Please give the answer in this form
{ (1 point) Find the solution to the linear system of differential equations x(0) = -9 and y(0) = -5. x(t) = = y(t) = x' y² = = -16x + 30y -12x + 22y satisfying the initial conditions

The linear program is as follows:

T - M ≤ -20,000

P - T ≤ -5,000

N - T ≤ -5,000

S - T ≤ -5,000

G - T - P ≤ 0

L - G ≤ -200

N + S - 2T - 2P ≤ 0

B - P ≤ 0

B - S ≤ 0

B + P ≤ 60,000

L - B - T ≤ 0

Let's define decision variables for each employee's salary as follows:

Let T, P, N, S, G, L, and B represent the salaries of Tom, Peter, Nina, Samir, Gary, Linda, and Bob, respectively.

Our objective is to minimize the salary of the highest paid employee. We can achieve this by introducing another variable, M, that represents the maximum salary among all employees. Therefore, our objective is to minimize M.

Minimize: M

Subject to:

T ≥ 20,000

P ≥ T + 5,000

N ≥ T + 5,000

S ≥ T + 5,000

G ≥ T + P

L ≥ G + 200

N + S ≥ 2(T + P)

B ≥ max(P, S)

B + P ≥ 60,000

L ≤ B + T

Now, we can write the linear program in standard form by moving all variables to the left-hand side of the constraints and adding slack variables:

Minimize: M

Subject to:

T - M ≤ -20,000

P - T ≤ -5,000

N - T ≤ -5,000

S - T ≤ -5,000

G - T - P ≤ 0

L - G ≤ -200

N + S - 2T - 2P ≤ 0

B - P ≤ 0

B - S ≤ 0

B + P ≤ 60,000

L - B - T ≤ 0

All variables are non-negative.

This linear program can be solved using a linear programming solver to find the minimum value of M that satisfies all the constraints. Once we have the optimal solution, we can retrieve the salaries of each employee from the linear program solution.

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The greatest monomial factor of 15x³y² + 45x²y² + 30x²y³ is  15x²y².

What is a monomial factor?

Each term of a given polynomial contains a monomial factor, which can be either a number, a variable, or a mix of both. A polynomial with only one term is called a monomial. An algebraic expression known as a "monomial" has a single term but can also have multiple variables and a higher degree.

Here, we have

Given: 15x³y² + 45x²y² + 30x²y³

We have to determine the greatest monomial factor.

= 15x³y² + 45x²y² + 30x²y³

We factor out a 15 and divide each term by 15 as well.

= 15x²y²(x + 3 + 2y)

The greatest common factor is 15x²y² because, according to our factored equation, it is most commonly factored out for all the terms in the original polynomial equation.

Hence, the greatest monomial factor of 15x³y² + 45x²y² + 30x²y³ is  15x²y².

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Answer:the answer is b

Step-by-step explanation: 3x+x=4x

                                              -4y-y=-5y

                                                z-2z=-z

Answer:

Answer:the answer is b

Step-by-step explanation:

Answer:

POINTFARMER.EXE=EZ

Step-by-step explanation:

Answer:

120 feet^2

Step-by-step explanation:

The correct equivalent expression is 6x - 24.

Calculating the equivalent expression in this question is a one step process and requires multiplication. We will simply multiply the values in bracket with number outside the bracket. In the process, ensure copying the correct sign while writing the result.

Rewriting the expression 6(x - 4)

Equivalent expression = 6×x - 6×4

Performing multiplication on Right Hand Side of the equation

Equivalent expression = 6x - 24

Thus, the desired equivalent expression is 6x - 24.

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The complete question is -

Which expression is equivalent to 6(x-4)? 6x + 4 6x - 4 0 6x-24 0 46x + 24

An investment strategy with an expected return of 14 percent and a standard deviation of 8 percent has the potential for higher returns, but also comes with a higher level of risk. It is important to carefully consider the trade-off between risk and return before making an investment decision.

An investment strategy with an expected return of 14 percent and a standard deviation of 8 percent means that the investment has a higher potential for return, but also a higher risk.

The standard deviation is a measure of the variation or dispersion of a set of data values. In this case, the standard deviation of 8 percent indicates the degree of variation in the investment returns. A higher standard deviation means that the investment returns are more spread out and there is a higher chance of extreme values, both positive and negative.

