the production department of celltronics international wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. as an experiment, two employees were assigned to assemble the subassemblies. they produced 15 during a 1-hour period. then four employees assembled them. they produced 25 during a 1-hour period. the complete set of paired observations follows. number of assemblersone-hour production (units) 215 425 110 540

The solution to the given system of differential equations is x(t) = C₁e^(√46t) + C₂e^(-√46t) and y(t) = x - 1 + Ce^(-3t), where C₁, C₂, and C are constants determined by initial conditions or additional constraints specified for the system.

To solve the given system of differential equations using systematic elimination, we'll eliminate one variable at a time. Here's the step-by-step solution:

Step 1: Write the system of differential equations:

dx/dt = 6x + 10y

dy/dt = x - 3y

Step 2: Choose one equation to eliminate a variable. Let's eliminate the variable x by differentiating the first equation with respect to t:

d²x/dt² = d/dt(6x + 10y)

d²x/dt² = 6(dx/dt) + 10(dy/dt)

d²x/dt² = 6(6x + 10y) + 10(x - 3y)

d²x/dt² = 36x + 60y + 10x - 30y

d²x/dt² = 46x + 30y

Step 3: Substitute the expression for d²x/dt² back into the second equation:

d²x/dt² = 46x + 30y

dy/dt = x - 3y

Step 4: Now we have a second-order differential equation in terms of x only and a first-order differential equation in terms of y only. We can solve them separately.

To solve the second-order differential equation:

d²x/dt² = 46x + 30y

We assume a solution of the form x(t) = e^(rt), where r is a constant.

Taking the derivatives, we have:

dx/dt = re^(rt)

d²x/dt² = r²e^(rt)

Substituting these derivatives into the differential equation:

r²e^(rt) = 46e^(rt) + 30y

Since e^(rt) is a non-zero function, we can divide both sides by e^(rt):

r² = 46 + 30y/e^(rt)

Since this equation must hold for all t, the coefficients of e^(rt) must be equal on both sides:

r² = 46

r = ±√46

So, the general solution for the second-order differential equation is:

x(t) = C₁e^(√46t) + C₂e^(-√46t)

Step 5: Now let's solve the first-order differential equation for y:

dy/dt = x - 3y

Rearranging the equation:

dy/dt + 3y = x

We can use an integrating factor to solve this equation. The integrating factor is given by e^(∫3dt) = e^(3t):

e^(3t)dy/dt + 3e^(3t)y = xe^(3t)

Applying the product rule on the left side:

d/dt (e^(3t)y) = xe^(3t)

Integrating both sides with respect to t:

e^(3t)y = ∫xe^(3t) dt

e^(3t)y = ∫x d(e^(3t))

e^(3t)y = xe^(3t) - ∫e^(3t) dx

e^(3t)y = xe^(3t) - e^(3t) + C

Dividing both sides by e^(3t):

y = x - 1 + Ce^(-3t)

Step 6: Combine the solutions for x(t) and y(t):

x(t) = C₁e^(√46t) + C₂e^(-√46t)

y(t) = x - 1 + Ce^(-3t)

Therefore, the solution to the given system of differential equations is:

x(t) = C₁e^(√46t) + C₂e^(-√46t)

y(t) = x - 1 + Ce^(-3t)

where C₁, C₂, and C are constants determined by initial conditions or additional constraints specified for the system.

Therefore, The solution to the given system of differential equations is x(t) = C₁e^(√46t) + C₂e^(-√46t) and y(t) = x - 1 + Ce^(-3t), where C₁, C₂, and C are constants determined by initial conditions or additional constraints specified for the system.

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To determine which differential equation(s) are linear, we need to examine the form of each equation. A linear differential equation is one that can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x), b(x), c(x), and g(x) are functions of x.

The differential equation 2xy" - 5xy' + y = sin(3x) is linear. It can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x) = 2x, b(x) = -5x, c(x) = 1, and g(x) = sin(3x).
The differential equation (v)² + xy = In(x) is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (v)², where v represents the derivative of y with respect to x. This term does not have a linear coefficient.
The differential equation y' + sin(y) = e^(3x) is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = sin(y), and g(x) = e^(3x).
The differential equation (x²+1)y" - 3y - 2x³y = -x - 9 is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (x²+1)y", where the coefficient is a function of x.
The differential equation y' + xy = y" is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = x, and g(x) = y".

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At the given rate, the athlete could run 10.584 miles in 1.5 hours.

To determine how many miles the athlete could run in 1.5 hours at the given rate, follow these steps:

Step 1: Calculate the athlete's speed in miles per minute.

The athlete can run 6 miles in 51 minutes, so their speed is:

Speed = Distance ÷ Time = 6 miles ÷ 51 minutes ≈ 0.1176 miles per minute.

Step 2: Convert 1.5 hours to minutes.

