A piece of machinery depreciates $6000 the first year,
$5700 the second year, and $5400 the third year. If the
rate of depreciation is constant, what is the amount of
depreciation of the piece of machinery in the sixth year?

Answer:

x=4

Step-by-step explanation:

1. 2x+4=12

2. 2x+4-4=12-4

3. 2x=8

4. 2x/2=8/2

5. x=4

Answer:

x=4

Step-by-step explanation:

2x+4=12

Step 1: subtract both sides by 4

4-4=0 and 12-4=8

Now you are left with 2x=8

Step 2: divide 2 on both sides

2/2=1x and 8/2=4

Therefore, x=4

Answer:

look in explanation

Step-by-step explanation:

what is the probability of the ball hitting u in dodge ball in pe

what is the ratio of your computer to everyone else's in comp science

how much of your essay did you finish (in a fraction)

how many people are there in psychology class for every notebook?

we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

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The following are the percentage increase or decrease of each employee to the nearest whole number;

Ruiz = 13%

Aria = 36%

Jack = 6%

The employee who had an increase of at least 10% and sold $425 or more in product is Ruiz.

Ruiz:

Percent increase = change in sales / march sales × 100

= ($450 - $400) / $400 × 100

= $50/$400 × 100

= 13%

Aria:

Percent increase = change in sales / march sales × 100

= ($420 - $310) / $310 × 100

= $110/$310 × 100

= 36%

Jack:

Percent decrease = change in sales / march sales × 100

= ($460 - $432) / $460 × 100

= $28/$460 × 100

= 6%

Therefore, Ruiz is the only employee who receives a bonus.

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Therefore, a westbound driver will travel 16 miles more by taking the detour than if they could stay on the highway. Among the given options, the closest value to 16 is 14 that is option G.

To determine the additional distance traveled by taking the detour compared to staying on the highway, we can calculate the distances traveled in each direction.

On the map, the detour involves:

Traveling 1 mile straight west

Traveling 2 miles straight north

Traveling 6 miles straight west

Traveling 3 miles straight south

Traveling 1 mile straight east

Traveling 3 miles straight south

Adding up these distances, we get:

1 + 2 + 6 + 3 + 1 + 3 = 16 miles.

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The driver taking the detour will travel an additional 9 miles compared to the direct distance on the highway.

The question is about calculating the extra distance that a driver would need to travel while taking a detour compared to the direct distance on a straight, flat highway. The detour includes going 1 mile west, 2 miles north, 6 miles west, 3 miles south, 1 mile east, and 3 miles south. These individual distances add up to a total of 16 miles. The original highway is a straight line, which can be viewed as 7 miles west on a flat map (1 mile west before the detour and 6 miles west as part of the detour). Therefore, the driver taking the detour will have to travel an additional 9 miles.

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Answer:

\(\frac{1}{81}\)

Step-by-step explanation:

\(\frac{1}{3}\) × \(\frac{1}{3}\) × \(\frac{1}{3}\) × \(\frac{1}{3}\)

1 × 1 × 1 × 1 = 1

3 × 3 × 3 × 3 = 81

\(\frac{1}{81}\)

Answer:

b

Step-by-step explanation:

0.22x4

= 0.22+0.22+0.22+0.22

=0.88

Or

0.22*100=22

22*4=88

88:100=0.88

If f'(x)= (x-1)^2(x+4), then the function y=f(x) has: (C) one local minimum and one local maximum.

To determine the local minimums and maximums of y=f(x), we need to find the critical points where f'(x)=0 or where f'(x) does not exist.

In this case, f'(x)= (x-1)^2(x+4), which equals zero at x=1 and has a vertical tangent at x=-4.

To determine the behavior of the function around these critical points, we can use the first derivative test.

- At x=1, f'(x) changes from negative to positive, indicating that the function has a local minimum at x=1.
- At x=-4, f'(x) is negative on both sides, indicating that the function has a local maximum at x=-4.

Therefore, the answer is (C) one local minimum and one local maximum.

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The way that errors can be introduced are;

Giving the questionnaire to all participants when they arrive for their appointment does not follow the protocol;

The participant could fill out the questionnaire before experiencing the therapy session.

