A survey shows that in one year, the average number of bilingual employees in an office was 42. Assume that the standard deviation is 12 and the number of bilingual employees is Normally distributed. Include an appropriately labeled and shaded Normal curve for each part. There should be three separate curves. (a) What percentage of offices have more than 45 bilingual employees? (2 points) (b) What percentage of offices have less than 38 bilingual employees? (2 points) (c) What percentage of offices have between 40 and 45 bilingual employees? (

Answer:

2

Step-by-step explanation:

slope : ( The amount y increases , when x is increased by 1 )

slope : { y2 - y1 / x2 - x1 }

slope : y2 = 2

           y1 = -4

           x2 = 5

           x1 = 2

You must minus the values in the formula to find the slope line that passes through the points:

slope : { y2 - y1 / x2 - x1 }

slope : (2) - (-4) / (5) - (2)

=> 2 + 3 / 3

=> 6/3

=> 2

Text explanation:

Difference between both y-coordinates. = 6

Difference between both x-coordinates. = 3

Divide the difference between y and x. =

y/x =2

Which means the slope of the line that passes through the points (2,-4) and (5,2) is 2.

Hope this helps! Sorry it took so long! ⸜(｡˃ ᵕ ˂ )⸝ xx

The slope of the line that passes through the points (2, -4) and (5, 2) is 2.

A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

slope = (y₂-y₁)/(x₂-x₁)

The slope of the line that passes through the points (2, -4) and (5, 2) can be calculated as shown below,

Slope = (y₂-y₁)/(x₂-x₁) =  [2 - (-4)] / (5 - 2)= 6/3 = 2

Hence, the slope of the line that passes through the points (2, -4) and (5, 2) is 2.

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To find the points {a, b, c, d} from the given Discrete Fourier Transform ({1, i, 0, 4i}), we can apply the inverse Discrete Fourier Transform (IDFT) algorithm. The IDFT will reveal the original values of the sequence.

To find the points {a, b, c, d} by applying the inverse Discrete Fourier Transform (DFT), we can use the formula:

X(k) = (1/N) * Σ(x(n) * \(e^{(2\pi i * nk/N)}\))

where X(k) represents the DFT coefficients, x(n) represents the input sequence, N is the length of the sequence, i is the imaginary unit, and Σ denotes the summation.

Given that the DFT of the four-point sequence (a, b, c, d) is {1, i, 0, 4i}, we can write the equation as:

1 = (1/4) * (a + b + c + d)

i = (1/4) * (a - b - c + d)

0 = (1/4) * (a + b - c - d)

4i = (1/4) * (a - b + c - d)

Let's solve this system of equations to find the values of a, b, c, and d.

Multiplying the first equation by 4 and adding the second equation:

4 + i = (a + b + c + d) + (a - b - c + d)

4 + i = 2a + 2d

Multiplying the third equation by 4 and adding the fourth equation:

0 + 4i = (a + b - c - d) + (a - b + c - d)

0 + 4i = 2a - 2d

Now, let's solve these two equations simultaneously.

From the first equation, we have:

2a + 2d = 4 + i --> Equation 1

From the second equation, we have:

2a - 2d = 4i --> Equation 2

Adding Equation 1 and Equation 2:

4a = 4 + i + 4i

Simplifying:

4a = 4 + 5i

Dividing both sides by 4:

a = 1 + (5/4)i

Substituting the value of a back into Equation 1:

2(1 + (5/4)i) + 2d = 4 + i

Simplifying:

2 + (5/2)i + 2d = 4 + i

Rearranging terms:

2d = 4 - 2 - i - (5/2)i

2d = 2 - (7/2)i

Dividing both sides by 2:

d = 1 - (7/4)i

Now, let's substitute the values of a and d back into the original equations to find b and c.

Using the second equation:

i = (1/4) * (a - b - c + d)

i = (1/4) * ((1 + (5/4)i) - b - c + (1 - (7/4)i))

Simplifying:

i = (1/4) * (2 - b - c - (2/4)i)

Multiplying both sides by 4:

4i = 2 - b - c - i

Rearranging terms:

b + c + 5i = 2

Using the third equation:

0 = (1/4) * (a + b - c - d)

0 = (1/4) * ((1 + (5/4)i) + b - c - (1 - (7/4)i))

Simplifying:

0 = (1/4) * (2 + b - c + (5/4)i + (7/4)i)

0 = (1/4) * (2 + b - c + (12/4)i)

Multiplying both sides by 4:

0 = 2 + b - c + 3i

Rearranging terms:

b - c + 3i = -2

Now, we have two equations:

b + c + 5i = 2 --> Equation 3

b - c + 3i = -2 --> Equation 4

Let's solve this system of equations to find the values of b and c.