1.5 hours = 1.5 × 60 = 90 minutes.

Step 3: Calculate the distance the athlete can run in 1.5 hours.

Distance = Speed × Time = 0.1176 miles per minute × 90 minutes ≈ 10.584 miles.

Therefore, at the given rate, the athlete could run approximately 10.584 miles in 1.5 hours.

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Answer:

Volume of cylinder = pi*r^2 * h

4300 = (22/7)*(r^2)((1.9*5280)

r^2 =30100/220704 =0.1364

r = √0.0364 = 0.369 = 0.37 ft.

There is only one such rectangle with the Largest area, since the derivative of A changes sign from positive to negative at x = sqrt(7/3), indicating that the function is increasing to the left of this point and decreasing to the right of this point.

The rectangle with the largest area that can be inscribed under the curve of the parabola y = 7 - x^2, with one side of the rectangle lying along the x-axis.Let's assume that the base of the rectangle is x units long, so its height is y = 7 - x^2. The area of the rectangle is then A = x(7 - x^2).

We can find the maximum area of the rectangle by finding the value of x that maximizes the area. To do this, we can take the derivative of A with respect to x and set it equal to zero:

dA/dx = 7 - 3x^2 = 0

Solving for x, we get:

x = sqrt(7/3)

This value of x gives the maximum area of the rectangle. To find the height of the rectangle, we substitute x = sqrt(7/3) into the equation for the parabola:

y = 7 - x^2 = 7 - 7/3 = 14/3

So the height of the rectangle is y = 14/3.

Therefore, the dimensions of the rectangle with the largest area that can be inscribed under the parabola y = 7 - x^2, with one side of the rectangle lying along the x-axis, are:

Base: x = sqrt(7/3)

Height: y = 14/3

that there is only one such rectangle with the largest area, since the derivative of A changes sign from positive to negative at x = sqrt(7/3), indicating that the function is increasing to the left of this point and decreasing to the right of this point.

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The variance of X is 2.92.

The variance of a random variable measures how much its values vary or spread out from the expected value. In this case, X represents the uppermost face of a fair die, which has six equally probable sides numbered from 1 to 6. The expected value of X, denoted as E(X), is the average of these numbers, which is (1+2+3+4+5+6)/6 = 3.5.

To calculate the variance, we need to find the squared difference between each possible outcome and the expected value, and then weigh them by their respective probabilities. The formula for variance is \(Var(X) = E[(X - E(X))^2]\).

For X, the possible outcomes are {1, 2, 3, 4, 5, 6}. So, the calculation becomes:

\(Var(X) = [(1-3.5)^2 * (1/6)] + [(2-3.5)^2 * (1/6)] + [(3-3.5)^2 * (1/6)] + [(4-3.5)^2 * (1/6)] + [(5-3.5)^2 * (1/6)] + [(6-3.5)^2 * (1/6)] = [(-2.5)^2 * (1/6)] + [(-1.5)^2 * (1/6)] + [(-0.5)^2 * (1/6)] + [(0.5)^2 * (1/6)] + [(1.5)^2 * (1/6)] + [(2.5)^2 * (1/6)]\)

      = 6.25/6 + 2.25/6 + 0.25/6 + 0.25/6 + 2.25/6 + 6.25/6

      = 17.25/6

      ≈ 2.92

Therefore, the variance of X is approximately 2.92.

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The volume of a right circular cone that has a height of 3.5 ft and a radius of 18.9 ft is given as follows:

1308.6 ft³.

The volume of a cone of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height, and then divided by 3.

V = πr²h/3.

The parameters for the cone in this problem are given as follows:

Hence the volume of the cone is given as follows:

V = 3.14 x 18.9² x 3.5/3

V = 1308.6 ft³.

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Rational equations can be used to solve a variety of problems that involve rates, times and work. Using rational expressions and equations can help you answer questions about how to combine workers or machines to complete a job on schedule.

Answer:

-8/5

Step-by-step explanation:

slope is rise over run. it's going down so it's negative. therefore, -8 over 5 is -8/5

Answer:

slope = -8/5

Step-by-step explanation:

slope =( -4-4)/(4-(-1)

= -8/5

Answer:

\(52^{\circ}\)

Step-by-step explanation:

Explanation is attached below.

Answer:

1.49 x 10^8

Step-by-step explanation:

(5.1x10^8) - (3.61x10^8)

(5.1-3.61) x 10^8

The value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

The history of pi dates back thousands of years, and over time, various civilizations have attempted to calculate its value with varying degrees of accuracy. One of the most inaccurate versions of pi was recorded by the ancient Babylonians around 2000 BC.

The Babylonians calculated the value of pi as 3.125, which is off by more than 6% from the actual value. It is believed that the Babylonians arrived at this value by using a rough approximation of a circle as a hexagon. They measured the perimeter of the hexagon and divided it by the diameter to get their approximation of pi.