In terms of investment strategy, it is important to consider the trade-off between risk and return. While a higher expected return is desirable, it often comes with a higher level of risk. Therefore, it is important to carefully consider the standard deviation and the potential risks associated with an investment before making a decision.

In conclusion, an investment strategy with an expected return of 14 percent and a standard deviation of 8 percent has the potential for higher returns, but also comes with a higher level of risk. It is important to carefully consider the trade-off between risk and return before making an investment decision.

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No, the use of the binomial distribution may not be appropriate for calculating the probability that exactly six 18-20 year olds consumed alcoholic beverages in a random sample of ten.

The binomial distribution assumes that the trials are independent, there are only two possible outcomes (success or failure), and the probability of success remains constant throughout the trials. In the case of consuming alcoholic beverages, the assumption of independence may not hold, as one person's decision to consume alcohol may influence another person's decision. Additionally, the probability of consuming alcohol may not remain constant throughout the sample, as some people may have stronger tendencies or preferences for drinking than others.

A more appropriate distribution for this scenario may be the hypergeometric distribution, which takes into account the finite population size (i.e. the total number of 18-20 year olds from which the sample is drawn) and the varying probabilities of success (i.e. the varying number of individuals in the population who consume alcohol).

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As long as the measures of the three angles of a triangle add up to less than 180 degrees, and none of the angles measures more than 90 degrees, the triangle will be acute.

An acute triangle is a triangle that has three acute angles, which are angles that measure less than 90 degrees. All three angles of an acute triangle must be acute, so they must measure less than 90 degrees. The measures of the three angles of an acute triangle can be any combination of angles that add up to less than 180 degrees.

Here are some examples of the measures of the three angles of an acute triangle:

45 degrees, 45 degrees, 90 degrees

30 degrees, 60 degrees, 90 degrees

35 degrees, 40 degrees, 105 degrees

60 degrees, 60 degrees, 60 degrees (this would be an acute equilateral triangle)

As long as the measures of the three angles of a triangle add up to less than 180 degrees, and none of the angles measures more than 90 degrees, the triangle will be acute.

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Answer:

Where is the Question?

Step-by-step explanation:

The distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

We can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the coordinates of M(6, 16) and Z(-1, 14), we get:

d = √((-1 - 6)² + (14 - 16)²) = √(49 + 4) = √53 ≈ 7.1

Therefore, the distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

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ANSWER and EXPLANATION

We are given that m<8 = 23 degrees.

First, let us find m<7.

m<7 and m<8 are angles on a straight line. Angles lying on a straight line sum up to 180 degrees.

This means that:

23 + m<7 = 180

m<7 = 180 - 23

m<7 = 157 degrees

Since m<8 and m<5 also lie on a straight line, we have that:

m<5 = 157 degrees

m<8 and m<6 are vertically opposite angles. Vertically opposite angles are equal, therefore:

m<6 = 23 degrees

m<8 and m<4 are corresponding angles, based on their positions. Corresponding angles are equal, therefore:

m<4 = 23 degrees

m<4 and m<2 are vertically opposite angles, therefore:

m<2 = 23 degrees

m<5 and m<1 are corresponding angles, therefore:

m<1 = 157 degrees

m<1 and m<3 are vertically opposite angles, therefore:

m<3 = 157 degrees

The geometric figures which could be this three-dimensional figure are:

A cross section can be defined as an exposed surface or shape that is formed when a cut is made through a three-dimensional figure.

In this scenario, the geometric figures which could be this three-dimensional figure are:

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-2x-6 =3x-21

Move all the variable terms ( the ones that have the x variable) to the left side of the equation:

-2x-3x = -21+6

Combine like terms

-5x = -15

Divide both sides of the equation by -5:

-5x/-5 = -15 /-5

x = 3

Answer: They can be arranged 720 different ways

Answer:

9 /4

Step-by-step explanation:

The slope of a line is given by

m = (y2-y1)/(x2-x1)

   = (5 - -4)/(3 - -1)

   = (5+4)/(3+1)

   = 9 /4

First, let us calculate the forecast for week 7. The naïve method (most recent value) is used to make the forecast. The most recent value is 15, so the forecast for the next week, which is week 7, is 15.

