if A is a square matrix such that some row of A^2 is a linear combination of the other rows of A^2, show that some column of A^3 is a linear combination of the other columns of A^3.

The value of x in the given circle is 12

From the given circle we have

61+5x-1=10x+1

We have to find value for x

60+5x=10x+1

Take the variable terms on one side and constant on other side

5x=59

Divide both sides by 5

x=59/5

x=11.8

Hence, the value of x in the given circle is 12

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The value of the expression is 295.

We can simplify the expression by grouping the terms that have the same value:

26 + (25 + 25) + (24 + 24) - (23 + 23) - (22 + 22) - (21 + 21) - (20 + 20) + (19 + 19) + (18 + 18) + 17 - (16 + 16) + (15 + 15) + (14)

= 26 + 50 + 48 - 46 - 44 - 42 - 40 + 38 + 36 + 17 - 32 + 30 + 14

= 295

The given expression involves a series of numbers where some of them are added and some of them are subtracted. To simplify this expression, we need to group the terms that have the same value. We can see that the expression has pairs of numbers that add up to the same value, such as (25 + 25), (24 + 24), and so on. We can combine these pairs and simplify the expression further.

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To find the extreme values of a function subject to a given constraint, Lagrange multipliers can be used. The method involves finding the critical points of the function and the constraint equation, and then solving a system of equations using the Lagrange multiplier. The resulting solutions will give the maximum and minimum values of the function subject to the given constraint.

Suppose we have a function f(x,y,z) and a constraint equation g(x,y,z) = 0. We can set up the Lagrangian function L(x,y,z,λ) = f(x,y,z) - λg(x,y,z) and then find the partial derivatives of L concerning x, y, z, and λ. Setting these partial derivatives to zero and solving the resulting system of equations will give us the critical points and the corresponding values of λ.

Once we have the critical points and values of λ, we can evaluate the function f(x,y,z) at these points to find the maximum and minimum values subject to the given constraint. It is important to note that not all critical points will necessarily correspond to maximum or minimum values, so we must evaluate the function at each point to determine which points give the extreme values.

Overall, Lagrange multipliers provide a powerful method for finding the extreme values of a function subject to a given constraint. The method involves setting up a Lagrangian function, finding the critical points and values of λ, and then evaluating the function at these points to find the maximum and minimum values. This approach can be applied to a wide range of optimization problems in mathematics, physics, and engineering.

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Answer:

h = -1.25

Step-by-step explanation:

isolate the variable by dividing each side by factors that don't contain the variable.

The probability is approximately 0.0549 or 5.49%. So, there is a 5.49% probability that all three randomly selected homes in the Quail Creek area have a security system.

To answer your question, we'll use the concept of probability. In this case, we want to find the probability that all three randomly selected homes in the Quail Creek area have a security system.

1. First, determine the probability that the first home has a security system:
There are 5 homes with security systems out of 14 total homes, so the probability is 5/14.

2. Next, determine the probability that the second home also has a security system:
Since one home with a security system has been "selected," there are now 4 homes with security systems out of the remaining 13 homes. So, the probability is 4/13.

3. Finally, determine the probability that the third home has a security system:
Since two homes with security systems have been "selected," there are 3 homes with security systems left out of the remaining 12 homes. So, the probability is 3/12, which simplifies to 1/4.

4. Multiply the probabilities from steps 1, 2, and 3 to get the probability that all three selected homes have a security system:
(5/14) * (4/13) * (1/4) = 20/364.

5. Round your answer to 4 decimal places:
The probability is approximately 0.0549 or 5.49%.

So, there is a 5.49% probability that all three randomly selected homes in the Quail Creek area have a security system.

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The distance between the given points which are (1, 2) and (1, -10) is equal to 12 units.

To find the distance between two points in a coordinate plane, we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Where d is the distance between the two points, (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Using this formula, we can find the distance between (1, 2) and (1, -10):

d = √((1 - 1)² + (-10 - 2)²)

= √(0² + (-12)²)

= √(144)

= 12

We can also visualize this by drawing a straight line segment connecting the two points and measuring its length.

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The area of the sector to the nearest hundredth is 308.57units²

The space bounded by two radii and an arc is called a sector of a circle. There is minor sector and major sector.

