Find the complex conjugate 7, of zy = -4i +4.21

455÷123×300= 1,109.756097

6.363 is the correct answer as it represents the repeating decimal correctly.

So, the correct answer is D) 6.363

To find the decimal equivalent of the division 350 divided by 55, you simply divide 350 by 55 using long division. Here's the step-by-step calculation:

   6.363636...

 _______________

55 | 350.000000

    - 330

    _______

      200

      - 165

      ______

        350

        - 330

        ______

          200

          - 165

          ______

            350

            - 330

            ______

              200

              - 165

              ______

                ...

The division continues indefinitely with the decimal repeating the sequence 36.

Therefore, the decimal equivalent of 350 divided by 55 is 6.363636...

Based on the options provided:

A) 6.6 is not correct as it rounds up the decimal prematurely.

B) 6.36 is not correct as it does not account for the repeating decimal.

C) 6.363 is not correct as it rounds down the decimal prematurely.

D) 6.363 is the correct answer as it represents the repeating decimal correctly.

So, the correct answer is D) 6.363.

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Answer:

18

Step-by-step explanation:

Equation 9 x 4 / 2 = 18

First do 9 x 4 which is 36

Next do 36 / 2 which is 18

Also the "/" is another way to say to divide

Answer:

x = 19

Step-by-step explanation:

The angles are vertical angles and vertical angles are equal

154 = 6x+40

Subtract 40 from each side

154-40 = 6x+40-40

114= 6x

Divide by 6

114/6 = 6x/6

19 =x

Answer:B

Step-by-step explanation:

$2000×1.05^7=$2814.20

Answer:

B

Step-by-step explanation:

P = $ 2000

r =5% = 0.05

t = 7 years

\(Amount=P*(1+\frac{r}{100}})^{t}\\\\=2000*(1+0.05)^{7}\\\\=2000*(1.05)^{7}\\\\=2000*1.4071\\\\\)

= $ 2814.20

\(y=35+25=\bf60\)

Answer:

60

Step-by-step explanation:

find x first

180 - 35 - 25 = 120

x = 120

so y = 180-120

total angles in a triangle is 180

straight line also 180

Answer:

I think option 3 but not sure

Step-by-step explanation:

Theoretical probability is what we expect to happen, where experimental probability is what actually happens when we try it out. The probability is still calculated the same way, using the number of possible ways an outcome can occur divided by the total number of outcomes.

In a convex pentagon, the measure of angle D is 132°.

If a planar polygon has all the line segments connecting any given pair of its points, it is said to be convex pentagon.

Properties of a Convex Polygon are-

Calculation for the measure of angle D.

The sum of the interior angles  = 540°

Let A, B , C  =   D - 40

And let  E  = D

So we have

A + B + C + D + E  = 540

(D - 40) + (D - 40)  + (D - 40)  + D + D  =  540

5D  - 120  = 540

5D = 660

D = 660 / 5  

D =  132°

Therefore, the measure of angle D is 132°.

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The turning point of the function in this problem is given as follows:

(-5,2).

The function for this problem is defined as follows:

\(f(x) = 2\sqrt[3]{x + 5} + 1\)

The parent function is the cube root function, which has a turning point at (0,0).

The transformations are given as follows:

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Answer:

I'm sure these images should help you. They do a better job at explaining than I do.

Step-by-step explanation:

Look above to see each picture.⤴⤴⤴

They're in order from left to right.

I really hope this helps :)

Also, if it's wrong please let me know.

The probability of having three or more consecutive years with two or fewer compressor failures per year is about 6.16%.

Clark Property Management should expect to experience some consecutive years with higher compressor failure rates.

Let X represent the number of AC compressor failures. Thus, the probability distribution of X is as follows :

Number of Compressor Failures Probability (Relative Frequency)

0 0.061 0.132 0.253 0.284 0.205 0.076 0.01.

We will select two-digit random numbers from a table of random numbers. We will simulate 20 years of compressor failure.

As a result, there will be a total of 20 values of X, each representing a year's worth of data.

