prove that a square matrix and its transpose have the same characteristic polynomial, and therefore the same set of eigenvalues. g

The appropriate distribution to answer questions about the New York Lotto is the hypergeometric distribution, which is used to calculate the probability of a certain number of successes in a sample of items drawn without replacement from a population.

The New York Lotto is a lottery game where participants select six numbers from a set of 51 numbers, 1 to 51. Then, six balls are randomly drawn from a barrel without replacement to determine the six winning numbers. To answer questions about the probability of various outcomes in this game, the appropriate probability distribution is the hypergeometric distribution. This distribution is used to calculate the probability of a certain number of successes in a sample of items drawn without replacement from a population. In the case of the New York Lotto, the population is the set of 51 numbers from 1 to 51, and the sample is the six numbers selected by the participant. The hypergeometric distribution can be used to calculate the probability of matching exactly two of the winning numbers.

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The Point-Slope equation is Z = 15X - 19Y + 204.

What is the slope-point form?

The slope-point form of a line in 3-dimensional space is a equation of the form:

Z = m_x (X - X_0) + m_y (Y - Y_0) + Z_0

where (X_0, Y_0, Z_0) is a point on the line, m_x is the x-slope, and m_y is the y-slope.

Given:

point (2, -12, 4) and x-slope 15 and y-slope -19, we can use the point-slope form to find the equation of the plane:

Z = 15 (X - 2) - 19 (Y + 12) + 4

Hence, the point-slope equation of the plane passing through the point (2, -12, 4) and having x-slope 15 and y-slope -19 is:

Z = 15X - 30 - 19Y + 228 + 4

Z = 15X - 19Y + 204

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The simplified form of 6 log₃x - 7 log₃y + 4 log₃z is  log₃{(x⁶z⁴)/y⁷}.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6.

The simplification of the provided logarithmic expression can be done as follows:-

6 log₃x - 7 log₃y + 4 log₃z,

= log₃x⁶ - log₃y⁷ + log₃z⁴ {Using the Power law}

= log₃x⁶ + log₃z⁴ - log₃y⁷

= log₃x⁶z⁴ - log₃y⁷ {Using the Product law}

= log₃{(x⁶z⁴)/y⁷} {Using the Quotient law}.

Hence, the simplified form of 6 log₃x - 7 log₃y + 4 log₃z is  log₃{(x⁶z⁴)/y⁷}.

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Answer:

21 miles per hour

Step-by-step explanation:

2x(5x + 1) / (4x - 1) is the final expression.

Option D is the correct answer.

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,

(4x³ - 12x²) / (4x² + 7x - 2) / (2x² - 6x) / (5x² + 11x + 2)

= (4x³ - 12x²) x (5x² + 11x + 2) / (4x² + 7x - 2) x (2x² - 6x)

Now,

(4x³ - 12x²) = 4x² (x - 3) _____(1)

And,

(5x² + 11x + 2)

Middle term factorizing

= 5x² + (10 + 1)x + 2

= 5x² + 10x + x + 2

= 5x (x + 2) + 1(x + 2)

= (x + 2) (5x + 1) ______(2)

And,

(4x² + 7x - 2)

Middle term factorizing

= 4x² + (8 - 1)x - 2

= 4x² + 8x - x - 2

= 4x(x + 2) - 1(x + 2)

= (4x - 1) (x + 2) ______(3)

And,

(2x² - 6x) = 2x (x - 3) ______(4)

From (1), (2), (3), and (4) we get,

(4x³ - 12x²) x (5x² + 11x + 2) / (4x² + 7x - 2) x (2x² - 6x)

= [ 4x² (x - 3) x (x + 2) (5x + 1) ] / [ (4x - 1) (x + 2) x 2x(x - 3) ]

(x + 2) and (x - 3) gets canceled.

