Can someone help me with this question plz?

Answer: A. 14,841

Step-by-step explanation:

To construct the matrix A using eigenvectors and eigenvalues, we normalize the given eigenvectors to obtain orthonormal vectors. We then form an orthogonal matrix P by arranging the orthonormal eigenvectors as columns. Next, we create a diagonal matrix D with the eigenvalues along the diagonal. Finally, we compute A using the formula A = PDPT.

(a) To normalize the eigenvectors, we divide each vector by its magnitude to obtain unit vectors. The normalized eigenvectors are:
v₁ = [1/√2, 1/√2, 0]
v₂ = [1/√3, -1/√3, 1/√3]
v₃ = [1/√6, -1/√6, -2/√6]
(b) To construct the matrix A, we form an orthogonal matrix P using the orthonormal eigenvectors as columns:
P = [v₁, v₂, v₃] = [[1/√2, 1/√3, 1/√6], [1/√2, -1/√3, -1/√6], [0, 1/√3, -2/√6]]
Next, we create a diagonal matrix D with the eigenvalues along the diagonal:
D = diag, -3, 12])
Finally, we compute A using the formula A = PDPT:
A = PDPT = [[1/√2, 1/√3, 1/√6], [1/√2, -1/√3, -1/√6], [0, 1/√3, -2/√6]] diag([8, -3, 12]) [[1/√2, 1/√3, 1/√6].T, [1/√2, -1/√3, -1/√6].T, [0, 1/√3, -2/√6].T]
Performing the matrix multiplication, we obtain the matrix A:
A = [[4, 0, 0], [0, -1, 0], [0, 0, 12]]
Therefore, the matrix A, constructed using the given eigenvectors and eigenvalues, is:
A = [[4, 0, 0], [0, -1, 0], [0, 0, 12]]

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Given:

Consider the given equation is

[tex]y=\dfrac{2}{5}x-1[/tex]

To find:

The equation of a line that is perpendicular to the graph of given line.

Solution:

Slope intercept form of a line is

[tex]y=mx+b[/tex]

where, m is slope and b is y-intercept.

Equation of given line is

[tex]y=\dfrac{2}{5}x-1[/tex]

Here, slope is [tex]\dfrac{2}{5}[/tex].

We know that, product of slopes of two perpendicular lines is -1.

[tex]m_1\times m_2=-1[/tex]

[tex]\dfrac{2}{5}\times m_2=-1[/tex]

[tex]m_2=-\dfrac{5}{2}[/tex]

The slope of perpendicular line is [tex]-\dfrac{5}{2}[/tex].

Only in option C, the slope of the line is [tex]-\dfrac{5}{2}[/tex].

Therefore, the correct option is C.

From the given option the slope of the line -5/2 is shown by the equation  [tex]y=-\dfrac{5}{2}x-4[/tex]   that is option B) and this can be determined by using the slope-intercept form.

Given :

Equation --    [tex]y=\dfrac{2}{5}x-1[/tex]     ---- (1)

First, determine the slope of the given line by using the slope-intercept form. The slope-intercept is given by the equation:

y = mx + c

Now, compare equation (1) with the above equation.

[tex]\rm m_1 =\dfrac{2}{5}[/tex]

c = -1

For a line to be perpendicular to the other line the product of the slope of both the line is equal to -1, that is:

[tex]\rm m_1m_2 = -1[/tex]

So, the slope of the line perpendicular to the line [tex]y=\dfrac{2}{5}x-1[/tex]  is:

[tex]\rm m_2 = -\dfrac{5}{2}[/tex]

So, from the given option the slope of the line -5/2 is shown by the equation  [tex]y=-\dfrac{5}{2}x-4[/tex]   that is option B).

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Answer:

This is correct

Step-by-step explanation:

Paul has made no mistakes but he probably is wondering if the 4x that he got in the equation is correct.  He might second guess that he shouldn't have subtracted the 3x from the 7x but instead divided the two numbers.

After approximately 2.4744 days, the number of bacteria in the culture will reach 7,144,200.

To find the number of days (x) after which the number of bacteria in the culture reaches 7,144,200, we need to solve the equation B(x) = 7,144,200.

The given equation for the growth of bacteria is B(x) = 9800(3)^x.

Setting B(x) equal to 7,144,200, we have:

9800(3)^x = 7,144,200

To solve for x, we can take the logarithm of both sides using base 3 logarithm:

log₃(9800(3)^x) = log₃(7,144,200)

Using logarithmic properties, we can simplify the equation:

log₃(9800) + log₃(3)^x = log₃(7,144,200)

Since log₃(3)^x is equivalent to x (since log₃(3) = 1), we can rewrite the equation as:

log₃(9800) + x = log₃(7,144,200)

Now, we can solve for x by isolating it:

x = log₃(7,144,200) - log₃(9800)

Using a calculator, we can compute the values:

x ≈ 5.2456 - 2.7712

x ≈ 2.4744

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Answer:

Step-by-step explanation:

Angle 1  = Angle 7

Angle 4  = Angle 8

Answer:

i need more information

Step-by-step explanation:

Answer:

1100 for $1200

Step-by-step explanation: it is

1200/1100 is 1.09

1100/1000 is 1.1

Answer:

Sod installation in an average 1/5-acre, or 8,712 square foot, yard costs $8,715 to $17,430. ... Expect sod installation to cost $1,000 to $6,000 for small yards that are between 1,000 and 3,000 square feet. ... Tulsa, Oklahoma, $1,100-$2,300.