Using the naïve method as the forecast for the next week, the following measures of forecast accuracy are calculated.The given data is as follows:

Week 1 2 3 4 5 6Value 19 13 16 10 18 15.

Now we will calculate the Mean absolute error:

Mae = (19-13)+(13-16)+(16-10)+(10-18)+(18-15) / 5=6+3+6+8+3 / 5=6.4.

Therefore, the Mean absolute error is 6.4.

Mean squared error can be calculated as follows:

Mse = [(19-13)²+(13-16)²+(16-10)²+(10-18)²+(18-15)²] / 5=196 / 5=39.2.

Therefore, the Mean squared error is 39.2.

Now let us calculate Mean absolute percentage error:

Map = [ (6/19) + (3/13) + (6/16) + (8/10) + (3/18) ] / 5= 0.962.

Therefore, the Mean absolute percentage error is 0.96.

The forecast for week 7 is 15. Mean absolute error is 6.4. Mean squared error is 39.2. Mean absolute percentage error is 0.96.

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To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

What the first person said

Answer:

Area = 40 m^2

Step-by-step explanation:

The formula for any triangles is A = h x b / 2

In this problem, h = 8 m and b = 10 m

So area = 8 x 10 / 2 m^2 = 40 m^2

Answer:

You are Amazing and Beautiful. I hope you have the greatest day and be happy and safe always! I don't have much to say but I hope you have an amazing year ahead and be successful always :)

Answer:

I hope everyone is safe during this quarantine. It is times like these where we are better together. We (my family and I) are praying for all those who have been affected or knows someone who has beed affected. Hope everyone is safe and healthy. And thanks to you, I am able to say something nice to those who need to hear it!

Step-by-step explanation:

The position function x(t) is x(t) = e²(-4t)(5cos(2t) + 12sin(2t)),c = 16 and c-c = 8√5 =17.89. Since c < c-c, the motion is underdamped ,The position function x(t) in the form Ce²at cos(bt - α) is: x(t) = 13e²(-4t)cos(2t - 1.176).

To find the position function x(t) for the given system, to solve the second-order linear differential equation that describes the motion of the object. The equation is given by: m × d²x/dt² + c × dx/dt + k × x =0 where m is the mass, c is the damping constant, and k is the spring constant.

a. Find the position function x(t):

The differential equation. Substituting the given values,

2 × d²x/dt² + 16 × dx/dt + 40 × x = 0

This equation, a solution of the form x(t) = e²(rt), where r is a constant. Substituting this into the equation,

2 × r² × e²(rt) + 16 × r × e²(rt) + 40 × e²(rt) = 0

Dividing through by e²(rt),

2 ×r² + 16 × r + 40 = 0

Dividing the equation by 2 to simplify,

r² + 8r + 20 = 0

Using the quadratic formula,

r = (-b ± √(b²- 4ac)) / (2a)

a = 1, b = 8, and c = 20. these values into the formula:

r = (-8 ± √(8² - 4 × 1 × 20)) / (2 × 1)

= (-8 ± √(64 - 80)) / 2

= (-8 ± √(-16)) / 2

Since the discriminant is negative,

r = (-8 ± 4i) / 2

= -4 ± 2i

Therefore, the solution to the differential equation is of the form:

x(t) = e²(-4t)(C₁cos(2t) + C₂sin(2t))

To find the values of C₁ and C₂. The initial conditions x(0) = 5 and v(0) = 4. Differentiating x(t) with respect to t,

dx/dt = -4e²(-4t)(C₁cos(2t) + C₂sin(2t)) + e²(-4t)(-2C₁sin(2t) + 2C₂cos(2t))

At t = 0, x(0) = 5:

5 = e²0(C₁cos(0) + C₂sin(0))

5 = C₁

At t = 0, v(0) = 4:

4 = -4e²0(C₁cos(0) + C₂sin(0)) + e²0(-2C₁sin(0) + 2C₂cos(0))

4 = -4C₁ + 2C₂

4 = -20 + 2C₂ (substituting C₁ = 5)

24 = 2C₂

C₂ = 12

b. Is the motion overdamped, critically damped, or underdamped? Give your reasoning.

