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Here is the graph of a function describing the relationship between the height y, in feet, of the tip of a windmill blade and the angle of rotation Θ made by the blade. Describe the windmill.

The ratio in the form of 1 :n is 1:300.

Ratio of two number A and B is the comparison of A with respect to B and when two ratios are equal they are said to be in proportion.

It is given that a ratio is

6mm : 180cm

It has to be simplified in the form of

1:n

1 cm = 10mm

therefore

180 cm = 1800 mm

6mm:180cm = 6/ 1800

= 1/300

Therefore the ratio in the form of 1 :n is 1:300.

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Number of roots in the RHP of the complex plane: 31.2. Number of roots in the RHP of the complex plane: 0

The Routh-Hurwitz stability criterion is a technique for deciding the stability of linear time-invariant systems.

The Routh-Hurwitz criteria are a collection of necessary and sufficient conditions for the stability of a polynomial whose coefficients are real numbers.

It can be used to calculate the location of the roots of a polynomial's characteristic equation. Below are the solutions to the given polynomial equations:

Solution 1: Using Routh-Hurwitz criterion for s⁵ + 3s⁴ + 9s³ + 8s² + 65 + 4= 0:

Routh table is given below: s⁵ = 1 3 4 0 0

s⁴ = 3 8 65 0

s³ = 2.36 16.6 0

s² = 8.9 65 0

s¹ = 68 0

s⁰ = 4

There are three poles in the right half plane (RHP) of the complex plane for the given equation.

Hence, the system is unstable.

Solution 2: Using Routh-Hurwitz criterion for s⁵ + 6s³ + 5s² + 8s + 20=0:

Routh table is given below: 

s⁵ = 1 5

s⁴ = 6 8

s³ = 2 20

s² = 4 -20

s¹ = -10

s⁰ = 20

There are no poles in the RHP of the complex plane for the given equation.

Therefore, the system is stable.

Hence, the answer is:1.1

Note: When the roots of the characteristic equation are located on the imaginary axis, the Routh-Hurwitz criteria fail.

A little change in the equation coefficients leads to no information on stability.

Hence, we cannot conclude the stability of the system.

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If every individual in a population has an equal chance of being selected for a sample, the sample is said to be a "random sample" or a "simple random sample."

A random sample is a sampling technique used in statistics to gather data from a population. It is considered one of the most unbiased and reliable methods for selecting a sample. In a random sample, each individual in the population has an equal probability of being selected, regardless of their characteristics or attributes.

This equal chance of selection eliminates any systematic bias and ensures that the sample is representative of the population.

The process of obtaining a random sample involves assigning a unique identifier to each individual in the population and using a randomization method to select the desired number of individuals.

Random sampling can be conducted through various techniques, such as simple random sampling, where individuals are selected directly from the population using a random number generator or a randomization table.

The goal of a random sample is to reduce the potential for selection bias and increase the generalizability of the findings to the larger population. By giving every individual an equal opportunity to be included in the sample, researchers can make more accurate inferences and draw conclusions about the population as a whole.

This type of sampling method ensures that each member of the population has an equal opportunity to be included in the sample, making it a representative subset of the population.

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Answer:

u must sketch what u see when u close ur

Answer:

Since we are attempting to sell a store owner a new product.

The plan of a free trial option will be used to use the product for six months. Additionally, we will display a graph to them demonstrating how using this product will increase sales.

Moreover, the testimonials from other store owners who spoke well of the product.

They are all the most successful presentation techniques

Step-by-step explanation:

Answer: All of the above is the correct answer

Step-by-step explanation: Confirmed correct on test

Without specific information about the data set, it is not possible to determine which equation is the best fit.

To determine the linear function equation that best fits the data set, we need more information about the data set itself. Without the data points or any other details, we cannot accurately determine which linear function equation is the best fit.

However, I can provide a general explanation of the four options:

y = -2x + 5: This is a linear equation with a negative slope of -2. It represents a line that decreases as x increases. The y-intercept is 5.

y = 2x + 5: This is a linear equation with a positive slope of 2. It represents a line that increases as x increases. The y-intercept is 5.

y = -1/2x + 5: This is a linear equation with a negative slope of -1/2. It represents a line that decreases at a slower rate as x increases. The y-intercept is 5.

y = 1/2x - 5: This is a linear equation with a positive slope of 1/2. It represents a line that increases at a slower rate as x increases. The y-intercept is -5.

Without specific information about the data set, it is not possible to determine which equation is the best fit. The best fit would depend on how well the equation aligns with the actual data points.

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Answer:

$2520

Step-by-step explanation:

→ Work out the area of the drive way

18 m × 4 m= 72 m²

→ Multiply the area by the cost per square metre

72 m² × $35 = $2520

The cost of paving a driveway that is 18m long and 4 m wide, if the paving costs $35 per square metre is $2520.

To calculate the cost of paving the driveway, you need to find the total area of the driveway and then multiply it by the cost per square meter.

The total area of the driveway can be calculated using the formula:

Area = length × width.

