20 points!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

The producers' surplus if the market price is set at $8/unit is $21000

Given that

Price, p = 36 + 2.8x

The quantity  function is

q = 100x

So, the revenue at $8/unit is

R = 100x * 8

R = 800x

The total cost is calculated as

T(x) = (36 + 2.8x) * 100x

By calculation, we have the producers' surplus function to be

P = (36 + 2.8x) * 100x - 800x

Differentiate and set to 0

-560x - 2800 = 0

So, we have

x = 5

Recall that

P = (36 + 2.8x) * 100x - 800x

So, we have

P = (36 + 2.8 * 5) * 100 * 5 - 800 * 5

P = 21000

Hence, the producers' surplus is 21000

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The area of the given sector for the following parameter in which radius and central angle are given is = 165.792 sq .

What about sector?

A sector refers to a region of a circle that is bounded by two radii and an arc of the circle between them. The two radii of the sector form an angle at the center of the circle, and the length of the arc between them determines the size of the sector. The area of a sector can be calculated using the formula A =(θ/360)\(\pi r^2\) , where θ is the central angle of the sector in degrees, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14159. Sectors are often used in geometry and trigonometry to calculate the area and other properties of circular shapes.

Define central angle:

A central angle is an angle that is formed by two radii of a circle that share a common endpoint at the center of the circle. A central angle's measurement is the same as the circumference of the circle's path that it intercepts.  In other words, if a central angle has a measure of x degrees, then the arc intercepted by that angle on the circumference of the circle will also have a measure of x degrees.

According to the given information:

The area of the sector = /\(360^{o}\) (\(r^{2}\))

⇒ Where  = \(132^{o}\) and radius = 12

⇒ Area of the sector = \(\frac{132^{o} }{360^{o} }\) x \(\pi r^{2}\)

⇒ Area of the sector = 0.366 x 3.14 x 144

                                   = 165.792 sq .

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The equation of the ellipse in standard form is x² / 36 + y² / 25 = 1.

In this problem we have the representation of an ellipse set on Cartesian plane, whose standard form is shown below:

(x - h)² / a² + (y - k)² / b² = 1

Where:

If we know that a = 6, b = 5 and (h, k) = (0, 0), then the standard form of the equation of the ellipse is:

x² / 36 + y² / 25 = 1

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Answer:

I think I've answered this before

There is no solution to the equation 3x + 2 = 20 for x = 5.

To solve the equation 3x + 2 = 20 for x = 5, we substitute x with 5 and solve for the unknown variable.

First, we substitute x = 5 into the equation:

3(5) + 2 = 20

Simplifying the left side of the equation, we get:

15 + 2 = 20

Adding 15 and 2, we get:

17 = 20

This is not a true statement, since 17 is not equal to 20.

Therefore, there is no solution to the equation 3x + 2 = 20 for x = 5.

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Answer:

6

Step-by-step explanation:

f(x)=5x-4

f(2)=5(2)-4

10-4=6

Answer:

(h-1)(7h-3)

Step-by-step explanation:

Use quadratic formula (you can search it up). Also, the +- is plus or minus (there is no symbol for it.)

(10+-\(\sqrt{100-4(7)(3)}\))/2(7)

(10+-\(\sqrt{100-84}\))/14

(10+-\(\sqrt{16}\))/14

(10+-4)/14

14/14

or

3/7

14/14 simplifies to 1

However for 3/7, we need to simplify it.

x=3/7

7x=3

7x-3=0

Answer:

18

Step-by-step explanation:

First, we know that the total is equal to 100%. We then know that 14 students make up 43.75%, and eight grade students make up the rest, at 100-43.75=56.25%.

One way we can figure this out to find how many students make up each percent. To find this, we can simply divide the number of students (14) by their percent (43.75) to get 14 students/43.75 percent = 0.32 students per percent. We can then multiply this by 56.25 to get 18 as our answer for the number of eight graders.

Answer: 18

Step-by-step explanation:

14/43.75% = 0.32

56.25 × 0.32 = 18

Therefore, 18 is the answer to this equation.

Answer:

Based on the given information, it is not possible to definitively determine whether the number generator is fair or not. However, we can make some observations and inferences:

We know that 70% of the socks in the drawer are black, which means that in a random selection of 10 socks, we would expect to see around 7 black socks on average.

The dot plot shows the number of black socks in 10 trials of the number generator. We can see that the number of black socks varies from 0 to 10, with some frequencies being higher than others.

Without knowing the exact frequencies or probabilities, we can see that the dot plot does not appear to be centered around 7 black socks, which is what we would expect from a fair number generator. However, it is difficult to determine whether the deviations from 7 are statistically significant or not, without more information.