To determine the nature of the motion, the damping coefficient c to the critical damping coefficient c-c. The critical damping coefficient is given by:

c-c = 2 × √(m × k)

c-c = 2 × √(2 × 40)

= 2 × √80

= 2 × 4√5

= 8√5

If c > c-c, the motion is overdamped.

If c = c-c, the motion is critically damped.

If c < c-c, the motion is underdamped.

c. If it is underdamped, write the position function in the form Ce²at cos(bt - α).

The position function x(t) to be:

x(t) = e²(-4t)(5cos(2t) + 12sin(2t))

Comparing this to the desired form Ce²at cos(bt - α),

x(t) = e²(-4t)√(5² + 12²)cos(2t - α)

where √(5² + 12²) = 13 and α = atan(12/5) ≈ 1.176.

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The value of A such that the binary number is 35, must be A = 1.

We want to find the value of A such that:

1000A1 represents the number 35.

Remember that each of these numbers are the coefficient of the correspondent powers of 2, then we can write:

1000A1 = 1*2⁰ + A*2¹ + 0*2² + 0*2³ + 0*2⁴ + 1*2⁵

Solving that we will get:

1*2⁰ + A*2¹ + 0*2² + 0*2³ + 0*2⁴ + 1*2⁵ = 1 + 2A + 32

And that must be equal to 35, then:

1 + 2A + 32 = 35

2A = 35 - 33

2A = 2

A = 2/2 = 1

That is the value of A.

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Therefore, the value of c is 10.

Given: s(n) 4n2 -4n+ 5, then s(n) = 2s(n − 1) – s(n − 2) + c

for all integers n > 2.

The formula given is:

s(n) = 2s(n − 1) – s(n − 2) + c

Let's use this formula to find s(n) for n = 3.

s(n) = 2s(n − 1) – s(n − 2) + c

Substituting n = 3,

s(3) = 2s(3 − 1) – s(3 − 2) + c

s(3)= 2s(2) - s(1) + c

We know that s(2) and s(1) by using the given equation are as follows:

s(2) = 4(2)2 - 4(2) + 5

s(2) = 12s(1)

s(2) = 4(1)2 - 4(1) + 5

s(2) = 5

Substituting the values in the above equation:

s(3) = 2(12) - 5 + c

s(3) = 19 + c

Now we need to solve for c.

For that, we need to know the value of s(3).

s(3) is given by:

s(3) = 4(3)2 - 4(3) + 5

s(3)= 29

Substituting s(3) in the above equation, we get:

19 + c = 29

c = 29 - 19

c = 10

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Answer:6(17/21)

Step-by-step explanation:13/7*11/3

=143/21

=6(17/21)

Answer:

Option C

Step-by-step explanation:

Assuming P represents the number of outcomes, n the number of competitors and r the number of places to be awarded....

\(P = n! / ( n - r )!\\P = 8! / ( 8 - 3 )!\\P = 8! / 5!\\\\Algebra, P = 336 \\Solution = Option C\)

There are 336 different possible ways for the winners to be chosen.

Hope that helps!

Answer:

C

Step-by-step explanation:

Answer:

The diameter is 40

Step-by-step explanation:

The indefinite integral of |cosec(x) tan(2x)| dx is |cosec(x)| + C.

To find the indefinite integral of |cosec(x) tan(2x)| dx, we can split the absolute value into two cases based on the sign of cosec(x).Case 1: If cosec(x) > 0, then the integral becomes ∫(cosec(x) tan(2x)) dx. By using the substitution u = cos(x), du = -sin(x) dx, we can rewrite the integral as ∫(-du/tan(2x)). The integral of -du/tan(2x) can be evaluated using the substitution v = 2x, dv = 2dx. Substituting these values, we get -∫(du/tan(v)) = -ln|sec(v)| + C = -ln|sec(2x)| + C.Case 2: If cosec(x) < 0, then the integral becomes ∫(-cosec(x) tan(2x)) dx.

By using the substitution u = -cos(x), du = sin(x) dx, we can rewrite the integral as ∫(du/tan(2x)). Using the same substitution v = 2x, dv = 2dx, we get ∫(du/tan(v)) = ln|sec(v)| + C = ln|sec(2x)| + C.Combining the results from both cases, the indefinite integral of |cosec(x) tan(2x)| dx is |cosec(x)| + C, where C is the constant of integration.

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