a + x + p + 8 = r
solve for x

all help is appreciated!!

The solution is \(\(x=\dfrac{\pi}{3}+2n\pi,\dfrac{5\pi}{3}+2n\pi\)\) where \(n\) is any integer.

The given equation is:\($$\sqrt{3}\csc x-2=0$$\)

We will isolate the term \(\(\csc x\)\) and solve it for \(x\).

First, we will add 2 to both sides of the equation.

\($$ \begin{aligned}\sqrt{3}\csc x &= 2 \\ \csc x &= \frac{2}{\sqrt{3}}\end{aligned} $$\)

Next, we will convert this into sin x.

Using the reciprocal property of csc we get,

\($$ \begin{aligned}\csc x &= \frac{1}{\sin x} \\ \frac{2}{\sqrt{3}} &= \frac{1}{\sin x} \\ \sin x &= \frac{\sqrt{3}}{2} \end{aligned} $$\)

Hence, the solution to the equation is given by

\($$x = \frac{\pi}{3} + 2n\pi, \quad \frac{5\pi}{3}+2n\pi.$$\)

Therefore, the solution is

\(\(x=\dfrac{\pi}{3}+2n\pi,\dfrac{5\pi}{3}+2n\pi\)\)

where \(n\) is any integer.

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Answer:

Two sets of dimensions are possible:

              L(m)   W(m)   Area(m^2)   Fence (m) Perimeter

Set 1         19        16       304              51

Set 2         32      9.5      304              51

Step-by-step explanation:

Let's set L and W for the Length and Width of the perimeter.  We know that:

Area = L*W

Area = 304 m^2

Perimeter = 51 m

Let's say that the side bounded by the river is the length side.   No fence is required for that portion, so the fencing for the perimeter is given by:

Perimeter, P = L + 2W

P = 51 m

We can write:   L+2W=51 m

Rearrange to isolate one of the two variables.  Lets pick L:

 L+2W=51

 L=51-2W

L = (51-2W)

Now use this in the area equation:

304 m^2 = L*W

304 m^2 = (51-2W)*W

304 m^2 = (51-2W)*W

304 m^2 = 51W-2W^2

Arrange this in the standard form of a quadratice equation and solve:

-2W^2+51W-304 m^2 = 0

W = 16 and 9.5 meters

W = 16 m

Since L=51-2W

 L=51-2*(16)

L = 51-32

L = 19 m

Area = L*W

L*W = 304 m^2

(19m)W = 304 m^2

W =  16 m

Check:

Does a length (L) of 19 m and a width (W) of 16 m give an area of 304 m^2 and a fencing perimeter of 51 m if one of the L sides is the river?

Area = (19 m)*(16 m) = 304 m^2  YES

Per.  = 2*(16)+ 19 = 51 m  YES

W = 9.5 m

Ding the same calculation for a width of 9.5 m also satisfies all the equations, as per above.  

Both values of W are valid, so the twos sets of possible dimensions are:

                   L(m)    W(m)   Area(m^2)   Fence (m) Perimeter

Set 1          19      16       304              51

Set 2          32      9.5      304              51

Answer:

Step-by-step explanation:

23(9x+6)=6x+4

Expand it

207x+138 = 6x+4

Simplify it

201x = -134

Divide everything by 201

x=-134/201

Simplify it again

x=-2/3

The population, in this case, would be option B: Collection of all commuters in South Africa.

The population refers to the total group of individuals or objects that the survey or study is interested in investigating.

In this case, the study or survey was carried out on a sample of 500 commuters.

A sample is a subset of the population that is taken to obtain information about the population.

This sample may or may not be representative of the population.

However, the population includes all commuters in South Africa, regardless of whether they were surveyed or not.

It is important to note that the sample is always a subset of the population.

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If Jacqueline bought a bicycle at wholesale cost for $210 dollars. If the bicycle is normally $300 from the local bike shop, Then 30% markup the bike shop adds to the wholesale cost

Percentage, a relative value indicating hundredth parts of any quantity.

Given,

Jacqueline bought a bicycle at wholesale cost for $210 dollars.

The actual price of bicycle is normally $300 from the local bike shop.

We need to find the percent markup the bike shop adds to the wholesale cost.

For this we need to find the difference and we have to divide it by actual price

300-210/300=90/300=0.3

Now multiply 0.3 with 100 as hundredths to get the percentage value

0.3×100=30

Hence 30 percent markup the bike shop adds to the wholesale cost

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The given expression, log₃(6c) + log₃₁(12), can be simplified as log₃(72c) with a coefficient of 1.