This is my answer i think its correct tell me if it is..........?

Answer:

12$!❤️

Step-by-step explanation:

Answer:

x>-2  and x<5

-2 <x<5

Step-by-step explanation:

We have open circles at -2 and 5 and are between the two numbers so we have and AND statement. It can be written either

x>-2  and x<5

or

-2 <x<5

Answer: 100*1000

Step-by-step explanation:

You would multiply 100 by 1000. So it would be 100*1000 and it would equal 100000.

Answer:

the rate of change is $1.50 per mile

Step-by-step explanation:

this is because x is the amount of miles, so if it is $1.50 for every mile then every mile that is traveled you are to pay $1.50

Answer:

I think that's 1

Step-by-step explanation:

but not sure

Answer:

I'd say A because this question is just like y and xays.

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

the question is asking to subtract a from b, which is the same as asking to find a-b

answer = 5/6 - 3/4

= 10/12 - 9/12 (lowest common multiple of 6 and 4 is 12)

= 1/12

if you dont know how to find lowest common multiple by prime factorisation, you can make the common denominator 6x4 instead which is 24, so

5/6 - 3/4 = 20/24 - 18/24

=2/24 = 1/12

Answer:

Think

Step-by-step explanation:

Think its 2.

Answer:

n=-6

Step-by-step explanation:

-3n-4n-17=25

-7n-17=25

-7n=42

n=-6

Answer:

n = -6

Step-by-step explanation:

-3n-4n-17=25

Combine like terms

-7n -17 = 25

Add 17 to each side

-7n -17+17 = 25+17

-7n = 42

Divide each side by -7

-7n/-7 = 42/-7

n = -6

Answer:

See below

Step-by-step explanation:

Given a polygon with vertices

Translation rule is

New coordinates are

Answer:his answer is right

Step-by-step explanation:

Answer:

x ≥ $14.05

Step-by-step explanation:

I subtracted 45.95 from 60 to find how much she had left, which amounts to 14.05. I used x as the amount she can spend, and the inequality is as such.

Answer: she can spend $14.05

Step-by-step explanation:

$60-$45.95=$14.05

-2

Its this number because its the number right outside of the ()

Answer:

-2

Step-by-step explanation:

Step 1: Write expression

3 - 2(x + 1) + 5x - 4

We see here that we have parenthesis around (x + 1) and a number in front of it. If we were to expand this:

3 - 2x - 2 + 5x - 4

We would see that we would distribute a negative 2.

Answer:

B

Step-by-step explanation:

You need to multiply both numbers inside the parentheses by 5:

5 times x  = 5x

5 times 7  = 35

and then you'll get B

hope this helped UwU

Answer:

3. B. P = 134x + 20y

4. J. (10, 150), I(40, 120), G(60, 100), C(60, 0) and E(10, 0)

5. C. 60 mopeds 100 bicycles

Step-by-step explanation:

3. The given information are;

The number of mopeds the company must produce per month = 10

The number of mopeds the company can produce month = 60

The number of bicycles the company can produce per month = 120

The total sum of the produced mopeds and bicycles ≤ 160

The profit on a moped = $134

The profit on a bicycle = $20

Given that the number of moped produced = x and the number of bicycles produced = y

Therefore, we have;

Profit, P = $134 × x + $20 × y

Which gives;

B. P = 134x + 20y

4) From Desmos, using the following constraints;

x + y ≤ 160

10 ≤ x ≤ 60

0 ≤ y ≤ 120 we have;

The vertices of the constraint for the feasible region are;

J. (10, 150), I(40, 120), G(60, 100), C(60, 0) and E(10, 0)

5) We note that since the profit from each moped is more than the profit from the sale of each bicycle, the maximum possible number of moped should be produced, while the rest should be used to produce bicycles

Therefore, given that from the vertices, the maximum possible number of moped = 60, the number of bicycles to be produced should be 160 - 60 = 100 bicycles

Which gives;

C. 60 mopeds 100 bicycles.

3. The objective function should be option B. P = 134x + 20y

4. The vertices of the feasible region, given the constraints should be J(10, 150), I(40, 120), G(60, 100), C(60, 0) and E(10, 0)

5. The number of each product that should be manufactured per month should be option C. 60 mopeds 100 bicycles

3.