The area of a sector is expressed as;

A = tetha/360 × πr²

where r is the radius and tetha is the angle formed by the two radii.

A = 98/369 × 3.14 × 19²

A = 111086.92/360

A = 308.57 units²( nearest hundredth)

therefore the area of the sector is 308.57 units²

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Answer:

3 centimeters

Step-by-step explanation:

The law of total probability, we can find the average time a computer is in the shop as:

E(T) = (1/4)P(X=0) + (1/4)P(X=1) + (1/4)P(X=2) + (1/8)P

a) To determine the probability that an extra technician is used, we need to find the probability that there are three or more computers in the shop. Let X be the number of computers in the shop. Then:

P(X ≥ 3) = P(X = 3) + P(X = 4)

To find P(X = 3), we need to use the Poisson distribution with λ = 4 (since there are already 3 computers in the shop):

P(X = 3) = e^(-4) * 4^3 / 3! ≈ 0.1954

To find P(X = 4), we need to use the Poisson distribution with λ = 3 (since there are already 4 computers in the shop):

P(X = 4) = e^(-3) * 3^4 / 4! ≈ 0.1680

Therefore, the probability that an extra technician is used is:

P(extra technician) = P(X ≥ 3) ≈ 0.3634

b) Let Y be the number of computers in the shop awaiting service. We can use the law of total probability to find the expected value of Y:

E(Y) = E(Y|X=0)P(X=0) + E(Y|X=1)P(X=1) + E(Y|X=2)P(X=2) + E(Y|X=3)P(X=3) + E(Y|X=4)P(X=4)

Using the given information, we have:

E(Y|X=0) = 5, E(Y|X=1) = 4, E(Y|X=2) = 4, E(Y|X=3) = 7, E(Y|X=4) = 0

P(X=0) = e^(-5) * 5^0 / 0! ≈ 0.0067

P(X=1) = e^(-4) * 4^1 / 1! ≈ 0.0733

P(X=2) = e^(-4) * 4^2 / 2! ≈ 0.1465

P(X=3) = e^(-3) * 3^3 / 3! ≈ 0.2240

P(X=4) = e^(-0) * 0^4 / 4! = 0

Therefore, the expected number of computers in the shop awaiting service is:

E(Y) = 5(0.0067) + 4(0.0733) + 4(0.1465) + 7(0.2240) + 0(0) ≈ 3.6182

c) Let T be the amount of time that a computer is in the shop. We know that the technician can repair a computer at a rate of 4 per day, and when an extra technician is used, they can repair computers at a rate of 8 per day. So:

If there are 0, 1, or 2 computers in the shop, the average time a computer is in the shop is 1/4 day.

If there are 3 or 4 computers in the shop, the average time a computer is in the shop is 1/8 day.

Using the law of total probability, we can find the average time a computer is in the shop as:

E(T) = (1/4)P(X=0) + (1/4)P(X=1) + (1/4)P(X=2) + (1/8)P

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The value of F(3) -F(0). d) In which area is the probability of entering F (3) -F (0) is "0 ≤ X < 3".

a) The function of distribution by regions is:

For x < -4: F(x) = 0

For -4 ≤ x < -2: F(x) = 0.2

For -2 ≤ x < 0: F(x) = 0.2 + 0.1 = 0.3

For 0 ≤ x < 1: F(x) = 0.3 + 0.25 = 0.55

For 1 ≤ x < 3: F(x) = 0.55 + 0.2 = 0.75

For 3 ≤ x < 5: F(x) = 0.75 + 0.2 = 0.95

For x ≥ 5: F(x) = 1

b) Expressing the result obtained as  F(x) =:

F(x) = {0, x < -4

0.2, -4 ≤ x < -2

0.3, -2 ≤ x < 0

0.55, 0 ≤ x < 1

0.75, 1 ≤ x < 3

0.95, 3 ≤ x < 5

1, x ≥ 5

c) F(3) - F(0) = 0.95 - 0.55 = 0.4

d) The probability of entering F(3) - F(0) is the probability of the random variable falling between 0 and 3. This can be expressed as:

P(0 ≤ X < 3) = F(3) - F(0) = 0.4

Therefore, the answer is "0 ≤ X < 3".

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The result is stored in the array `X`, which represents the frequency of the gene over time.