= [4x² (5x + 1)] / [(4x - 1) 2x]

= 2x(5x + 1) / (4x - 1)

Thus,

2x(5x + 1) / (4x - 1)

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The value of the side lengths x and y are 29.4 units and 17 units

From the information given, we have that;

Using the cosine identity'

sin 30 = y/34

find the value

0. 5000 (34) = y

Multiply

y = 17 units

Using the cosine identity

cos 30 = x/34

multiply

x = 34(0.8660)

x = 29. 4 units

Hence, the values are  17 units and 29. 4 units

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Answer:

Supernova

Step-by-step explanation:

A supernova is a powerful and luminous explosion of a star, which is what the sun is.

Answer:

pop'n = 358000*(1-0.25%)^t

Step-by-step explanation:

pop'n = 358000

decreasing rate = 0.25%

after t years

pop'n = 358000*(1-0.25%)^t

Answer:

The two angles are 32 degrees and 48 degrees.

Step-by-step explanation:

If one angle of a triangle is 100 degrees, then the sum of the other two angles is 80 degrees (180 - 100). If the magnitude of the other two angles is in the ratio 2:3, then we can call the first angle 2x and the second angle 3x. The sum of these two angles is 5x, so 5x = 80, and x = 16. So, the two angles are 2x = 32 degrees and 3x = 48 degrees.

Answer: Final Balance is $11,591.87 and the total compound interest is $1,731.87.

Step-by-step explanation:

Therefore, the values of x that make the equation distance between (11,6) and (x,-9) equal to 17 are x = 19 and x = 3.

The formula y=mx+b is used to draw a simple regression graph. The inclination is B, and the y-intercept is m. It is frequently referred to simply as a "simple method combining many variables," despite the fact that the section before it is divided into distinct sections. Bivariate linear equations have two variables. For problems involving linear equations in applications, there are no proven solutions. Y=mx+b, also known as mx+b, provides a number of straightforward formulae.

Here,

Using the distance formula:

sqrt((x - 11)^2 + (-9 - 6)^2) = 17

Simplifying:

sqrt((x - 11)^2 + 225) = 17

Squaring both sides:

(x - 11)^2 + 225 = 289

(x - 11)^2 = 64

Taking the square root:

x - 11 = ±8

x = 11 + 8 or x = 11 - 8

x = 19 or x = 3

Therefore, the values of x that make the equation distance between (11,6) and (x,-9) equal to 17 are x = 19 and x = 3.

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The quotient and remainder, when written as partial fractions, of 8x²³-21²-67x-24 is represented by 2x²-x-21.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

given that,

Which expression represents the correct form for the quotient and remainder?

(8x³-21²-67x-24) = (2x²-x-21) + (6x¹-42)

This is done by dividing 8x²³-21²-67x-24 by 2x² and using long division to find the remainder.

The result of the division is a quotient of 4x²-33x+12 and a remainder of 2x²-x-21.

The remainder is the expression which represents the quotient and remainder, written as partial fractions, of 8x²³-21²-67x-24.

To illustrate this further, we can break down the long division process into steps. First, divide 2x² into 8x²³.

The result is 4x².

Then, subtract 4x² from 8x²³ to get the remainder of 4x³.

Next, divide 4x² into 21².

The result is 33x.

Then, subtract 33x from 4x³ to get the remainder of 4x²-33x.

Finally, divide 4x²-33x into 67x.

The result is 12. Subtract 12 from 4x²-33x to get the remainder of 2x²-x-21.

This remainder is the expression which represents the quotient and remainder, written as partial fractions, of 8x²³-21²-67x-24.

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Angelique needs 3 8/15 hours to completely build the fence.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Angelique builds a fence and she can build 5/8 of the fence in 2 5/6 = 17/6 hours.

We know a number multiplied to its reciprocal is 1.

Therefore, The amount of time Angelique needs to complete the fence is,

(5/8)×(8/5) the complete fence in (17/6)×(8/5) hours.

= 136/30 hours.

= 3 16/30 hours.

