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The total salary of all employees is obtained by adding the amount each of the employees earns in the company.

The mean salary of the employees is obtained by dividing the total salary of all employees by the number of employees given.Here is how to find the mean salary of the employees:Total salary for all employees = $20,700 + $24,000 + $325,200 + $31,600 + $146,200 = $547,700Number of employees = 10 + 2 + 8 + 1 + 5 = 26Mean salary for all employees = Total salary for all employees / Number of employees= $547,700 / 26= $21,061.54

Therefore, the mean salary for the employees is $21,062 (rounded to the nearest whole number).

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We have to find the mean salary for the employees. For this we will use the formula:Mean = Sum of all data values / Total number of data valuesThe given data values are as follows:$20,700, $24,000, $25,200, $25,200, $25,200, $25,200, $25,200, $25,200, $31,600, $146,200We need to find the sum of all data values, then divide by total number of data values. Sum of all data values = $20,700 + $24,000 + $25,200 + $25,200 + $25,200 + $25,200 + $25,200 + $25,200 + $31,600 + $146,200= $325,100Total number of data values = 10Mean = Sum of all data values / Total number of data values= $325,100 / 10= $32,510Therefore, the mean salary for the employees is $32,510 (rounded to the nearest hundred).

Answer: first option

Step-by-step explanation:

Triangle pairs are similar polygons if they have the same shape but not necessarily the same size. In order for two triangles to be similar, they must satisfy the following conditions:

They must have the same angles. This means that the measures of the angles in one triangle must be the same as the measures of the corresponding angles in the other triangle.

The lengths of the sides must be in the same ratio. This means that if you divide the lengths of the corresponding sides of one triangle by the lengths of the corresponding sides of the other triangle, you must get the same ratio for all pairs of sides.

For example, if triangle ABC is similar to triangle DEF, the ratios of AB/DE, AC/DF, and BC/EF must all be the same.

To determine if two triangles are similar, you can use one of several theorems and postulates, such as the Side-Side-Side (SSS) Similarity Theorem, the Side-Angle-Side (SAS) Similarity Theorem, or the Angle-Angle (AA) Similarity Postulate. These theorems and postulates provide different sets of conditions that must be satisfied in order for two triangles to be similar.

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Answer:

infinitely many solutions because both equations are the same

Step-by-step explanation:

The rule is reflection in y=x (x, y)→(y, x) and reflection in y=-x (x, y)→(-y, -x).

Given that, a rotation and reflection composition is equivalent to other compositions.

Reflection is flipping an object across a line without changing its size or shape. Rotation is rotating an object about a fixed point without changing its size or shape.

Rotation rule:

Rotation of a point through 180°, about the origin when a point A (x, y) is rotated about the origin O through 180° in the anticlockwise or clockwise direction, it takes a new position A' (-x, -y).

Reflection rule:

A vertical reflection reflects a graph vertically across the x-axis, while a horizontal reflection reflects a graph horizontally across the y-axis.

Therefore, the rule is reflection in y=x (x, y)→(y, x) and reflection in y=-x (x, y)→(-y, -x).

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The bottom width and depth of the trapezoidal channel are 2.25 m and 1.67 m, respectively.

In Windsor area of New South Wales, flood flow needs to be drained from a small locality at a rate of 120 m³/s in uniform flow using an open channel (n=0.018) Given the bottom slope as 0.0013 calculate the dimensions of the best cross section if the shape of the channel is (a) circular of diameter D and (b) trapezoidal of bottom width b.

(a) Circular channel:

For a circular channel, the best hydraulic section can be achieved by using the formula,

Q = (1 / n) x (A / P)2 / 3 x S0.5

where Q is the discharge; A is the area of the flow section; P is the wetted perimeter, S is the slope of the channel; and n is the roughness coefficient of the channel.

Assuming that the channel is flowing at full capacity, the depth of flow can be calculated using the following formula,

Q = (1 / n) x (π / 4) x D2 / 2 x D1 / 2 x S0.5

where D is the diameter of the channel; S is the slope of the channel; and n is the roughness coefficient of the channel.