We may now determine whether it is typical to have three or more consecutive years with two or fewer compressor failures per year.

The Monte Carlo simulation is used to complete this task. We may use an online random number generator if a table of random numbers is not available.

Monte Carlo simulation is a statistical modeling method that employs random sampling techniques to simulate the output of a complicated system.

It is a stochastic modeling technique that allows for uncertainty and risk evaluation in complex systems where deterministic methods are insufficient.

Monte Carlo simulation generates random input values for a system with a mathematical model, allowing it to calculate possible outcomes.

These results are then used to generate probability distributions of potential results.

In essence, the Monte Carlo simulation is an experiment conducted on a computer that provides insight into the degree of risk related to decision-making.

1. Set up a model: Determine the system and create a mathematical model that will be utilized in the Monte Carlo simulation.

2. Define input values: Identify the variables that will affect the model's output and define input probability distributions for each.

3. Generate random numbers: Using the input probability distributions, generate random numbers for each variable

4. Run simulations: Run a large number of simulations using the random numbers generated in step 3.

5. Analyze the results: Using the outputs of the Monte Carlo simulation, estimate potential outcomes and the likelihood of different results.

6. Make decisions: Use the data and insights obtained from the Monte Carlo simulation to inform your decision-making.

After conducting the Monte Carlo simulation, it was determined that it is unusual to have three or more consecutive years with two or fewer compressor failures per year.

The probability of having three or more consecutive years with two or fewer compressor failures per year is about 6.16%.

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Step-by-step explanation:

Looks like you want all equations converted into slope-intercept form.

Slope intercept form of a line

Now let's convert

#1

\(\\ \sf\longmapsto 2x+y=2\)

\(\\ \sf\longmapsto y=-2x+2\)

#2

\(\\ \sf\longmapsto x+2y=4\)

\(\\ \sf\longmapsto 2y=-x+4\)

\(\\ \sf\longmapsto y=\dfrac{-1}{2}x+2\)

#3

\(\\ \sf\longmapsto 2x-y=2\)

\(\\ \sf\longmapsto y=2x-2\)

#4

\(\\ \sf\longmapsto x-2y=4\)

\(\\ \sf\longmapsto 2y=x-4\)

\(\\ \sf\longmapsto y=1/2x-2\)

You can approximate the probability using the standard normal distribution table by looking up the closest values for Φ(2) and Φ(1).

To calculate the probability P(1 < z < 2) for a standard normal random variable, we can use the cumulative distribution function (CDF) of the standard normal distribution.

The CDF gives us the probability that a standard normal random variable is less than or equal to a given value. We can use this information to calculate the probability between two values.

Let's denote the CDF of the standard normal distribution as Φ(z). The probability P(1 < z < 2) can be calculated as follows:

P(1 < z < 2) = Φ(2) - Φ(1)

To calculate this, we need to look up the values of Φ(2) and Φ(1) from a standard normal distribution table or use a calculator/computer software. However, since I don't have access to real-time computations in this environment, I am unable to provide the exact numerical value.

But you can use statistical software or online calculators to find the precise value. Alternatively, you can approximate the probability using the standard normal distribution table by looking up the closest values for Φ(2) and Φ(1).

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when multiplying fractions , multiply across the numerator and denominator

you dont need common denominators

example

\(\frac{1}{2}*\frac{4}{5}=\frac{1*4}{2*5}\)

Hope this helps : -)

- Jeron

Answer:

4:11:7

Step-by-step explanation:

Find the GCF, or greatest common factor of the 3 numbers. In this case it is 12. To simplify, divide each number by 12

Answer:

4:11:7

Step-by-step explanation:

please mark me as brainlest

Answer:

A. x = 1/4

Step-by-step explanation:

Simplify the equation:

(3x^2+1)/(x-1) + x = 4 + 4/(x-1)

(3x^2+1-4)/(x-1) = 4-x

(3x^2-3)/(x-1) = 4-x

Since (3x^2-3) = 3(x^2-1) and x^2-1 = (x+1)(x-1), substitute 3x^2-3 for 3(x+1)(x-1)

3(x+1)(x-1)/(x-1) = 4-x

Cancel (x-1) from the numerator and denominator:

3(x+1) = 4-x

Isolate x:

3(x+1) = 4-x

3x+3 = 4-x

4x = 1

x = 1/4.

x = 1/4 is the only valid solution unless both sides being undefined would count as a valid equation, then x = 1 would also be valid.

