*p. 7 2 ant is hese cases, find 1 Sec. 7.2 Cyclic Decompositions and the Rational Form Find the characteristic polynomial for T. Consider the cases a = b = 1;c = b = 0; a = 0,6 = 1. In each minimal polynomial for T and non- zero vectors Qi, . . . , Q, which satisfy the conditions of Theorem 3. 11. Prove that if A and B are 3 x 3 matrices over the field F, a necessary and sufficient condition that A and B be similar over F is that they have the same characteristic polynomial and the same minimal polynomial. Give an example which shows that this is false for 4 X 4 matrices. 12. Let F be a subfield of the field of complex numbers, and let A and B ben Xn matrices over F. Prove that if A and B are similar over the field of complex num- bers, then they are similar over F. (Hint: Prove that the rational form of A is the ama hather A is yiewed as a matrix over F or a matrix over C; likewise for B.)

Answer:

2 1/4kms = how many meters?

Step-by-step explanation:

You're welcome.

Answer:

M = 2250

Step-by-step explanation:

First of all solve the mixed number which is 9/4 and as a decimal it is 2.25

Now as the meters it is....

2250!!!!

Hope this helps, have a great day!!!!!!

(Multiply 2.25 times 1000 and that gives you 2250)

Answer

58.3 in^3

Explanation

The volume of a square base pyramid is given by:

A sample size of at least 34 consumers is necessary to generate a 95% confidence interval for the percentage of customers who alter their plans with a margin of error of 0.12.

To estimate the sample size needed for a 95% confidence interval with a margin of error of 0.12, we can use the formula:

n = (Z^2 * p* q) / E^2

Where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (95% confidence level corresponds to a Z-score of approximately 1.96)

p = proportion of clients who changed their vacation plans in the preliminary study (19/132 ≈ 0.144)

q = complement of p (1 - p)

E = desired margin of error (0.12)

Plugging in the values, we can calculate the required sample size:

n = \((1.96^2 * 0.144 * (1 - 0.144)) / 0.12^2\)

n ≈ (3.8416 * 0.144 * 0.856) / 0.0144

n ≈ 0.4899 / 0.0144

n ≈ 33.89

Rounding up to the nearest whole number, the estimated sample size needed is approximately 34.

Therefore, to obtain a 95% confidence interval for the proportion of customers who change their plans with a margin of error of 0.12, a sample size of at least 34 clients is required.

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Answer:

Step-by-step explanation:

what is questio ?

Answer:

∠ABD = 48

Step-by-step explanation:

use symbolab

(x+15)=(4x-12)

x+15-15=4x-12-15

x=4x-27

x-4x=4x-27-4x

-3x=-27

divide both sides by 3 and you get x=9

then put 9 in to replace x

((9) + 15) + (4 (9) - 12)

=24 + (4 (9) - 12)

= 24 + 24

=48

ur welcome

Answer:

A

Step-by-step explanation:

The population decreased by 5,400 people from 2015 to 2020.

Also known as population decline, means the reduction in a human population size

Population in 2015 = Population in 2010 + Growth from 2010 to 2015

Population in 2015 = 167,000 + (8% of 167,000)

Population in 2015 = 167,000 + 13,360

Population in 2015 = 180,360

Population in 2020 = Population in 2015 - Decrease from 2015 to 2020

Population in 2020 = 180,360 - (3% of 180,360)

Population in 2020 = 180,360 - 5,411.8

Population in 2020 = 174,948.2

The population decrease from 2015 to 2020 is:

= Population in 2015 - Population in 2020

= 180,360 - 174,948.2

= 5,411.8

= 5,400 to nearest 100 people.

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The remaining eigenvalue is λ = -0.007. Thus, the eigenvalues of A are:
X1 = 0
X2 = 0
X3 = -0.007
Arranging them in ascending order, we get:
X1 = -0.007
X2 = 0
X3 = 0

To find the characteristic polynomial of A, we first need to compute the determinant of (A - λI), where I is the identity matrix and λ is a scalar variable:

|0-λ  0.00 0.007|
|0.00 0-λ  0.00 |
|0.00 0.00 0-λ  |

Expanding along the first row, we get:

(0-λ) |0-λ  0.00| - 0.00 |0.00 0-λ | + 0.007 |0.0 0.00|
       |0.00 0-λ |            |0.0 0.00|                 |0.00 0-λ |