Solving for D,

D = (8Q / πnD12S0.5)

For the given values of Q, n, and S,

D = (8 × 120 / π × 0.018 × 0.00132 × 120.5)

D = 1.98 m

Therefore, the diameter of the circular channel is 1.98 m.

(b) Trapezoidal channel:

For a trapezoidal channel, the best hydraulic section can be achieved by using the formula,

Q = (1 / n) x (A / P)2 / 3 x S0.5

where Q is the discharge; A is the area of the flow section; P is the wetted perimeter, S is the slope of the channel; and n is the roughness coefficient of the channel.

Assuming that the channel is flowing at full capacity, the depth of flow can be calculated using the following formula,

Q = (1 / n) x ((b + y) / 2) y / ((b / 2)2 + y2)0.5 x ((b / 2)2 + y2)0.5 x S0.5

where b is the bottom width of the channel; y is the depth of flow in the channel; S is the slope of the channel; and n is the roughness coefficient of the channel.

Rewriting the equation,

120 = (1 / 0.018) x ((b + y) / 2) y / ((b / 2)2 + y2)0.5 x ((b / 2)2 + y2)0.5 x (0.0013)0.5

Simplifying the equation,

658.5366 = (b + y) y / ((b / 2)2 + y2)0.5 x ((b / 2)2 + y2)0.5

Squaring both sides,

433407.09 = (b + y)2 y2 / ((b / 2)2 + y2) x ((b / 2)2 + y2)

Multiplying both sides by ((b / 2)2 + y2),

433407.09 ((b / 2)2 + y2) = (b + y)2 y2 x ((b / 2)2 + y2)

Simplifying the equation,

216703.545 = b2 y3 / 4 + b y4 / 2 + y5 / 4

Solving the above equation by using trial and error, the bottom width and depth of the trapezoidal channel are 2.25 m and 1.67 m, respectively.

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Answer:

3

Step-by-step explanation:

3

Answer:

3

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

5 x 4 x 2 = 40

length x width x height = volume

Answer:

=>A. -6x - 4

Step-by-step explanation:

=>-4(x + 2) - 2x + 4

=> -4x-8-2x+4

=> -6x-4

Answer:

25) A 26) B 27) y=-3/5-6 28) y=-15/18+4 29) y=5/4+12 30) y=-4x+3

Step-by-step explanation:

25) the line perpendicular would have the equation of y=-1/4x+b. In A, I plug in those to coordinated and they both have b as equal to -2 so they are both in the same line.

26) Find the slope of those two points (-1). Parallel lines means same slope but different y-intercepts and only B has a slope of -1.

27) Substitute those two points into the formula equation y=mx+b and solve for b

28) Solve for the slope and then solve for b by substituting

29) Write that equation into slope intercept form (y=5/4x-1). Parallel lines has the same slope but different y-intercepts. Use that slope of 5/4 and substitute those coordinates

30) Write the equation into slope intercept form (y=1/4x-5). Perpendicular lines have opposite reciprocal slopes. Find the opposite reciprocal of that slope and then substitute those coordinates

Hopefully I was able to help

Answer:

∠ GJK = 22°

Step-by-step explanation:

∠ HJI = ∠ JHG ( alternate angles ), then

7x - 16 = 5x + 8 ( subtract 5x from both sides )

2x - 16 = 8 ( add 16 to both sides )

2x = 24 ( divide both sides by 2 )

x = 12 , so

∠ KJI = 7x - 16 = 7(12) - 16 = 84 - 16 = 68°

Then

∠ GJI = 90° ( vertex of a rectangle )

∠ GJK = 90° - 68° = 22°

Answer:

He would have to use the method of polling

Step-by-step explanation:

Polliong would be the method used to solve hope this help

Yes because 60% is .60.

Answer:

no  0.345 would be 34.5%

The type of sampling described in the scenario is c. Cluster sampling.

Cluster sampling involves dividing the population into clusters or groups and randomly selecting some of these clusters. In this case, the state is subdivided into counties, which act as the clusters. Seven counties are selected at random, and further sampling is concentrated on these seven counties.

Cluster sampling is commonly used when it is not feasible or practical to directly sample individuals from the entire population. Instead, clusters or groups are randomly selected, and then a sample is taken from each of these clusters. This approach can be more efficient and cost-effective compared to other sampling methods, especially when the clusters are internally heterogeneous.