To express the given expression as a single logarithm with a coefficient of 1, we can use the product rule of logarithms. The product rule states that the sum of logarithms of two numbers multiplied together is equal to the logarithm of their product.

Apply the product rule to combine the two logarithms:

log₃(6c) + log₃₁(12) = log₃(6c * 12)

Simplify the expression inside the logarithm:

6c * 12 = 72c

Rewrite the expression using a single logarithm:

log₃(72c)

Therefore, the given expression, log₃(6c) + log₃₁(12), can be simplified as log₃(72c) with a coefficient of 1.

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Answer:

B log3 c/2

Next C log7 2 + log 7 49

Next log7 49 = 2

Next log 7 98 = 2.356

Step-by-step explanation:

Based on the equation in the question , the R2 would be 0.934.

To compute R2, we need to use the formula:

R2 = SSR / SST

Given that SSR = 14,141.7 and

SST = 15,128.4,

We can substitute these values into the formula:

R2 = 14,141.7 / 15,128.4

R2 ≈ 0.934

b. To compute Ra2, we need to subtract R2 from 1:

Ra2 = 1 - R2

Substituting the value of R2 we calculated in part a:

Ra2 ≈ 1 - 0.934

Ra2 ≈ 0.066

c. A large R2 value indicates that the estimated regression equation explains a large amount of the variability in the data.

In this case, R2 is approximately 0.934, which means that the estimated regression equation explains about 93.4% of the variability in the data.

So, the answer is "Yes".

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The value of the computer with initial value $4600 after 3 years using the exponential model is equal to $2422.39 (approximately).

Cost of new computer = $4600

Book value after 2 years = $3000

use the exponential model,

y = a × \(e^{(-kt)}\)

where y is the value of the computer after t years,

a is the initial value of the computer when t=0,

k is a constant,

and e is the base of the natural logarithm.

Find the value of k using the information given,

y(2) = 3000

⇒3000 = a × \(e^{(-2k)}\)

y(0) = 4600

⇒ 4600 = a × e⁰

⇒ 4600  = a

Dividing the two equations, we get,

⇒3000/4600 =  \(e^{(-2k)}\)

⇒0.6522 =   \(e^{(-2k)}\)

Taking the natural logarithm of both sides, we get,

⇒ -2k = ln (0.6522 )

Solving for k, we get,

⇒ k = -0.4276 /2

⇒ k = - 0.2138

So the exponential model for the value of the computer is,

y = 4600 × \(e^{(-0.2138 \times t)}\)

To find the value of the computer after 3 years, we can plug in t=3,

y(3) = 4600 × \(e^{(-0.2138 \times 3)}\)

      = 4600 × \(e^{(-0.6413)}\)

      = 4600 × 0.5266

      = 2422.39

Therefore, the value of the computer after 3 years using the exponential model is approximately $2422.39.

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Answer:

divide $70 by 0.2

Step-by-step explanation:

Answer:

multiply $70 by 0.2

Step-by-step explanation:

Answer:

A) y>=-1

Step-by-step explanation:

The line itself is y=-1, but it is also filled in. Therefore, we are down to either A or C as the right answer

Since (0,0) is a solution to the inequality as indicated by the shade, we know that since y=0 in the origin, 0 is greater than -1, so therefore A is the correct answer.

Answer:

-1

Step-by-step explanation:

x=(-2)

2(-2) +3

-4 +3

= -1 .

As the law of supply and demand states, there is an effect on the price of a product depending on its availability.

If there is a low supply and a high demand, there is an increase in price and vice versa.

Last 2012, there was a virus which infected millions of chicken. It was known as Avian influenza or bird flu. It resulted to scarcity of eggs.

As the law of supply and demand states, there is an effect on the price of a product depending on its availability.

For example we can use water. If a product becomes scarce its price would increase due to supply in demand.

If drinkable water became scarce its price would be greatly increased to its need and being in extreme demand.

In short,  if there is a low supply and a high demand, there is an increase in price and vice versa.

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According to the sample data, the best conclusion supported by the sample data is that approximately 30% of all largemouth bass in the pond weigh more than 2 pounds. The answer is (D) Approximately 30% of all largemouth bass in the pond weigh more than 2 pounds.

The conclusion that is best supported by the sample data is that approximately 30% of all largemouth bass in the pond weigh more than 2 pounds, which is based on the fact that the sample contained 150 largemouth bass, of which 30% weighed more than 2 pounds.