Therefore, based on the given information, the most accurate statement is:

The number generator's fairness cannot be determined with certainty from the given data, but there are indications that it may not be perfectly fair.

Step-by-step explanation:

Answer:

\( \frac{x + 2}{ {x}^{2} - x - 20 } \)

Step-by-step explanation:

Since the roots are -4 and 5, we can write that as

\((x + 4)(x - 5)\)

Apply foil method to find our denominator.

We get

\( {x}^{2} - x - 20\)

So that our denominator.

Since our denomiater gives us interger asymptote, our degree in our numerator must be 1 so the answer has to be a single interger or a single term.

Since our x intercepts is -2, we use

\((x + 2)\)

So our rational denomiater is

\( \frac{x + 2}{ {x}^{2} - x - 20 } \)

Answer:

-2x + (-3) = x

x = -1

Step-by-step explanation:

-2x + (-3) = x

add 2x to each side

-3 = 3x

divide each side by 3

-1 = x

The relationship between x and y is a strong negative relationship.

For this question, we need to determine the correlation coefficient,

Thus,

The correlation coefficient

= (21 - 5*6)/ \(\sqrt{9 * 10}\)

= -0.948

The above answer is too close to -1. Therefore correlation coefficient is a strong negative.

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Answer:

Step-by-step explanation:

x- intercept is the point (x, 0)

y-intercept is the point (0, y)

Answer:

Range: the difference between the highest and lowest values.

Step-by-step explanation:

Range is the difference of highest value and lowest value.

What is range of a function ?

Range of a function can be defined as the all possible values that x could be .

The definition of a range as follows

Range can be defined as the difference of highest value and lowest value.

Example :

Let the data be 1,55,1,70,8,8,55

So from the given data  ,

The highest term = 70

lowest = 1

Range could be = 70 - 1

= 69

Therefore, Range is the difference of highest value and lowest value.

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Given:

Consider the given equation is

\(y=\dfrac{2}{5}x-1\)

To find:

The equation of a line that is perpendicular to the graph of given line.

Solution:

Slope intercept form of a line is

\(y=mx+b\)

where, m is slope and b is y-intercept.

Equation of given line is

\(y=\dfrac{2}{5}x-1\)

Here, slope is \(\dfrac{2}{5}\).

We know that, product of slopes of two perpendicular lines is -1.

\(m_1\times m_2=-1\)

\(\dfrac{2}{5}\times m_2=-1\)

\(m_2=-\dfrac{5}{2}\)

The slope of perpendicular line is \(-\dfrac{5}{2}\).

Only in option C, the slope of the line is \(-\dfrac{5}{2}\).

Therefore, the correct option is C.

From the given option the slope of the line -5/2 is shown by the equation  \(y=-\dfrac{5}{2}x-4\)   that is option B) and this can be determined by using the slope-intercept form.

Given :

Equation --    \(y=\dfrac{2}{5}x-1\)     ---- (1)

First, determine the slope of the given line by using the slope-intercept form. The slope-intercept is given by the equation:

y = mx + c

Now, compare equation (1) with the above equation.

\(\rm m_1 =\dfrac{2}{5}\)

c = -1

For a line to be perpendicular to the other line the product of the slope of both the line is equal to -1, that is:

\(\rm m_1m_2 = -1\)

So, the slope of the line perpendicular to the line \(y=\dfrac{2}{5}x-1\)  is:

\(\rm m_2 = -\dfrac{5}{2}\)

So, from the given option the slope of the line -5/2 is shown by the equation  \(y=-\dfrac{5}{2}x-4\)   that is option B).

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Answer:

6:6=x

7:16=y

8:20=z

Step-by-step explanation:

For 6, since BD is a perpendicuar bisector, that means 15x=90. Divide 90 by 15 and you get 6

for 7, if bd is a angle bisector, you can set 3y=48. divide 48 by 3 and you get 16

for 8, since Bd is a median, you can set 2z-3=z+17. Isolate the variable and you will get 2z-z=17+3. Add like terms together and you get z=20

Just so you know, a perpendicular bisector will make both angles equal to 90, an angle bisector make both angles equal to each other, and medians make it so that it hit a line in the center therefor you can set both sides of the line to be equal

The statement "the expected value of an unbiased estimator is equal to the parameter whose value is being estimated" is true.

An estimator is a function of the sample data used to estimate the value of a population parameter. An estimator is said to be unbiased if its expected value is equal to the true value of the population parameter. In other words, if we were to repeatedly take samples from the population and calculate the estimator for each sample, the average value of the estimator over all the samples would be equal to the true value of the population parameter. The expected value of an unbiased estimator is a key property because it ensures that the estimator is not systematically overestimating or underestimating the population parameter. Instead, the estimator provides an unbiased estimate of the population parameter on average across all possible samples. It is important to note that not all estimators are unbiased. Biased estimators may systematically overestimate or underestimate the population parameter, leading to incorrect conclusions. Therefore, unbiasedness is a desirable property for an estimator to have.