Simplifying, we obtain:

-λ³ + (-0.007)λ² = 0

Factoring out λ², we get:

λ²(-λ - 0.007) = 0

Therefore, the characteristic polynomial of A is:

p(A) = λ³ + 0.007λ²

To find the eigenvalues of A, we need to solve the equation p(A) = 0. We can see that one of the roots is λ = 0, which has multiplicity 2 (since it appears as a factor of λ² in the characteristic polynomial). To find the third eigenvalue, we need to solve:

λ³ + 0.007λ² = 0

Factoring out λ² again, we obtain:

λ²(λ + 0.007) = 0

Therefore, the remaining eigenvalue is λ = -0.007. Thus, the eigenvalues of A are:

X1 = 0
X2 = 0
X3 = -0.007

Arranging them in ascending order, we get:

X1 = -0.007
X2 = 0
X3 = 0

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The cost of the bike is $40 and that accessories is $6.65

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Let the cost of the accessories be x, therefore, the cost of the bike is 6x,

According to the equation,

6x × x = 266

6x² = 266

x² = 44.33

x = 6.65

Therefore, the cost of the bike is = 6 × 6.65 = 39.94 ≈ 40

Hence, the cost of the bike is $40 and that accessories is $6.65

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If the whole diameter of sphere is 6 inch(means radius is 3 inch) & thickness of material is 1 inch, so the radius of the hollow part should be 2 inch (3-1=2)

The total volume of the ball will be;

= Total volume - Volume of hollow part

= 4/3πr³ - 4/3πr³

= 4/3 × 3.14 × (3)³ - 4/3×3.14×(2)³

= 4 × 3.14 × 9 - 4/3 × 3.14 × 8

= 113.04 - 33.52

= 79.52

If the density of the material is 3.25 g/in3, then the density of 79.52 inch³ should be;

= 79.52 × 3.25

= 258.44 g

Now, if there are 8 spheres in one box, the weight if box will be;

= 258.44 × 8

= 2,067.52 g

_____________________________

Ahh! Finally done with this, if you have any doubt just do ask me :)

The real zeros of the polynomial function P(x) = x⁵ − 50x³ + 49x are -1, 0, and 1.

To find the zeros of this function, we can factor it by first factoring out an x to get P(x) = x(x⁴ − 50x² + 49). Then, we can factor the quadratic expression inside the parentheses using the difference of squares formula, which gives us P(x) = x(x² − 1)(x² − 49). Simplifying further, we have P(x) = x(x − 1)(x + 1)(x - 7)(x + 7).

Therefore, the zeros of P(x) are the values of x that make each factor equal to zero. This gives us x = -7, -1, 0, 1, and 7. Since all of these values are real, we conclude that the number of real zeros of P(x) is 5.

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Answer:

Therefore, -8(2x-4) simplifies to -16x + 32.

Step-by-step explanation:

-8 * 2x - (-8 * 4)

Simplifying this expression further gives:

-16x + 32

Therefore, -8(2x-4) simplifies to -16x + 32.

Answer:

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

x/3+2=3 (subtract 2)

x/3=1 (multiply by 3)

x=3

Answer:

97

Step-by-step explanation:

x has to be more than 60 and less than 100

the primes between those are 61,67,71,73,79,83, 89, 97

97 is two less in the ones than in the tens so it completes all of the requirements of the riddles therefore, 97 is the answer.

Answer:

It is 79

Step-by-step explanation:

9-7 is 2

Answer:

  Slope = 7/4

Step-by-step explanation:

You are given coordinate values and a formula that tells you what to do with them. All you need to do is put the values in the formula and do the arithmetic.

You are given points (2, -3) and (6, 4). The slope formula refers to the two points as (x1, y1) and (x2, y2). It does not matter which is which.

If we use the points in the same order they are given, then we can see that ...

Using these values in the given formula, we find the slope to be ...

  \(m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4-(-3)}{6-2}=\dfrac{7}{4}\)

The slope of the line through the given points is 7/4.

The first derivatives for the given functions are:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For  \(y = 100200x + 7x,\) the first derivative is dy/dx = 100207.

For \(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

To find the first derivative for each of the given functions, we'll use the power rule, constant rule, and chain rule as needed.