In this scenario, the initial random selection of the seven counties represents the cluster sampling, as subsequent sampling is focused on these specific clusters.

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Answer:

Step-by-step explanation:

its (x+1,y+-3)

Answer:5,200ft and 145in is less than a mile and 40in

Step-by-step explanation: I got this answer by first figuring out how many feet are in 145in so i did 145 divided by 12 which gave me 12.083... so I added just 12 to 5,200 which gives 5,212

Then I know that there are 5,280ft in 1 mile which is already bigger than 5,212 then I still add 40 divided by 12 which equals 3.3... to the total which gives me 5,283ft which is more than 5,212

Hope this Helps!

Answer:200 ounces

Step-by-step explanation: multiply 12.5 by 16

The measures of the angles are ∠1 = 127°, ∠2 = 53°, ∠3 = 127°, ∠4 = 37°, ∠5 = 53°, ∠6 = 90°, ∠7 = 37°, ∠8 = 143°, ∠9 = 37° and ∠10 = 143°

From the question, we have the following parameters that can be used in our computation:

The transversal lines and the other lines

So, we have

∠1 = 180 - 53

Evaluate

∠1 = 127°

Also, we have

∠5 = 53°

By vertical angles, we have

∠2 = 53°

∠3 = 127°

Next, we have

∠4 = 127 - 90°

∠4 = 37°

Solving further, we have

∠6 = 90°

By corresponding angles, we have

∠7 = 37°

∠9 = 180 - 90 - 53°

∠9 = 37°

∠10 = 90 + 53°

∠10 = 143°

∠8 = 143°

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Answer:

The person solving the problem first subtracted 6 from 15. Since the cube root is next to the six, the problem should be read as \(15-6(\sqrt[3]{\frac{-1000}{27} } )\) rather than \((15-6)(\sqrt[3]{\frac{-1000}{27} } )\).

please lmk if anything is wrong with my answer, hope this helps :)

Answer:

3x + 2y = 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - \(\frac{3}{2}\) , then

y = - \(\frac{3}{2}\) x + c ← is the partial equation

To find c substitute (6, - 8 ) into the partial equation

- 8 = - 9 + c ⇒ c = - 8 + 9 = 1

y = - \(\frac{3}{2}\) x + 1 ( multiply through by 2 to clear the fraction )

2y = - 3x + 2 ( add 3x to both sides )

3x + 2y = 2 ← in standard form

To find the Nth order Taylor Polynomial of the function f(x) = xe^(-x) expanded around x₀ = 1, we can use the Taylor series expansion formula.

We are asked to find the Taylor Polynomial for N = 4. By plotting the Taylor Polynomial and the original function for N = 0, 1, 2, 3, and 4, we can observe that the Taylor Polynomial approaches the original function as N increases.

The Taylor Polynomial P_N(x) is given by:

P_N(x) = f(x₀) + f'(x₀)(x - x₀) + f''(x₀)(x - x₀)²/2! + ... + f^N(x₀)(x - x₀)^N/N!

Substituting f(x) = xe^(-x) and x₀ = 1 into the formula, we can compute the coefficients for each term of the polynomial. The graph of P_N(x) and f(x) in the domain 0.5 ≤ x ≤ 1.5 shows that as N increases, the Taylor Polynomial approximates the function more closely.

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When moving from a 95% confidence interval to a 90% confidence interval, the width of the interval will decrease. (option b).

To understand this, let's consider a simple example. Suppose we want to estimate the mean height of all high school students in a particular region. We take a sample of 100 students and calculate the mean height to be 65 inches, with a 95% confidence interval of (63, 67) inches. This means that if we were to repeat this process many times, we would expect the true population mean height to be within this interval 95% of the time.

Now, if we were to calculate a 90% confidence interval instead, we would obtain a narrower interval because we are now willing to accept a greater risk of being wrong.

It is important to note that the width of the confidence interval depends on the sample size and the variability of the data.

As the sample size increases or the variability decreases, the confidence interval will become narrower. Conversely, as the sample size decreases or the variability increases, the confidence interval will become wider.