Therefore, options A and C are incorrect. The sample data does not provide enough information to determine the average weight of all fish in the pond, so option B is also incorrect.

The correct answer is D) Approximately 30% of all largemouth bass in the pond weigh more than 2 pounds. This conclusion is supported by the sample data because the study specifically included a sample of 150 largemouth basses, of which 30% weighed more than 2 pounds. The other options are not supported by the sample data because the study does not include data on any other types of fish or the average weight of all fish in the pond.

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Here we want to find the possibles magnitudes of the sum of two vectors.

Sadly, the options are not given, so I will give you the range of all the possible magnitudes of the sum of these two vectors.

We will find that any magnitude in the range: 58cm ≤ M ≤ 100cm is a possible magnitude or the resultant vector.

How we can find that range?

What we need to do is find the maximum and minimum.

The minimum is the case where the two displacements are in opposite directions, in that case, the magnitude of the sum will be:

79cm - 21cm = 58cm

The maximum is when both displacements are in the same direction, thus we must add the displacements, then we have:

79cm + 21cm = 100cm

Thus, any magnitude in the range:

58cm ≤ M ≤ 100cm

Is a possible magnitude for the resultant vector.

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The closest answer for each area is B. 0.052, D. 0.015, and C. 0.936, respectively.

(a) The area to the left of 32 on a N(45, 8) distribution. The area to the left of 32 on a N(45, 8) distribution is given by: P(Z < (32 - 45)/8)P(Z < -1.625)= 0.052, approximately. So, the closest answer is B. 0.052.

(b) The area to the right of 12 on a N(9.4, 1.2) distribution. The area to the right of 12 on a N(9.4, 1.2) distribution is given by: P(Z > (12 - 9.4)/1.2)P(Z > 2.166)= 1 - P(Z < 2.166)= 1 - 0.985= 0.015. So, the closest answer is D. 0.015.

(c) The area between 43 and 100 on a N(75, 15) distribution. The area between 43 and 100 on a N(75, 15) distribution is given by: P((43 - 75)/15 < Z < (100 - 75)/15)P(-1.5333 < Z < 1.6666)= P(Z < 1.6666) - P(Z < -1.5333)= 0.9525 - 0.0624= 0.8901. So, the closest answer is C. 0.936.

In conclusion, the closest answer for each area is B. 0.052, D. 0.015, and C. 0.936, respectively.

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Answer:

Step-by-step explanation:

You want to know how to determine the y-intercepts of a rational function, and their possible number.

A rational function f(x) is the ratio of two polynomial functions p(x) and q(x):

  f(x) = p(x)/q(x)

As such, both numerator and denominator have single function values for any value of the independent variable. The y-intercept of f(x) is ...

  f(0) = p(0)/q(0)

The values of p(0) and q(0) are simply the constant terms in those respective functions.

The simple way to find the y-intercept is to look at the ratio of the constant terms in the polynomial functions making up the rational function. If that is defined, there is one y-intercept. If it is undefined (q(0)=0), then there are no y-intercepts.

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Answer:

\(x = 110 \\ (exterio \: angles \: of \: a \: traingle \: sum \: up \: to \: 360)\)

Answer:

x = 110

Step-by-step explanation:

Assuming you require the value of x

The sum of the external angles of a triangle = 360°

The 3 angles shown are external angles.

Subtract the sum of the 2 given angles from 360 for x

x = 360 - (140 + 110) = 360 - 250 = 110

Answer:  "How do u calculate the diameter of a circle"?

Step-by-step explanation:  Calculating diameter is easy you just need the radius, the circumference, or the area. Even if you don't have any of those dimensions, you can still find the diameter if you have a drawing of the circle.

The probability that none of the 4 light bulbs work is 0.0256, or approximately 2.56%.

Since each light bulb works independently of the others, we can treat the outcome of each bulb as a Bernoulli trial with a probability of success (working) p = 0.6 and a probability of failure (not working) q = 0.4.

To find the probability that none of the 4 light bulbs work, we need to find the probability of having 0 successful trials out of 4. This can be calculated using the binomial distribution:

P(X=0) = (4 choose 0) * (0.6)^0 * (0.4)^4 = 0.4^4 = 0.0256

Where (4 choose 0) is the number of ways to choose 0 successful trials out of 4, which is 1.

In summary, we can use the binomial distribution to find the probability that none of the 4 light bulbs work, since each bulb works independently of the others. Using this method, we find that the probability is 0.0256 or approximately 2.56%.