Given that the driveway is 18 meters long and 4 meters wide, the area would be:

Area = 18m × 4m

Area = 72 square meters.

Now,  find the cost of paving the driveway by multiplying the area by the cost per square meter:

Cost = Area × Cost per square meter

Cost = 72 square meters × $35/square meter

Cost = $2520.

So, the cost of paying the driveway would be $2520.

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For sp3d hybridized central atoms, the only possible molecular geometry is trigonal bipyramidal.

Hybridisation (or hybridization) is a process of mathematically combining two or more atomic orbitals from the same atom to form an entirely new orbital different from its components and hence being called as a hybrid orbital.

In this case, if all the bonds are in place, the shape is also trigonal bipyramidal.

In chemistry, a trigonal bipyramid formation is a molecular geometry with one atom at the center and 5 more atoms at the corners of a triangular bipyramid.

Bond angle(s): 90°, 120°

Coordination number: 5

Point group: D3h

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Answer:

its 3 and 5

Step-by-step explanation:

i know this because i took the quiz and its simple

Answer:

Step-by-step explanation:

P = 2( L + W)

To solve for L first divide both sides by 2

That's

\( \frac{P}{2} = L + W\)

Move W to the other side of the equation to make L stand alone

We have the final answer as

\(L = \frac{P}{2} - W \\ \)

Hope this helps you

The equilibrium price is the price at which the quantity demanded equals the quantity supplied.

Looking at the graph, we can see that the demand curve intersects the supply curve at a quantity of approximately 200 million boxes. To find the corresponding equilibrium price, we need to find the price level at this quantity.

From the graph, we can observe that the price axis ranges from $20 to $40. Since the graph is not accurately scaled, we can estimate the equilibrium price to be around $30 per box based on the midpoint of the price range.

Therefore, the equilibrium price in this market is approximately $30 per box.

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Answer: you would have somewhat $41.000 to $42.000

Answer:

Range y≥-3

Step-by-step explanation:

Answer:

D. Range: y ≥ -3.

Step-by-step explanation:

(x - 4)^2 - 3

= x^2 - 4x - 4x + 16 - 3

= x^2 - 8x - 13

Since this is a parabola, there are no limits to the x-values, but there is a limit on the y-values: the y-values cannot exceed the highest or lowest point of the parabola, the vertex.

To find the vertex...

-b / 2a

8 / 2 = 4

(4 - 4)^2 - 3

= 0 - 3

= -3

So, your answer is D. Range: y ≥ -3.

Hope this helps!

Answer:

3.1

Step-by-step explanation:

There are 45 eels in the aquarium.

The ratio of pufferfish to starfish is 2 : 5.

So, 2 pufferfish / 5 starfish = 8 pufferfish / x starfish

2x = 8 (5)

2x = 40

x = 40 / 2

x = 20

So there are 20 starfish in the aquarium.

Next, we're given the ratio of starfish to eels as 4 : 9.

4 starfish / 9 eels = 20 starfish / y eels

4y = 20 (9)

4y = 180

y = 180 / 4

y = 45

Therefore, there are 45 eels in the aquarium.

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Answer:

sinA = ± \(\sqrt{1-cos^2A}\)

Step-by-step explanation:

Using the Pythagorean identity

sin²A + cos²A = 1 ( subtract cos²A from both sides )

sin²A = 1 - cos²A ( take the square root of both sides )

sinA = ± \(\sqrt{1-cos^2A}\)

Answer:

a, 6

Step-by-step explanation:

7x + 2y = 48

7x + 2(3) = 48

7x + 6 = 48

7x = 48 - 6

7x = 42

x = 42 / 7

x = 6

Answer:

2.5

Step-by-step explanation

Pi R squared

radius is half diameter, so .9

Square the .9

Multiple that to 3.142

An equation for the line perpendicular to 4x - 8 = y and has a y-intercept of 2 is y = (-1/4)x + 2.To find the equation for the line perpendicular to 4x - 8 = y and has a y-intercept of 2, we need to use the properties of perpendicular lines. Perpendicular lines have opposite reciprocal slopes.

The given equation, 4x - 8 = y, is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Therefore, we can rewrite the equation as y = 4x - 8 and see that the slope is 4.

Since we want a line perpendicular to this line, we need to find the opposite reciprocal slope. The opposite reciprocal of 4 is -1/4.

Now we have the slope of the perpendicular line, -1/4, and the y-intercept, 2. We can use the point-slope form of a line to find the equation:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line. In this case, (x1, y1) = (0, 2) since the y-intercept is 2.

Plugging in the values, we get:

y - 2 = (-1/4)(x - 0)

Simplifying, we get:

y = (-1/4)x + 2

Therefore, an equation for the line perpendicular to 4x - 8 = y and has a y-intercept of 2 is y = (-1/4)x + 2.