= 3 8/15 hours.

Q. Angelique builds a fence. After working for 2 5/6 hours, she has built 5/8 of the fence, how much time she needs to complete the fence?

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Answer:

52

Step-by-step explanation:

my boy its 52 she said times it means multiply

Answer:

Step-by-step explanation:

9/12 + 10/12

How the ffffffffffffffffffffffffffffffffffffffffff

Answer:

x = 9

Step-by-step explanation:

x + 3 = 2x - 6
3 + 6 = 2x - x
9 = x
x = 9

Hope this helped have a great day!

Answer:

2

Step-by-step explanation:

10-5=5.....the ones she ate

5-2=3 .... the 2 she gave to Mary

3-1 =2.....the one she threw away

2 mangoes!

10 - 5 = 5

5 - 2 = 3

3 - 1 = 2

All other things being equal, outliers tend to have a greater effect on the value of the mean, as compared to the value of the median. The given statement is true.

What is the mean and median?

Outliers are values that are significantly different from the other values in a data set, and their presence can greatly affect the value of measures of central tendency, such as the mean and the median.

The mean is a measure of central tendency that is calculated as the sum of all the values in a data set divided by the number of values. The presence of outliers can greatly affect the mean because outliers can have a large impact on the sum of the values in the data set. For example, if a data set has a few very large outliers, the mean will be pulled up to be much higher than the median, which represents the midpoint of the data set.

On the other hand, the median is a measure of central tendency that is calculated as the middle value of a data set when the values are arranged in order. The median is not as sensitive to outliers as the mean because outliers do not affect the median unless the number of outliers is so large that it changes the value of the middle value.

Hence, all other things being equal, outliers tend to have a greater effect on the value of the mean than on the value of the median.

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Answer: 63 sedans

Step-by-step explanation:

21 * 3

The optimum sampling strategy is (iii), which is listed below.

By selecting a student's initial name from each page of the cam pus phone book, you may measure the heights of the chosen pupils.

Sampling is a technique for selecting a small group of people or a subset of the population in order to make generalizations and estimate the features of the population. In order to acquire relevant information without studying the entire society, researchers commonly use a variety of sampling approaches in market research.

To ascertain the average height of all students at a certain institution and guarantee that the result is statistically reliable, the sampling process must be applied.

a. Measure the heights of 50 students found in the gym during basketball intramurals.

This approach is not ideal since you would only sample basketball players while leaving all other university students out; hence, your sample would not be representative of all students, simply those who play basketball.

b. Measure the heights of all engineering majors.

This approach is flawed since the sample exclusively includes engineering majors, leaving out students studying other courses.

c. Measure the heights of the students selected by choosing the first name on each page of the campus phone book.

This strategy, which is the finest of the three, allows you to select students independent of the sport or subject they are pursuing. It is more representative of the university student population.

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The p-value for the two-tailed test is 2 mincdf(x), 1 - cdf (x) because a study team believes that less than 48% of Americans are affected.

A type of data hypothesis known as both a null hypothesis claims that a certain collection of data has no statistically significant results. The viability of hypotheses be evaluated using sample. Sometimes refers to as "zero," and symbolized as H0. The premise made by the researchers is that there is a correlation between the variables. The h0, on the other hand, says that such an association doesn't quite exist. Despite its inability to seem significant, the null hypothesis is a crucial component of a study.

given

Calculating the p-value requires knowledge of the distribution of your test statistic under the assumption that the null hypothesis is true.

Cdf as the p-value for the left-tailed test (x).

Right-tail test: p-value = 1 - cdf (x).

The two-tailed test's p-value is 2 mincdf(x), 1 - cdf (x).

The p-value for the two-tailed test is 2 mincdf(x), 1 - cdf (x) because a study team believes that less than 48% of Americans are affected.

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The center of dilation is (1, -4).

Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.

