Which equation best represents the relationship between x and y in the graph?

The maximum population density evaluated is 1200 citizens per square mile, under the condition that the city is 30 miles long and two-thirds as wide, and 555,000 citizens currently live there.

Now to evaluate the maximum population density that is considered in the mayor's calculation is
Let us first calculate the area of the city which is (2/3) × (30 miles)
= 20 miles.
So, now we can calculate the current population density which is
555,000 / (20 × 20)
= 1387.5 citizens per square mile.
Hence the mayor evaluates that at least 75,000 people must transfer out of the city for adequate services to be exercised, we can find the new population as
555,000 - 75,000
= 480,000 citizens.
Therefore, the new population density would be 480,000 / (20 × 20)
= 1200 citizens per square mile

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Total cost = VC(80) + Fixed cost = 1325.34 + 200 = $1525.34

To find the total cost of producing 80 barstools, we need to calculate the variable cost and add it to the fixed cost.

First, integrate the marginal cost function to find the variable cost function:

VC(x) = ∫[tex](20 - 0.5\sqrt{x dx} )[/tex]

VC(x) = [tex]20x - (1/3)x^(^3^/^2^) + C[/tex]

The constant C is irrelevant in this case, as we are interested in the difference between VC(80) and VC(0).

Now, evaluate the variable cost function at x = 80:

VC(80) = 20(80) - [tex](1/3)(80^(^3^/^2^))[/tex]

VC(80) = 1600 - [tex](1/3)(80\sqrt{80} )[/tex]

VC(80) ≈ 1325.34

Finally, add the fixed cost:

Total cost = VC(80) + Fixed cost = 1325.34 + 200 = $1525.34

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The dimensions of the pasture that require the least amount of fence are approximately 600 meters by 300 meters.

To minimize the amount of fence needed, we want to maximize the length of the side next to the canal. Let's call this side x and the other two sides y.

We know that the area of the rectangle must be 180,000 m², so we have x*y = 180,000. We want to minimize the amount of fence, which is the perimeter of the rectangle: P = x + 2y

To solve for the dimensions that require the least amount of fence, we need to eliminate one variable. We can do this by using the area equation to solve for one variable in terms of the other:
y = 180,000/x

Substituting this into the perimeter equation, we have:
[tex]P = x + 2(180,000/x)[/tex]

To find the minimum value of P, we take the derivative with respect to x and set it equal to zero:
[tex]P' = 1 - 360,000/x^2 = 0x = sqrt(360,000) ≈ 600[/tex]

Substituting this back into the area equation, we find:
[tex]y = 180,000/x ≈ 180,000/600 ≈ 300[/tex]

So, the dimensions of the pasture which require the least amount of fence are approximately 600 meters by 300 meters.

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Answer:

See explanation.

Step-by-step explanation:

The arc BX, central angle BCX, and inscribed angle BNX are connected through the following relationships:

1. The central angle BCX subtends the arc BX. This means that the central angle is formed by two radii connecting the center of the circle to the endpoints of the arc BX.

2. The inscribed angle BNX subtends the same arc BX. This means that the inscribed angle is formed by two chords connecting a point on the circumference of the circle to the endpoints of the arc BX.

3. The relationship between the central angle BCX and the inscribed angle BNX is given by the Inscribed Angle Theorem, which states that the measure of an inscribed angle is half the measure of the central angle subtending the same arc. In other words, if θ is the measure of the central angle BCX and α is the measure of the inscribed angle BNX, then:

[tex]\alpha =\frac{1}{2}[/tex] θ

Answer:

Sure. Here are the steps on how to solve for x^3 - 1/x^3:

1. **Cube both sides of the equation x - 1/x = 3.** This will give us the equation x^3 - 3x + 1/x^3 = 27.

2. **Subtract 1 from both sides of the equation.** This will give us the equation x^3 - 1/x^3 = 26.