We have,
To generate random variates according to the standard normal distribution in Python, you can use the `numpy` library:

```python
import numpy as np

# Generate random variates according to the standard normal distribution
random_variates = np.random.randn(1024)
```

Now that you have the random variates, you can simulate an approximate realization of the Brownian motion using the Euler-Maruyama method with Δt = 1:
```python
# Set the parameters
delta_t = 1
X = np.zeros(len(random_variates) + 1)

# Initialize the gene frequency
X[0] = 0.5

# Use the Euler-Maruyama method to simulate the Brownian motion
for i in range(len(random_variates)):
   dW = random_variates[i] * np.sqrt(delta_t)
   X[i + 1] = X[i] + X[i] * (1 - X[i]) * dW
```

With this code, you have generated an approximate realization of the Wright-Fisher model using a numerical method (Euler-Maruyama) for a Brownian motion with Δt = 1.

Thus,

The result is stored in the array `X`, which represents the frequency of the gene over time.

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The probability of observing 13 or more successes out of 15 trials, assuming no difference in preference between Simply Significant and Starbucks coffee, is 0.9437.

Assuming a null hypothesis that there is no difference in preference between Simply Significant and Starbucks coffee, the number of successes (preferred Simply Significant coffee) out of 15 trials follows a binomial distribution with parameters n=15 and p=0.5 (under the null hypothesis).

To calculate the probability of observing 13 or more successes, we can use the cumulative distribution function (CDF) of the binomial distribution:

P(X ≥ 13) = 1 - P(X < 13)

Using a binomial calculator or statistical software, we can find:

P(X < 13) = 0.0563

Therefore,

P(X ≥ 13) = 1 - P(X < 13) = 1 - 0.0563 = 0.9437

So the probability of observing 13 or more successes out of 15 trials, assuming no difference in preference between Simply Significant and Starbucks coffee, is 0.9437.

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If we consider the two vectors a and b with known magnitudes of 1 m and 10 m respectively, but unknown directions, we can still perform some calculations with these vectors. However, without knowing their directions, we cannot determine the resultant vector of their addition or subtraction.

The direction of a vector is a crucial component in determining the overall effect of the vector. Therefore, to fully understand the impact of vectors a and b, we need to know their directions as well.
Based on the information given, you have two vectors: vector a with a magnitude of 1 m and vector b with a magnitude of 10 m. However, since the directions of these vectors are unknown, you cannot determine their specific position, direction, or any further information about their relationship to each other. To analyze or perform operations on these vectors, you would need additional information regarding their directions.

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a)We have x2 = 21.44 as our test statistic.

b) the critical value for a chi-squared distribution with 4 degrees of freedom and a 10% significance level is 7.78.

c) the distribution of appointments is not the same for all weekdays.

a. To calculate the test statistic for the chi-squared goodness-of-fit test, we need to find the expected frequency for each day of the week if the appointments were distributed evenly. Since there are five days of the week, we would expect 500/5 = 100 appointments for each day of the week.

Day Appointment Observed Frequency Expected Frequency (O - E)^2 / E Monday 98 100 (98-100)^2/100 = 0.04 Tuesday 116 100 (116-100)^2/100 = 2.56 Wednesday 122 100 (122-100)^2/100 = 4.84 Thursday 98 100 (98-100)^2/100 = 0.04 Friday 66 100 (66-100)^2/100 = 13.96 Total:

The test statistic is the sum of the squared differences between the observed and expected frequencies, divided by the expected frequencies for all categories:

x2 = Σ(Observed - Expected)² / Expected

x2 = (0.04 + 2.56 + 4.84 + 0.04 + 13.96)

x2 = 21.44

We have x2 = 21.44 as our test statistic.

b. To determine the critical value(s) for the hypothesis test, we need to use the chi-squared distribution table with (5 - 1) = 4 degrees of freedom and a significance level of 10%. Looking at the table, the critical value for a chi-squared distribution with 4 degrees of freedom and a 10% significance level is 7.78.

c. To conclude whether to reject the null hypothesis or not based on the test statistic, we compare it with the critical value. Since our test statistic (21.44) is greater than the critical value (7.78), we reject the null hypothesis that the appointments are distributed evenly from Monday to Friday each week. This means that the distribution of appointments is not the same for all weekdays.

d. We reject the null hypothesis.