Adding Equation 3 and Equation 4:

(b + c + 5i) + (b - c + 3i) = 2 + (-2)

Simplifying:

2b + 8i = 0

Dividing both sides by 2:

b + 4i = 0

Therefore, b = -4i.

Substituting the value of b back into Equation 3:

(-4i) + c + 5i = 2

Rearranging terms:

c + i = 2 + 4i

Subtracting i from both sides:

c = 2 + 3i

Finally, we have found the values of a, b, c, and d:

a = 1 + (5/4)i

b = -4i

c = 2 + 3i

d = 1 - (7/4)i

So, the points {a, b, c, d} obtained by applying the inverse Discrete Fourier Transform are {1 + (5/4)i, -4i, 2 + 3i, 1 - (7/4)i}.

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Answer:

R=5.0095

D=25.0955

Step-by-step explanation:

C=r^2(3.14)

C=d(3.14)

78.8/3.14=d

Square root diameter to get radius.

The two column proof is completed by

Statement                                            Justification

1. DE || KL                                        1. Given

2. < DFE ≅ < LF-K                            2. Vertical Angles Theorem

3. < DEF ≅ < LKF                            3. Alternate Interior Angles Theorem

4. Δ FDE ≅ Δ FLK                           4. AAS postulate

According to the AAS Postulate, triangles are congruent if two angles and the non-included side of one triangle are congruent with two angles and the non-included side of another triangle.

In the given problem the side is non included and the angels are congruent and hence completes the proof

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Answer:

The 3rd one

Step-by-step explanation:

Obtuse triangles have 1 angle greater than 90 degrees

An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees.

It would be the third option <3

Find the probabilities

We can make a easy comparison by finding the percentage of the two

The percentage that a freshman has a summer job will be 64%

Now the seniors

26.2% of the seniors have a summer job.

So, the obvious comparison is that "a senior is less likely to have a job then a freshman" or the second option. Since the percentage that a freshman will have a job is much higher then the percentage a senior will have a job.

Here is the answer for the problem I believe

There are 16 possible 2-letter code words letters can be repeated. There are 12 possible 2-letter code words adjacent letters must be different.

If letters can be repeated, the number of possible 2-letter code words that can be formed from the given letters is determined by the formula:

Number of possibilities = (number of choices for the first letter) * (number of choices for the second letter)

Since we have 4 letters available (W, C, M, J), and we can repeat letters, the number of choices for each letter is 4.

Therefore, the number of possible 2-letter code words with repeated letters is:

4 * 4 = 16

If adjacent letters must be different, the number of possible 2-letter code words is determined as follows:

Number of possibilities = (number of choices for the first letter) * (number of choices for the second letter, excluding the previously chosen letter)

For the first letter, we have 4 choices. For the second letter, we have 3 choices because we need to choose a letter different from the first letter.

Therefore, the number of possible 2-letter code words with adjacent letters different is:

4 * 3 = 12

To summarize:

The number of possible 2-letter code words with repeated letters is 16.

The number of possible 2-letter code words with adjacent letters different is 12.

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Answer:

there will only be one 3

Step-by-step explanation:

see cause the first 3 of both numbers are 2 but only the last one of both numbers are 3 .

the function f(x) = 6x - 2 correctly models the given sequence. We conclude that the correct option is C.

Here we have the sequence {4, 10, 16, 22, ...} we want to find which function models this, we should have that:

f(1) = 4

f(2) = 10

f(3) = 16

etc...

If you look at the third option:

f(x) = 6x - 2

Evaluating it in x = 1 we get:

f(1) = 6*1 - 2 = 4

in x = 2

f(2) = 6*2 - 2 = 12 - 2 = 10

in x = 3

f(3) = 6*3 - 2 = 18 - 2 = 16

in x = 4

f(4) = 6*4 - 2 = 24 - 2 = 22

So the function f(x) = 6x - 2 correctly models the given sequence. We conclude that the correct option is C.

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Answer:

------------------

Convert 5 3/4 to an improper fraction:

Multiply both denominator and numerator by 3:

Equivalent fraction is 69/12.

