What is solution to this system of equations? x + 4y = 12 and x = 0
PLSSS hurry​

The solution to the equation is y₂ = -13.51.

To find the exact value of y₂ without rounding, we will use the method of corner points. This method involves finding the corner points of the feasible region and evaluating the objective function at each corner point to determine the optimal solution.

Step 1: Setting up the inequalities:

Let's rewrite the constraints with variables in terms of a fraction:

Constraint 1: 5y₁ + 9y₂ + 4y₃ < 15 ... (1)

Constraint 2: 5y₁ + 18y₂ + 2y₃ > 8 ... (2)

Step 2: Solving for y₂:

To solve for y₂, we will express y₂ in terms of the other variables in the constraints.

From constraint (1), we have:

5y₁ + 9y₂ + 4y₃ < 15

9y₂ < 15 - 5y₁ - 4y₃

y₂ < (15 - 5y₁ - 4y₃)/9

From constraint (2), we have:

5y₁ + 18y₂ + 2y₃ > 8

18y₂ > 8 - 5y₁ - 2y₃

y₂ > (8 - 5y₁ - 2y₃)/18

Step 3: Analyzing the constraints:

Now we have the inequalities for y₂ in terms of y₁, y₃, and constants. Let's examine the conditions to satisfy the constraints:

y₂ > (8 - 5y₁ - 2y₃)/18 ... (3)

y₂ < (15 - 5y₁ - 4y₃)/9 ... (4)

Considering the constraints y₁ > 0, y₃ > 0, and y₂ > 0, we need to find the range of values for y₁ and y₃ that satisfy these inequalities.

Analyzing the inequalities:

Let's examine the intervals for y₁ and y₃ that satisfy the constraints:

From inequality (3):

y₂ > (8 - 5y₁ - 2y₃)/18

For y₁ > 0 and y₃ > 0, the numerator 8 - 5y₁ - 2y₃ should be positive to maintain y₂ > 0.

Simplifying the numerator:

8 - 5y₁ - 2y₃ > 0

8 > 5y₁ + 2y₃

This implies that 5y₁ + 2y₃ < 8.

From inequality (4):

y₂ < (15 - 5y₁ - 4y₃)/9

For y₁ > 0 and y₃ > 0, the numerator 15 - 5y₁ - 4y₃ should be positive to maintain y₂ > 0.

Simplifying the numerator:

15 - 5y₁ - 4y₃ > 0

15 > 5y₁ + 4y₃

This implies that 5y₁ + 4y₃ < 15.

Step 5: Finding the corner points:

To find the corner points, we need to determine the intersection of the lines 5y₁ + 2y₃ = 8 and 5y₁ + 4y₃ = 15.

Solving the system of equations:

5y₁ + 2y₃ = 8 ... (5)

5y₁ + 4y₃ = 15 ... (6)

Multiplying equation (5) by 2, we get:

10y₁ + 4y₃ = 16 ... (7)

Subtracting equation (6) from equation (7):

(10y₁ + 4y₃) - (5y₁ + 4y₃) = 16 - 15

5y₁ = 1

Dividing both sides by 5:

y₁ = 1/5

Substituting y₁ = 1/5 into equation (5):

5(1/5) + 2y₃ = 8

1 + 2y₃ = 8

2y₃ = 8 - 1

2y₃ = 7

y₃ = 7/2

Therefore, one corner point is (y₁, y₂, y₃) = (1/5, ?, 7/2).

Step 6: Evaluating the objective function:

Now, let's evaluate the objective function at the corner point (1/5, ?, 7/2) to find the value of y₂.

Substituting the corner point into the objective function:

w = 35y₁ + 72y₂ + 65y₃

w = 35(1/5) + 72y₂ + 65(7/2)

w = 7 + 72y₂ + 2275/2

w = 7 + 72y₂ + 1137.5

w = 1144.5 + 72y₂

172 = 1144.5 + 72y₂

Let's start by subtracting 1144.5 from both sides of the equation:

172 - 1144.5 = 1144.5 + 72y₂ - 1144.5

This simplifies to:

-972.5 = 72y₂

To isolate y₂, we can divide both sides of the equation by 72:

-972.5 / 72 = 72y₂ / 72

Simplifying further:

-13.51 = y₂

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Complete Question:

Solve. Minimize: w = 35y₁ + 72y₂ +65y₃

Subject to: 5y₁ +9y₂ + 4y₃ < 15

5y₁ + 18y₂ + 2y₃ > 8

With: y₁ > 0; y₂ > 0; y₃ > 0

Write only the exact value for y₂.