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We can solve a common base exponential equation of the form:

With the one-to-one property to get:

(a) In this case, we can take 4 as the common base, to get:

For f(x), we can use a linear equation of the form mx + b like 6x + 9, and for g(x) we can make it equal to -x² (we can use whatever equation we want because we are creating the complex exponential equation), then we get:

Since we have common bases, by means of the one-to-one property, we rewrite the above equation to get:

Simplifying and factoring:

6x + 9 + x² = x² - x²

6x + 9 + x² = 0

(x + 3)² = 0

Then, the solution to this equation is -3

(b) Similarly, taking logarithms on both side we get:

By dividing both sides by Log(4), we get:

As you can see, we got the same equation as in part (a), then the solution will be the same and it is x = -3

Answer:

108 pens

Step-by-step explanation:

48/4=x/9

4x=432

x=108

Answer:

Since there are 12 pens packed in each box, because there are 48 packed in 4 boxes, there will be ( 12 times 9 ) 108 pens in 9 boxes.

Answer:

the answer is C

Step-by-step explanation:

In pent-2-en, the trans isomer would have one hydrogen atom and one methyl group on each side of the double bond.

For pent-2-ene, there are two geometric isomers: cis-pent-2-ene and trans-pent-2-ene. In cis-pent-2-ene, the two alkyl groups (CH3 and CH2CH2CH3) are on the same side of the double bond. In trans-pent-2-ene, these two alkyl groups are on opposite sides of the double bond. These isomers have different physical and chemical properties due to the spatial arrangement of their atoms.

Pent-2-en is a five-carbon molecule with a double bond between the second and third carbon atoms. Therefore, it has two possible geometric or cis/trans isomers. The first isomer is the cis isomer, also known as Z-isomer, where the two substituents on the double bond are on the same side of the molecule. In pent-2-en, the cis isomer would have the two hydrogen atoms on one side of the double bond, and the two methyl groups on the other side.  The second isomer is the trans isomer, also known as the E-isomer, where the two substituents on the double bond are on opposite sides of the molecule. In pent-2-en, the trans isomer would have one hydrogen atom and one methyl group on each side of the double bond.

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To find the probability of the call lasting less than 230 seconds, we have to find P(X<230). Here X follows normal distribution with mean = 290

The given data: Meanμ = 290 seconds

Standard deviation σ = 30 seconds

Sample size n = 1000a) and

standard deviation = 30.

We get the value of 0.0228, which represents the area left (or below) to z = -2. Therefore, the probability that the call lasted less than 230 seconds is 0.0228 (or 2.28%). By using z-score formula;

Z=(X-μ)/σ

Z=(230-290)/30

= -2P(X<230) is equivalent to P(Z < -2) From z-table,

0.6384 (or 63.84%) P(230330) is equivalent to 1 - P(X<330)Here X follows normal distribution with mean = 290 and standard deviation = 30.From part b,

We already have P(X<330).Therefore, P(X>330) = 1 - 0.9082 = 0.0918, which is equal to 9.18%. Therefore, the probability that the call lasted more than 330 seconds is 0.1356 (or 13.56%).Answer: 0.1356 (or 13.56%). In parts a, b, and c, the final probabilities are rounded off to four decimal places as needed, as per the instructions given. However, these values are derived from the exact probabilities and can be considered accurate up to that point.

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The error made in subtracting the two rational expressions 1/(x - 2) - 1/x is that the common denominator is not correctly identified and applied.

To subtract rational expressions, we need to find a common denominator and then subtract the numerators. In this case, the common denominator should be (x - 2) * x. However, the error lies in neglecting the parentheses in the first expression, leading to a miscalculation of the common denominator.

The correct subtraction of the given expressions should be: (x - 2)/(x - 2) - 1/(x * (x - 2)). Simplifying this expression further would result in (x - 2 - 1)/(x * (x - 2)), which can be simplified as (x - 3)/(x * (x - 2)).

Therefore, the error made in the subtraction lies in incorrectly identifying and applying the common denominator, which resulted in an inaccurate calculation of the expression.

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If earth days merely 2 hours long, which means the rotation period of the earth is 2 hours, your weight will become 1/144 of your actual weight.

The weight or gravitational force on a mass can also be considered as centripetal force.

The formula for the centripetal force is:

F = m v²/R

In this case,

m = your mass

v = tangential velocity or earth's rotation speed

R = earth's radius

Recall that speed = distance / time. In the problem, the distance is the circumference of the earth and the travelled time is the rotation period.

v = C/t

t₁ = 24 hours

t₂ = 2 hours

Since the units are the same, we do not need to convert the unit when comparing them.

Notice that the centripetal force is directly proportional to the square of rotation speed.

F ∝ v²

Hence,

F₁ : F₂ = v₁² : v₂²

But v is inversely proportional to rotation period. Hence,

F₁ : F₂ = t₂² :  t₁²

F₁ / F₂ = (t₂ /t₁)²

F₁ / F₂ = (2 /24)²

F₁ / F₂ = (1 /12)²

F₁ / F₂ = 1/144

Hence, your weight will be 1/144 of your actual weight.

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Answer:

The actual dimensions would be 3.375 feet by 3.5 feet. The area of the room would be 11.8 square feet.

Step-by-step explanation: