the equation for the graph

The price at which the demand drops to 584 units is $20.80 per unit.

The formula given is:

D = 1000 - 20P

To find the price at which the demand drops to 584 units, we can set D equal to 584 and solve for P:

584 = 1000 - 20P

20P = 1000 - 584

20P = 416

P = 416/20

P = 20.8

Therefore, the price at which the demand drops to 584 units is $20.80 per unit.

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Answer:

x ≈ 7.1

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos27° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{KL}{KM}\) = \(\frac{6.3}{x}\) ( multiply both sides by x )

x × cos27° = 6.3 ( divide both sides by cos27° )

x = \(\frac{6.3}{cos27}\) ≈ 7.1 ( to the nearest tenth )

The expressions for ar and ao are: ar = α₁(1 - r₁/r₂) - (r₁/r₂)²(dω₁/dt) and ao = α₁(r₁r₂/r) + (rd/r)w

Given, a₁ = ²2-rw²₁ ao = 2 & w+rd

The expressions for ar and ao are to be derived.

First, let's see what these terms mean: a₁ is the initial angular acceleration, measured in rad/s².

It is the angular acceleration of the driving wheel of a vehicle at the moment it starts to move.

ar is the angular acceleration of the wheel and rd is the distance between the centers of the driving and driven wheels.

w₁ and w₂ are the angular velocities of the driving and driven wheels, respectively.

r₁ and r₂ are the radii of the driving and driven wheels, respectively.

So, to derive the expression for ar, we have:

r₂w₂ = r₁w₁

Let's differentiate both sides w.r.t time.

The result is:

r₂α₂ + r₂dw₂/dt = r₁α₁ + r₁dw₁/dt

We know that α₁ = a₁/r₁, and we need to find α₂.

To do this, we can use the formula:

ω₂ = (r₁ω₁)/r₂

Thus, dω₂/dt = (r₁/r₂)dω₁/dt

We can differentiate this equation again to get:

α₂ = (r₁/r₂)α₁ - (r₁/r₂)²dw₁/dt

Next, we can substitute the value of α₂ in the previous equation to get:

r₂((r₁/r₂)α₁ - (r₁/r₂)²dw₁/dt) + r₂dw₂/dt

= r₁α₁ + r₁dw₁/dt

Simplifying this equation, we get:

ar = α₁(1 - r₁/r₂) - (r₁/r₂)²(dω₁/dt)

To derive the expression for ao, we can use the formula:

ao = 2&w+rd

We know that w = (r₁w₁ + r₂w₂)/(r₁ + r₂)

Thus, ao = 2((r₁w₁ + r₂w₂)/(r₁ + r₂)) + rd

Now, we can substitute the values of w₁, w₂, and w from the previous equations to get:

ao = (r₁r₂/r)α₁ + (rd/r)(r₁w₁ + r₂w₂),

where r = r₁ + r₂.

Now, we can simplify this equation to get:

ao = α₁(r₁r₂/r) + (rd/r)w, where

w = (r₁w₁ + r₂w₂)/(r₁ + r₂)

Thus, the expressions for ar and ao are:

ar = α₁(1 - r₁/r₂) - (r₁/r₂)²(dω₁/dt)

ao = α₁(r₁r₂/r) + (rd/r)w

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Wheres the ? n answers at for #3 n #4

The numbers of the jerseys of 5 randomly selected Carolina Panthers would fall under the category of quantitative discrete data.

Quantitative data are numerical measurements or counts that can be added, subtracted, averaged, or otherwise subjected to arithmetic operations. Discrete data, on the other hand, can only take on specific, whole number values, as opposed to continuous data which can take on any value within a range.

Qualitative data, on the other hand, are non-numerical data that cannot be measured or counted numerically. Examples include colors, names, opinions, and preferences. Since the numbers of the jerseys are specific numerical values, they are considered quantitative data.