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No, 4 in, 2 in, and 8 in do not make a triangle.

We have,

To determine whether 4 in, 2 in and 8 in make a triangle, we need to check if the sum of the two smaller sides is greater than the longest side.

If this condition is satisfied, then the three sides can form a triangle.

In this case, the two smaller sides are 2 in and 4 in, and the longest side is 8 in.

Therefore, we need to check if:

2 in + 4 in > 8 in

This simplifies to:

6 in > 8 in

Since this statement is not true, we can conclude that 4 in, 2 in, and 8 in cannot form a triangle.

Thus,

No, 4 in, 2 in, and 8 in do not make a triangle.

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This is because the amount Rachel owes her parents increases by $75 every week, which is represented by the linear term 75x. The starting amount she owes her parents is $800, which is represented by the constant term 800. Therefore, the linear model for this situation is f(x) = 800x + 75.

Since Rachel is paying back $75 every week, the relationship between the amount owed and the number of weeks is linear. We can represent this linear model relationship as a function f(x), where x is the number of weeks.

Now, let's look at the given options and identify the correct linear model:

a. f(x) = 800x + 75
b. f(x) = 800x - 75
c. f(x) = 75x + 800
d. f(x) = 75 - 800
e. f(x) = -75 + 800
f. f(x) = -75 - 800

Since Rachel initially owes $800 and is paying back $75 every week, the correct model should have a starting value of 800 and a decrease of 75 for each week. The model that represents this is:

f(x) = -75x + 800

Comparing this to the given options, we can see that the correct answer is:
c. f(x) = 75x + 800

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H. 0.270 is equal in value to 27% in the given case. Option 3 is correct

A percentage is a way of expressing a number as a fraction of 100. The symbol for percentage is the percent sign (%).

To convert a percentage to a decimal, we divide the percentage by 100. For example, 50% is equal to 0.50 as a decimal.

To convert a percentage to a decimal, we divide the percentage by 100.

So to convert 27% to a decimal, we divide 27 by 100:

27/100 = 0.27

Therefore, 27% is equal to 0.27 as a decimal.

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The equation x³ + y³ + z³ = k Is not possible to solve because it is an equation of  degree 3.

We have,

The equation x³ + y³ + z³ = k represents a surface of constant values in a 3D coordinate system.

If we want to solve for one of the variables in terms of the others, it is not possible because it is an equation of degree 3.

However, you can analyze the equation by graphing it and observing the shape of the surface.

It is a special case of an algebraic surface known as an elliptic cone.

If you have a specific value for k, you can plot the surface and observe its shape.

For example, if k = 1, the surface is a twisted cubic curve that intersects the coordinate axes at (1,0,0), (0,1,0), and (0,0,1).

Thus,

The equation is not possible to solve because it is an equation of

degree 3.

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The surface area of the prism is 200 cm².

The total surface area of the prism is calculated by applying the formula for total surface area of prism.

S.A = bh + (s₁ + s₂ + s₃)L

where;

The surface area of the prism is calculated as;

S.A = 8 cm (15 cm) + (8 cm + 15 cm + 17 cm) x 2cm

S.A = 120 cm² + 80 cm²

S.A = 200 cm²

Thus, the surface area of the prism is calculated using the formula for surface of right prism.

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With a 10% margin of error in either direction, the price range for replacing the hot water boiler is $7,470 to $9,130.

To provide a margin of error of 10% in each direction, we need to calculate the high and low range by adding and subtracting 10% of the current cost from the current cost itself.

To calculate the high range, we can add 10% of the current cost to the current cost:

High range = $8,300 + (10% of $8,300)

High range = $8,300 + $830

High range = $9,130

To calculate the low range, we can subtract 10% of the current cost from the current cost:

Low range = $8,300 - (10% of $8,300)

Low range = $8,300 - $830

Low range = $7,470

Therefore, the price range for replacing the hot water boiler with a margin of error of 10% in each direction is between $7,470 and $9,130.

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The given statement is an alternative hypothesis that can be used in a statistical hypothesis test to determine whether the mean amount of a certain diet soda is at least 12 oz.

The given statement is an alternative hypothesis. An alternative hypothesis is a statement that is used to test against the null hypothesis in a statistical hypothesis test. In this case, the alternative hypothesis states that the mean amount of a certain diet soda is at least 12 oz. This statement is used to test against the null hypothesis, which is usually a statement that there is no significant difference between two groups or no significant effect of a treatment. However, the null hypothesis is not given in this statement.