Statistical errors are defined as errors that describe the difference that exists between a value obtained from a data collection process and the 'true' value for the population. Thus, the greater the error, the less representative the data will be of the population.

There are two main errors in this case which are type I error and type II error.

A type I error is called false-positive and it occurs if an investigator rejects a null hypothesis that is actually true in the population.

A type II error is called false-negative and it occurs if the investigator fails to reject a null hypothesis that is actually false in the population.

Now, from the question, since the data collection protocol alls for a questionnaire to be administered to patients having knee replacement surgery after the third physical therapy appointment, then we can introduce an error by;

Giving the questionnaire to all participants when they arrive.

The participant could fill out the questionnaire before experiencing the therapy session.

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Giving a questionnaire to all par-ticipants follows the timing of theprotocol.

BReading the questionnaire to par-ticipants with poor reading skillsfollows the timing of the protocol.

CGiving the questionnaire to allparticipants when they arrive fortheir appointment does not fol-low the protocol; the participantcould fill out the questionnairebefore experiencing the therapysession.

DGiving the questionnaire to theparticipants after the appoint-ment to be completed while theyhave a snack follows the timingof the protocol.

Answer:

B

Step-by-step explanation:

i took the test

18 7/10 liters of milk does he milk from both cows.

According to the question

Mr. benjamin milk 8 1/5 from the black cow and 10 1/2 liters of the brown cow

Milk from both cows

= 8 1/5 + 10 1/2

converting mixed fraction into proper fraction

8 1/5 = \(\frac{8 \times 5 +1}{5}\) = 41/5

10 1/2 = \(\frac{10 \times 2 +1}{2}\) = 21/2

= \(\frac{41}{5} +\frac{21}{2}\)

= \(\frac{2 \times 41+21 \times 5}{10}\)

= \(\frac{82+105}{10}\)

= \(\frac{187}{10}\)

converting fraction into mixed fraction

= \(\frac{180+7}{10}\)

= 18 7/10

Therefore,

18 7/10 liters of milk does he milk from both cows.

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The equation of the line is y = -(3/4)x - 6.

A line is a perfectly straight, one-dimensional shape that extends endlessly in both directions and has no thickness.

Given that, the line passes through the points (-4,-3) and has a slope of -3/4.

The equation of the line in point-slope form is:

y - y₁= m (x -x ₁)

Substitute (x₁,y₁) = (-4,-3) and m = -3/4 into the above equation,

y - (-3) = -3/4 (x - (-4))

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

y = -(3/4)x -3 -3

y = -(3/4)x - 6

Hence, the equation of the line is y = -(3/4)x - 6.

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The number of days when they are both on the same page will be 8 days.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Nevaeh and Keshawn are perusing a similar book. Toward the start of the month, Nevaeh was on page 42 and Keshawn was on page 10. Nevaeh will peruse 11 pages each day and Keshawn will peruse 15 pages each day.

Let 'N' be the number of pages of the book and 't' be the number of days. Then the equations are given as,

N = 42 + 11 t            ...1

N = 10 + 15 t           ...2

From equations 1 and 2, then we have

15 t + 10 = 42 + 11 t

        4 t = 32

           t = 8

The number of days when they are both in the total agreement will be 8 days.

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Answer:

Yep I got that to! 20480

Step-by-step explanation:

I multiplyed them together

The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.

Let the area be y .

Area = (base) × (height)

Base = 2x

Height = h

Let the area of the rectangular pens be y .

∴ y = 2xh

Perimeter of all the fencing = 4x+3h

∴ 4x+3h = 120

now we solve for h

3h = 120-4x

h = 40 - 4/3 x

Now we will substitute this value in the above first equation:

y = 2xh

or, y = 2x (40 - 4/3 x)

or, y = 80x - 8/3 x²

Now for the maximum area we have to find the first order differentiation of y

now,

dy /dx = 80 - 16/3 x

At dy/dx = 0 we get the value of x for which y is maximum.

80 - 16/3 x = 0

or, - 16/3 x = -80

or, x = 15 feet

Hence height =  40 - 4/3 x = 40 - 20 = 20feet

Maximum area = 2xh = 2×15×40 = 1200 square feet

The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.

Disclaimer : The missing figure for the question is attached below.

