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To solve the given linear programming (LP) problem using the graphical LP approach, we will plot the feasible region, identify the corner points, and determine the optimal solution.

Here are the steps:

Step 1: Plot the constraints:

- Plot the line 5x + y = 32, which represents the constraint 5x + y ≤ 32. To do this, find two points that lie on this line by assigning values to x and solving for y. For example, when x = 0, y = 32, and when x = 6, y = 2. Connect these points to draw the line.

- Plot the line x + 3y = 12, representing the constraint x + 3y ≥ 12. Again, find two points on this line and connect them. For instance, when x = 0, y = 4, and when x = 12, y = 0.

- Draw the lines representing x = 20 and y = 20 as vertical and horizontal lines passing through x = 20 and y = 20, respectively.

Step 2: Identify the feasible region:

- Shade the area that satisfies all the constraints. The feasible region is the intersection of the shaded regions.

Step 3: Identify the corner points:

- Find the coordinates of the corner points of the feasible region. These points are the intersections of the lines representing the constraints.

Step 4: Evaluate the objective function:

- Calculate the objective function Z = 3x + 12y for each corner point.

Step 5: Determine the optimal solution:

- Identify the corner point that gives the minimum value of the objective function Z. This point corresponds to the optimal solution of the LP problem.

Once you have completed these steps, you will have the complete solution to the LP problem using the graphical LP approach.

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Answer: it is P(x)

Step-by-step explanation:

Just joking my mind wants to say the 1 or second

Answer:

-5, -2, -2/5, 5/2, 5.2

Step-by-step explanation:

1: y=x-1

2: y=-x+9

I need to write at least 20 characters so here’s a sentence you just read

Answer: 4/25

Step-by-step explanation:

(2/5)^2 or can write as 2/5 times 2/5

2/5 times 2/5 = 4/25

Answer:

0.08

Step-by-step explanation:

2/5 = 0.4 x 0.4

The residuals should show no pattern around the horizontal axis.

You obtain a line of best fit when you execute simple linear regression (or any other kind of regression analysis). Typically, the data points are dispersed rather than falling exactly on this regression equation line. The vertical separation between a data point and the regression line is known as a residual. There is one residual for every data point. As follows:

If they are above the regression line and below it, they are positive and vice versa, respectively.

If the regression line actually crosses the spot, the result is zero.

Hence, the residuals should show no pattern around the horizontal axis.

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The correct question is:

We can plot the residuals sequentially over time to look for correlated observations. if there is no violation, then what would you see?

The residuals should show normal pattern around the vertical axis.

The residuals should show normal pattern around the horizontal axis.

The residuals should show no pattern around the horizontal axis.

The residuals should show no pattern around the vertical axis.

The graph of the function f(x) = 151 / (4e^(-0.2x)) has a horizontal asymptote at y = 0 and a vertical asymptote at x = -∞.

Horizontal Asymptote: As x approaches infinity (x → ∞), the exponential term \(e^(-0.2x)\) approaches 0. This is because the exponential function decreases rapidly as the exponent becomes more negative. Therefore, the value of f(x) approaches 151 / 4 as x approaches infinity. Hence, the horizontal asymptote is y = 151 / 4

Vertical Asymptote: The exponential function \(e^(-0.2x)\) will never equal zero for any finite x-value. Therefore, there are no vertical asymptotes for the given function.

In summary, the graph of f(x) = 151 / (\(4e^(-0.2x))\) has a horizontal asymptote at y = 151 / 4, representing the behavior of the function as x approaches infinity. There are no vertical asymptotes in the graph.

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The tax rate given as a percentage, can be used to find out the amount

to be paid as tax.

Correct response:

The given parameters are;

Susan Wong's taxable income last year = $52,915

The income tax rate = 2%

Required:

Susan Wong's tax last year

Solution:

The tax rate is given as a percentage of the taxable income.

The amount payable as tax = The tax rate × The taxable income

Therefore;

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Using compound interest, it is found that Dante was 6.6 years old when the balance in the account reached $13,000.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

In this problem, we have that the parameters are given as follows:

A(t) = 13000, A(0) = 10000, r = 0.04, n = 12.

Hence the time in years is found as follows:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(13000 = 10000\left(1 + \frac{0.04}{12}\right)^{12t}\)

\((1.0033)^{12t} = 1.3\)

\(\log{(1.0033)^{12t}} = \log{1.3}\)

\(12t\log{1.0033} =  \log{1.3}\)

\(t = \frac{\log{1.3}}{12\log{1.0033}}\)

t = 6.6

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Answer:

La raíz cuadrada de 16 es 4. Es la solución positiva de la ecuación x2 = 16. El número 16 es un cuadrado perfecto.