Since they can only take on specific, whole number values (i.e. the jersey numbers are not continuous values like weights or heights), they are considered discrete data. Therefore, the correct option for the given question is option "quantitative discrete".

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The value of x in the first question is 11 and the value of y is 3.

The value of x in the second question is 4 and the value of y is 4.

The value of x in the third question is -5 23/26 and the value of y is -1/13

2x + y = 25 equation 1

2x - 3y = 13 equation 2

The first step is to subtract equation 2 from equation 1:

-4y = -12

Divide both sides of the equation by -4

y = -12 / -4

y = 3

Substitute for y in equation 1:

2x + 3 = 25

2x = 25 - 3

2x = 22

x = 22 / 2

x = 11

-3x + 4y = -18 equation 1

x = -2y - 4

x + 2y = -4 equation 2

Multiply equation 2 by 2

2x + 4y = -8 equation 3

Subtract equation 3 from equation 2:

-5x = -20

Divide both sides of the equation by -5

x = -20 / -5

x = 4

Substitute for x in equation 2:

4 + 2y = -4

4 + 4 = 2y

8 = 2y

y = 8/2

y = 4

-2x + 3y = -15 equation 1

3x + 2y = -23 equation 2

Multiply equation 1 by 3 and equation 2 by 2

-6x + 9y = -45 equation 3

6x + 4y = -46 equation 4

Add equation 3 and equation4 together

13y = -1

y = -1/13

Substitute for y in equation 1:

-2x + 3(-1/13) = -15

-2x  -3/13 = -15

-2x = -15 + 3/13

-2x = 11 10/13

x = 11 10/13 ÷ -2

x = 153/13 x -1/2

x = -153/26

x =-5 23/26

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The quotient of 462 and 28 is 16.5 when written in decimal notation.

To calculate this, you divide 462 by 28:

462 ÷ 28 ≈ 16.5

The division process involves dividing the digits of the dividend (462) by the divisor (28) and obtaining the result. In this case, the result is approximately 16.5. The decimal point is placed after the digit 5, indicating the presence of a fractional part.

Please note that this is an approximation because the exact result would involve an infinite decimal expansion, which is typically rounded to a certain number of decimal places for practical purposes.

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Answer:

64

Step-by-step explanation:

The vertex of the parabola y = f(x + 1) is (1, -1).

To find the vertex of the parabola given by the equation y = f(x + 1), we need to determine the effect of the transformation on the vertex coordinates.

The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) represents the vertex coordinates.

In the given equation, y = f(x + 1), we can see that the transformation is a horizontal shift of 1 unit to the left. This means that the new vertex will be located 1 unit to the left of the original vertex.

Given that the original vertex is (2, -1), shifting 1 unit to the left would result in a new x-coordinate of 2 - 1 = 1. The y-coordinate remains the same.

Therefore, the vertex of the parabola y = f(x + 1) is (1, -1).

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Answer:

Step-by-step explanation:

Total marbles = 5  + 6 + 2 = 13

P( getting blue ball from first draw) = 5/13

The marble is not replaced. So, Now total marbles will be 12 & number blue marbles will be 4

P( getting blue ball from second draw) = 4/12 = 1/3

P(getting two blues) = \(\frac{5}{13}*\frac{1}{3}\\\)

                                  = 5/39

Answer:

One: x =  3/32

Two: y =  3/10

Step-by-step explanation:

One

y = k*x

1/4 = k* 1/8                    Multiply both sides by 8

8(1/4) = 8*k*(1/8)

8/4 = k

k = 2

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

3/16 = 2*x                      Divide by 2

3/32 = x

Two

y = 2/5

x = 1/3

2/5 = k * 1/3                   Multiply both sides by 5

2 = 5*k * 1/3

2 = 5/3 * k                     Multiply both sides by 3

6 = 5 * k                        Divide both sides by 5

6/5 = k

y = 6/5 * x

x = 1/4

y = 6/5 * 1/4

y = 6/20 = 3/10

Based on the given information, we know that x must be 2 since it is the only even prime number. We also know that y must be either 11, 13, 17, or 19 since those are the only prime numbers between 10 and 20.