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Answer:

Step-by-step explanation:

⅔n - 5 = ⅓n + 7

⅓n = 12

n = 36

Answer:

the last option

2(x-9)=12;x=15

Answer:

2(x-9) = 12; x = 15

Step-by-step explanation:

Have a nice day

Answer:

Look at attachment

Step-by-step explanation:

The cost of 1 pencil and 1 eraser is $0.10 and 3 pencils and 5 erasers is $0.38.

To clear up this problem, we are able to use simultaneous equations to locate the value of 1 pencil and 1 eraser. Let x be the price of 1 pencil and y be the price of 1 eraser. Then we are able to write  equations based totally on the given records:

1x + 2y = 0.14 and 2x + 3y = 0.24

To take away y, we can multiply the first equation by using -3 and add it to the second equation:

-3x - 6y = -0.42 and  2x + 3y = 0.24

-x - 3y = -0.18

Then we can divide both sides by way of -1 to get:

x + 3y = 0.18

To dispose of x, we are able to multiply the first equation through -2 and upload it to the second equation:

-2x - 4y = -0.28 and  2x + 3y = 0.24

-y = -0.04

Then we are able to divide both sides by -1 to get:

y = 0.04

This method that one eraser fee of $0.04. To locate the cost of one pencil, we can replace y in both equations. For instance, the usage of the primary equation:

1x + 2(0.04) = 0.14

1x + 0.08 = 0.14

1x = 0.14

- 0.08 1x = 0.06

This approach is that one pencil is priced at $006.

Therefore, the cost of:

i.) one pencil and one eraser is $0.06 + $0.04 = $0.10

ii.) 3 pencils and 5 erasers is 3($0.06) + 5($0.04) = $0.18 + $0.20 = $0.38.

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The region enclosed by the given curves are integrated with respect to x and the area is 4.2724 square units.

In this question,

The curves are y = 2/x, y = 2/x^2, x = 4

The diagram below shows the region enclosed by the given curves.

From the diagram, the limit of x is from 1 to 4.

The given curves are integrated with respect to x and the area is calculated as

\(A=\int\limits^4_1 {\frac{2}{x} } \, dx -\int\limits^4_1 {\frac{2}{x^{2} } } \, dx\)

⇒ \(A=2[\int\limits^4_1 {\frac{1}{x} } \, dx -\int\limits^4_1 {\frac{1}{x^{2} } } \, dx]\)

⇒ \(A=2[\int\limits^4_1( {\frac{1}{x} } - {\frac{1}{x^{2} } } )\, dx]\)

⇒ \(A=2[lnx-\frac{1}{x} ] \limits^4_1\)

⇒ \(A=2[(ln4-\frac{1}{4} )-(ln1-\frac{1}{1} )]\)

⇒ A = 2[(1.3862-0.25) - (0-1)]

⇒ A = 2[1.1362 + 1]

⇒ A = 2[2.1362]

⇒ A = 4.2724 square units.

Hence we can conclude that the region enclosed by the given curves are integrated with respect to x and the area is 4.2724 square units.

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The general solution to the differential equation y'' + 16y = 0 is y(x) = (c₁ + c₂) * cos(4x)

To solve the differential equation y'' + 16y = 0 using reduction of order, we'll assume a second solution of the form y₂(x) = u(x) * y₁(x), where y₁(x) is a known solution and u(x) is an unknown function.

Given y₁(x) = cos(4x), we'll differentiate it to find y₁'(x) and y₁''(x):

y₁'(x) = -4sin(4x)

y₁''(x) = -16cos(4x)

Now we substitute y₂(x) = u(x) * y₁(x) into the original differential equation:

y'' + 16y = 0

(-16cos(4x)) + 16(u(x) * cos(4x)) = 0

Simplifying the equation:

-16cos(4x) + 16u(x) * cos(4x) = 0

cos(4x)(-16 + 16u(x)) = 0

For this equation to hold for all values of x, we must have (-16 + 16u(x)) = 0.

Solving for u(x):

-16 + 16u(x) = 0

16u(x) = 16

u(x) = 1

Now we have the second solution:

y₂(x) = u(x) * y₁(x)

y₂(x) = 1 * cos(4x)

y₂(x) = cos(4x)

Therefore, the general solution to the differential equation y'' + 16y = 0 is:

y(x) = c₁ * y₁(x) + c₂ * y₂(x)

y(x) = c₁ * cos(4x) + c₂ * cos(4x)

y(x) = (c₁ + c₂) * cos(4x)

Where c₁ and c₂ are arbitrary constants.

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