3. **The answer is 26.**

Here is the solution in detail:

1. **Cube both sides of the equation x - 1/x = 3.**

```

(x - 1/x)^3 = 3^3

```

```

x^3 - 3x + 1/x^3 = 27

```

2. **Subtract 1 from both sides of the equation.**

```

x^3 - 1/x^3 - 1 = 27 - 1

```

```

x^3 - 1/x^3 = 26

```

3. The answer is 26.

Possible number of death rays (D) and claws (C) that Archimedes can build are given by the following system of inequalities: 350D + 200C ≤ 3000. D, C ≥ 0

The first inequality represents the fact that the total amount of gold used to build the machines cannot exceed the 3000 lbs of gold given by the city. The second inequality ensures that the number of death rays and claws cannot be negative.

To explain this system, let us assume that Archimedes builds x death rays and y claws. The amount of gold required to build x death rays and y claws is given by 350x + 200y. The first inequality ensures that this value cannot exceed 3000 lbs of gold. The second inequality ensures that the number of death rays and claws cannot be negative.

Therefore, the solution to this system of inequalities gives us all the possible combinations of death rays and claws that Archimedes can build with the given amount of gold.

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The equation for the plane through the points Po(-3,-2,4), Qo(-5,-1,2), and Ro(1,1,5) is:

3x - 3y + 2z - 11 = 0

Using a coefficient of 7 for x, the equation of the plane is:

21x - 3y + 2z - 11 = 0

To find the equation of the plane, we can use the cross product of the vectors formed by the points Qo-Po and Ro-Po.

Let's call the vector formed by Qo-Po "u" and the vector formed by Ro-Po "v". Then, we can find the normal vector to the plane by taking the cross product of "u" and "v":

u = Qo - Po = (-5+3, -1+2, 2-4) = (-2,1,-2)

v = Ro - Po = (1+3, 1+2, 5-4) = (4,3,1)

n = u x v = (1(2) - (-2)(3), (-2)(4) - 1(1), (-2)(3) - 1(4)) = (8,-7,-10)

Now that we have the normal vector to the plane, we can find the equation of the plane by using the point-normal form of the equation of a plane:

n · (P - Po) = 0

where "·" denotes the dot product, P is any point on the plane, and Po is one of the given points on the plane.

Let's use the point Po(-3,-2,4) to find the equation of the plane:

n · (P - Po) = 0

(8,-7,-10) · (x+3, y+2, z-4) = 0

8(x+3) - 7(y+2) - 10(z-4) = 0

8x - 7y - 10z + 11 = 0

So the equation of the plane through the points Po, Qo, and Ro is:

3x - 3y + 2z - 11 = 0

To use a coefficient of 7 for x, we can simply multiply both sides of the equation by 7:

21x - 21y + 14z - 77 = 0

Simplifying, we get:

21x - 3y + 2z - 11 = 0

Therefore, the equation of the plane with a coefficient of 7 for x is 21x - 3y + 2z - 11 = 0.

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Answer:

Step-by-step explanation:

Without a diagram, I cannot determine the equation of the curve. However, I can provide you with the general steps to find the equation of a quadratic curve given three points on the curve.

Let the three points be (x1, y1), (x2, y2), and (x3, y3). Then the equation of the quadratic curve in the form ax²+bx+c can be found using the following system of equations:

y1 = a(x1)² + b(x1) + c

y2 = a(x2)² + b(x2) + c

y3 = a(x3)² + b(x3) + c

Solving this system of equations simultaneously will give us the values of a, b, and c, which we can use to write the equation of the quadratic curve.

However, since you have only provided three y-values (32, 2.0, and 8.0), without their corresponding x-values or the diagram, it is not possible to determine the equation of the curve.

Answer:

y = (x + 5)/3

Step-by-step explanation:

To make y the subject, you need to isolate y on one side of the equation.

x = 3y - 5

Add 5 to both sides:

x + 5 = 3y

Divide both sides by 3:

y = (x + 5)/3

Therefore, y is the subject of the formula when it is expressed as:

y = (x + 5)/3

the integral by reversing the order of integration. the result will be F(β) - F(α), which is the integral evaluated after reversing the order of integration.