Do not round. If necessary, write as a fraction or improper fraction. Show your work on separate paper.

1) Let's rewrite it into the z=a +bi form.

2) So we can write out the following noticing that i² =-1 as well as √-1=i

Note that in this number the real part "a" is equal to 0.

Answer: 5.099

Step-by-step explanation:

Scatter plot is best for analyzing relationship between two variables.

What is scatter ?

In statistics and data visualization, a scatter plot (also called a scatter graph or scatter chart) is a type of graph used to display the relationship between two sets of data. It is a two-dimensional plot that uses Cartesian coordinates to display values for typically two variables for a set of data.

A scatter plot is a graph that uses dots to represent values for two numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point. Scatter plots are a useful tool for visualizing the relationship between two variables, such as how changes in one variable may be associated with changes in another variable.

Scatter plots can show the following types of relationships:

Positive correlation: as one variable increases, the other variable increases.

Negative correlation: as one variable increases, the other variable decreases.

No correlation: there is no relationship between the two variables.

Non-linear relationship: the relationship between the two variables is not linear.

Scatter plot is best for analyzing relationship between two variables.

Complete Question: Which of the following types of graph is the best kind to use for analyzing how two variables are related?

Line Graphs, Bar Graphs, Pie Charts, Scatter Plots

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hi

A fraction has two parts  :  

- numerator           ( number on the top of fraction bar )

- and  denominator  ( number under the fraction bar )

To compare two fractions, they must have the same denominator.

When it is the case, you check for numerator.  

Then, you just ask the same question you would do, as you would with two numbers.

Now what do we have here ?     8/10 and  5/10

As 10 is denominator for both , let compare numerator.  we have 8 and 5

well, we both know that  8 ≥ 5 ,   so   8/10 ≥ 5/10  

Each person eats at least one fruit. Hence 39% of people eat both orange and apple using the probability.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics. From the given data

n(O)=0.63

n(A)=0.76

n(A∪O)=1 as every person eats at least one fruit

n(A∪O)=n(A)+n(O)−n(A∩B)

1=0.63+0.76−n(A∩B)

n(A∩B)=1.39−1

n(A∩B)=0.39

A∩B=0.39×100=39

Hence 39% of people eat both orange and apple

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The confidence interval 0.039 < p < 0.479 in the form of (p) hat ± E is 0.259 ± 0.22.

(p) is given by the sum of confidence divided by 2

(p) hat = sum of confidence interval / 2

The confidence interval is 0.039 < p < 0.479

(p) hat = ( 0.039 + 0.479 ) / 2

(p) hat = 0.518 / 2

(p) hat = 0.259

E =  margin of error

The margin of error is the difference in confidence divided by 2

E = Difference of confidence interval / 2

E = (0.479 - 0.039) / 2

E = 0.44 / 2

E = 0.22

(p) hat ± E = 0.259 ± 0.22

Hence the confidence interval 0.039 < p < 0.479 in the form of (p) hat ± E is  0.259 ± 0.22.

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Rounding to the nearest hundredth, the area of the sector is approximately 152.30 cm².

To find the area of a sector, you can use the formula:

\(Area = (\theta /360) \times \pi \times r^2\)

where θ is the central angle and r is the radius.

Plugging in the given values:

θ = 144°

r = 11 cm

π = 3.14

\(Area = (144/360) \times 3.14 \times 11^2\)

Simplifying:

\(Area = (0.4) \times 3.14 \times 121\)

\(Area = 48.4 \times 3.14\)

\(Area = 152.296 cm^2.\)

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Answer:

No estoy seguro, intenta preguntarle a tu profesor

Step-by-step explanation:

Answer:

C. 0.26

Step-by-step explanation:

Answer:

(0,0), (0,1), (1,2), (1,3)

Step-by-step explanation:

To determine what makes ordered pairs a function, we have to make sure each input (x) goes to exactly one output (y).

The reason this is the answer is that each input doesn't have exactly one output. (0 goes to 0 and 1. 1 goes to 2 and 3).

Answer:

Step-by-step explanation:

1. Let us assume that we are solving for the frame of the deck alone

2. And also from the given parameters the deck has a rectangular shape

we know that the total amount of woods to be used is same as the perimeter of the rectangle.

Given that

length l= 60 ft

width w= 8 ft

The formula for the perimeter of a rectangle is given as

Perimeter= 2l+2w

perimeter= 2*60+ 2*8

perimeter= 120+16

perimeter= 136 ft

Hence in other to construct the frame of the deck Adam needs a total of 136 ft of woods

The probability that both randomly selected people own a dog is approximately 0.0361, or 3.61%.

