Using the reduction of order method solve the differential equation 8y" – 12y' = 21. A. None of these. B. 12x / 8 y = Cie +C2 Oc. y = 23 xC x+c,ex 18+c2 + C2 12 OD. y = 21 2 12x / 8 x² + C, el +C2

Answer: \(g(x)=(x+3)^2\)

Step-by-step explanation:

When shifting a function left \(3\) units, \(f(x) \to f(x+3)\).

Therefore, \(g(x)=(x+3)^2\).

Answer:

8

Step-by-step explanation:

Intersecting chord theorem

12 * 4 = 6x

48 = 6x

x = 8

Answer:

9^ x -^ 5

Step-by-step explanation:

There are 560 ways to fill the 5 positions on the shelf, with the first 2 positions occupied by math books and the last 3 positions occupied by computer science books.

To determine the number of ways to fill the positions on the shelf, we need to consider the different combinations of books for each position.

First, let's select the math books for the first two positions. Since Mike has 8 different math books, we can choose 2 books from these 8:

Number of ways to choose 2 math books = C(8, 2) = 8! / (2! * (8-2)!) = 28 ways

Next, we need to select the computer science books for the last three positions. Since Mike has 6 different computer science books, we can choose 3 books from these 6:

Number of ways to choose 3 computer science books = C(6, 3) = 6! / (3! * (6-3)!) = 20 ways

To find the total number of ways to fill the positions on the shelf, we multiply the number of ways for each step:

Total number of ways = Number of ways to choose math books * Number of ways to choose computer science books

= 28 * 20

= 560 ways

Therefore, there are 560 ways to fill the 5 positions on the shelf, with the first 2 positions occupied by math books and the last 3 positions occupied by computer science books.

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Answer:

Option (2)

Step-by-step explanation:

Given function is,

9y - 6 = 3x

y = \(\frac{3x+6}{9}\)

To find the inverse of the given function,

1). Substitute x in place of y and y in place of x.

x = \(\frac{3y+6}{9}\)

2). Now we have to solve this equation for the value of y.

9x = 3y + 6

3y = 9x - 6

y = (3x - 2)

Therefore, inverse of the given function is y = (3x - 2)

Option (2) will be the answer.

WLS involves multiplying observation i by 1/ h_i, the WLS method will be viable without any further adjustments, this statement is True.

To use Weighted Least Squares (WLS) for estimating the Linear Probability Model (LPM) the steps are:

Step 1: Estimate the model using OLS and obtain the residuals, u_i.

Step 2: Determine whether all of the P(y|x1,x2) are inside the unit interval. If so, proceed to step 3. If not, adjust them so that all values fit inside the unit interval.

Step 3: Construct the estimated variance h_i = p(x_i) (1 - p(x_i)).

Step 4: Estimate the original model with weights equal to 1/ h_i.

Thus, the correct answer is True.

Suppose, for some i, y^i = −2.

Although WLS involves multiplying observation i by 1/ h_i, the WLS method will be viable without any further adjustments, this statement is True.

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The answer of 5+7-2+5=15

Answer:

2. 90+240= 330 m cubed

3. (24*2)+96= 144 cm cubed

Answer:

-0.8

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

Hello, I am also working on graphs at the moment!

Step-by-step explanation:

it is -8 units. If you place the points on a graph, you can see that it is going from point (4,5) and (4,-3) (the points given) now all you do is count the units between them.

Thus, the distance between the two points is, -8 units. Hope this helps! let me know if its right pls :) thx <3 (can also be written as- (0,-8) because its decreasing)

Answer:

yep

Step-by-step explanation:

bc I said something about math lol no used a caulqter

Can't spell, if my life depended on him.

Answer:

200+426x234 = 99884

Here is your answer

Looking at the sequence 2, 4, 6, 8, 10, ..., we can see that the first element is 2 and each subsequent element is 2 units more than the previous element.

Knowing that, we can write the equations:

Therefore the correct option is A.

The formula in getting possible zeros in rational root theorem is given as ± p / q.

According to rational root theorem if a polynomial expression which is written in descending order of the exponents and has integer coefficients, then any rational zero must be of the form ± p / q

Here, p is a factor of the constant term or the numerator and q is a factor of the leading coefficient or the denominator.

As the name implies, the rational root theorem is used to find the rational solutions to a polynomial equation . Polynomial roots or zeros are the solutions we get when we solve a  polynomial equation. A polynomial does not need required rational zeros only.

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Answer:

c. CBA = PQR

Step-by-step explanation:

after 3 trips, the probabilities for the driver's locations are approximately 0.524 for airport A, 0.274 for hotel B, and 0.202 for hotel C. If the driver starts at hotel B, after 3 trips, we expect them to be at hotel B with a probability of approximately 0.46. The stationary distribution of the chain indicates that, in the long run, the driver is most likely to be found at the airport (state A) with a probability of approximately 0.4167.

(a) To find the transition probability matrix, we assign the values A = 0, B = 1, and C = 2. The matrix will have dimensions 3x3, with each entry representing the probability of transitioning from one state to another.

Let's denote the transition probability matrix as P. The entries of P are given by:

P = [[0, 1/4, 3/4],

[4/5, 0, 1/5],

[4/5, 1/5, 0]]

(b) If the driver is initially at the airport (state A), we can find the probability of their location after 3 trips by multiplying the initial state vector [1, 0, 0] by the transition probability matrix P three times:

[1, 0, 0] * \(P^3\)= [0.524, 0.274, 0.202]

Therefore, after 3 trips, the probabilities for the driver's locations are approximately 0.524 for airport A, 0.274 for hotel B, and 0.202 for hotel C.

