminating numbers( or)Non-recurring numbers

Non-terminating numbers( or) Recreating numbers

How to convert fragments to decimal numbers?

To convert fragments to numbers, divide the numerator by the denominator value.

To know more about decimal number, visit: brainly.com/question/4708407

#SPJ4

In this case, I will choose the McDonald's QSR menu. Here are three menu items and their respective food cost percentages and contribution margins.

Breakfast: Sausage McMuffinIngredients: English muffin, sausage patty, pasteurized American cheeseFood Cost: $0.50 + $0.35 + $0.15 = $1.00Selling Price: $2.99Food Cost Percentage: ($1.00 ÷ $2.99) x 100 = 33.44%Contribution Margin: $2.99 - $1.00 = $1.99Lunch: Big MacIngredients: Bun, beef patty, lettuce, cheese, pickles, Big Mac sauce, onionsFood Cost: $0.50 + $0.75 + $0.05 + $0.10 + $0.10 + $0.15 + $0.05 = $1.70Selling Price: $4.79

Food Cost Percentage: ($1.70 ÷ $4.79) x 100 = 35.53%Contribution Margin: $4.79 - $1.70 = $3.09Dinner: 10-piece Chicken McNuggetsIngredients: Chicken, breading, cooking oilFood Cost: $2.50 + $0.25 + $0.25 = $3.00Selling Price: $4.49Food Cost Percentage: ($3.00 ÷ $4.49) x 100 = 66.81%Contribution Margin: $4.49 - $3.00 = $1.49I found this information on the McDonald's website and verified it with current prices at a local McDonald's restaurant.

Learn more about GFS here,1. Should GFS market GFS Crane DCIM as Business Continuity or as Green IT solution?

2. What Intellectual Property (IP) w...

https://brainly.com/question/31004352

#SPJ11

True. The coefficient of determination (R²) measures the proportion of the variation in the dependent variable that is explained by the regression model.

In statistics, the coefficient of determination (denoted R² or r² and pronounced "R squared") is used in the context of statistical models whose main purpose is either the prediction of future results or the testing of hypotheses, on the basis of other related information.

It is also known as the multiple correlation coefficient or the multiple determination coefficient. It is the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

In a simple regression model, this is the square of the correlation between the dependent variable and the single independent variable.

Hence, the given statement is True.

To know more about the "regression model": https://brainly.com/question/25987747

#SPJ11

Equation: 80 - 6.75x = 19.25

Sandwiches: 9

(x=9)

Answer:

answer by your own

Step-by-step explanation:lol

Answer:

D.

Step-by-step explanation:

The first step is to subtract 2 on both sides, so

3(y - 5) + 2 - 2 = 5 - 2

3(y - 5) = 3

Next, multiply by or distribute the 3 on the left side.

3y - 15 = 3

Then, add 15 on both sides.

3y - 15 + 15 = 3 + 15

3y = 18

Finally, divide by 3 on both sides.

3y/3 = 18/3

y = 6

The volume of the solid can be calculated by integrating the area of the cross section over the entire height of the solid.

The washer method is a way to calculate the volume of a solid that is created when a region is rotated about a certain line.

Here you find the area of this cross section, and multiply it by the circumference of a circle with the same radius as the cross section.

To use the washer method to find the volume of the solid created when the region bounded by

=> y = 12x², y=0, and x=2 is rotated about the line y=3,

we first need to find the cross section of the solid at different heights along the line of rotation.

To do this, we need to find the points where the plane perpendicular to the line of rotation intersects the original region. This is done by finding where the equation of the plane and the equation of the original region intersect.

Next, we find the area of the cross section and multiply it by the circumference of a circle with the same radius.

Finally, we add up all of these washer volumes to find the total volume of the solid.

To know more about volume here.

https://brainly.com/question/11168779

#SPJ4

The rules AAS, ASA, SSS and SAS are congruence rule of triangle  and the each rules has been explained

The rules AAS, ASA, SSS and SAS are congruence rule of triangle

SSS rule is side-side-side rule, it states that if three sides of the one triangle and three sides of the other triangles are equal, then both triangles are congruent

SAS rule is side-angle-side rule, it states that if two sides and one included angles between the sides of the one triangle is equal to  the two sides and one included angles between the sides of the other triangle, then both triangles are congruent

ASA rule is angle-side-angle rule, it states that if two angles and one included side between the angle of the one triangle is equal to the two angles and one included sides between the angles of the other triangle, then both triangles are congruent

AAS rules is angle-angle-side rule, it states that if two angles and one non included sides of the one triangle is equal to the two angles and one non included sides of the another triangle, then both triangles are congruent

Therefore, the AAS, ASA, SSS and SAS are the rules of congruence of the triangle

Learn more about congruence rule here

brainly.com/question/29548914

#SPJ4