Six guests invited by Mr. And Mrs. Bernardo to dinner. They are to be all
seated around a
circular table. How many ways can they be seated?
1. If the couple must sit together?
2. If the couple must not be together?

Nul(A) = Nul(B) , Col(A) = Col(B) in integer matrices.

Describe matrix using an example?

A matrix is a collection of numbers that have been put in rows and columns to make a rectangular array. The entries of the matrix are the numbers, which are referred to as its elements.

                                 In addition to many other areas of mathematics, matrices have extensive applications in the fields of engineering, physics, economics, and statistics.

The null space of any matrix A consists of all the vectors

 X  such that Ax = 0

And the column space of a matrix A is the span of its column vectors.

Let  A = [tex]\left[\begin{array}{ccc}1&0&0 \\0&1&0\\0&0&1\end{array}\right][/tex]

Therefore, Nul(A) = {(0,0,0,w ) w∈ Z }

 Col(A) = span{ (1,0,0), (0,1,0) , (0,0,1) }

By using definition of Null space of matrix and column space of matrix.

 Let B = [tex]\left[\begin{array}{ccc}1&1&0\\0&1&0\\0&0&1\end{array}\right][/tex]        

Nul(A) = {(0,0,0,w ) w∈ Z }

 Col(A) = span{ (1,0,0), (0,1,0) , (0,0,1) }

Hence Nul(A) = Nul(B) , Col(A) = Col(B)

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The required probability that a randomly selected lid will fit on a randomly selected cup is 0.9772, or 97.72%.

Normal distributions can be altered to standard normal distributions by the formula:

Z = (X - μ)/σ

The difference in diameter between the lid and cup, D = L - C, is also a normal distribution with mean μ(D) = μ(L) - μ(C) = 3.98 - 3.96 = 0.02 inches and standard deviation σ(D) = √(σ² (L)+ σ²(C)) = 0.03 inches.

The probability that a randomly selected lid will fit on a randomly selected cup is the probability that D is between 0 and 0.06 inches. To find this probability, we can standardize D using the z-score formula and find the corresponding area under the standard normal curve.

Let z = (D - μ) / σ.
Then, the required probability is,
P(0 < D < 0.06) = P(0 < z < (0.06 - 0.02) / 0.03) = P(0 < z < 2).

We can use a standard normal table or a calculator to find the area under the standard normal curve between 0 and 2. This area represents the required probability. For example, using a standard normal table, we can find that P(0 < Z < 2) = 0.9772.

Therefore, the probability that a randomly selected lid will fit on a randomly selected cup is 0.9772, or 97.72%.

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The Probability that all four of the light bulbs work is 0.004 approx.

The probability that all four light bulbs work can be calculated by taking the product of the probability that each individual light bulb works. If each light bulb works independently of the other light bulbs, then the probability that all four light bulbs work is:

P(all 4 bulbs) = P(bulb 1) * P(bulb 2) * P(bulb 3) * P(bulb 4)

P(all 4 bulbs) = 0.25 * 0.25 * 0.25 * 0.25

P(all 4 bulbs) = 0.25^4

P(all 4 bulbs) = 0.00390625

So, the probability that all four light bulbs work is 0.00390625 or approximately 0.004.

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Answer:

28 lawns

Step-by-step explanation

If there is 7 lawns for 4 hours there will be 14 lawns in 8 hours. and 28 lawns in 16 hours

Answer:

Step-by-step explanation:20

factorials with algebraic expressions still be correct if you substitute the letter with a number.

Factorial is a mathematical operation denoted by the exclamation mark (!). It is used to find the product of all positive integers from 1 to a given number. For example, the factorial of 4 (written as 4!) is:

4! = 4 × 3 × 2 × 1 = 24

Given by the question.

if you substitute a numerical value for the algebraic expression, the resulting factorial can be computed and evaluated as a numerical expression.

For example, consider the factorial expression n! where n is an algebraic expression such as n = x + 2. Substituting a numerical value for x, say x = 3, we get n = 3 + 2 = 5, and hence we can compute 5! = 5 x 4 x 3 x 2 x 1 = 120.