First, let's rewrite your integral more clearly:

∫∫ R 7x dy dx, where R is the region of integration.

To reverse the order of integration, we first need to determine the limits of integration for R in terms of x and y. Let's assume the current limits are a to b for x and c(y) to d(y) for y.

Now, we need to express these limits in terms of y and x. Let's denote the new limits as α to β for y and γ(x) to δ(x) for x.

After finding the new limits, we can rewrite the integral as:

∫∫ R 7x dx dy

Now, evaluate the integral by integrating first with respect to x and then with respect to y:

1. Integrate 7x with respect to x: (7/2)x^2 + C₁(x)
2. Apply the limits of integration for x: [(7/2)δ(x)^2 + C₁(δ(x))] - [(7/2)γ(x)^2 + C₁(γ(x))]
3. Integrate the result with respect to y: ∫[α, β] [(7/2)(δ(y)^2 - γ(y)^2)] dy
4. Apply the limits of integration for y: F(β) - F(α)

The final result will be F(β) - F(α), which is the integral evaluated after reversing the order of integration.

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Answer:

A. There is an asymptote at x = 0.

D. There is an asymptote at y = 23.

The scatterplot  that would describe is Option A.

A scatter plot is described as  a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data.  

The slope - intercept form of the equation of a line is:

y = mx + c

where m =  the slope

c = the y-intercept

Only in the first scatterplot can the line of best fit intersect the y-axis at 2 if a line of best fit is drawn on each of the scatterplots. Only when a line of best fit is established on the first scatterplot is a slope of 1/2 conceivable.

That is, c = 2

m = 1/2

In conclusion, only the first scatterplot would have the line of best fit represented by the equation y = 1/2 x + 2.

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Answer: As the Integers being positive or negative depends on the 0 As it is reference present on  the centre of the number line

Numbers on the left side are negative while that on right side being positive

Step-by-step explanation:

The approximate APR for Morgan's sofa purchase is 1.7%.

To calculate the approximate APR (Annual Percentage Rate) for Morgan's sofa purchase, we can use the formula:

APR ≈ (finance charge / # of months) x 12 / amount financed

Here, the finance charge is $25, the number of months is 15, and the amount financed is the total cost of the sofa minus the finance charge, which is:

financed= $216.00 - $25.00 = $191.00

on substitution:

APR ≈ (25 / 15) x 12 / 191

APR ≈ 0.2778 x 0.06283

APR ≈ 0.01743

Rounding the answer to the nearest tenth, we get:

APR ≈ 1.7%

Therefore, the approximate APR for Morgan's sofa purchase is 1.7%.

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Emmanuel weighs 150 pounds and he has normal liver function. It will take him approximately 1 hour to metabolize one standard drink. Metabolism of alcohol is primarily done in the liver where it is broken down into acetaldehyde, which is then further broken down into water and carbon dioxide.

The liver can only metabolize a certain amount of alcohol per hour, which is why it takes time for the body to process and eliminate alcohol. However, other factors such as age, gender, body composition, and food consumption can also affect how quickly alcohol is metabolized.

It is important to drink responsibly and be aware of how alcohol can affect your body.

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Answer:

100

Step-by-step explanation:

i think this is right

After considering all the given data we conclude that  the coordinates of k so that the ratios of JK to KL is 3 to 4 is (-16x₁x₂-16y₁y₂)

The two values of X and Y are the coordinates of K. Let us assume that the coordinates of points J and L are (x₁, y₁) and (x₂, y₂) respectively.
Then, the coordinates of point K can be placed as (x, y), here x and y are unknowns that we need to find.
Now, we know that the ratio of JK to KL is 3:4. This means that:
JK/KL = 3/4
We can use the distance formula to find the distances JK and KL in terms of their coordinates:
JK = √((x-x₁)²+(y-y₁²) KL = √((x-x₂)²+(y- y₂)²)

