Problem 2
Let A= [ 9 2 -22]
[ 0 -2 0 ]
[ 1 0 -4 ]
a) find the characteristic polynomial of A
b) Find the two eigenvalues of A
(c) Find a basis for the eigenspace corresponding to the smallest eigenvalue. (d) Find a basis for the eigenspace corresponding to the largest eigenvalue.

a.   It will take you 2 seconds to catch up to your friend.

b.  You will be 60 feet ahead of your friend when you cross the finish line.

a. This is because you are skating at a rate of 12 feet per second and your friend has a head start of 20 feet, so you must cover 20 feet in 2 seconds (20 feet/12 feet per second).

b. You will be 60 feet ahead of your friend when you cross the finish line.

This is because your friend is skating at a rate of 10 feet per second, and you are skating at a rate of 12 feet per second, so you will gain an additional 2 feet per second.

Therefore, in the 180-foot race, you will have gained an additional 60 feet over your friend (180 feet/2 feet per second).

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Answer:

30%

Step-by-step explanation:

First, I added up the number of minutes in 2 1/2 hours. 2 hours is 120 minutes, and 1/2 hour is 30 minutes. 120 + 30 = 150.

Next, divide 45 (which is the number out of 150 we are determining the percentage for) by 150 (which is the total number of minutes). Multiply that number by 100 to get 30. The answer is 30%.

15 + 2x = Price

The price of a medium-sized pizza at Desminos Pizza's online menu is $15 plus $2 per topping. The equation for this is 15 + 2x = Price, where x represents the number of toppings.

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The linear inequality answer using interval notation are [10/63, ∞]

To solve the linear inequality 3x+(1)/(3)>=(3)/(2)x+(4)/(7), we need to isolate the variable on one side of the inequality.

Here are the steps to do so:

1. Subtract (3)/(2)x from both sides of the inequality: 3x-(3)/(2)x+(1)/(3)>=(4)/(7)

2. Combine like terms on the left side of the inequality: (3/2)x+(1)/(3)>=(4)/(7)

3. Subtract (1)/(3) from both sides of the inequality: (3/2)x>=(4)/(7)-(1)/(3)

4. Find a common denominator and combine the fractions on the right side of the inequality: (3/2)x>=(12-7)/(21)

5. Simplify the fraction on the right side of the inequality: (3/2)x>=(5)/(21)

6. Multiply both sides of the inequality by the reciprocal of (3/2) to isolate the variable: x>=(5)/(21)*(2)/(3)

7. Simplify the fraction on the right side of the inequality: x>=(10)/(63)

The solution to the inequality is x>=(10)/(63). In interval notation, this is expressed as [10/63, infinity).

So the answer is [10/63, infinity]

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Answer: B

Step-by-step explanation:

A perfect square is in the name: square!

Any number squared means that it can represent a square, since the side lengths are equal. In this example, 6^2 is a perfect square since a square with equal side lengths of 6*6 would be perfect; any other length measures would not make it a square. Hope this helps explain it!

Answer:

6^2

Step-by-step explanation:

62 = (6 ×  6) = 36. Here, 36 is a perfect square because it is the product of two equal integers, 6 × 6 = 36.

Using coordinate geometry, we can find that Theo is 5.61 units closer to the tube slide than the wave pool.

Using the formula obtained from Pythagoras' theorem, distance can be computed. In coordinate geometry, the formula for distance is:

√ [(x2 – x1) ² + (y2 – y1) ²].

Given,

Theo is at point (5,0)

Wave pool is at point (-8, -12)

Tube Slide is at point (10,11)

We must first figure out how far Theo is from each ride in order to gauge how near he is to any of them. The distance formula can be used to achieve this.

By distance formula to find distance between two points (x1, y1) and (x2, y2), d= √[(x2-x1) ² + (y2-y1) ²]

Distance between Theo and wave pool is=

d= √ [(-13) ² + (-12) ²]

d= √313

d= 17.69 units.

Distance between Theo and tube slide is=

d= √ [5² + 11²]

d= √146

d = 12.08 units.

Difference between the two distances = 17.69 - 12.08

= 5.61 units.

Therefore, Theo is 5.61 units closer to the tube slide than the wave pool.

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yes

im not sure though try it!

Answer:

Let's assume that the original price of petrol is x per liter.

After the increase of R1 per liter, the new price of petrol is (x+1) per liter.