Similarly, if we have an expression like (n+1)! /(n-1)! where n is an algebraic expression, we can substitute a numerical value for n and compute the resulting value. For example, if we substitute n = 4, we get (4+1)!/(4-1)! = 5!/3! = (5 x 4 x 3 x 2 x 1)/(3 x 2 x 1) = 60.

It's important to note that substituting numerical values for algebraic expressions only works if the resulting expression is well-defined and doesn't lead to any undefined or indeterminate forms (such as division by zero).

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The circumcenter of the triangle is (-3, -4), units.

The circumcenter is the intersection point of the perpendicular bisectors of sides of a triangle. It is the Centre of a triangle's circumcircle.

For a right-angled triangle, the circumcenter lies on the hypotenuse.

The middle of the horizontal length of the triangle = - 3

The  middle of the vertical length of the triangle = - 4

The circumcenter of the triangle is located at (x, y ) = ( -3, -4 )

Thus, the circumcenter of the triangle is determined from the interception point of the horizontal length and vertical length.

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The prime factorization of 35 is 5 * 7

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

Number = 35

Express 35 as the product of its factors

So, we have the following representation

Number = 5 * 7

None of the factors 5 and 7 can be further simplified

This means that the prime factorization of 35 is 5 * 7

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164 pounds is equal to 74.389 kilograms (kg). To convert pounds to kilograms, you can use the conversion factor of 0.45359237, which is the number of kilograms in one pound.

To convert 164 pounds to kilograms, you can use the conversion factor of 0.45359237, which represents the number of kilograms in one pound. Multiplying 164 pounds by this conversion factor gives the result in kilograms. Using this method, 164 pounds is equivalent to 74.389 kilograms. This conversion is useful in many situations, such as when traveling to countries that use the metric system, or when working with scientific measurements that use metric units. Understanding the relationship between pounds and kilograms can help to make conversions easier, and allow for more accurate and consistent measurements across different systems of measurement.

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The equation of the circle that models the circumference of the circular area the bees were foraging in is given as follows:

(x - 3)² + (y - 7)² = 41.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

A beehive is located at (3, 7), hence the center is located at (3,7), thus:

(x - 3)² + (y - 7)² = r².

The farthest patched was located at (-1,2), hence the radius is obtained as follows:

(-1 - 3)² + (2 - 7)² = r²

r² = 41.

Hence the equation is:

(x - 3)² + (y - 7)² = 41.

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Analyzing a distribution's form and the placements of its mean, median, and mode in relation to one another can reveal its symmetry.

Therefore by analyzing a distribution's form and the placements of its mean, median, and mode in relation to one another can reveal its symmetry. The following techniques can be used to determine a distribution's symmetry: Examining a distribution's histogram, box plot, or probability density function visually is one technique to identify a distribution's symmetry. If the distribution's shape appears to be symmetrical, it probably is. The subjective nature of this approach means that it might not give an accurate indication of symmetry.

Skewness is a measurement of a distribution's asymmetry. It may be calculated manually or with the aid of statistical tools. Examining a distribution's histogram, box plot, or probability density function visually is one technique to identify a distribution's symmetry. If the distribution's shape appears to be symmetrical, it probably is. Skewness is zero for a symmetric distribution. When the skewness is positive, the distribution is skewed to.

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Answer:

10y - 3

Step-by-step explanation:

(y + 9y) + (-10 - 3)

(1 + 9) x y + (-10 - 3)

10y - 13

Answer: To compare the costs between the two suppliers, we need to find the total cost of 83 bushes and 22 trees from each supplier.

For Pinedale Plants:

The first order was for 10 bushes and 5 trees, so the cost per bush is $393.6 / 10 = $39.36.

The second order was for 5 bushes and 2 trees, so the cost per bush is $177.32 / 5 = $35.464.