For the function\(y = 3x^2 + 5x + 10:\)

Taking the derivative term by term:

\(d/dx (3x^2) = 6x\)

d/dx (5x) = 5

d/dx (10) = 0

Therefore, the first derivative is:

dy/dx = 6x + 5

For the function y = 100200x + 7x:

Taking the derivative term by term:

d/dx (100200x) = 100200

d/dx (7x) = 7

Therefore, the first derivative is:

dy/dx = 100200 + 7 = 100207

For the function \(y = ln(9x^4):\)

Using the chain rule, the derivative of ln(u) is du/dx divided by u:

dy/dx = (1/u) \(\times\) du/dx

Let's differentiate the function using the chain rule:

\(u = 9x^4\)

\(du/dx = d/dx (9x^4) = 36x^3\)

Now, substitute the values back into the derivative formula:

\(dy/dx = (1/u) \times du/dx = (1/(9x^4)) \times (36x^3) = 36x^3 / (9x^4) = 4/x\)

Therefore, the first derivative is:

dy/dx = 4/x

To summarize:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For y = 100200x + 7x, the first derivative is dy/dx = 100207.

For\(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

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The proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

We have,

A normal distribution located between z = 0.50 and z = -0.50,

So,

Now,

From the Z-score table,

We get,

The Probability corresponding to the Z score of -0.50,

i.e.

P(-0.50 < X < 0) = 0.191,

And,

The Probability corresponding to the Z score of -0.50,

i.e.

P(0 < X < 0.50) = 0.191,

Now,

The proportion of a normal distribution,

i.e.

P(Z₁ < X < Z₂) = P(Z₁ < X < 0) + P(0 < X < Z₂)

Now,

Putting values,

i.e.

P(-0.50 < X < 0.50) = P(-0.50 < X < 0) + P(0 < X < 0.50)

Now,

Again putting values,

We get,

P(-0.50 < X < 0.50) = 0.191 + 0.191

On solving we get,

P(-0.50 < X < 0.50) = 0.382

So,

We can write as,

P(-0.50 < X < 0.50) = 38.2%

So,

The proportion of a normal distribution is 38.2%.

Hence we can say that the proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

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Answer:

20y-14y+4=16

20y+(-14y) -4   -4

6y=12

y=2

Step-by-step explanation:

Combine like terms

subtrate 4 from each side

Divide 6 by 6 and 12 by 6

There for y=2

The equation for calculating the total population after t years \(f(t) = ae^r^t\)

Given;

A city has a current population of 45,000 people and is losing 2% of its residents annually.

To get the formula for determining the total population after a period of t years;

⇒ \(f(t) = ae^r^t\)

Here, a → Initial population

          r → Rate of reduction

          t → Time or period

As r is decreasing rate r = -0.02

Assume t = 4;

\(f(4) = 45000e^-^0^.^0^2^(^4^)\)

\(f(4) = 45000*0.923\\ f(4) = 41535\)

Hence, the formula for determining the total population after a period of t years is \(f(t) = ae^r^t\).

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The range is the most convenient measure of dispersion because it is simple to calculate and understand. The range is the most imprecise measure of variability because can be greatly affected by outliers or extreme values and may not accurately reflect the true variability of the data.

The range is used to evaluate a small data set such as the grades of a small group of students.

The range is the difference of the maximum and minimum values of a data set. The range is calculated by subtracting the smallest value from the largest value in a data set.

For example, if the smallest value in a data set is 2 and the largest value is 10, the range would be 8 (10-2=8).

However, the range is also the most imprecise measure of variability because it only takes into account the two extreme values in the data set and does not consider the values in between.

The range is most useful when you want to quickly assess the dispersion of a data set or when the data set is small and does not have any outliers. It is also useful when you want to compare the dispersion of two or more data sets. However, if the data set is large or has outliers, it is better to use other measures of dispersion and variability, such as the standard deviation or interquartile range.

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The clock minutes rotate 270 degrees in 45 minutes.

While rotating, the clock's hands are seen to move at a speed of six degrees per minute.

The number of degrees for a clock minute is solved by

60 minutes  = 360 degrees

1 minute = ?

cross multiplying

60 * ? = 360

? = 360 / 60

? = 6

hence 1 minute is 6 degrees

The formula to use to get the calculation is multiplying the number of minutes by 6

Number of degrees in 45 minutes = 45 * 6

Number of degrees in 45 minutes = 270 degrees

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The total weight of the loaves of bread remaining is 1.5 lbs

From the problem it can be deduced that'

There are 3.5 loaves of bread

each weighing 1.5 lbs

Anton's family eats 2.5 loaves of bread

the total weight of the loaves of bread that are left = ?