Hence the correct option is (b)

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The four experimental design concepts were applied in the 111-student research trial. Replication is necessary to establish that responses remain due to treatment, supplements, and social assistance.

In 1972, 111 youngsters were subjected to the experiment. They are healthy but impoverished infants. Social workers provided dietary supplements to infants.

Rules of experimental design are:

To determine the outcome of lurking variables, two classes must be used.

Before therapy, we must create equal classes using random assignments. To ensure that the difference in outcomes was caused by treatment rather than a random variable.

The results are tracked using 2 classes and comparison with hidden variables. The children are placed into two groups.

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Answer:

In problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. To find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

Step-by-step explanation: i hope this helps if it does vote me the brainliest or like and rate 5 starts if u cant vote me

Answer:

Solution : a value of the variable that makes an algebraic sentence true

Equation : a mathematical statement that shows two expressions are equal using an equal sign

Solution set : a set of values of the variable that makes an inequality sentence true

Order of operations: a system for simplifying expressions that ensures that there is only one right answer

Infinite : increasing or decreasing without end

Commutative property : a property of the real numbers that states that the order in which numbers are added or multiplied does not change the value

Answer:

standard form:   y = x² - 2x - 8

vertex form:  y = (x − 1)² - 9

factorized form:  y = (x + 2)(x - 4)

Step-by-step explanation:

From inspection of the graph:

Standard quadratic form:   y = ax² + b x + c

Vertex form of a quadratic equation:   y = a(x − h)² + k

If a > 0 then the parabola opens upwards

If a < 0 then the parabola opens downwards

(h, k) is the vertex

c is the y-intercept

Inputting the vertex into the vertex form gives:

y = a(x − 1)² - 9

  = a(x² - 2x + 1) - 9

  = ax² - 2ax - 8

Using the x-intercepts to create a quadratic equation:

y = a(x + 2)(x - 4)

  = a(x² - 2x - 8)

  = ax² - 2ax - 8a

Comparing the y-intercepts:

-8 = -8a  ⇒  a = 1

Therefore,   y = x² - 2x - 8

Sylvia's holdings in Maxima Growth add to her taxable income for the year assuming she decides not to sell the fund this year is $50.

Dividend income is a sort of revenue received by shareholders of certain companies. Dividend income is generated by company's profits and distributed on a per-share basis.

Some key features regarding income dividend are-

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The complete question is-

Sylvia owns 100 shares of Maxima Growth mutual fund.

In December she received a check for $50, payment of ordinary income dividend distributions and capital gains distributions.

Sylvia also noticed in her daily newspaper listings that Maxima Growth is now worth $2 per share more than what she purchased it for at the beginning of the year.

How much will Sylvia's holdings in Maxima Growth add to her taxable income for the year assuming she decides not to sell the fund this year?

The parameterization for the curve that satisfies the given conditions is:

x = (-ct)^(1/3) / 2^(1/3), y = 4 + ct, z = 0.

To find a parameterization for the curve that satisfies the given conditions, we need to express the equation of the curve in vector form. Let's define the vector function r(t) = ⟨x(t), y(t), z(t)⟩, where t is the parameter.

Since the curve is parallel to the xy-plane, we know that the z-coordinate of any point on the curve is 0. Therefore, we have z(t) = 0.

We also know that the curve passes through the point (0, 4, 2) when t = 0. Therefore, we have x(0) = 0, y(0) = 4, and z(0) = 2.

Now we just need to find an expression for x(t) and y(t) that satisfies the equation of the curve y = 4 - 8x³.

We can rewrite this equation as x³ = (4 - y)/8 and take the cube root of both sides to get:

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

Substituting this expression into our vector function, we get:

r(t) = ⟨(4 - y(t))^(1/3) / 2^(1/3), y(t), 0⟩

Now we just need to find an expression for y(t) that satisfies the initial conditions. Since y(0) = 4, we can take y(t) = 4 + ct, where c is a constant. This gives us:

r(t) = ⟨(4 - (4 + ct))^(1/3) / 2^(1/3), 4 + ct, 0⟩

Simplifying, we get:

r(t) = ⟨(-ct)^(1/3) / 2^(1/3), 4 + ct, 0⟩

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