To find the average cost per bush from Pinedale Plants, we can take the average of the two costs: ($39.36 + $35.464) / 2 = $37.412

The total cost from Pinedale Plants for 83 bushes would be 83 * $37.412 = $3108.976

The total cost from Pinedale Plants for 22 trees would be 22 * $35.464 (since the cost per tree was not specified), which is $777.75

The total cost from Pinedale Plants for 83 bushes and 22 trees would be $3108.976 + $777.75 = $3886.726

For Sierra Shrubs:

The cost per bush from Sierra Shrubs is $18.27

The total cost from Sierra Shrubs for 83 bushes would be 83 * $18.27 = $1510.01

The cost per tree from Sierra Shrubs is $41.96

The total cost from Sierra Shrubs for 22 trees would be 22 * $41.96 = $923.12

The total cost from Sierra Shrubs for 83 bushes and 22 trees would be $1510.01 + $923.12 = $2433.13

So, we can see that the total cost from Sierra Shrubs for 83 bushes and 22 trees is lower than the total cost from Pinedale Plants. The company would save $3886.726 - $2433.13 = $1453.596 by ordering from Sierra Shrubs.

Step-by-step explanation:

According to hing theorem, the following inequalities describe each triangle:

According to Euclidean geometry, the hing theorem states that if two triangles with two pairs of congruent sides and the former triangle has larger internal angle, then the third side of the former triangle is longer than the third side of the latter triangle.

Mathematically speaking, the relationship between the third can be expressed in terms of inequalities. Now we proceed to express the inequalities in terms of variable x for each case below:

The letter e has been eliminated from hing[e] due to profanity detector.

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The initial value (initial fee) for the picnic is $40. Then the correct options are A, B, and D.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

Let 'x' be the number of people and 'y' be the total cost.

From the table, the two points are (6, 52) and (9, 58). Then the equation of the line is given as,

(y - 52) = [(58 - 52) / (9 - 6)](x - 6)

y - 52 = 2x - 12

y = 2x + 40

The initial value (initial fee) for the picnic is $40. Then the correct options are A, B, and D.

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The values of x is 13.42, y is 12 and z is 26.83 for right angle triangle ABC shown below.

The Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides, is a fundamental property of right triangles.

By the figure apply Pythagorean theorem in right angle ΔABC;

x² + z² = (24+6)² = 30²

x² + z² = 900         (eq. 1)

Apply Pythagorean theorem in right angle ΔAEB;

y² + 24² = z²

z² - y² = 576          (eq. 2)

Apply Pythagorean theorem in right angle ΔAEC;

y² + 6² = x²

x² - y² = 36            (eq. 3)

subtract eq. 2 and 3; then we get,

z² - x² = 540      (add this eq. with eq. 1)

2z² = 1440

z = √720  = 26.83

put in eq. 1

x² + 720 = 900

x = √180 = 13.42  

put x value in eq. 3

180 - y² = 36

y = 12

Therefore, the values of x is 13.42, y is 12 and z is 26.83

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Multistage sampling is a probability sampling technique that involves sampling in stages or multiple steps. In this technique, a large population is divided into smaller subgroups, and then a random sample is selected from each subgroup.

Here is an example of multistage sampling:

Suppose we want to conduct a study on the prevalence of a certain disease among high school students in a particular country. The population of high school students in the country is very large, so it is not feasible to sample all of them. Instead, we can use multistage sampling to select a representative sample.

In the first stage, we randomly select a certain number of schools from different regions of the country. Let's say we select 20 schools.

In the second stage, we randomly select a certain number of classes from each of the selected schools. Let's say we select 2 classes from each of the 20 schools, resulting in a total of 40 classes.

In the third stage, we randomly select a certain number of students from each of the selected classes. Let's say we select 10 students from each of the 40 classes, resulting in a total of 400 students.

This process of selecting a sample in stages is an example of multistage sampling. By selecting schools, classes, and students in a random and systematic way, we can obtain a representative sample of high school students in the country, which can be used to estimate the prevalence of the disease.

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Answer:is this real

Step-by-step explanation:

1 =727

Answer:

B isa the answer for me it might be wrong for you or switch them

Step-by-step explanation:

Answer:

Step-by-step explanation:

Based on the information given, we can calculate the change in the depth of the river between the years 1846, 1847, and 1848.

Change in depth between 1846 and 1847:

The depth of the river dropped from 5 feet in 1846 to 4.9 feet in 1847. The change in depth can be calculated as:

Change in depth = 4.9 - 5 = -0.1 feet

So, the depth of the river dropped by 0.1 feet between 1846 and 1847.