Staging these distances into the above equation, we get:
√(x-x₁)²+(y-y₁))/√((x-x₂)²+(y-y₂)²) = 3/4
Squaring both sides and simplifying, we get:
16(x-x1)²+16(y-y₁)²= 9(x-x₂)²+9(y-y₂)²
Expanding and simplifying, we get:

7x²-14xx₁-9x₂²+ 7y2-14yy₁-9y₂²= -16x₁x₂-16y₁y₂

This is a quadratic equation in x and y. We can solve this equation to find the values of x and y that satisfy the given conditions. The solution to this quadratic equation gives two values of x and y, which are the coordinates of point K.

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Answer:

mmm, well, not much we can do per se, you'd need to use a calculator.

I'd like to point out you'd need a calculator that has regression features, namely something like a TI83 or TI83+ or higher.

That said, you can find online calculators with "quadratic regression" features, which is what this, all you do is enter the value pairs in it, to get the equation.

Step-by-step explanation:

The conditional probability that she tosses two heads, given she has tossed one head already is: 1/3

Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

We are given that she has two coins.

She has tossed one head already

Let A be the event that two heads result and B the event that there is at least one head.

If S denote the sample space, then S={(H,H),(H,T)(T,H)(T,T)}

A={(H,H)}

B={(H,H),(H,T)(T,H)}

So, A∩B = {H,H}

P(B)= 3/4

P(A∩B)= 1/4

​

Hence P(A∣B) = P(A∩B)/P(B)

P(A∣B) = (1/4)/(3/4)

​= 1/3

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The volume of the large diamond is approximately 3.51 cm³.

To find the volume of the large diamond with a mass of 481.3 grams and a density of (g/3.51 cm), you can use the formula:

Volume = Mass / Density

The volume of the large diamond, we can use the formula Volume = Mass / Density. Given that the mass is 481.3 grams and the density is (g/3.51 cm), we can substitute these values into the formula.

Simplifying the equation, we find that the volume is equal to 3.51 cm³. This means that the large diamond occupies a space of approximately 3.51 cubic centimeters.

1. First, rewrite the density as a fraction: g/3.51 cm = 481.3 g / 3.51 cm³
2. Next, solve for the volume by dividing the mass by the density: Volume = 481.3 g / (481.3 g / 3.51 cm³)
3. Simplify the equation: Volume = 481.3 g * (3.51 cm³ / 481.3 g)
4. Cancel out the grams (g): Volume = 3.51 cm³

So, the volume of the large diamond is approximately 3.51 cm³, rounded to the nearest hundredth.

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Answer:

Step-by-step explanation:

Density = mass

               volume  

We have density (3.51 cm) and we have mass (481.3)

We need to solve for V (volume)

3.51 =     481.3

               V

Multiply both sides by V to clear the fraction:

3.51 V = 481.3

Divide both side by 3.51

3.51 V = 481.3

3.51         3.51

V = 137.122cm³

rounded to 137.12 cm³

[tex]\cfrac{\stackrel{\textit{longer side}}{12}}{\underset{\textit{shorter side}}{3\sqrt{3}}}\implies \cfrac{4}{\sqrt{3}}\implies \cfrac{4}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}}\implies \cfrac{4\sqrt{3}}{3}[/tex]

Answer:

To determine the best measure of variability for the data, we need to consider the type of data we are dealing with. In this case, the data is numerical and discrete, so the best measure of variability would be the range or the interquartile range (IQR).

The range is the difference between the maximum and minimum values in a dataset, while the IQR is the range of the middle 50% of the data. The IQR is less sensitive to outliers than the range, so it is often a better measure of variability.

To calculate the range and IQR for each player, we first need to order the data:

Player A: 1, 2, 2, 2, 3, 3, 3, 4, 8

Player B: 1, 1, 2, 2, 2, 3, 4, 4, 6

Player A has a range of 8 - 1 = 7, and an IQR of Q3 - Q1 = 4 - 2.5 = 1.5.