So, the sum of x and y can be 2 + 11 = 13, 2 + 13 = 15, 2 + 17 = 19, or 2 + 19 = 21.

Out of these four possible sums, only 13, 17, and 19 are prime numbers. Therefore, we can say that the sum of x and y may or may not be a prime number, depending on the specific values of x and y.

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Answer:

136 1/2 cubic inches

Step-by-step explanation:

Volume is equal to length times width times height.

For width and height, use the decimal version of the mixed fractions to make calculations easier.

5 1/4 = 5.25

6 1/2 = 6.5

4 x 5.25 x 6.5 = 136.5, or 136 1/2

Answer:

1. Semi-regular tessellations are made from multiple regular polygons.

2. There are an infinite number of figures that form irregular tessellations!

3. You can create irregular polygons that tessellate the plane easily, by cutting out and adding symmetrically.

An irregular tessellation

An irregular tessellation is simply a group of figures which does not include any regular polygons.

In other words, an irregular tessellation is a group of irregular shapes.

The number of irregular tessellations

There are several irregular shapes and figures that make up an irregular tessellation.

This means that the number of irregular tessellation is non-finite.

How to create an irregular tessellation

There are several ways to do this. Some of them include;

See attachment for an instance of an irregular tessellation

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Answer:

A)

Step-by-step explanation :

This question isn't too hard, but you would have to use similar triangles.

To prove the assertion (p→¬q), (r → (p ∧ q)) ⇒ ¬r using a proof sequence. Here's the step-by-step justification:

1. (p→¬q) - Given as a premise
2. (r → (p ∧ q)) - Given as a premise
3. Assume r - Assumption for a proof by contradiction
4. (p ∧ q) - From 2 and 3, using Modus Ponens
5. p - From 4, using the Simplification rule (Conjunction elimination)
6. ¬q - From 1 and 5, using Modus Ponens
7. q - From 4, using the Simplification rule (Conjunction elimination)
8. (¬q ∧ q) - From 6 and 7, using the Conjunction Introduction rule
9. ¬r - From 3 and 8, using a proof by contradiction (Reductio ad absurdum)

The proof sequence shows that, given the premises (p→¬q) and (r → (p ∧ q)), the assertion ¬r can be proven.

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The height of the rectangle, given the breadth, can be found to be 200 cm

In a two - dimensional shape such as a rectangle, there would be certain terms that mean the same thing. An example of such terms are height and breadth. The height and the breadth of a rectangle is considered to be the same thing.

The height of this rectangle would therefore be the same as the breadth which means the height is 2 meters.

However, seeing as the length is in centimeters, the height would need to be in centimeters as well.

A single meter is 100 centimeters so 2 meters would be :

= 2 x 100

= 200 cm

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Answer:

Yes

Step-by-step explanation:

If you would like me to explain why I would love to explain

slope = −2

Once you know the slope of the line, plug it in for m in y = mx +

Step-by-step explanation:

Answer:

EC = 8/9 ft

Step-by-step explanation:

ΔADE ≈ ΔABC

set up a proportion based on corresponding sides

AD/AE = AB/AC

9/4 = 11/(4 + EC)

9(4 + EC) = 44

36 + 9EC = 44

9EC = 8

EC = 8/9

Answer: Domain (3, infinity); Asymptote x = 3

Step-by-step explanation:

log(x) domain is (0, infinity), but in this function the (x - 3) shifts the graph 3 to the right

The asymptote is 3 because log(3-3) = log(0) which does not exist (and any number that is negative inside log too) the function can't reach 3 which makes it the asymptote

The value of ML = 3, using the mid-point theorem of triangles.