To find the probability that both randomly selected people own a dog, we need to multiply the probabilities of each event occurring.

Given that 19% of people own dogs, the probability that a randomly selected person owns a dog is 0.19.

Since we're selecting two people independently, the probability that both of them own a dog can be calculated by multiplying the probabilities:

P(both own a dog) = P(owning a dog for person 1) * P(owning a dog for person 2)

P(both own a dog) = 0.19 * 0.19 = 0.0361

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The value of the integral after evaluating them is given by

a. ∫\(e^\sqrt{x}\) dx is equal to  2√x × \(e^\sqrt{x}\) - 2\(e^\sqrt{x}\) + C.

b.  ∫ [-∞, 0] x\(e^{-x\) dx is equal to  -x\(e^{-x\) - \(e^{-x\) + C.

a. To evaluate the integral ∫\(e^\sqrt{x}\)dx, we can use a substitution.

Let's substitute u = √x.

Then, differentiating both sides with respect to x,

we have du/dx = 1 / (2√x).

Solving for dx, we get dx = 2√x du.

Substituting these values into the integral, we have,

∫\(e^\sqrt{x}\) dx

= ∫\(e^u\) × 2√x du

= 2∫\(e^u\) × √x du.

Now, express the integral in terms of u only.

Since u = √x, we can rewrite √x as u,

∫\(e^\sqrt{x}\) dx = 2∫\(e^u\) × u du.

This integral can be evaluated using integration by parts.

Let's differentiate u and integrate \(e^u\) to apply the integration by parts formula,

d/dx (u)

= d/du (u) × du/dx

= 1 × 1 / (2√x)

= 1 / (2√x),

∫\(e^u\) du = \(e^u\)

Applying the integration by parts formula, we have,

∫\(e^\sqrt{x}\) dx

= 2 × ∫\(e^u\) × u du

= 2 × (u × \(e^u\) - ∫\(e^u\) × du)

= 2u × \(e^u\) - 2∫\(e^u\)du

= 2u × \(e^u\) - 2× \(e^u\)  + C,

where C is the constant of integration.

Substituting u = √x back into the expression, we get the final result:

∫\(e^\sqrt{x}\) dx = 2√x × \(e^\sqrt{x}\) - 2\(e^\sqrt{x}\) + C.

b. To evaluate the integral ∫ [-∞, 0] x\(e^{-x\) dx, we can use integration by parts.

Let's choose u = x and dv = \(e^{-x\)dx.

Then, differentiate u and integrate dv,

du = dx,

v = ∫\(e^{-x\) dx

  = -\(e^{-x\)

Using the integration by parts formula ∫u dv = uv - ∫v du, we have,

∫x\(e^{-x\) dx

= uv - ∫v du

= x × (-\(e^{-x\)) - ∫(-\(e^{-x\)) dx

= -x\(e^{-x\) + ∫\(e^{-x\) dx.

The integral ∫\(e^{-x\) dx is simply the negative of \(e^{-x\) so we have,

∫x\(e^{-x\) dx = -x\(e^{-x\) - \(e^{-x\) + C,

where C is the constant of integration.

Therefore, the value of the integral a. ∫\(e^\sqrt{x}\) dx = 2√x × \(e^\sqrt{x}\) - 2\(e^\sqrt{x}\) + C.

b.  ∫ [-∞, 0] x\(e^{-x\) dx = -x\(e^{-x\) - \(e^{-x\) + C.

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The above question is incomplete, the complete question is:

Evaluate the following integral:

\((a) \( \int e^{\sqrt{x}} d x \) (b) \( \int_{-\infty}^{0} x e^{-x} d x \)\)

50%

since 98/2 = 49

Thats it

Answer:111m^2

Step-by-step explanation:

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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Answer:

In expanded form:

2^3 = 2 * 2 * 2 = 8

In standard form :

2^3

Step-by-step explanation:

Given the numbers in range (0 to 10)

Write an exponential expression :

Choosing from the range for the Base and the exponent

Base = 2

Exponent = 3

where ; 2 = base. ; 3 = exponent

In expanded form:

2^3 = 2 * 2 * 2 = 8

In standard form :

2^3

Answer:

Radius = 1.02493

Answer:

1/36

Step-by-step explanation:

If the cubes are numbered from 1 to 6 there is just one way that the sum of both of them equals 12 and this is when Marsha gets 6 in the first cube and 6 in the other.