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Answer:

--1-- (of set 23456)

2   4

5 3

 6

--2-- (of set 23456)

2   3

5 4

 6

--3-- (of set 23456)

2   5

6 3

 4

--4-- (of set 23456)

2   3

6 5

 4

--5-- (of set 23456)

3   5

4 2

 6

--6-- (of set 23456)

3   2

4 5

 6

--7-- (of set 23456)

3   6

5 2

 4

--8-- (of set 23456)

3   2

5 6

 4

--9-- (of set 23456)

3   5

6 4

 2

--10-- (of set 23456)

3   4

6 5

 2

--11-- (of set 23456)

4   5

3 2

 6

--12-- (of set 23456)

4   2

3 5

 6

--13-- (of set 23456)

4   6

5 3

 2

--14-- (of set 23456)

4   3

5 6

 2

--15-- (of set 23456)

5   4

2 3

 6

--16-- (of set 23456)

5   3

2 4

 6

--17-- (of set 23456)

5   6

3 2

 4

--18-- (of set 23456)

5   2

3 6

 4

--19-- (of set 23456)

5   6

4 3

 2

--20-- (of set 23456)

5   3

4 6

 2

--21-- (of set 23456)

6   5

2 3

 4

--22-- (of set 23456)

6   3

2 5

 4

--23-- (of set 23456)

6   5

3 4

 2

--24-- (of set 23456)

6   4

3 5

 2

--1-- (of set 34567)

3   5

6 4

 7

--2-- (of set 34567)

3   4

6 5

 7

--3-- (of set 34567)

3   6

7 4

 5

--4-- (of set 34567)

3   4

7 6

 5

--5-- (of set 34567)

4   6

5 3

 7

--6-- (of set 34567)

4   3

5 6

 7

--7-- (of set 34567)

4   7

6 3

 5

--8-- (of set 34567)

4   3

6 7

 5

--9-- (of set 34567)

4   6

7 5

 3

--10-- (of set 34567)

4   5

7 6

 3

--11-- (of set 34567)

5   6

4 3

 7

--12-- (of set 34567)

5   3

4 6

 7

--13-- (of set 34567)

5   7

6 4

 3

--14-- (of set 34567)

5   4

6 7

 3

--15-- (of set 34567)

6   5

3 4

 7

--16-- (of set 34567)

6   4

3 5

 7

--17-- (of set 34567)

6   7

4 3

 5

--18-- (of set 34567)

6   3

4 7

 5

--19-- (of set 34567)

6   7

5 4

 3

--20-- (of set 34567)

6   4

5 7

 3

--21-- (of set 34567)

7   6

3 4

 5

--22-- (of set 34567)

7   4

3 6

 5

--23-- (of set 34567)

7   6

4 5

 3

--24-- (of set 34567)

7   5

4 6

 3

Step-by-step explanation:

This javascript code is extremely brute-force, but it does the job:

function checkIfInSet(i, set) {

   return i.toString().split('').sort().join('') === set;

}

function checkIfMagic(s) {

   return (parseInt(s[0]) + parseInt(s[1]) == parseInt(s[3]) + parseInt(s[4]))

}

function printMagic(s) {

   console.log(`${s[0]}   ${s[4]}`);

   console.log(` ${s[1]} ${s[3]}`);

   console.log(`  ${s[2]}\n`);

}

function checkSet(set) {

   let counter = 1;

   for(let i=1; i<99999; i++) {

       if (checkIfInSet(i, set) && checkIfMagic(i.toString())) {

           console.log(`--${counter++}-- (of set ${set})`);

           printMagic(i.toString());

       }

   }

}

checkSet('23456');

checkSet('34567');

1st 2nd and last

Step-by-step explanation:

simplify your inequality

6x >= 3 + 4(2x -1)

6x >= 3 + 8x - 4

2x >= 1

x >= 1/2

so indeed the

1st one , the 2nd and the last one

first, second, last

Hope it helps

Answer:

Step-by-step explanation:

Your solution is in the picture format

The question number from the top is 6 then 5 , 4 , 3 ,2 and at last one is 1 so don't be confused

The three angle bisector of a triangle intersect at a single point that point of concurrency of the angle of bisectors is called the incenter.