This value was later refined by the ancient Egyptians and Greeks, who were able to calculate pi with greater accuracy. The Greek mathematician Archimedes, for instance, was able to calculate pi to within 1% accuracy by using a method of exhaustion.

It wasn't until the development of calculus in the 17th century that mathematicians were able to derive an exact formula for pi. Today, the value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

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The equation of the locus of the moving point that maintains a distance of 4 units from the X-axis is y = ±4, representing two parallel horizontal lines.

To find the equation of the locus of a point that always maintains a distance of 4 units from the X-axis, let's analyze the given information.

Let P(x, y) be the moving point and Q(x, 0) be the fixed point on the X-axis. The distance between P and Q is denoted by PQ. According to the problem, PQ is always 4 units.

Using the distance formula, we have:

PQ² = (x - x)² + (y - 0)²

Since the x-coordinate of both P and Q is the same (x - x = 0), the equation simplifies to:

PQ² = y²

Substituting the value of PQ as 4 units:

4² = y²

16 = y²

Taking the square root of both sides:

\(\sqrt{16 } = \sqrt{y^2}\)

±4 = y

Therefore, the y-coordinate of the moving point P can be either positive or negative 4, giving us two possible solutions for the y-coordinate.

Hence, the locus of the moving point P that maintains a distance of 4 units from the X-axis is given by the equation:

y = ±4

This equation represents two horizontal lines parallel to the X-axis, with y-coordinates at +4 and -4. Any point (x, y) on these lines will always be at a constant distance of 4 units from the X-axis.

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By solving a system of equations we will see that she sold 80 phones and 240 accessories.

Let's define the variables:

x = number of phones.

y = number of accessories.

We know that she makes $160 on commissions, and that she sold 3 times as many accessories as phones, so we can write the system of equations:

y = 3x

x*$8 + y*$4 = $160

To solve the system, we can replace the first equation into the second one.

x*$8 + (3x)*$4 = $160

x*$8 + x*$12 = $160

x*$20 =  $160

x  = $160/$20 = 80

She sold 80 phones, and the number of accessories is:

y = 3x

y = 3*80 = 240

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The slope of the line is undefined.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (-4, 6) and (-4, 1)

Now,

Since, The equation of line passes through the points (-4, 6) and (-4, 1)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (1 - 6) / (-4 - (-3))

m = - 5 / 0

m = ∞

Thus, The slope of the line is undefined.

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Answer:

Step-by-step explanation:

1. ✔️Using Pythagorean Theorem, thus the missing length, x, would be:

x² = 19² - 17² = 72

x = √72

x = 8.5 (nearest tenth)

✔️Area = ½*b*h

b = 17

h = 8.5

Area = ½*17*8.5 = 72.25 units²

✔️Perimeter = 19 + 17 + 8.5 = 44.5 units

2. ✔️Using Pythagorean Theorem, thus the missing length, x, would be:

x² = 5² + 13² = 194

x = √194

x = 13.9 (nearest tenth)

✔️Area = ½*b*h

b = 13

h = 5

Area = ½*13*5 = 32.5 units²

✔️Perimeter = 13 + 5 + 13.9 = 31.9 unit

3. ✔️Using Pythagorean Theorem, thus the missing length, x, would be:

x² = 20² - 10² = 300

x = √300

x = 17.3 (nearest tenth)

✔️Area = ½*b*h

b = 17.3

h = 10

Area = ½*17.3*10 = 86.5 units²

✔️Perimeter = 17.3 + 10 + 20 = 47.3 unit

4. ✔️Using Pythagorean Theorem, thus the missing length, x, would be:

x² = 5² + 14² = 221

x = √221

x = 14.9 (nearest tenth)

✔️Area = ½*b*h

b = 14

h = 5

Area = ½*14*5 = 35 units²

✔️Perimeter = 14.9 + 14 + 5 = 33.9 unit

Answer:i think its 115 degres

Step-by-step explanation:

Answer: 100

Step-by-step explanation:

Because 88.9% of the data falls between approximately 47.62 and Blank.

Answer:

174 Sq feet

Step-by-step explanation:

30+90+54 just add.

Answer:

174 sq ft

Step-by-step explanation:

Formula:

A = Lw

Note:

A rectangle has 3 set of different side.

Solve:

A = Lw

A = 5 × 9

A = 45 ×  2

A = 90

A = Lw

A = 5 × 3

A = 15× 2

A = 30

A = Lw

A = 3 × 9

A = 27× 2

A = 54

90 + 30 + 54 = 174 sq ft

Kavinsky

(a) Condition 2: Constant variance: The variance of the series is constant for all t, i.e., Var(Yt) = σ², where σ² is a constant for all t. Condition 3: Autocovariance is independent of time: Cov(Yt, Yt-h) = Cov(Yt+k, Yt+h+k) for all values of h and k for all t. (b) The test statistics for the Dickey-Fuller test is DFE = p - ρ / SE(p).

