2) a right rectangular prism has a square base, and its height is triple the base
edge. find the ratio of its surface area to volume.​

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

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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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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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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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

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.

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.

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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The odds in favor of the event are 1.

The probability of an event is the ratio between the total number of favorable outcomes and the total number of outcomes.

The odds in favor of an event are the ratio of the total number of favorable outcomes and the total number of unfavorable outcomes. If the probability of the event is given, we can find the odds in favor by using the formula of odds in favor:

odds in favor = probability of event/probability of not event

In this case question, the probability of an event is given as 0.5 which means that the total number of favorable outcomes is 50 out of 100

So the probability of not having an event is also 0.5 (the other half of the part.)

So, odds in favor = 0.5/0.5 = 1

The probability of the happening of an event is the same as the probability of not happening of an event. This means that the odds in favor of the event are 1 to 1, or simply 1.

Therefore,  the odds in favor of the event are 1.

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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.

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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Nora will be able to cut 52 equal pieces of yarn for her Science project.

To find out how many equal pieces of yarn Nora can cut for her Science project, we need to divide the total length of the yarn by the length of each piece.

Total length of yarn: 67.6 inches
Length of each piece: 1.3 inches

Step 1: Divide the total length by the length of each piece.
67.6 inches ÷ 1.3 inches = 52

Nora will have 52 equal pieces of yarn, each 1.3 inches long, for her Science project.

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The scale factor used is 2.

It is one of the simplest polygon shapes and is commonly used in mathematics and geometry. The sum of the internal angles of a triangle is always 180 degrees.

The vertices of a triangle are the three points in a two-dimensional (2D) or three-dimensional (3D) space that define the corners or corners of the triangle. In a 2D plane, the vertices are typically denoted as A, B, and C, and in a 3D space, they can be represented as (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) where (x, y, z) are the coordinates of each vertex along the x, y, and z axes respectively. The vertices of a triangle are connected by three line segments, known as edges, to form the sides of the triangle. The combination of the three vertices and the edges connecting them determines the shape and size of the triangle.

To find the scale factor used to dilate triangle ABC to A'B'C', we can compare the corresponding side lengths of the two triangles.

The distance between A(-3, -3) and B(3, 3) is √((3-(-3))^2 + (3-(-3))^2) = 6√2.

The distance between A'(-6, -6) and B'(6, 6) is √((6-(-6))^2 + (6-(-6))^2) = 12√2.

So the scale factor used to dilate triangle ABC to A'B'C' is:

scale factor = length of corresponding side in A'B'C' / length of corresponding side in ABC

            = (12√2) / (6√2)

            = 2

Therefore, the scale factor used is 2.

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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 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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If length of rectangle is 5 more than twice it's width and having perimeter as 88 feet, then the dimensions of the rectangle are, length is 31 feet, width is 13 feet.

Let width of the rectangle be represented as = "w" feet.

It is given that, the length of rectangle is 5 more than twice it's width,

So, Length can be represented as "2w + 5" in feet;

We use formula for perimeter of rectangle, which is "P = 2Length + 2Width", where P = perimeter, L = length, and W = width.

In this case, we know that the perimeter is 88 feet, so we substitute the values,

We get,

⇒ 88 = 2(2w + 5) + 2w;

⇒ 88 = 4w + 10 + 2w,

⇒ 88 = 6w + 10,

⇒ 78 = 6w,

⇒ w = 13,

So the width is 13 feet. We use this value of width to find length of the rectangle:

⇒ L = 2w + 5,

⇒ L = 2(13) + 5,

⇒ L = 31

Therefore, the dimensions of the rectangle are 31 feet by 13 feet.

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Answer:

A. There is an asymptote at x = 0.

D. There is an asymptote at y = 23.

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: 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.

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:

100

Step-by-step explanation:

i think this is right

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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Cif a = 2.74 mi, b = 3.18 mi and ZC = 41.9° and c^2 = a^2 + b^2 - 2ab*cos(C)where C is the angle opposite to side c, c comes to be ≈ 4.26 mi.

The Law of Cosines is a numerical formula that relates the side lengths and points of any triangle. It expresses that the square of any side of a triangle is equivalent to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them. To get side c, we can use the law of cosines, which states that c² = a² + b² - 2ab cos(C).
Plugging in the given values, we get:
c² = (2.74)² + (3.18)² - 2(2.74)(3.18)cos(41.9°)
c² ≈ 18.126
Taking the square root of both sides, we get:
c ≈ 4.26 mi
Rounding to 2 decimal places, c ≈ 4.26 mi.
Therefore, the answer is: c ≈ 4.26 mi.

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[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]

The total number of bikes that can be painted in an hour would be 60 bikes.

With three identical machines,

the number of bikes machine can paint per hour = 20,

the number of machines bought again = 2,

so the total number of machines will be = 3,

when there are two same machines the productivity will be = 20 * 3 = 60 bikes.

This is because each machine works independently and can paint bikes simultaneously.

By adding two additional machines to the existing one,

the productivity of the painting process can be significantly increased. The new machines will not only increase the overall capacity but also reduce the turnaround time required for painting a large number of bikes.

By investing in additional machines,

the business can increase its output and generate more revenue,

which can be used to expand the operations further.

It's important to note that the investment in additional machines needs to be justified by the demand for painted bikes and the expected return on investment.

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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

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