Answer:

30.4

Step-by-step explanation:

17+28+32+35+59+20+19+33+30+31=304

304/10=30.4

Answer:

The values of a and b are:

Step-by-step explanation:

We know that the slope-intercept form of the line equation

y = ax+b

where

From the diagram of the line graph, we can fetch the two points

Determining the slope between (0, 2) and (-1, 0)

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(\left(x_1,\:y_1\right)=\left(0,\:2\right),\:\left(x_2,\:y_2\right)=\left(-1,\:0\right)\)

\(a=\frac{0-2}{-1-0}\)

\(a=2\)

Thus, the value of a = 2

We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

From the graph, it is clear

at x = 0, y = 2

Thus, the y-intercept b = 2

now substituting a = 2 and b = 2 in the slope-intercept form of the line equation

y = ax+b

y = 2x + 2         ∵ a = 2 , b = 2

Thus, the line of equation is:

y = 2x+2

now comparing with y = ax+b

Here:

a = 2

b = 2

Therefore, the values of a and b are:

Answer:

।बवछॅनछॅठै रटटृ रटटृरटॅलठट

Answer:

40

Step-by-step explanation:

4/5 * q = 32

First you divide 4/5 by itself so you can eliminate it from the equation and then you have to divide 32 by 4/5 n when you do that you get 40. So q = 40.

Answer: 4x-9y=27 is this equation in standard form.

Answer:

I dont know

Step-by-step explanation:

I was looking for the same answer to this question☠

The expression x + 80 represents the number of coins Arthur has now, since he x pennies and an additional 6 dimes and 4 nickels.

We shall convert the pennies, dimes and nickels into same unit before adding to get the expression for the number of coins Arthur will have in total.

A penny = 1 cent, so

x pennies = x cents

A dime = 10 cents so;

6 dimes = 6 × 10cents

6 dimes = 60 cents

A nickel = 5 cents so;

4 nickels = 4 × 5 cents

4 nickels = 20 cents

Arthur's coins in total = (x + 60 + 40) cents

Arthur's coins in total = (x + 80) cents.

Therefore, the expression expression x + 80 represents the number of coins Arthur will have in total, wether in pennies, dimes or nickels.

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Answer:

Step-by-step explanation:

c = 10h

h is the independent variable.

c is the dependent variable.

Answer:

An acute angle is greater than 0 and less than 90

Step-by-step explanation:

An acute angle is greater than 0 and less than 90

A right angle is 90 degrees

An obtuse angle is greater than 90 and less than 180

Answer:

Between 0 and 90 because think of a cute baby they are small put it to angles they are smaller than an obtuse angle and so on.

Step-by-step explanation:

Answer:

y=1 1/2x

Step-by-step explanation:

y= mx+c

1st point : (2,3)

2nd point : (4,6)

m= 3-6/2-4

= -3/-2

= 1 1/2

y=1 1/2x

The solution curve represents a spiral that converges towards the origin.

(a) To classify the behavior of the system, we can use the (A,T) chart. Here, A is the sum of the elements in each row of the system matrix and T is the sum of the absolute values of the off-diagonal elements.

The system matrix for this scenario is:

[ 0   1 ]

[-1   1 ]

So, A = 1 for both rows, and T = 1 (absolute value of the off-diagonal element).

Using the (A,T) chart, we can see that the system is a focus.

(b) To find the eigenvalues and eigenvectors of the system, we need to solve the characteristic equation:

| 0-lambda  1       |   |u|    |0|

| -1        1-lambda| \(\times\) |v| =  |0|

Expanding the determinant, we get:\(\lambda^2\) -\(\lambda\) + 1 = 0

Solving for lambda using the quadratic formula, we get:\(\lambda\) = (1 +/- sqrt(3)i) / 2

So, the eigenvalues are complex conjugates with a real part of 1/2. The eigenvectors can be found by solving the system of linear equations:(0 - lambda)u + v = 0

(-1)u + (1 - lambda)v = 0

For lambda = (1 + sqrt(3)i) / 2, we get:u = [1, -1 + sqrt(3)i]

For lambda = (1 - sqrt(3)i) / 2, we get:u = [1, -1 - sqrt(3)i]

(c) To sketch the solution curve that starts at R(0) = 1, J(0) = 1, we can use the eigenvectors and eigenvalues. The general solution for the system can be written as:[x(t), y(t)] = \(c_1 \times u_1 \times e^(l \ambda1 \times t) + c2 \times u2 \times e^(\lambda2 \times t)\)

where c1 and c2 are constants determined by the initial conditions, u1 and u2 are the eigenvectors, and lambda1 and lambda2 are the eigenvalues.