Change in depth between 1847 and 1848:

The depth of the river rose from 4.9 feet in 1847 to 6.4 feet in 1848. The change in depth can be calculated as:

Change in depth = 6.4 - 4.9 = 1.5 feet

So, the depth of the river increased by 1.5 feet between 1847 and 1848.

A unit of measurement which is equal to one thousands meters is known as one kilometers.

Therefore, the given units of measurement equal to one thousand meters is called one - kilometers.

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[tex]\dfrac{2}{3}x=6[/tex]

[tex]\dfrac{\frac{2}{3}x}{\frac{2}{3}}=\dfrac{6}{\frac{2}{3}}\\\\x=\dfrac{6}{\frac{2}{3}}\\\\x=6\div\dfrac{2}{3}[/tex]

[tex]x=6\times\dfrac{3}{2}\\\\x=\dfrac{18}{2}\\\\x=9[/tex]

x = 9

The side length QR = 34 derived using the Pythagoras rule, and the following are the values of the trigonometric ratio:

sin Q = 30/34, cos Q = 16/34 , tan Q = 30/16, sin Q = 30/34, cos Q = 16/34, and tan Q = 30/16

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

QR² = 16² + 30²

QR = √(256 + 900) {take square root of both sides}

QR = √1156

QR = 34

since we have QR = 34, RS = 30, and SQ = 16, then:

Considering the angle Q for the right triangle;

sin Q = 30/34 {opposite/hypotenuse}

cos Q = 16/34 {adjacent/hypotenuse}

tan Q = 30/16 {opposite/adjacent}

Considering the angle R for the right triangle;

sin R = 16/34 {opposite/hypotenuse}

cos R = 30/34 {adjacent/hypotenuse}

tan R = 16/30 {opposite/adjacent}

Therefore, the side length QR = 34 derived using the Pythagoras rule, and the following are the values of the trigonometric ratio:

sin Q = 30/34, cos Q = 16/34 , tan Q = 30/16, sin Q = 30/34, cos Q = 16/34, and tan Q = 30/16.

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Answer:

ky - c

Step-by-step explanation:

K(Y) - C

(K*Y) - C

A yearly salary of $47,000 is equivalent to an hourly rate of approximately $22.60 per hour.

To convert a yearly salary to an hourly rate, you need to divide the annual salary by the number of working hours in a year.

Assuming a typical workweek of 40 hours and 52 weeks in a year, the total number of working hours in a year is:

40 hours/week x 52 weeks/year = 2,080 hours/year

To calculate the hourly rate for a yearly salary of $47,000, you can divide the annual salary by the total number of working hours in a year:

$47,000 / 2,080 hours = $22.60 per hour

Therefore, a yearly salary of $47,000 is equivalent to an hourly rate of approximately $22.60 per hour.

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The value of y is -2.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

2 (y + 6) = 8

Using the distributive operation of multiplication over addition.

2y + 12 = 8

2y = 8 - 12

2y = -4

y = -2

Thus,

y = -2.

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The statements that are not characteristics of a normal curve are III, IV, and VI. The answer is B.

A normal curve is a bell-shaped probability distribution that is commonly used in statistics. It has several key characteristics that make it useful in modeling real-world data. These include the fact that the mode and median occur at the mean, the curve is symmetric about the mean, and the total area under the curve and above the horizontal axis is equal to 1.

In addition, the normal curve is asymptotic to the horizontal axis on both sides. However, not all normal curves are asymptotic to the horizontal axis on both sides, as this is only true for curves with a finite standard deviation.

Finally, the probability that a normal random variable is equal to a specific discrete value is always zero, since the normal variable is continuous, and the probability that the variable is between two values is given by the area under the curve between those values and the horizontal axis.

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In the given figure , the measure of angle p is 41 degrees.

A quadrilateral is a closed figure that has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

It is given that the kite is shares a side with an equilateral triangle to form a new quadrilateral.

The side of kite which is attatched to triangle contains an angle of 79 degree.

the other end of side which is attatched to the triangle contains angle of 120 degree because it is attatched to the side of triangle which makes a straight line and the triangle is having each angle of 60 degrees.

So, the angle opposite to it will also be of 120 degrees.

Now in the kite, the angles are,

79+120+p+120=360

p=360-319

p=41 degrees

Hence, the measure of angle p is 41 degrees.

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