According to the problem, with the new price, you can buy 7 liters less for R504, so we can write:

7(x+1) = 504

Simplifying this equation, we get:

7x + 7 = 504

Subtracting 7 from both sides, we get:

7x = 497

Dividing both sides by 7, we get:

x = 71

Therefore, the original price of petrol was Rx71 per liter.

The percentage of those standing is 60%

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

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

Seated : Standing = 1 : 2

Standing : VIP = 6 : 1

Multiply Seated : Standing = 1 : 2 by 3

Seated : Standing = 3 : 6

Standing : VIP = 6 : 1

Combine the ratios

Seated : Standing : VIP = 3 : 6 : 1

So, we have

Standing = 6/(3 + 6 + 1) * 100%

Evaluate

Standing = 60%

Hence, the percentage is 60%

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The end behavior is that as x moves toward negative infinity, f(x) moves toward negative infinity and as x moves toward positive infinity, f(x) moves toward positive infinity. F(x) only has one x-intercept, which is x = 3.

The given function is f(x) = -x³ + 2x² + 3

1. End behavior:

As the leading coefficient of f(x) is negative, -x^3 dominates the behavior of the function as x moves towards -∞ or +∞. Therefore, the end behavior of the function is:

2. X-intercepts:

To determine the x-intercepts of the function, we have to calculate the equation f(x) = -x^3 + 2x^2 + 3 = 0. We can factor out a common factor of -1 to simplify the equation:

-x^3 + 2x^2 + 3 = 0

x^3 - 2x^2 - 3 = 0

Applying synthetic division or long division, one of the roots of this equation is x = 3. We can then factor out (x - 3) using polynomial division to find the other two roots:

x^3 - 2x^2 - 3 = (x - 3)(x^2 + x + 1)

The factor of x^2 + x + 1 has no real roots, so the only x-intercept of f(x) is x = 3.

3. Positive/negative:

To determine the sign of f(x) for different values of x, we can look at the sign of each factor in the polynomial:

Putting these together, we can make the following sign chart for f(x):

x                         f(x)

x < 0                   -

0 < x < 3                  +

x > 3                  -

4. Multiplicity: The single root of f(x) has multiplicity 1 and is given by x = 3. This indicates that at x = 3, the graph of f(x) crosses the x-axis and switches signs.

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The project is expected to generate a return of 16.1% per year, which is higher than the company's cost of capital.

To calculate the IRR of the project, we need to find the discount rate at which the present value of the cash inflows equals the initial cost of the investment. We can use the following formula to find the IRR:

NPV = 0 = CF0 + CF1/(1+IRR)¹ + CF2/(1+IRR)² + CF3/(1+IRR)³ + CF4/(1+IRR)⁴

Where:

CF0 = initial investment = -$10,000

CF1, CF2, CF3, CF4 = cash flows in years 1, 2, 3, and 4, respectively

IRR = the discount rate we want to find

Using the given values, we can plug them into the formula and solve for IRR using a financial calculator or Excel. Alternatively, we can use a trial-and-error method to find the discount rate that makes NPV equal to zero.

Here is one way to solve for IRR using Excel:

In Excel, create a new spreadsheet.

In cells A1 to A5, enter the cash flows: -10000, 6000, 7500, 7000, and 2000.

In cell B1, enter the formula: =IRR(A1:A5)

Press Enter. The IRR of the project is displayed in cell B1 as a percentage.

Using this method, we find that the IRR of the project is approximately 16.1%.

Therefore, the Internal Rate of Return (IRR) of the project is calculated to be 16.1%, which indicates that the project is expected to generate a return that is greater than the cost of capital for the company. Hence, investing in this project is considered financially viable for Big Wolf Demolition.

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g(x) = -f(x) - 4

===========================================================

Explanation:

The point (0,1) is on the the red f(x) curve. It's the y-intercept.

If we reflected that point over the x axis, then it moves to (0,-1). Shift it down 4 units to get to (0,-5)

The point (0,-5) is on the purple g(x) curve.

This process of...

is applied to every point on the red curve to arrive at a corresponding point on the purple curve. The order of the transformations matters. We can't shift down first before reflecting (or else g(x) will be in a different spot).

We stick a negative sign in front of the f(x) to reflect over the x axis. This is to change the sign of the y coordinate from positive to negative. Our answer choices are narrowed to either B or C.

The answer is choice B since that -4 at the end means "shift each point 4 units down". We're subtracting 4 from each y coordinate.

GeoGebra and Desmos are two useful tools to help verify the answer.