Given:

the 3 angle bisectors of a triangle intersect.

when three angle bisector of a triangle intersect then that point of concurrency is called incenter.

Incenter:

The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle. In other words, it can be defined as the point where the internal angle bisectors of the triangle cross. This point will be equidistant from the sides of a triangle, as the central axis’s junction point is the center point of the triangle’s inscribed circle.

Incenter formula:

= (ax1+bx2+x3 / a+b+c  , ay1+by2+y3 / a+b+c).

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When measuring wind speed with a cup anemometer on a sailboat trip across the Atlantic Ocean, there are a few situations that may arise, as shown below:1. When the bearing of the axle is old, the type of error that occurs is systematic error. To reduce or overcome this error, you would need to replace the bearing to avoid it.

2. When there is turbulent flow, the type of error that occurs is random error. To overcome this error, you would have to wait for the wind to stabilize or take an average of many measurements.  3. When there is icing on the cups, the type of error that occurs is also random error.

To overcome this error, you would need to remove the ice or wait for it to melt before continuing the measurement.4. When there is strong tumbling of the sailboat, the type of error that occurs is systematic error. To overcome this error, you would need to find a way to stabilize the boat or take measurements when the boat is less unstable.

It is not well posed to use a cup anemometer to measure in-cabin air flow in a quiet environment because the device is not sensitive enough. The device needs a minimum wind speed to provide accurate readings, and it is not designed to measure low wind speeds. Therefore, it may not be the right tool for the job, and a different instrument may be more appropriate.

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Answer: m= -1/2

Step-by-step explanation:

m is the gradient of a line. and the formula for gradient is (y2-y1)/(x2-x1)

first, find a point on the line, (-2,1) and that is equal to (x1,y1)

then find another point on the line, (2,-1) and that is equal to (x2,y2)

then substitute your points into the formula above and that is equal to

(-1-1)/(2-(-2))

= -2/4

= -1/2

that is your answer

Answer:

-x-3 = y

Step-by-step explanation:

The analyst should use the alpha aesthetic. The alpha aesthetic makes some points on a plot more transparent than others to call out specific data points.

A set of points plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of correlation, if any, between the values of observed quantities or phenomena, scatter plots are crucial in statistics (called variables). In an effort to demonstrate the degree to which one variable is influenced by another, scatter plots are used to plot data points on a horizontal and vertical axis. The values of the columns set on the X and Y axes determine the position of the marker that represents each row in the data table.

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Answer: 2pi

\(l=\frac{\pi .4.90 }{180}=2\pi\)

Step-by-step explanation:

hope it's helpful ❤❤❤

THANK YOU.

The probability of the quadratic equation having real roots is 3/5 or 0.6.

To determine the probability that the quadratic equation 4x^2 + 4Yx + Y + 2 = 0 has real roots, we need to analyze the discriminant, which is the value inside the square root in the quadratic formula. The discriminant, Δ, is given by:

Δ = b^2 - 4ac

For the given quadratic equation, a = 4, b = 4Y, and c = Y + 2. So,

Δ = (4Y)^2 - 4(4)(Y + 2)

Δ = 16Y^2 - 16(Y + 2)

The equation has real roots if Δ ≥ 0. So, we need to find the probability that 16Y^2 - 16(Y + 2) ≥ 0, given that Y is uniformly distributed over (0, 5).

First, let's find the range of Y values for which the inequality holds true:

16Y^2 - 16(Y + 2) ≥ 0
16Y^2 - 16Y - 32 ≥ 0
Y^2 - Y - 2 ≥ 0

Factoring the quadratic, we get (Y - 2)(Y + 1) ≥ 0. The inequality holds for Y ∈ (-∞, -1) ∪ (2, ∞).

Now, let's find the probability:

Since Y is uniformly distributed over (0, 5), the total length of the interval is 5 (from 0 to 5). The interval where the inequality holds true within the given range is (2, 5), which has a length of 3 (from 2 to 5).

So, the probability of the quadratic equation having real roots is the ratio of the length of the interval (2, 5) to the length of the interval (0, 5):

Probability = Length of (2, 5) / Length of (0, 5) = 3 / 5

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Answer:

a)54 b)48 c)49 d)91

Step-by-step explanation:

here is your answer

MARK ME AS BRILLIANT