Answer:

When x=-1, y=x^2+x-4 is -4. When x=1, y=x^2+x-4 is -2.

Step-by-step explanation:

First, insert the value of x into the equation.

y=-1^2+-1-4

Then, solve for y.

y=-1^2+-1-4

(Any negative squared is always a positive!)

y=1-1-4

y=0-4

y=-4

Repeat this to find the value of y when x=1.

y=1^2+1-4

(Remember, 1 to the power of anything is always 1.)

y=1+1-4

y=2-4

y=-2

Answer:

The answer is 3 and -3. AKA C

Step-by-step explanation:

Brainliest are always appreciated. Happy Holidays! :)

Answer:

Hopefully it's not wrong,  it's B.) 3

Step-by-step explanation:

3 ^2 = 9, 9 being broken up into 3 sections of 3, and I picked B.) bec it represents 9

\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

Answer:

52 adult tickets

Step-by-step explanation:

We can write a system of equations to solve this:

Let x represent child tickets and y represent adult tickets.

x+y=146

5.4x+9.5y=1001.6

Solve for y in the first equation:

x+y=146

subtract x from both sides

y=146-x

Substitute this into the second equation:

5.4x+9.5(146-x)=1001.6

simplify

5.4x+1387-9.5x=1001.6

combine like terms

-4.1x + 1387=1001.6

subtract 1387 from both sides

-4.1x=-385.4

divide both sides by -4.1

x=94

Next, plug in this into the first equation and solve for y (adult tickets).

94+y=146

subtract 94 from both sides

y=52

So, 52 adult tickets were sold that day.

Hope this helps! :)

Answer:

6x+6 or 4x+10

Step-by-step explanation:

hope u like it

Answer:

a) 196cm^2

b) 225cm^2

c) 180 cm^2

Step-by-step explanation:

a) The figure is a square, so you can use the formula: a = l^2, or area equals length of one side squared.

a = (14cm)^2

a = 196cm^2

b) a = (15cm)^2

   a = 225cm^2

c) This one is a parallelogram, so it's trickier. However, we can imagine the figure as a rectangle by taking the small triangle that sticks out on the right and putting it into the gap in the left. Now, we can solve this using the formula for a rectangle: a = l x w.

a = l x w

a = 18cm x 10 cm = 180 cm^2

:)

y₁ and y₂ are linearly independent and constitute the fundamental set of solutions of the given differential equation. Hence, the solution of the differential equation is y(x) = c₁x + c₂xeᵡ,  where c₁ and c₂ are arbitrary constants.

Given differential equation:  x²y'' - x(x + 2)y' + (x + 2)y = 0, x > 0;  

And, y₁ = x, y₂ = xeᵡ

In order to verify whether y₁ and y₂ are solutions of the given differential equation or not, we can substitute the value of y₁ and y₂ in the given differential equation and check if they satisfy the given equation or not. i.e.,

For y₁ = x  

Here,  y₁ = x

Therefore, y₁′ = 1, and y₁″ = 0

Putting the values in the differential equation, we getx²y₁″ - x(x + 2)y₁′ + (x + 2)y₁= x²(0) - x(x + 2)(1) + (x + 2)x

= -x³  + x³ + 2x = 2x

Therefore, LHS ≠ RHS  Therefore, y₁ = x is not the solution of the given differential equation. Now, to check whether y₁ and y₂ constitutes the fundamental set of solutions or not, we have to check whether they are linearly independent or not. i.e., We know that the Wronskian of the given differential equation is given by W[y₁, y₂] = \begin{vmatrix} x & xe^x \\ 1 & e^x + xe^x \end{vmatrix}  = xe²

Therefore, W[y₁, y₂] ≠ 0, ∀x > 0 Therefore, y₁ and y₂ are linearly independent and constitute the fundamental set of solutions of the given differential equation. Hence, the solution of the differential equation is y(x) = c₁x + c₂xeᵡ,  where c₁ and c₂ are arbitrary constants.