(c) If the driver is initially in hotel B (state B), we can calculate the probability of their location after 3 trips by multiplying the initial state vector [0, 1, 0] by the transition probability matrix P three times:

[0, 1, 0] *\(P^3\)= [0.46, 0.46, 0.08]

Therefore, after 3 trips, we expect the Uber driver to be at hotel B with a probability of approximately 0.46.

(d) To find the stationary distribution of the chain, we need to solve the equation π = π * P, where π is the stationary distribution vector. This equation represents the balance between entering and leaving each state in the long run. Solving this equation yields the following vector:

π = [0.4167, 0.2778, 0.3056]

Interpretation: The stationary distribution indicates the long-term probabilities of the Uber driver's location in the Markov chain. In this case, the Uber driver is most likely to be found at the airport (state A) with a probability of approximately 0.4167. Hotel C has the second highest probability of approximately 0.3056, while hotel B has the lowest probability of approximately 0.2778. This suggests that, on average, the Uber driver spends the most time at the airport, followed by hotel C, and the least time at hotel B.

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Answer:

C

Step-by-step explanation:

you can add that they meet at a 90° angle

\(f(x)=3x^2-6x+6\\\\f(x)=3(x^2-2x)+6\\\\f(x)=3(\underbrace{x^2-2x+1}-1)+6\\\\ f(x)=3[(x-1)^2-1]+6\\\\f(x)=3(x-1)^2-3+6\\\\f(x)=3(x-1)^2+3\)

Answer:

The 4 pint ketchup bottle was the better bargain.

Step-by-step explanation:

To find which bottle was the better bargain, find which one had the most amount of ketchup in it.

In one quart, there are 2 pints.

Convert the 1.25 quart bottle to pints by multiplying 1.25 by 2:

1.25(2)

= 2.5

Since 4 is larger than 2.5, the 4 pint bottle of ketchup has more.

So, the 4 pint ketchup bottle was the better bargain.

The Laplace transform of the given function f(t) = {0, 0 < t < 1, t², t ≥ 1} is 2s⁻³.

Given the function f(t) = {0, 0 < t < 1, t², t ≥ 1}, we need to find its Laplace transform. The Laplace transform of a function f(t) is denoted by F(s) and is defined as follows:

F(s) = L{f(t)} = ∫[0,∞) f(t)e⁻ᵃˣdt,

where s is a complex variable.

To find the Laplace transform of the given function, we need to split the function into two parts: one for 0 < t < 1 and another for t ≥ 1. For 0 < t < 1, f(t) = 0, so the integral becomes:

L{0} = ∫ 0e⁻ᵃˣdt = 0.

For t ≥ 1, f(t) = t², so the integral becomes:

L{t²} = ∫ t²e⁻ᵃˣdt.

To evaluate this integral, we can use integration by parts. Let u = t² and dv = e⁻ᵃˣdt, then du/dt = 2t and v = (-1/s) e⁻ᵃˣ. Using the integration by parts formula, we get:

L{t²} = ∫ t²e⁻ᵃˣdt = (-t²/s)e⁻ᵃˣ∣∣∣[0,∞) + (2/s)∫[0,∞) te⁻ᵃˣdt.

The first term in the above equation evaluates to zero because e⁻ᵃˣapproaches zero as t approaches infinity. Using integration by parts again for the second term, we get:

L{t²} = (-t²/s)e⁻ᵃˣ∣∣∣[0,∞) + (2/s)(-t/s)e⁻ᵃˣ∣∣∣[0,∞) + (2/s²)∫[0,∞) e⁻ᵃˣdt.

The first two terms in the above equation evaluate to zero for the same reason as before. The integral in the last term evaluates to (1/s²), so we get:

L{t²} = 2/s³.

Therefore, the Laplace transform of the given function f(t) is:

L{f(t)} = L{0} + L{t²} = 0 + 2/s³ = 2s⁻³.

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Check the picture below.

\(tan(\theta )=\cfrac{11}{10}\implies tan^{-1}[tan(\theta )]=tan^{-1}\left( \cfrac{11}{10} \right) \\\\\\ \theta =tan^{-1}\left( \cfrac{11}{10} \right)\implies \theta \approx 47.73^o\)

Make sure your calculator is in Degree mode.

Katelyn needs to mow 3 lawns to have enough money to buy the skateboard.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Let, 'x' be the no. of lawns she has to mow.

Given, Katelyn wants to buy a $75.00 skateboard and she has $25.00 saved and she mows lawns to make extra money and earns $20.00 for each lawn he mows.

Therefore the inequality that represents this context is,

20x + 25 ≥ 75.

20x ≥ 75 - 20.

20x ≥ 55.

x ≥ 55/20.

x ≥ 2.75, But she has to mow a lawn completely to get paid so she must mow 3 lawns.

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Answer:

3 lawns

Step-by-step explanation:

25 is what she haves now

3x20(how much she gets paid)=60

25+60=85

85-75=10 (she has 10 dollars left after she buys the skateboard

Answer:

answer choice A

Step-by-step explanation:

you make two equations.

Answer:

Step-by-step explanation:

Given expression:

Factor out 1/4:

Correct choice is A

Let's check one by one

#1

\(\\ \tt\longmapsto 1/4(n-64)=1/4n-64/4=1/4n-16\checkmark\)

#2

\(\\ \tt\longmapsto 1/4(n-4)=1/4n-1\)

#3

\(\\ \tt\longmapsto 4(n-4)=4n-16\)

#4

\(\\ \tt\longmapsto 4(n-64)=4n-256\)

4x+5x+=6+11

9x=17

x=17/9

☞ user58580~ ♥

Answer:

x= 17/9

Step-by-step explanation:

4x+5x=6+11

Combine like terms

9x=17

x=17/9

Answer:

I think it's C. 0

Step-by-step explanation:

On Edge