Plugging in the values, we get:

\([x(t), y(t)] = c_1 \times [1, -1 +\ sqrt(3)i] \times e^{((1 + \sqrt(3)i)t} / 2) + c_2\times [1, -1 - \sqrt(3)i] \times e^{((1 - \sqrt(3)i)t} / 2)\)

Using the initial condition R(0) = 1, J(0) = 1, we get:

\(c_1 + c_2 = 1\)

(-1 + sqrt(3)i)c1 + (-1 - sqrt(3)i)c2 = 1

Solving for \(c_1\) and \(c_2\), we get:

\(c_1\) = (1 + sqrt(3)i) / (2\(\times\) sqrt(3)i)

\(c_2\)= (1 - sqrt(3)i) / (2 \(\times\) sqrt(3)i)

Plugging in these values, we get:

[x(t), y(t)] = [1, 0] \(\times\) e^((1 + sqrt(3)i)t / 2) + [0, 1] \(\times\)  e^((1 - sqrt(3)i)t / 2)

This solution curve represents a spiral that converges towards the origin.

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Answer:

Step-by-step explanation:

Is the given equation factorable?

(x - 7)(x - 2) = x^ - 9x + 14 That doesn't work.

-7 * - 2  = 14 but the middle term is - 9 not - 5

x - 7 is not a factor  of x^ - 5x + 14

What is?

Something very ugly (x - 2.5 +/- 2.783 i )

Answer:

Option 2

Step-by-step explanation:

Answer:

it option 2

Step-by-step explanation:

Answer:

Step-by-step explanation:both are 1/6 of a chance

One possible argument that is time dependent is related to the concept of inflation. Inflation is the rate at which the general level of prices for goods and services is increasing over time, and it is typically measured by the Consumer Price Index (CPI). If we look at historical data for the CPI, we can see that it tends to fluctuate over time, with periods of high inflation (e.g. in the 1970s) followed by periods of low inflation (e.g. in the 1990s).

This time-dependent nature of inflation has important implications for various aspects of the economy, such as wages, interest rates, and investment decisions. For example, if inflation is high, workers may demand higher wages to keep up with the rising cost of living, which can lead to higher prices and further inflation. Similarly, if interest rates are low during a period of high inflation, investors may be less willing to lend money, which can slow down economic growth.

Without detailed computation, we can see that the time-dependent nature of inflation is a key factor that affects many aspects of the economy, and it is important to take this into account when making decisions or analyzing trends over time.
To provide an argument that is time dependent without detailed computation, let's consider the example of radioactive decay.

Radioactive decay is a process where an unstable atomic nucleus loses energy by emitting radiation. This decay is time dependent because the rate at which a radioactive substance decays is not constant, but instead is determined by its half-life. The half-life is the time it takes for half of the substance to decay.

Without going into detailed computations, we can argue that radioactive decay is time dependent by focusing on the concept of half-life. As time progresses, the amount of radioactive material decreases, and so does the rate at which it decays. This means that the rate of decay is not constant, but rather dependent on the amount of time that has passed since the process began.

In conclusion, radioactive decay serves as an example of a time-dependent process, as its rate is not constant but is instead governed by the half-life of the substance involved. This argument demonstrates the time dependence without going into detailed computations.

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The first step in constructing a segment congruent to a given segment is to draw a vertex and a ray.

Step 1: draw a vertex and a ray

Step 2: Draw a line segment that is longer than the specified line segment if we are not given the line segment on which we are to create the congruent section. The portion we just sketched will be known as the second line segment.

Step 3: Place the needle of the compass at an endpoint of the second line segment.

Step 4: Draw an arc of the circle so that it intersects the line segment.

Step 5: Label the point where we placed the needle and the point of intersection using two letters. The congruent line segment we want is the line segment formed by these two endpoints.

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Answer:

y=  -69/8  (negative 69 over 8)

Step-by-step explanation:

First, you have to simplify both sides of the equation:

\(-2/3y+ -3/4 =5\)

Second, add 3/4 to both sides:

-2/3y +-3/4 + 3/4=5 +3/4

-2/3y= 23/4

Next, multiply both sides by 3/(-2) (3 over -2)

(3/-2)*(-2/3y)= (3/-2) * (23/4)

y= -69/8

The number in scientific notation is 4.901 * 10^7

The number is given as:

Number = 49,010,000

A number in scientific notation is represented as:

a * 10^b

Where a is any number between 1 and 10.

So, we have:

Number = 4.901 * 10^7

Hence, the number in scientific notation is 4.901 * 10^7

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