From the given graph,

Vertices of RSTV are R(1, -4), S(2, 0), T(1, 2) and V(-2, 1).

Vertices of R'S'T'V' are R'(1, -4), S'(4.5, 2), T'(2, 5) and V'(-2.5, 3.5).

Here, the center of dilation is (1, -4).

The transformation is enlargement by scale factor 1.5

Therefore, the center of dilation is (1, -4).

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Answer:

Step-by-step explanation:

Cost of goods available for sale:

Starting inventory: 150 units * $6/unit = $900

Purchase on June 1: 450 units * $7/unit = $3150

Purchase on June 23: 400 units * $8/unit = $3200

Total cost: $900 + $3150 + $3200 = $7450

Moving Average Unit Cost:

June 1: $7450 / (150 + 450) = $7/unit (rounded to 3 decimal places)

June 12: $7450 / (150 + 450 + 400) = $7.36/unit (rounded to 3 decimal places)

June 15: $7450 / (150 + 450 + 400 + 500) = $7.51/unit (rounded to 3 decimal places)

June 23: $7450 / (150 + 450 + 400 + 500) = $7.51/unit (rounded to 3 decimal places)

June 27: $7450 / (150 + 450 + 400 + 500 + 420) = $7.43/unit (rounded to 3 decimal places)

Cost of ending inventory using perpetual inventory system:

FIFO: $7.51/unit * 80 units = $604 (rounded to 3 decimal places)

LIFO: $7/unit * 80 units = $560 (rounded to 3 decimal places)

Average Cost: $7.43/unit * 80 units = $594.4 (rounded to 3 decimal places)

Taking the quotient between the total distance and the gallons consumed we can see that:

Mpg = 37 miles per gallon.

It is just given by the quotient between the number of miles traveled and the number of gallons used.

We know that at the start the odometer reads 69247 miles and at the end the odometer reads 69765 miles, taking the difference we can see that the total distance traveled is:

69765 mi - 69247 mi = 518 mi

And you consumed 14 gallons of gas, then the miles per gallon is:

Mpg = 518mi/14 gal = 37 miles per gallon.

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Answer:

Gross salary =G

Number of worked hours =x

Dollar per hour =$12

substitute the given data into the gross salary formula and simplify.

Gross salary = (number of worked hours)

G =(x) (12)

G =12x

Therefore, G(x) =12x

Hence the function is G(x) = 12x

The regression equation is Y = 95.0 + 0.84X.The regression line is a mathematical model that is used to predict the value of a dependent variable (Y) based on the value of an independent variable (X).

In this case, the regression line is used to predict Y from X using the following data: X = 10, 20, 30, 40, 50, 60 and Y = 111, 109, 110, 94, 92, 93. By using a regression analysis tool such as StatKey, we can calculate the regression equation that best fits this data. The regression equation is Y = 95.0 + 0.84X, where 95.0 is the intercept and 0.84 is the slope. This equation can be used to make predictions about the value of Y for a given value of X. The rounded answer for the intercept is 95.0 and the rounded answer for the slope is 0.84.

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Answer:

B. 9[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Rewriting the two fractions in the expression:

=[tex]\frac{[(8)(2)]+1}{8} + \frac{[(8)(7)]+3}{8}[/tex]

=[tex]\frac{17}{8} + \frac{59}{8}[/tex]

Since the denominators of both the fractions is the same, then the denominator of the resulting simplified fraction will also be the same. In addition, everything written in the numerator level will be copied down as it is:

=[tex]\frac{17 + 59}{8}[/tex]

=[tex]\frac{76}{8}[/tex]

Divide the numerator and denominator by the Highest Common Factor '4':

= [tex]\frac{19}{2}[/tex]

Apply Long Division since:

Choose the highest quotient to be multiplied by 2 to give a number closest to 19 but still less than 19. The quotient turns out to be 9. The remainder is 1

∴ Sum of the expression = 9[tex]\frac{1}{2}[/tex]