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Answer:

OC. $57.28

Step-by-step explanation:

It depends on how much she sells them for.

Let's say Anne sells them for $x.

Then her profit is:

8x-(8*7.16)

=8x-57.28

To make a minimum to at least make even is $57.28 and sell for $7.16 a piece.

Anne makes a profit of $57.28 on the sale of these 8 canvases. which is the correct answer would be option (C).

The profit is equal to the difference between the selling price and the original cost price.

Anne purchases art supplies for her business from a wholesaler. She spends $7.16 on eight 16 by 20-inch canvases.

To calculate the profit that Anne makes on the sale of these 8 canvases, you need to know the price at which she sells them and the cost of buying them from the wholesaler. If the cost of each canvas is $7.16 and she buys 8 of them, the total cost of the canvases is :

⇒ 8 × $7.16

Apply the multiplication operation and we get

⇒ $57.28.

Therefore, she makes a profit of $57.28 on the sale of these 8 canvases.

Hence, the correct answer would be an option (C).

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the percent of cash the Fire branch raised is 5.833 and the pre-sale rate of the TV is $300.

A price or ratio that can be said as a fragment of one hundred is called a percent in mathematics. If we want to compute a percent of a number, we need to divide it with the aid of using its complete after which multiply it with the aid of using one hundred. The percentage consequently refers to an issue in keeping with a hundred. Per one hundred is what the time period percentage signifies. The letter "%" stands for it.

Given,  The fire department hopes to raise $30,000 to repair a firehouse. So far the department has raised $1,750.00

From the general formula of Percentage, we have to divide the value by the total value and then multiply the resultant by 100.

Percentage = (1750/30,000) * 100 = 5.833%

Also given, A TV is advertised for sale. It is 35% off and has a new price of $195.

Price of TV before Sale = (195 / 65) * 100

Price of TV before Sale = 300$

Therefore, the percentage of money the Fire department raised is 5.833 and the pre-sale price of the TV is $300.

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Answer:

the answer is 7p

Step-by-step explanation:

p(5)+p(2)=7p

The text discusses a production function and addresses various aspects of a firm's decision-making. It covers profit maximization, factor demand functions, supply function, profit function, Hotelling's lemma, cost minimization, conditional factor demand functions, and the cost function. These concepts are derived using mathematical calculations and formulas. Hotelling's lemma is verified, and the cost function is determined.

(a) The firm's profit maximization problem can be stated as follows: Maximize profits (π) by choosing the optimal levels of inputs (z and zo) that maximize the output (y) given the prices of output (p) and inputs (w, w₂).

(b) To derive the firm's factor demand functions, we need to find the conditions that maximize profits.

The first-order condition for input z is given by:

∂π/∂z = p * (∂f/∂z) - w = 0

Substituting the production function f(z) = z^(1/4) / z^(1/2) into the above equation, we have:

p * (1/4 * z^(-3/4) / z^(1/2)) - w = 0

Simplifying, we get:

p * (1/4 * z^(-7/4)) - w = 0

Solving for z, we find:

z = (4w/p)^(4/7)

Similarly, for input zo, the first-order condition is:

∂π/∂zo = p * (∂f/∂zo) - w₂ = 0

Substituting the production function f(zo) = z^(1/4) / z^(1/2) into the above equation, we have:

p * (1/2 * z^(1/4) * zo^(-3/2)) - w₂ = 0

Simplifying, we get:

p * (1/2 * z^(1/4) * zo^(-3/2)) - w₂ = 0

Solving for zo, we find:

zo = (2w₂ / (pz^(1/4)))^(2/3)

(c) To derive the firm's supply function, we need to find the level of output (y) that maximizes profits.

Using the production function f(z), we can express y as a function of z:

y = z^(1/4) / z^(1/2)

Given the factor demand functions for z and zo, we can substitute them into the production function to obtain the supply function for y:

y = (4w/p)^(4/7)^(1/4) / (4w/p)^(4/7)^(1/2)

Simplifying, we get:

y = (4w/p)^(1/7)

(d) The firm's profit function is given by:

π = p * y - w * z - w₂ * zo

Substituting the expressions for y, z, and zo derived earlier, we have:

π = p * ((4w/p)^(1/7)) - w * ((4w/p)^(4/7)) - w₂ * ((2w₂ / (pz^(1/4)))^(2/3))

(e) To verify Hotelling's lemma, we need to calculate the partial derivatives of the profit function with respect to the prices of output (p), input z (z₁), and input zo (z₂).