The loaves of bread that are left

= 3.5 loaves - 2.5 loaves

= 1 loaf

Since 1 loaf weighs  1.5 lbs the weight of the left over bread is 1.5 lbs

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IF THE SLOPE IS 0 IT MEANS THAT THERE IS NO CHANGE IN THE Y COORDINATE OF THE LINE.FOR ANY VALUE OF X GIVEN

THEREFORE THE EQUATION WILL BE

\(y = (0)( - 6) - 2 \\ y = - 2\)

THE EQUATION IS

\(y = - 2\)

HOPE THIS HELPS

Answer:

The slope-intercept form would be: y = 0x - 2

A quadratic approximation to \displaystyle f(x,y)=xe^{y} e^xf(x,y)=xe y e x near the origin is \displaystyle Q(x,y)=xy+xy^{2} Q(x,y)=xy+xy^2.

A quadratic approximation to a function \displaystyle f(x,y) f(x,y) can be constructed using Taylor's formula. In this case, we are looking to approximate the function \displaystyle f(x,y)=xe^{y} e^xf(x,y)=xe y e x near the origin. Taylor's formula allows us to express a function as a sum of its partial derivatives evaluated at a specific point, multiplied by the corresponding power of the variables.

To find the quadratic approximation, we start by calculating the first-order partial derivatives of \displaystyle f(x,y) f(x,y) with respect to \displaystyle x x and \displaystyle y y, which are \displaystyle f_{x}=e^{y}+ye^{y} x+e y +y e and \displaystyle f_{y}=xe^{y} x e y , respectively. Evaluating these derivatives at the origin \displaystyle (0,0) (0,0), we get \displaystyle f_{x}(0,0)=1 f_x(0,0)=1 and \displaystyle f_{y}(0,0)=0 f_y(0,0)=0.

Using the Taylor expansion, the quadratic approximation \displaystyle Q(x,y) Q(x,y) can be written as:

\displaystyle Q(x,y)=f(0,0)+f_{x}(0,0)x+f_{y}(0,0)y+\frac{1}{2}\left[f_{xx}(0,0)x^{2}+2f_{xy}(0,0)xy+f_{yy}(0,0)y^{2}\right]

Since the second-order partial derivatives \displaystyle f_{xx},f_{xy},f_{yy} f_xx, f_xy, f_yy are not given, we consider only the terms up to the quadratic order. Plugging in the values we obtained, the quadratic approximation to \displaystyle f(x,y)=xe^{y} e^xf(x,y)=xe y e x near the origin becomes:

\displaystyle Q(x,y)=xy+xy^{2}

This approximation provides a reasonable estimate of the function \displaystyle f(x,y) f(x,y) in the neighborhood of the origin, capturing the linear and quadratic behavior of the function. However, it should be noted that as we move away from the origin, the accuracy of the quadratic approximation decreases.

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Answer:

36 units squared

Step-by-step explanation:

Multiply the base by the height, so 6 by 12, then divide by 2

The inequality that correctly describes the number of ounces of water, w, that tom drinks each day is d. 64<w.

Amount of water that the bottle can hold = 32 ounces

Bottles of water consumed = 2

A mathematical comparison and representation of the connection between two expressions is known as an inequality. It can be regarded as a generalisation of an equation and is denoted by signs such as <, > and =.

Tom consumes more than two complete bottles of water every day. Since each bottle can carry up to 32 ounces of water, we can describe Tom's daily water consumption as -

= w > 2 × 32

Therefore,

Simplifying the right side of the inequality:

w > 64

Complete Question:

Toms water bottle can hold up to 32 ounces of water. each day he drinks more than 2 full bottles of water. which inequality correctly describes the number of ounces of water, w, that tom drinks each day?

a. w>2

b. 32<w

c. w = 64

d. 64<w

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Answer:

The base is 90 sq

Step-by-step explanation:

Formula for Area= 1/2*b*h

where b is unknown and area = 54sq

1/2 *b*12 = 54sq

12b = 54*2

12b /12 = 54*2/12

b = 9sq