According to the midpoint theorem, "the line segment of a triangle crossing the midpoints of two sides of the triangle is said to be parallel to its third side and also half the length of the third side."

In the question, we are given that triangle ABC is an equilateral triangle, and L, M, and N are the midpoints of BC, AB, and CA respectively.

Thus, by the midpoint theorem, we can say that:

Assuming AB = BC = AC = x units, we get:

Thus, the triangle LMN is an equilateral triangle.

Thus, MN = ML = NL.

Given MN = 3, we can write the value of ML = 3.

Thus, the value of ML = 3, using the mid-point theorem of triangles.

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The given question is in Spanish. The question in English is:

"Triangle ABC is equilateral and L, M, and N are the midpoints of BC, AB, and CA respectively. If MN = 3, what is the value of ML?"

The lamina's moment of inertia about the origin is given by, \(I_0=640 \pi\).

Given:

Find the moment of inertia \(I_y\) and \(I_0\).

The lamina's moment of inertia about the x-axis is:

In the above equation, substitute the given value:

Make use of polar coordinates:

\(\begin{aligned}x &=r \cos \theta \\y &=r \sin \theta \\d A &=d x d y=r d r d \theta \\D &=\{(r, \theta) \mid 0 \leq r \leq 4,0 \leq \theta \leq 2 \pi\}\end{aligned}\)

As we all know, the general equation of a circle is:

The given circle equation is:

As a result, r ranges from 0 to 4.

And ranges from 0 to 2\(\pi\).

As a result, the integral is shown below; simply enter all of the values and then integrate.

\(\begin{aligned}&I_x=\iint_D 5 y^2 d A \\&I_x=\int_0^{2 \pi} \int_0^4 5(r \sin \theta)^2 r d r d \theta \\&I_x=\int_0^{2 \pi} \int_0^4 5 r^3 \sin ^2 \theta d r d \theta \\&I_x=5 \int_0^{2 \pi}\left(\frac{r^4}{4}\right)_0^4 \sin ^2 \theta d \theta \\&I_x=320 \int_0^{2 \pi} \sin ^2 \theta d \theta \\&I_x=320 \int_0^{2 \pi}\left(\frac{1-\cos 2 \theta}{2}\right) d \theta \\&I_x=320\left(\theta-\frac{\sin 2 \theta}{2}\right)_0^{2 \pi} \\&I_x=320\left(\frac{2 \pi}{2}\right) \\&I_x=320 \pi\end{aligned}\)

Now, calculate  \(I_y\) and \(I_0\).

Make use of polar coordinates.

\(\begin{aligned}&x=r \cos \theta \\&y=r \sin \theta \\&d A=d x d y=r d r d \theta \\&D=\{(r, \theta) \mid 0 \leq r \leq 4,0 \leq \theta \leq 2 \pi\}\end{aligned}\)

As we all know, the general equation of a circle is:

The given circle equation is:

As a result, r ranges from 0 to 4.

And ranges from 0 to 2\(\pi\).

As a result, the integral is shown below; simply enter all of the values and then integrate.

\(\begin{aligned}&I_y=\iint_D 5 x^2 d A \\&I_y=\int_0^{2 \pi} \int_0^4 5(r \cos \theta)^2 r d r d \theta \\&I_y=\int_0^{2 \pi} \int_0^4 5 r^3 \cos ^2 \theta d r d \theta \\&I_y=5 \int_0^{2 \pi}\left(\frac{r^4}{4}\right)_0^4 \cos ^2 \theta d \theta \\&I_y=320 \int_0^{2 \pi} \cos ^2 \theta d \theta \\&I_y=320 \int_0^{2 \pi}\left(\frac{1-\cos 2 \theta}{2}\right) d \theta \\&I_y=320\left(\theta-\frac{\sin 2 \theta}{2}\right)_0^{2 \pi} \\&I_y=320\left(\frac{2 \pi}{2}\right) \\&I_y=320 \pi\end{aligned}\)