(a) If we let t=1, we have Y1= E1+A E0

Now let t=2, then Y2=Y1+ E2+A E1

On applying recursive substitution up to time t, we get Yt= E(Yt-1)+A Σ i=0 t-1 Ei

From the above equation, we observe that if A≠-1, the process {Yt} will be non-stationary since its mean is non-constant. There are three conditions that ensure a covariance stationary process: Condition 1: Constant mean: The expected value of the series is constant, i.e., E(Yt) = µ, where µ is a constant for all t. If the expected value is a function of t, the series is non-stationary.

(b) The problem of applying the Dickey-Fuller test when testing for a unit root when the model of a time series is given by t = pxt-1+u, where the error term ut exhibits autocorrelation is that if the error terms are autocorrelated, the null distribution of the test statistics will be non-standard, so using the standard critical values from the Dickey-Fuller table can lead to invalid inference.

The null hypothesis for the Dickey-Fuller test is that the time series has a unit root, i.e., it is non-stationary, and the alternative hypothesis is that the time series is stationary. In DFE = p- ρ / SE(p), p is the estimated coefficient, ρ is the hypothesized value of the coefficient under the null hypothesis (usually 0), and SE(p) is the standard error of the estimated coefficient.

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The three formulas for volume are V = a3 for a cube, V = l x w x h for a rectangular prism, and V = πr2h for a cylinder. Calculations for each are done by substituting the relevant measurements for each formula.

The formula for the volume of a cube is V = a3, where a is the length of one side of the cube. For example, if the side of the cube is 5 cm, then the volume of the cube is 5 x 5 x 5 = 125 cm3.

The formula for the volume of a rectangular prism is V = l x w x h, where l is the length, w is the width and h is the height. For example, if the length is 10 cm, the width is 5 cm and the height is 7 cm, then the volume of the rectangular prism is 10 x 5 x 7 = 350 cm3.

The formula for the volume of a cylinder is V = πr2h, where r is the radius of the cylinder, and h is its height. For example, if the radius is 5 cm and the height is 10 cm, then the volume of the cylinder is π x 5 x 5 x 10 = 785.4 cm3.

The three formulas for volume are V = a3 for a cube, V = l x w x h for a rectangular prism, and V = πr2h for a cylinder. Calculations for each are done by substituting the relevant measurements for each formula.

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Answer:

C

Step-by-step explanation:

1000mg=1g

Answer:

C. 0.4691 grams

Step-by-step explanation:

Divide by a thousand

Answer:

9.17cm (3s.f.)

Step-by-step explanation:

Using Pythagoras Theorem,

5² = 2² + (Height of Triangle)²

Height of Triangle = 4.5826cm (5s.f.)

Area = ½ × 4 × 4.5826

= 9.1652cm (5s.f.)

= 9.17cm (3s.f.)

Answer:

Step-by-step explanation:

Step one:

given

we are told that the total number of students is =16

so 25% of these students preferred pizza

Firstly, we want to know what 25% of 16 will be

so

=25/100*16

=0.25*16

=4

This means that only 4 students preferred pizza

Answer:

2/5+4/10

first find the LCM =10

Mytiply both numerator and denominator to have the denominator same value 2×2/5×2 + 4×1/10×1=

4/10 + 4/10 add numerator 8 / 10 both number divisible by 2 answer is 4/5

hope so it will help, if so please mark me brainliest

Answer:

AB

Step-by-step explanation:

A ray has one endpoint and the rest is a line, so AB would be the only answer that would make sense in this situation (because it's starting from A and B is a point on the ray).

Answer: Jing-mei's mother wants her to be a prodigy because her friend Lindo Jong's daughter Waverly is a chess prodigy. She also wants her daughter to be successful.

Step-by-step explanation:

Answer:

it 31 for sure but if not that than some thing is wrong

Step-by-step explanation:

15+12+4=31

The statement that knowing the value of x tells you nothing about the value of y can be explained by several scenarios. One possible scenario is when the values of x and y are not related in any way. In other words, there is no mathematical or logical connection between them.

Another scenario where knowing the value of x tells you nothing about the value of y is when there are multiple possible values of y for a given value of x. This occurs when the relationship between x and y is not one-to-one. For instance, if x represents a person's age and y represents their height, knowing someone's age does not determine their height since there are different heights for different ages.

Furthermore, it is possible that there is a relationship between x and y, but the value of y is affected by other factors besides x. For example, if x represents the amount of time a student spends studying and y represents their grade on a test, knowing the value of x does not completely predict the value of y because other factors like natural ability and test-taking skills may also play a role in determining the grade.

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