Thus, to know what the probability that the total of numbers facing up will equal 12 we would have to calculate the probability that the first cube is 6 AND the second one is also 6.

The probability that the first cube has the number 6 is: 1/6

The probability that the second cube has the number 6 is: 1/6

We need to multiply this numbers because they both have to be 6 (rule of multiplication),

so: \(\frac{1}{6}(\frac{1}{6} )= \frac{1}{36}\)

Thus, the probability that the sum of them equals 12 is 1/36

Answer: Circumference = 18 π cm

Step-by-step explanation:

We can use this formula to find the circumference of a circle:

➜ r is equal to the radius, also known as half the width of a circle.

      C = 2πr

We will substitute our known values and solve for C by multiplying. Since the answer option includes π in our units, we do not multiply this into the 18.

      C = 2πr

      C = 2π(9)

      C = 18 π cm

Answer: 18π

Step-by-step explanation:

The circumference of a circle is equal to 2πr, with r being equal to the radius. The radius of a circle is defined as the length from any point on the circle to its middlemost point. In this case, we are given the value of the radius as defined by the line. The radius equals 9, which we can plug into the equation.

C= 2πr

C = 2π(9)

C = 18π = 56.55

Hope this helps!

To start, let's sketch the graph of the curve y = x from x = 0 to x = 20. This is simply a diagonal line that passes through the points (0,0) and (20,20), as shown below:

```
   |
20  |    *
   |   *  
   |  *  
   | *    
   |*    
0  --------------
  0   10   20
```

Now, we want to revolve this curve around the x-axis to create a solid shape. Specifically, we want to create a paraboloid, which is a three-dimensional shape that looks like an upside-down bowl.

To find the volume of this paraboloid, we need to use calculus. The basic idea is to slice the solid into very thin disks, and then add up the volumes of all the disks to get the total volume.

To do this, we'll use the formula for the volume of a cylinder, which is:

V = πr^2h

where r is the radius of the cylinder and h is its height. In our case, each disk is a cylinder with radius r and height h, where:

- r is equal to the y-value of the curve (i.e. r = y = x), since the disk extends from the x-axis to the curve.
- h is the thickness of the disk, which is a very small change in x. We can call this dx.

So, the volume of each disk is:

dV = πr^2dx
  = πx^2dx

To find the total volume of the paraboloid, we need to add up the volumes of all the disks. This is done using an integral:

V = ∫(from x=0 to x=20) dV
 = ∫(from x=0 to x=20) πx^2dx

Evaluating this integral gives us:

V = π/3 * 20^3
 = 8000π/3

So the exact volume of the paraboloid is 8000π/3.

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Answer:

In order:

\(\frac{y^{3}}{2x^{2}}\)

\(\frac{9r^2s}{2t^{3}}\)

\(23a^9b^8\)

\(34x^8y^{14}\)

Step-by-step explanation:

\(\frac{4x^3y^2 * 3x^6y^3}{24x^{11}y^2} \\\\\frac{12x^9y^5}{24x^{11}y^2} \\\\\frac{x^9y^5}{2x^{11}y^2} \\\\\\frac{y^5}{2x^{11-9}y^2} \\\\\frac{y^5}{2x^{2}y^2} \\\\\frac{y^{5-2}}{2x^{2}y^2} \\\\\frac{y^{3}}{2x^{2}}\)

\((3rs^2t^4)^2/21r^2s^3t^11\\\\\frac{9r^2s^4t^8}{2s^3t^{11}} \\\\\frac{9r^2s^{4-3}t^8}{2s^3t^{11-8}} \\\\\frac{9r^2s}{2t^{3}}\)

\((10a^4b^6)(3a^5b^2) -7a^9b^8\\\\30a^9b^8-7a^9b^8\\\\23a^9b^8\)

\((-5x^4y^7)^2 + 9x^8y^{14}\\\\25x^8y^{14}+9x^8y^{14}\\\\34x^8y^{14}\)

Hope this helps!

Answer: Debit card transactions usually go through a period where the purchase is pending before the funds are removed from your account. The funds will not be taken out of your account immediately. Therefore it is false

Answer:

Irrational, Rational, and Complex Roots

Step-by-step explanation:

Irrational roots cannot be written as a fraction, for example, √2 is an irrational root because 2 is not a square number

Rational roots can be written as a fraction. For example, √4 is a rational root because it can be either -2 or 2 which are both rational.

Complex/imaginary roots take the form of \(a+bi\) where "a" is the real part and "b" is the imaginary part. For example, √(-1) = i which is complex/imaginary.

Fitness mania is cheaper as $200 < $240