Step-by-step explanation:

Answer:

x = 20% acid = 60 ml

y = 45% acid = 40 ml

Step-by-step explanation:

Let

x = 20% acid

y = 45% acid

x + y = 100 (1)

.20x + .45y = .3 ×100

.20x + .45y = 30 (2)

From (1)

x + y = 100 (1)

x = 100 - y

Substitute x = 100 - y into (2)

.20x + .45y = 30

.20(100 - y) + .45y = 30

20 - .20y + .45y = 30

- .20y + .45y = 30 - 20

.25y = 10

y = 10/.25

y = 40 ml

Substitute y = 40 into (1)

x + y = 100

x + 40 = 100

x = 100 - 40

x = 60 ml

x = 20% acid = 60 ml

y = 45% acid = 40 ml

Answer:

Step-by-step explanation:

Heights of the flowers in his garden, in  inches:

Mean

Absolute deviation

MAD

Heights of the vegetable plants in his garden, in  inches:

Mean

Absolute deviation

MAD

===============================================

Answer:

i think 4 feet tall

Step-by-step explanation:

i think if it is wrong im sorry i tried

Answer:

37.7ft³

Step-by-step explanation:

1) The missing side lengths are:   Hypotenuse a = 4   Side b = 2√2

2) The missing side lengths are:   Leg x = 2√2   Leg y = 2√2

1) In a right triangle with a 90° angle and an opposite angle of 45°, we can use the trigonometric ratios to find the missing side lengths.

Let's denote the hypotenuse as a, the side opposite the 45° angle as c, and the remaining side as b.

Using the sine function, we have:

sin(45°) = c / a

Since sin(45°) = √2 / 2, we can substitute the values:

√2 / 2 = 2√2 / a

To solve for a, we can cross-multiply and simplify:

√2 * a = 2√2 * 2

a√2 = 4√2

a= 4

Therefore, the hypotenuse (a) has a length of 4.

To find side b, we can use the Pythagorean theorem:

a² + b² = c²

Plugging in the known values:

(2√2)²+ b² = 4²

8 + b² = 16

b²= 16 - 8

b² = 8

b = √8 = 2√2

So, the missing side lengths are:

Hypotenuse (c) = 4

Side b = 2√2

2) In a right triangle with a 45° angle and a hypotenuse of 4, we can find the lengths of the other two sides. Let's denote the length of one leg as x and the length of the other leg as y.

Using the Pythagorean theorem, we have:

\(x^2 + x^2 = 4^2\\2x^2 = 16\\x^2 = 16 / 2\\x^2 = 8\)

x = √8 = 2√2

Therefore, one leg (x) has a length of 2√2.

To find the other leg, we can use the fact that the triangle is isosceles (since both acute angles are 45°). Therefore, the other leg (y) has the same length as x:

y = x = 2√2

So, the missing side lengths are:

Leg x = 2√2

Leg y = 2√2

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The complete question is:

Find the missing side lengths. leave your answers as radicals in simplest form

Answer:

you got to do it

Step-by-step explanation:

Step-by-step explanation:

a1 = 27

r = -9/27 = -⅓

the formula :

an = a1. r^(n-1)

= 27. (-⅓)^(n-1)

= 3³(-3`¹)^(n-1)

= 3³(-3)^(1-n)

Answer: 7%

(Hope this is right.)

Step-by-step explanation:

Let's solve this using the information we have and an equation.

Shane: $32,000 - (Given)

Theresa: 18,000+14x, if x=1,160 - (Given)

---------------------------------------------------------------

Step two: (Theresa) 14(1,160) =16,240 (Algebra)

Step three: (Theresa) 18,000+16,240=34,240 (Algebra, given.) - cost of Theresa's car.

---------------------------------------------------------------

Finally,

They're asking for how much more she paid for her car as a percentage of what Shane paid.

34,240-32,000=2,240 and

2,240/32,000=0.07

0.07x100=7

Answer 7% more than what Shane paid.

Answer: 5

Step-by-step 10-5=5

Answer:

5 apples

Step-by-step explanation:

Liam has 10 apples and he gives 5 away to his friend cherry

10-5= 5

He has 5 apples left

The other elements of order 12 can be obtained by raising a to the powers k, where 1 ≤ k < 12 and gcd(k, 12) = 1.

To find the number of elements of order 10 in a cyclic group G, we can use the fact that the order of an element must divide the order of the group. Since 10 divides |G|, there exists at least one element of order 10. Let's call this element x.

Now, suppose there is another element y in G such that the order of y is also 10. This means that the cyclic subgroups generated by x and y have the same number of elements.

Since G is cyclic, it has a unique subgroup of order 10, which is generated by x. Therefore, there is only one element of order 10 in G.