To conduct a hypothesis test, a researcher would need to formulate a null hypothesis that is the opposite of the alternative hypothesis. For example, the null hypothesis in this case could be that the mean amount of a certain diet soda is less than 12 oz. Then, the researcher would collect data and conduct statistical tests to determine whether the null hypothesis can be rejected or not.

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The metal in the frame weighs 70.5 kg in total. If a rectangular frame measuring 5 metres in length and 12 metres in width is constructed from five straight pieces of metal.

Get the diagonal

d² = 52 + 122

d² = 25+ 144

d² = 169

d = 13m

Get the perimeter of the rectangular frame:

Perimeter of the frame = 2(5+12) + 13

Perimeter of the frame = 2(17) + 13

Perimeter of the frame = 34 + 13

Perimeter of the frame = 47m

If the weight of the metal is 1.5 kg per metre, the total weight will be expressed as:

Total weight = 47×1.5

Total weight = 70.5kg

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The complete question is

This rectangular frame is made from 5 straight pieces of metal.

5 m

12 m

The weight of the metal is 1.5 kg per metre.

Work out the total weight of the metal in the frame.

Answer:

17.2

Step-by-step explanation:

I took the test and got it wrong, but when it showed me the answer, it said 17.2

The probability that the randomly selected point is in the semicircular region is 628/3653.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

We have,

Radius of semicircle = 4 inches.

Side of Square= 11 inch

Now, area of semicircle = πr²/2

= 3.14 x 16/2

= 25.12 inch²

and, Area of square = s x s

= 11 x 11

= 121 inch²

So, the probability that the randomly selected point is in the semicircular region

= 25.12 / 146.12

= 2512 / 14612

= 628 / 3653

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The function g(x) increases faster than the function f(x).

We know, the quadratic function f(x) will be

f(x) = ax² + bx + c

At x = 1, f(x) will be 3

So,  a + b + c = 3 ...(1)

and x = 2, f(x) will be 6

4a + 2b + c = 6 ...  (2)

and, x = 3, f(x) will be 11

9a + 3b + c = 11 ...  (3)

On solving equations we get

a = 1, b = 0, and c = 2

So, the quadratic function will be

f(x) = x² + 2

Now, The exponential function g(x) will be given as

g(x) = abˣ

At x = 1, g(x) will be 3

ab = 3 .....(4)

and, x = 2, g(x) will be 9

ab² = 9 ...(5)

From equations 4 and 5 we get

a = 1 and b = 3

So, the exponential function will be

g(x) = [tex]3^x[/tex]

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The solutions are:

(a) 2Cu = (16C, 6C)

(b) 3v = (18, -21)

(c) V - u = (-2, -10)

(d) 2u + 5v = (46, -29)

To find the given values, we need to perform basic vector operations using the given vectors u and v.

(a) 2Cu

We need to multiply the vector u by 2C.

2Cu = 2C(8, 3)

= (16C, 6C)

So, 2Cu = (16C, 6C).

(b) 3v

We need to multiply the vector v by 3.

3v = 3(6, -7)

= (18, -21)

So, 3v = (18, -21).

(c) V - u

We need to subtract the vector u from the vector v.

V - u = (6, -7) - (8, 3)

= (-2, -10)

So, V - u = (-2, -10).

(d) 2u + 5v

We need to multiply vector u by 2 and vector v by 5 and then add the two vectors.

2u + 5v = 2(8, 3) + 5(6, -7)

= (16, 6) + (30, -35)

= (46, -29)

So, 2u + 5v = (46, -29).

Therefore, the solutions are:

(a) 2Cu = (16C, 6C)

(b) 3v = (18, -21)

(c) V - u = (-2, -10)

(d) 2u + 5v = (46, -29)

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Answer:

The correct graph is graph B.