Here we assume that the number of mopeds produced = x

and the number of bicycles produced = y

So, the profit equation should be

Profit, P = $134 × x + $20 × y

That provides P = 134x + 20y

4) From Desmos, we used the following constraints;

x + y ≤ 160

10 ≤ x ≤ 60

0 ≤ y ≤ 120 we have;

So, The vertices of the constraint should be

J. (10, 150), I(40, 120), G(60, 100), C(60, 0) and E(10, 0)

5) The maximum no of mopeds should be 60

And, the no of bicycles that need to be produced is

= 160 - 60

= 100 bicycles

That provides  60 mopeds 100 bicycles.

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To calculate the mean of a data set, we need to sum up all the values and then divide by the total number of values.

Sum of the data set = 33 + 42 + 49 + 49 + 53 + 55 + 55 + 61 + 63 + 67 + 68 + 68 + 69 + 69 + 72 + 73 + 74 + 78 + 80 + 83 + 88 + 88 + 88 + 90 + 92 + 94 + 94 + 94 + 94 + 96 + 100

Count of values = 31

Mean = (Sum of the data set) / (Count of values)

Now we can substitute the values and calculate:

Mean = (33 + 42 + 49 + 49 + 53 + 55 + 55 + 61 + 63 + 67 + 68 + 68 + 69 + 69 + 72 + 73 + 74 + 78 + 80 + 83 + 88 + 88 + 88 + 90 + 92 + 94 + 94 + 94 + 94 + 96 + 100) / 31

After evaluating this expression, we find that the mean of the given data set is approximately 71.29 (rounded to two decimal places).

Therefore, the mean of the data set is 71.29.

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Answer:

its the last graph

Step-by-step explanation:

It the graph that represents the function given in the table is the graph [3].

The point slope form of a line is given by -

y - y₁ = m(x - x₁)

Given is a line that passes through the points (-2, 5), (0, 3), (1, 2) and (4, -1).

The general equation of the straight line is -

y = mx + c

where -

m is the slope of line

c is the y - intercept

Now -

We can calculate the slope as follows -

m = (2 - 3)/(1 - 0) = -1/1 = -1

Now, at [x] = 0, [y] = 3

Which is the y - intercept.

The equation of the line will be -

y = - x + 3

We will plot the graph and match it with the given ones.

It can be seen that graph 3 is the correct choice.

Therefore, it the graph that represents the function given in the table is the graph [3]. It is plotted and attached with the answer for reference.

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Step-by-step explanation:

i hope u can understand that

The probability that the restaurant will receive two or more complaints in the next week is approximately 0.907.

Given that a fast food restaurant keeps record of the number of customer complaints per week and it has had 4 complaints per week. Assume that the number of complaints follows a Poisson distribution. We need to find the probability that the restaurant will receive two or more complaints in the next week. To find the probability of two or more complaints in the next week, we need to subtract the probability of zero or one complaint from 1, since the sum of all probabilities is 1.

So ,P(X ≥ 2) = 1 - P(X < 2). Now, the probability of having no complaints P(X = 0) = (e^-λλ^x)/x!

Putting x = 0 and λ = 4,P(X = 0) = (e^-4 4^0)/0! = 0.0183Approximately P(X = 0) = 0.02

Now, the probability of having one complaint P(X = 1) = (e^-λλ^x)/x!

Putting x = 1 and λ = 4,P(X = 1) = (e^-4 4^1)/1! = 0.0733Approximately P(X = 1) = 0.073

So, P(X < 2) = P(X = 0) + P(X = 1)P(X < 2) = 0.02 + 0.073 = 0.093

Therefore, P(X ≥ 2) = 1 - P(X < 2)P(X ≥ 2) = 1 - 0.093P(X ≥ 2) = 0.907

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Answer:

[tex]{7}^{3} [/tex]

Step-by-step explanation:

simplify numerator to get

[tex] {7}^{7} [/tex]

simplify denominator to get

[tex] { ({7}^{2} )}^{2} [/tex]

which simplifies to

[tex] {7}^{4} [/tex]

now that it's

[tex] \frac{ {7}^{7} }{ {7}^{4} } [/tex]

the exponents subtract to get our final answer

Answer:

Step-by-step explanation:

(16-9)^7

[(5+2)^2]^2

(16-9)^7

823543

[(5+2)^2]^2

(49)^2

2401

823543/2401 = 343

Answer: 24 miles. Yes

Step-by-step explanation:

1/2in = 3 miles so 1in = 6 miles

6 x 4 = 24 so he will need 24 miles worth of gas to make it.

Answer:

2.25 miles  no Ryan does not have enough gas.

Step-by-step explanation:

first draw your proportion

------------------=---------------------

Next fill it out

30 miles                2.25 miles

                        =

4 inches                 3 miles

Then multiply 30 miles by 3 miles and you get 90

After you mutliply 30 by 3 which is 90, divide 90 by 4 and you get 2.25 miles.

Ryan only has  enough gas in his jeeep to drive 30 miles he needs to travel 2.25 miles to get to the island, so he does not have enough gas to get to the island.