Now, let's consider the case where 12 divides |G|. Similar to the previous case, there exists at least one element a in G with order 12.

To find the other elements of order 12, we need to consider the powers of a. Specifically, we need to find the powers of a that generate distinct cyclic subgroups of order 12.

For example, if we let a^k be an element of order 12, where k is relatively prime to 12, then the powers of a^k will generate distinct cyclic subgroups.

Therefore, the other elements of order 12 can be obtained by raising a to the powers k, where 1 ≤ k < 12 and gcd(k, 12) = 1.

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The vertex form of the provided equation  y = (x 3)2 (x 4)2 is expressed as  (x+3.5)²+0.5.

Vertex form of parabola is the equation form of quadratic equation, which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.

The standard equation of the vertex form of parabola is given as,

y=a(x-h)^2+k

Here, (h, k) is the vertex point.

The given equation is

\(y = (x +3)^2 +(x+ 4)^2\\y=x^2+9+6x+x^2+16+8x\\y=2x^2+14x+25\)

To convert this equation, into the vertex form, follow the following steps,

\(y=2(x^2+7x+12.5)\\y=2((x+3.5)^2-12.25+12.5)\\y=(x+3.5)^2+0.5\)

Thus, the vertex form of the provided equation  y = (x 3)2 (x 4)2 is expressed as  (x+3.5)²+0.5.

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Answer:

Option A ( 86 Degrees)

Step-by-step explanation:

To convert Celsius to Fahrenheit formula is:

\(F = \frac{9}{5} C + 32\)

\(F = \frac{9}{5} 30 + 32\)

\(F = 54 + 32\)

\(F = 86 Degree\)

The integral of du/sqrt(a^2 - u^2) is arcsin(u/a) + C, where a is a constant and C is the constant of integration.

To evaluate the integral of du/sqrt(a^2 - u^2), we can use a trigonometric substitution. Let's substitute u = asin(theta), where theta is a new variable. Differentiating u with respect to theta gives du = acos(theta)*d(theta).

Now, let's substitute these expressions back into the integral:

∫(du/sqrt(a^2 - u^2)) = ∫((acos(theta)d(theta))/sqrt(a^2 - a^2sin^2(theta)))

Simplifying the expression under the square root:

= ∫((acos(theta)d(theta))/sqrt(a^2(1 - sin^2(theta))))

= ∫((a*cos(theta)d(theta))/(acos(theta)))

= ∫d(theta)

= theta + C

Since we made the substitution u = asin(theta), we need to express the result in terms of u. Using the relationship u = asin(theta), we can find theta = arcsin(u/a). Therefore, the integral becomes:

∫(du/sqrt(a^2 - u^2)) = theta + C = arcsin(u/a) + C

Hence, the integral of du/sqrt(a^2 - u^2) is arcsin(u/a) + C, where a is a constant and C is the constant of integration.

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The approximate probability that a randomly selected student spends at most 175 hours on the project is 0.8413 (rounded to four decimal places).

Hence, the answer is 0.8413.

Given that the mean time spent by a student on the project is 150 hours and the standard deviation is 25 hours.

To compute the approximate probability that a randomly selected student spends at most 175 hours on the project, we need to use the normal distribution formula.

Z = (X - μ) / σwhere

X = 175,

μ = 150 and

σ = 25

Substituting the values, we get; Z = (175 - 150) / 25

= 1P (X ≤ 175)

= P (Z ≤ 1)

We look for the probability from the standard normal distribution table or calculator.

Using the standard normal distribution table, we get P (Z ≤ 1) = 0.8413

Therefore, the approximate probability that a randomly selected student spends at most 175 hours on the project is 0.8413 (rounded to four decimal places).

Hence, the answer is 0.8413.

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The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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Answer:divideing by the whole number

Step-by-step explanation:

Answer:

Step-by-step explanation:

13.48x − 200 < 256.12

Using the addition property , add 200 to both sides

That's

13.48x + 200 - 200 < 256.12 + 200

13.48x < 456.12

Divide both sides by 13.48

\( \frac{13.48x}{13.48} < \frac{456.12}{13.48} \\ x < \frac{456.12}{13.48} \\ \: \: \: x < 33.83679\)

We have the final answer as

x < 33.84 to the nearest hundredth

Hope this helps you

Answer:

Thats good!

Step-by-step explanation:

Answer:

Step-by-step explanation:

It’s mean you are intellectual than me

Hello there! :)

The Distributive property states:

a(b+c)=ab+ac

So, we know what a is. It's 5.

b=3

c=0.4

5(3+0.4)

5*3+5*0.4

15+0.2

15.2

Hope it helps!

\(GraceRosalia\)

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