Answer: true, true, false, true

Step-by-step explanation:

1 True- 2 is a prime number

2- True 2 is a prime number

3 False 2,3,5,7 can be prime numbers as well

4 True 2 is a prime number

Fully  parenthesize form of arithmetic operation are -

1. For the expression x + y * z - x, you can fully parenthesize it as follows: ((x + (y * z)) - x)
2. For the expression y - z * x / w + z, you can fully parenthesize it as follows: (((y - ((z * x) / w)) + z)
3. For the expression (z - w + x) / z * w, you can fully parenthesize it as follows: (((z - w) + x) / z) * w
4. For the expression (x * w / z) - (x - y) * y, you can fully parenthesize it as follows: (((x * w) / z) - ((x - y) * y))
5. For the expression z - (w + x ) - y * z - y, you can fully parenthesize it as follows: (((z - (w + x)) - (y * z)) - y)
6. For the expression (x - y + z) * z / z, you can fully parenthesize it as follows: (((x - y) + z) * z) / z

Given arithmetic expressions: 1. x + y * z - x2. y - z * x / w + z3. (z - w + x) /z * w4. (x * w / z) - (x - y) * y5. z - (w + x ) - y * z - y6. (x - y + z) * z / z. To apply fully parenthesize form in solving the arithmetic operation, the given arithmetic expressions are:1. ((x) + ((y) * (z))) - (x)2. ((y) - (((z) * (x)) / (w))) + (z)3. ((((z) - (w)) + (x)) / (z)) * (w)4. ((((x) * (w)) / (z)) - ((x) - (y))) * (y)5. (z) - (((w) + (x)) - ((y) * (z))) - (y)6. (((x) - (y) + (z)) * (z)) / (z)

Therefore, the fully parenthesized form in solving the arithmetic operation for the given expressions is shown as above.

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Answer:

$445.10

Step-by-step explanation:

The amount withheld for federal income tax depends on several factors, including Steve's filing status, income, and deductions. However, we can make an estimate based on some assumptions.

Assuming Steve is paid weekly and is paid for 52 weeks a year, his gross income would be:

$255.75 x 52 = $13,293

We also assume that Steve is claiming two allowances. Each allowance reduces the amount of taxable income subject to federal income tax withholding. For 2021, each allowance is equal to $4,300.

Therefore, Steve's taxable income for federal income tax purposes would be:

$13,293 - (2 x $4,300) = $4,693

To estimate the federal income tax withholding, we can use the IRS tax tables. For a single person claiming two allowances and earning $4,693 per week, the estimated federal income tax withholding would be:

$445.10

However, this is just an estimate, and the actual federal income tax withholding may be different based on Steve's specific circumstances. It's always best to consult with a tax professional for accurate tax advice.

The first equation describing the given conditions is x - y = 2, as the difference between the two outputs of a firm is 2. The second equation is 8x = 10y, as eight times the larger quantity is 10 times the smaller quantity. The system of equations can be written as:

x - y = 2
8x = 10y

To solve the system, we can use the substitution method. First, we can solve for x in the first equation:

x = y + 2

Then, we can substitute this expression for x into the second equation:

8(y + 2) = 10y

Distributing the 8 gives:

8y + 16 = 10y

Subtracting 8y from both sides gives:

16 = 2y

Dividing by 2 gives:

y = 8

Finally, we can substitute this value of y back into the first equation to find x:

x = 8 + 2 = 10

So the two output levels are x = 10 and y = 8.

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The correct statement is (a) Regression coefficients estimated using least squares are always BLUE.

Therefore, statement (a) is true. The other statements are not correct. Statement (b) is incorrect because the omitted variable bias can be positive or negative, depending on the direction of the correlation between the omitted variable and the other explanatory variables. Statement (c) is incorrect because R2 j is obtained from the regression of the jth explanatory variable on the rest of the explanatory variables, not the dependent variable. Statement (d) is incorrect because statement (a) is true.

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Answer:if what im getting at is correct, 8000  cm for the part a then that means part b is probably in conversion of that to 80 m

Step-by-step explanation:

if what i think may be correct 1:1000 means that 8 cm would be 8000 then, if it wants to know the real length in meters then it would have to be converted making it 80 meters

___________________________________________________

Hope this is correct

Answer:

A) 8000 cm

B) 80m

Step-by-step explanation:

A) 1:1000 is 0.001 times that by 1000 you get 8 x 1000=8000

=8000cm

B) we know that in cm the ship size is 8000cm converting cm to meter is basically

8000÷100= 80meters

Answer:

x = 1

Step-by-step explanation:

17.25x+3.89=21.14
17.25x=17.25
x = 1

Answer:

The solution to the equation is x = 1

Step-by-step explanation:

Hi,

We need to isolate the term that contains the variable "x", so we will subtract 3.89.