Hotelling's lemma states that the partial derivatives of the profit function with respect to the prices are equal to the respective factor demands:

∂π/∂p = y - z * (∂y/∂z) - zo * (∂y/∂zo) = 0

∂π/∂z₁ = -w + p * (∂y/∂z₁) = 0

∂π/∂z₂ = -w₂ + p * (∂y/∂z₂) = 0

By calculating these partial derivatives and equating them to zero, we can verify Hotelling's lemma.

(f) The firm's cost minimization problem can be stated as follows: Minimize the cost of production (C) given the level of output (y), prices of inputs (w, w₂), and factor demand functions for inputs (z, zo).

(g) To derive the firm's conditional factor demand functions, we need to find the conditions that minimize costs. We can express the cost function as follows:

C = w * z + w₂ * zo

Taking the derivative of the cost function with respect to z and setting it to zero, we get:

∂C/∂z = w - p * (∂y/∂z) = 0

Simplifying, we have:

w = p * (1/4 * z^(-3/4) / z^(1/2))

Solving for z, we find the conditional factor demand for z.

Similarly, taking the derivative of the cost function with respect to zo and setting it to zero, we get:

∂C/∂zo = w₂ - p * (∂y/∂zo) = 0

Simplifying, we have:

w₂ = p * (1/2 * z^(1/4) * zo^(-3/2))

Solving for zo, we find the conditional factor demand for zo.

(h) The firm's cost function is given by:

C = w * z + w₂ * zo

Substituting the expressions for z and zo derived earlier, we have:

C = w * ((4w/p)^(4/7)) + w₂ * ((2w₂ / (pz^(1/4)))^(2/3))

This represents the firm's cost function.

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Answer:

-4

Step-by-step explanation:

I calculated it straight forward. lol

Answer:

the first option

To convert 4.42 kg into pounds, the starting place in the conversion process is to understand the conversion factor between kilograms and pounds.

The conversion factor between kilograms (kg) and pounds (lbs) is 1 kg = 2.20462 lbs. This means that 1 kilogram is equal to approximately 2.20462 pounds. To convert a given weight in kilograms to pounds, you need to multiply the weight in kilograms by the conversion factor.

In this case, you want to convert 4.42 kg into pounds. The starting place in the conversion process is to use the conversion factor:

4.42 kg * 2.20462 lbs/kg = 9.7314044 lbs

By multiplying the given weight in kilograms (4.42 kg) by the conversion factor (2.20462 lbs/kg), you find that 4.42 kg is approximately equal to 9.7314044 pounds. Therefore, when converting kilograms to pounds, the first step is to apply the appropriate conversion factor by multiplying the weight in kilograms by the conversion factor.

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The volume of the solid obtained by rotating the region enclosed by the curves \(y = x ^{\frac{1}{2} }\) and y = x about the x-axis is \(\frac{\pi}{6}\).

option A.

The volume of the solid obtained by rotating the region enclosed by the curves \(y = x ^{\frac{1}{2} }\) and y = x about the x-axis is calculated as follows;

The limit of the integration is calculated as follows;

 \(y = x ^{\frac{1}{2} } = \sqrt{x}\)

y = x

solve the two equation together;

x = √x

Square both sides of the equation;

x² = x

x² - x = 0

x(x - 1) = 0

x = 0 or  x - 1 = 0

x = 0 or 1

The radius of the solid formed is determined as;

\(r = (x^2 - x)\)

when it is rotated, the radius of the solid; r = x - x²

The volume function of the solid is calculated as follows;

dv = 2πxr

dv = 2πx (x - x²)

The volume of the solid is calculated as;

\(V = \int\limits^1_0 {2\pi x (x - x^2) } \, dx \\\\V = 2\pi \int\limits^1_0 {x( x- x^2) } \, dx\\\\V = 2\pi \int\limits^1_0 { (x^2- x^3) } \, dx\\\\V = 2\pi [\frac{x^{3 }}{3} - \frac{x^4}{4} ]^1_0\\\\V = 2\pi [\frac{(1)^{3 }}{3} - \frac{(1)^4}{4} ]\\\\V = 2\pi (\frac{1}{12} )\\\\V = \frac{2\pi}{12} \\\\V = \frac{\pi }{6}\)

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Answer:

Both have 4 points, and sides.  

Squares have 4 even sides

Rectangles have 2 short sides and 2 long sides.