Player B has a range of 6 - 1 = 5, and an IQR of Q3 - Q1 = 4 - 1.5 = 2.5.

Therefore, Player B has a higher range and a higher IQR, indicating more variability in their performance. Player A has a lower range and a lower IQR, indicating greater consistency in their performance. Therefore, the answer is: Player A is the most consistent.

Given:- ABCD is a parallelogram, and AE and CF bisect ∠A and ∠C respectively. To prove:- AE∥CF Proof:- Since in a parallelogram, opposite angles are equal.

A parallelogram is a geometric shape that has four sides and four angles. It is a type of quadrilateral, which means it has four sides, and its opposite sides are parallel to each other.

The opposite sides of a parallelogram are also equal in length. The opposite angles of a parallelogram are also equal in measure.

The shape of a parallelogram looks similar to a rectangle, but it differs from a rectangle in that its angles are not necessarily right angles. A square is a special case of a parallelogram in which all four sides are equal in length and all four angles are right angles

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If x, y, and z represent three rational numbers, such that y is 512 times x and z is 50. 25 more than x and y = 15.5 , then value of z = 50.280.

Let x, y, and z represent three rational numbers, such that y is 512 times x and z is 50.25 more than x. If y = 15.5, the value of z can be found as follows:

Find the value of x.
Since y is 512 times x, we have the equation:
y = 512x
Substitute y with 15.5:
15.5 = 512x

Now, divide both sides by 512 to find x:
x = 15.5 / 512
x ≈ 0.0302734375

Find the value of z.
Since z is 50.25 more than x, we have the equation:
z = x + 50.25
Substitute x with the value we found (x = 0.0302734375):
z ≈ 0.0302734375 + 50.25
z ≈ 50.2802734375

So, the value of z is approximately 50.2802734375.

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The probability that the students have to wait at most 4 periods for the teacher to trip is approximately 0.8215

The probability of the teacher not tripping during a single period is 1 - 0.35 = 0.65.

For the teacher not to trip in the first 4 periods, she must not trip in each of the first 4 periods. Since the periods are independent, we can multiply the probabilities together:

P(not tripping in first 4 periods) = 0.65 * 0.65 * 0.65 * 0.65 = 0.65^4 ≈ 0.1785

Now, we subtract this probability from 1 to find the probability that the students have to wait at most 4 periods for the teacher to trip:

P(at most 4 periods) = 1 - P(not tripping in first 4 periods) = 1 - 0.1785 ≈ 0.8215

So, the probability that the students have to wait at most 4 periods for the teacher to trip is approximately 0.8215, or 82.15%.

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Answer:

3/2

Step-by-step explanation:

f(x) = 2x+5

f-¹(x) = ?

to find f-¹(x)

let f(x) be y

y = 2x+5

then we'll make x the subject of formula

y-5 = 2x

x = y-5/2

change y to x and x to y

f-¹(x) = x-5/2

f-¹(8) = 8-5/2 = 3/2

4.20 cm² is the area of the triangle STU to the nearest 10th of a square centimeter.

Given, t = 3.4 cm, u = 6.9 cm and ∠S = 21°

We know that the formula for the area of the triangle = 1/2 * t*u *sin(S)

Substituting the values

Area = 1/2 × 3.4 × 6.9 × sin(21°)

Area = 11.73 × sin(21°)

Area = 11.73 ×  0.3583

Area = 4.2016

Rounding to the nearest 10th of a square centimeter .

Area = 4.20 cm²

Hence, 4.20 cm² is the area of the triangle STU to the nearest 10th of a square centimeter.

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Answer: 8.75

Step-by-step explanation:

We know that 4 goes into 35 eight times.

        35 - (4 * 8) = 3

Next, we know that 3/4 is equal to 0.75 by dividing.

This leaves us with 8.75. Eight wholes and a part of 0.75.