17.25x + 3.89 - 3.89 = 21.14 - 3.89

We obtain:

17.25x = 17.25

Dividing both sides by 17.25:

x = 1

Therefore, the solution to the equation is x = 1.

Good luck!

The risk premium of L2 is $19,000 - $18,000.5 = $999.5.

The utility function u(x) = 2x + 1 represents a risk-neutral individual. This is because the utility function is a linear function, meaning that the marginal utility of wealth is constant. Therefore, the individual is indifferent between a certain outcome and a risky outcome with the same expected value.

To determine which lottery the individual prefers, we can calculate the expected utility of each lottery and compare them. The expected utility of a lottery is the sum of the probabilities of each outcome multiplied by the utility of that outcome.

The expected utility of Li is:

EU(Li) = 1 * u($20,000 - $1,000) = 1 * u($19,000) = 1 * (2 * $19,000 + 1) = $38,001

The expected utility of L2 is:

EU(L2) = 0.9 * u($20,000 + $0) + 0.1 * u($20,000 - $10,000) = 0.9 * u($20,000) + 0.1 * u($10,000) = 0.9 * (2 * $20,000 + 1) + 0.1 * (2 * $10,000 + 1) = $36,001.1

Since the expected utility of Li is greater than the expected utility of L2, the individual prefers Li.

The risk premium of L2 is the difference between the certain outcome that gives the same utility as L2 and the expected value of L2. The certain outcome that gives the same utility as L2 is $18,000.5, since u($18,000.5) = $36,001.1. The expected value of L2 is $19,000. The risk premium of L2 is $19,000 - $18,000.5 = $999.5.

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Risk premium = $900

a) Since the utility function is increasing, this means you are risk-averse as increasing your position increases your utility.

b) In this case, you would prefer Lottery Li as it has lower risk of loss compared to Lottery L2. The risk premium of L2 can be calculated by finding the expected value of the lottery and subtracting the expected value of Li.
Expected Value of Li: (.9 x $20,000) - (.1 x $1,000) = $18,900
Expected Value of L2: (.9 x $20,000) - (.1 x $10,000) = $18,000

Risk premium = $18,900 - $18,000 = $900

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Answer: 60

Step-by-step explanation:

The least whole-number angle measure of a regular polygon would be 60 degrees.

For a regular polygon of any number of sides, the sum of its exterior angle is 360° (full angle).

Exterior angle is a measure of rotation between one extended side(we extend it virtually) of the polygon with its adjacent side which is not extended. Because the polygon being regular, let it be having 'n' sides, all the exterior angles are of the same measure, and therefore, their measure is (360/n)°.

We can conclude that  least whole-number angle measure of a regular polygon = 60 degrees.

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Answer:

Slope = -250

Interpretation: Every month the value of the car goes down $250.

Step-by-step explanation:

The slope of this linear function is -250 because every 4 months, the value goes down by $1000 so...

-1000/4 = -250

Interpretation: Every month the value of the car goes down $250.

Hope this helps!

f(a) is concave down on the interval -∞ to -4 and on the interval 0 to ∞, f(x) is concave up on the interval -4 to 0, inflection point for this function is at x = -2 and x = 2, the minimum for this function occurs at x = -4, the maximum for this function occurs at x = 0.

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, *, /, ^) that represents a value or a quantity. Expressions can contain variables, which are symbols that can take on different values. An expression can also be a combination of other expressions. Expressions are used to represent mathematical relationships, make calculations, and solve problems.

To answer these questions, we need to find the first and second derivatives of the function:

f(x) = x√(x²+16)

f'(x) = √(x²+16) + x(x²+16)[tex]^{(-1/2)}[/tex](2x)

f''(x) = (2x)/(x²+16)[tex]^{(3/2)}[/tex]+ (x²+16)[tex]^{(-1/2)}[/tex] + 2(x²+16)[tex]^{(-1/2)}[/tex]

A. f(a) is concave down on the interval -∞ to -4 and on the interval 0 to ∞.

To determine where the function is concave down, we need to find where the second derivative is negative. The second derivative is negative on the intervals (-∞, -4) and (0, ∞), so the function is concave down on those intervals.