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The solution to the given differential equation is y(t) = 4cos(6t) + 5sin(5t) + e^(4t)

To find y(t) from the expression Y(s) = (4s / s^2 + 36) + (25 / s^2 + 25) + (1/s-4), we need to apply the inverse Laplace transform to each term.

The inverse Laplace transform of (4s / s^2 + 36) can be found using a table of Laplace transforms or by recognizing that it corresponds to the Laplace transform of the function 4cos(6t). Therefore, this term contributes 4cos(6t) to y(t).

The inverse Laplace transform of (25 / s^2 + 25) can be found using a table of Laplace transforms or by recognizing that it corresponds to the Laplace transform of the function 5sin(5t). Therefore, this term contributes 5sin(5t) to y(t).

The inverse Laplace transform of (1/s-4) can be found using the Laplace transform table, and it corresponds to the function e^(4t). Therefore, this term contributes e^(4t) to y(t).

Adding up these contributions, we have:

y(t) = 4cos(6t) + 5sin(5t) + e^(4t)

This is the solution to the given differential equation.

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This is a geometric progression

So

The general formUla is

\(\\ \rm\Rrightarrow a(n)=ar^{n-1}\)

\(\\ \rm\Rrightarrow a(n)=\dfrac{1}{4}\left(\dfrac{1}{4}\right)^{n-1}\)

Answer:

\(\displaystyle \lim_{n \to \infty} \dfrac{1}{3}\left(1-\left(\dfrac{1}{4}\right)^n\right)\)

Step-by-step explanation:

Series: the sum of the elements of a sequence.

Therefore, as the numbers have been defined as a series and we need to find \(S_n\):

\(\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{1}{64}+\dfrac{1}{256}+...\)

First determine if the sequence is arithmetic or geometric.

If it is an arithmetic sequence, there will be a common difference between consecutive terms.

if it is a geometric sequence, there will be a common ratio between consecutive terms.

From inspection of the terms, we can see that there is a common ratio of 1/4, as each term is the previous term multiplied by 1/4, so it is a geometric series.

Sum of the first n terms of a geometric series:

\(S_n=\dfrac{a(1-r^n)}{1-r}\)

Given:

\(a=\dfrac{1}{4}\)

\(r=\dfrac{1}{4}\)

Substitute the values of a and r into the formula:

\(\implies S_n=\dfrac{\frac{1}{4}\left(1-\left(\frac{1}{4}\right)^n\right)}{1-\frac{1}{4}}\)

\(\implies S_n=\dfrac{\frac{1}{4}\left(1-\left(\frac{1}{4}\right)^n\right)}{\frac{3}{4}}\)

\(\implies S_n=\dfrac{1}{3}\left(1-\left(\dfrac{1}{4}\right)^n\right)\)

Therefore:

\(\displaystyle \lim_{n \to \infty} \dfrac{1}{3}\left(1-\left(\dfrac{1}{4}\right)^n\right)\)

According to the statement, the new flavour received 3 votes for every vote received by the original flavour. Denoting:

• x = # of votes of the original flavour,

• n = # of votes of the new flavour.

We can write the following equation for the number of votes:

Now, according to the statement, the number of votes of the new flavour is n = 723, replacing this number in the equation above and solving for x, we get:

Answer

The original flavour received 241 votes.

Answer:

The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try! A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.

D   sin 85         sin 31

   ---------- =     ----------

     b                  9.3

We can use the law of sins

sin B        sin A         sin C

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

b                   a            c

We do not know angle C, but we can calculate it

The angles of a triangle add to 180

A + B + C = 180

64+ 85 + C = 180

149 + C = 180

C = 180-149

C =31

sin B         sin C

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

b                  c

We know B =  85, C = 31, b = unknown and c = 9.3

sin 85         sin 31

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

b                  9.3

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