Answer:

65

Step-by-step explanation:

3x - y + 1 =0

d/dx (3x) - dy/dx + d/dx (1) = 0

dy/dx = 3

y = x2 + 4x - 16

dy/dx = 2x + 4

Hence

2x + 4 = 3

x= 3-4/2 = -1/2

at x = -1/2y = (-1/2)2 + 4 (-1/2) - 16 = 1/4 -2 -16

y = -71/4

so the point p (-1/2, -71/4)

equation of tangent

y - (-71/4) = 3 (x-(-1/2))

y + 71/4 = 3 ( x + 1/2)

3x - y = 71/4 - 3/2 = 71-6/4 = 65/4

12x - 4y = 65.

​

We get a total of 175 collars sold and 226 leashes sold for the week, and an average of 25.0 collars and 32.3 leashes sold per day.

We have,

Day       Collars      Leashes

Sunday        30          34

Monday        22          29

Tuesday        21               27

Wednesday   25          32

Thursday         17          30

Friday          26           39

Saturday          34           35

Total          175          226

Average          25.0  32.3

To complete the table, we can add up the number of collars and leashes sold each day to get the total for the week.

We can also calculate the average number of collars and leashes sold per day by dividing the total by 7.

Thus,

We get a total of 175 collars sold and 226 leashes sold for the week, and an average of 25.0 collars and 32.3 leashes sold per day.

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A can be diagonalized if it has 2 unit eigenvectors All two eigenvalues are distinct and the eigenvectors that correspond to distinct eigenvalues are orthogonal Eigenvalues of A are the roots of a quadratic polynomial. The third eigenvalue is 5.

Given that two eigenvalues of a 3 x 3 matrix A are λ1 = 3, λ2 = 4, and det(A) = 60.

We know that the product of all eigenvalues of a matrix is equal to its determinant. So, we have:

λ1 * λ2 * λ3 = det(A)

Substituting the given values, we get:

3 * 4 * λ3 = 60

Simplifying, we get:

λ3 = 5

Therefore, the third eigenvalue is 5.

Statement (a) is false because having 2 unit eigenvectors does not guarantee that a matrix can be diagonalized.

Statement (b) is false because even if the eigenvalues are distinct, the eigenvectors may not be orthogonal.

Statement (c) is true because eigenvectors that correspond to distinct eigenvalues are always orthogonal.

Statement (d) is true because the eigenvalues of a 2 x 2 real matrix are the roots of a quadratic polynomial.

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To evaluate the integral of 5.3x^2 dx using trapezoidal rule with n = 10, we first need to break the interval [0, 5.3] into 10 subintervals of equal width. The width of each subinterval, h, is given by:

h = (b - a) / n = (5.3 - 0) / 10 = 0.53

where a = 0 is the lower limit of integration and b = 5.3 is the upper limit of integration.

Next, we need to calculate the function values at the endpoints of each subinterval. Let xi be the left endpoint of the ith subinterval, then:

x1 = 0
x2 = 0.53
x3 = 1.06
x4 = 1.59
x5 = 2.12
x6 = 2.65
x7 = 3.18
x8 = 3.71
x9 = 4.24
x10 = 4.77

Using these values, we can calculate the function values at each endpoint:

f(x1) = 5.3(0)^2 = 0
f(x2) = 5.3(0.53)^2 = 0.769547
f(x3) = 5.3(1.06)^2 = 6.119948
f(x4) = 5.3(1.59)^2 = 15.013238
f(x5) = 5.3(2.12)^2 = 28.451232
f(x6) = 5.3(2.65)^2 = 46.433928
f(x7) = 5.3(3.18)^2 = 68.961326
f(x8) = 5.3(3.71)^2 = 96.033426
f(x9) = 5.3(4.24)^2 = 127.650228
f(x10) = 5.3(4.77)^2 = 163.811732

Now, we can apply the trapezoidal rule formula to approximate the integral:

∫[0,5.3] 5.3x^2 dx ≈ h/2 * [f(x1) + 2f(x2) + 2f(x3) + ... + 2f(x9) + f(x10)]

Substituting the values we calculated above, we get:

∫[0,5.3] 5.3x^2 dx ≈ 0.53/2 * [0 + 2(0.769547) + 2(6.119948) + 2(15.013238) + 2(28.451232) + 2(46.433928) + 2(68.961326) + 2(96.033426) + 2(127.650228) + 163.811732]

∫[0,5.3] 5.3x^2 dx ≈ 614.660107

Therefore, the approximate value of the integral of 5.3x^2 dx using trapezoidal rule with n = 10 is 614.660107.

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