B. f(x) is concave up on the interval -4 to 0.

To determine where the function is concave up, we need to find where the second derivative is positive. The second derivative is positive on the interval (-4, 0), so the function is concave up on that interval.

C. The inflection point for this function is at x = -2 and x = 2.

The inflection points occur where the concavity of the function changes. We found that the function is concave down on (-∞, -4) and (0, ∞), and concave up on (-4, 0). Therefore, the inflection points occur at x = -2 and x = 2.

D. The minimum for this function occurs at x = -4.

To find the minimum, we can either use the first derivative test or the second derivative test. Using the first derivative test, we look for where the first derivative changes sign from negative to positive, which indicates a local minimum. Using the second derivative test, we look for where the second derivative is positive, which indicates a local minimum. Either way, we find that the minimum occurs at x = -4.

E. The maximum for this function occurs at x = 0.

To find the maximum, we can either use the first derivative test or the second derivative test. Using the first derivative test, we look for where the first derivative changes sign from positive to negative, which indicates a local maximum. Using the second derivative test, we look for where the second derivative is negative, which indicates a local maximum. Either way, we find that the maximum occurs at x = 0.

Therefore, f(a) is concave down on the interval -∞ to -4 and on the interval 0 to ∞, f(x) is concave up on the interval -4 to 0, inflection point for this function is at x = -2 and x = 2, the minimum for this function occurs at x = -4, the maximum for this function occurs at x = 0.

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x<4 is the solution of the inequality 5 x < 20

A number system is defined as a system of writing to express numbers.

The given inequality is  5 x < 20

We have to solve for x

Divide both sides by 5

x<20/5

Divide numerator and denominator by 5

x<4

The graph of x<4 is given in the attachment.

Hence, x<4 is the solution of the inequality 5 x < 20

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Answer:

squareroot(256)

16

Step-by-step explanation:

im genius

The formula:

[tex]\huge\begin{array}{ccc}C=2\pi r\end{array}[/tex]

[tex]r[/tex] - radius

We have:

[tex]r=6.5m[/tex]

Substitute:

[tex]C=2\cdot6.5m\cdot\pi=13\pi m[/tex]

Use: [tex]\pi\approx3.14[/tex]

[tex]C\approx13m\cdot3.14=40.82m[/tex]

Answer:40.82 meters

The circumference of the circle.

The formula:

- radius

SOLUTION:

We have:

Substitute:

Use:

Step-by-step explanation:

Give bro above me the good stuff

The graph that best represents the amount of money that John still needs to save for camp is a bar graph.

A bar graph is a graphical representation of data that is used to compare different categories of data. It is composed of rectangular bars with lengths proportional to the values that they represent. A bar graph may contain either vertical or horizontal bars, and it is usually used to represent data that is grouped into categories.

This graph would have a vertical axis that represents the amount of money that still needs to be saved and a horizontal axis that represents the amount of time. The graph would start with the bar at $60 and gradually increase over time until it reaches the goal of $120. He could also use the graph to determine how much money he needs to save each week or month in order to reach the goal on time.

Additionally, the graph could show him how much he has saved so far and how much he needs to save in order to reach the goal.

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The given statement " If A is an m x n matrix and B is an n x n matrix, then A × B is an m x n matrix" is True.  Correct answer of (a) is T.

This statement is definately true because, it helps to consider the dimensions of a matrix. The dimensions of a matrix refer to the number of rows and columns it contains. In the case of an m x n matrix (A) and an n x n matrix (B), the dimensions of A are m rows and n columns, while the dimensions of B are n rows and n columns.

When A is multiplied by B, the result is an m x n matrix, meaning it contains m rows and n columns. This is due to the fact that the number of columns of the first matrix (A) must equal the number of rows of the second matrix (B) in order for the matrices to be compatible for multiplication.

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The difference in volumes between the total volume and initial volume is 40 milliliters.

Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫∫ F(x, y, z) dx dy dz

Given is the volume flask as shown in the image.

Initial volume in the container {I} : 360 milliliters

Total volume of the container {T} : 400 milliliters

The difference in volumes between the total volume and initial volume -

{T} - {I}

400 - 360

40 milliliters

Therefore, the difference in volumes between the total volume and initial volume is 40 milliliters.

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Step-by-step explanation:

[tex] \frac{1}{2} \times 5.4 \times 6.4 \\ = 17.28 \\ \frac{1}{2} \times 6.6 \times 6.4 \\ = 21.12 \\ 17.28 + 21.12 = 38.4 {in\\ }^{2} [/tex]