The lamina's moment of inertia about the origin is given by:

\(\begin{aligned}&I_0=\iint_D\left(x^2+y^2\right) d(x, y) d A \\&I_0=\iint_D 5 r^2 r d r d \theta \\&I_0=5 \int_0^{2 \pi} \int_0^4\left(\frac{r^4}{4}\right)_0^4 d \theta \\&I_0=320 \int_0^{2 \pi} d \theta \\&I_0=320(\theta)_0^{2 \pi} \\&I_0=640 \pi\end{aligned}\)

So, the moment of inertia is \(I_x=320 \pi\).

The worth of, \(I_y=320 \pi\).

Therefore, the lamina's moment of inertia about the origin is given by, \(I_0=640 \pi\).

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The correct question is given below:

Find the moment of inertia about the x-axis of a thin plate with density δ=5 bounded by the circle x2+y2=16. Then use your result to find Iy and Io.

The number of guests that were at the party is 26. This was illustrated in the probability.

From the information, it was stated that twenty six soft-drinks were consumed. Therefore, it implies that there were 26 people.

From the information, 9 guests had raspberry and 13 had cola while the remaining was shared equally. Therefore, the raspberry consumed will be 11 and 15 cola were drank.

The probability that a randomly chosen party guest had a cola drink will be:

= 15/26

The probability that a randomly chosen party guest had a raspberry drink will be:

= 11/26

The probability of the people who had both a raspberry and cola drink will be 0 since everyone had different drinks.

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Answer:

(a.) 27^4/3 = 81, (b.) 36^3/2 = 216, (c.) (1/8)^2/3 = 1/4, (d.) 128^5/7 = 32

Step-by-step explanation:

All these expressions can be converted in square roots.

In order to do this, we can picture the fractional exponents as exponent / index

(a.) So for this first problem, we would have the cube root of \(27^{\frac{4}{3} }\) or

\(\sqrt[3]{(27)^{4} }\).

We must do the equation inside the radical first (i.e., \((27)^{4}\)) to get \(\sqrt[3]{531,441}\) = 81

We can follow these same steps for the remaining equations:  

(b.) \(36^{\frac{3}{2} }\) = \(\sqrt{(36)^3}\) = \(\sqrt{46,656}\) = 216

(c.) \((\frac{1}{8})^\frac{2}{3}\) = \(\sqrt[3]{(\frac{1}{8})^{2} }\) = \(\sqrt[3]{(\frac{1^2}{8^2}) }\) = \(\sqrt[3]{(\frac{1}{64}) }\) = \(\frac{1}{4}\)

(d.) \(128^{\frac{5}{7} }\) = \(\sqrt[7]{(128)^{5} }\) = 32

In a shortest path problem, the right-hand side (RHS) value for the starting node has a value of 0. This indicates that the shortest path from the starting node to itself has a cost of 0.

In summary, the RHS value for the starting node in a shortest path problem is 0, indicating that the shortest path from the starting node to itself has a cost of 0.

The RHS value is used in the context of the Dijkstra's algorithm, which is commonly used to solve shortest path problems. In this algorithm, a priority queue is used to store the nodes that have not yet been visited, sorted based on their tentative distances from the starting node. Initially, the starting node is assigned a tentative distance of 0, indicating that it is the source node for the shortest path. The RHS value is used to update the tentative distance of a node when a shorter path is discovered. When a node is added to the priority queue, its tentative distance is compared to its RHS value, and the smaller of the two values is used as the node's priority in the queue. By setting the RHS value of the starting node to 0, we ensure that the starting node always has the highest priority in the queue and is processed first by the algorithm.

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\( - \frac{5}{4} \)

Step-by-step explanation:

It's going down 5 so it negative 5 and it moves to the right 4 times so it's positive 4.

Answer:

negative 5 over 4

Step-by-step explanation: