Find the area of a regular decagon with an apothem of 6. 2 units. Round your answer to the nearest hundredth.

Answer:

0.051

Step-by-step explanation:

Because the 10 is to the power of -2, you would move the decimal twice to the left to get 0.051.

Hope this helps!!

Answer:

The value of a is 6 and the value of b is -12

Step-by-step explanation:

Given identity is:

a(4x – 10) = 24x + 5b

We can use the comparison of coefficients method to find the values of a and b

So,

By simplifying the left hand side of identity

\(4ax-10a = 24x+5b\\4ax+(-10)a = 24x+5b\)

Comparing the co-efficient of x

\(4a = 24\\a = \frac{24}{4}\\a = 6\)

Comparing the constant terms

\(-10a = 5b\)

Putting the value of a

\(-10(6) = 5b\\-60 = 5b\\b = \frac{-60}{5}\\b = -12\)

Hence,

The value of a is 6 and the value of b is -12

Note that assuming that the instrument used was exogenous, one can conclude about the endogeneity of an explanatory variable if the OLS and 2SLS estimates are significantly different: "The explanatory variable is endogenous and therefore 2SLS should be considered." (Option C)

Two-stage least squares (2SLS) regression analysis is a statistical approach used in structural equation analysis. The OLS approach has been extended using this methodology. It is employed when the error terms of the dependent variable are associated with the independent variables.

The ordinary least squares (OLS) approach is a linear regression methodology used to estimate a model's unknown parameters. The strategy is based on reducing the sum of squared residuals between the expected and actual values.

2SLS is utilized as an alternate strategy when we encounter endogeneity Problems in OLS. Endogeneity arises when the explanatory variable correlates with the error word. Then we utilize 2SLS, which employs an instrumental variable. The outcome will be different because if there is endogeneity in the model, OLS will produce biased results.

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Full Question:
What can we conclude about the endogeneity of an explanatory variable if the OLS and 2SLS estimates are significantly different? Assume that the instrument used was exogenous. Select one:

a. The explanatory variable is not endogenous and therefore using 2SLS is ill-advised.

b. The explanatory variable is not endogenous and therefore OLS should not be used.

c. The explanatory variable is endogenous and therefore using 2SLS should be considered.

d. The explanatory variable is endogenous and therefore OLS should be used.

Answer:

your answer is the length of time is 7 hours and 15 minutes

Step-by-step explanation:

hope it helps

The line represented by the table is:

y = 2x + 40

A general linear relationship is written as:

y = ax + b

Where a is the slope and b is the y-intercept.

If the line passes through (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

We can use the first two pairs:

(6, 52) and (9, 58)

Then we will get:

a = (58 - 52)/(9 - 6)

a = 6/3 = 2

y = 2x + b

To find the value of b, we replace the values of one of the points, if we use the first one (6, 52), then we will get:

52 = 2*6 + b

52 = 12 + b

52 - 12 = b

40 = b

The line is:

y = 2x + 40

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Answer:

<

Step-by-step explanation:

-4.49 is greater than -4.5 because it is closer to a positive number.

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

Explanation:

Think of -4.5 as -4.50, then you would be able to see that -4.50 is further left compared to -4.49 and this makes -4.50 to be smaller than -4.49; therefore, -4.50 < -4.49

Keep in mind that these values are negative, so the more leftward you go, the larger the magnitude of the values will get. For example, -10 is even more to the left so it makes -10 even smaller compared to the other values mentioned. We would be able to say -10 < -4.5 and also -10 < -4.49

Side note: if the values were positive, then 4.50 > 4.49 because 50 > 49. The inequality sign flips when we change everything from positive to negative.

The given function is f(x) = (4-x)/29. We need to find the x-values where f is not continuous and determine whether the discontinuities are removable or nonremovable.

For this function, there are no nonremovable discontinuities. The only type of discontinuity that could occur is a removable discontinuity. This occurs when a point is undefined, but the limit exists and is finite. In other words, the function can be made continuous by redefining it at that point.

To find any possible removable discontinuities, we need to find the values of x for which the denominator becomes zero, because division by zero is undefined. The denominator is always 29, which is never zero, so there are no values of x for which the denominator is zero. Therefore, there are no removable discontinuities.

In conclusion, the function f(x) = (4-x)/29 is continuous for all values of x, and there are no removable or nonremovable discontinuities.

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It will take 14.87 years for $100 to reach $500 when it grows at 10 percent per year.

To find out how long it will take, we can use the formula for compound interest:

A = P(1 + r)^t

Where A is the final amount, P is the principal amount, r is the interest rate, and t is the number of years.

In this case, we want to find out how long it will take for $100 to reach $500 when it grows at 10 percent per year. So we can plug in the values and solve for t:

500 = 100(1 + 0.10)^t

5 = (1.10)^t

Taking the natural logarithm of both sides:

ln(5) = t ln(1.10)

t = ln(5) / ln(1.10)

t = 14.87 years

So it will take 14.87 years for $100 to reach $500 when it grows at 10 percent per year.

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Answer:

15

Step-by-step explanation:

To solve you have to get x by itself on one side.

x/3+7=12

First, you move the seven over.

x/3+7-7=12-7

Simplify.

x/3=5

Now to get x by itself you can multiply both sides by 3.

x/3*3=5*3

Simplify.

x=15

Answer:

x = 15

Step-by-step explanation:

x/3 + 3⋅7/3 = 12

x+3⋅7/3=12

x+21/3

X=15

The stationing of the end of the excavation is Station 2+080.

The volume of fill by end area method is 1440 cubic meters.

The volume of excavation by end area is 1080 cubic meters.

We have,

The stationing of the end of excavation can be determined by adding the given sections to the starting station.

Assuming the starting station is Station 2+020, the end of excavation would be at Station 2+080 (given as Station 2+020 + 60 meters).

To find the volume of fill by end area method, we need to calculate the area of the end section and multiply it by the distance between the start and end stations.

Given that the base for fill is 12 meters and the sideslope for fill is 2:1, the area of the end section can be calculated as follows:

Area of end section = (Base for fill) * (Sideslope for fill)

Area of end section = 12 * (2/1) = 24 square meters

Now, multiply the area of the end section by the distance between the start and end stations (60 meters) to find the volume of fill:

Volume of fill = Area of end section * Distance

Volume of fill = 24 * 60 = 1440 cubic meters

Therefore, the volume of fill by end area method is 1440 cubic meters.

Similarly, to compute the volume of excavation by end area, we calculate the area of the end section (base for cut * sideslope for cut) and multiply it by the distance between the start and end stations. Given that the base for cut is 12 meters and the sideslope for cut is 1.5:1, the area of the end section can be calculated as follows:

Area of end section = (Base for cut) * (Sideslope for cut)

Area of end section = 12 * (1.5/1) = 18 square meters

Multiply the area of the end section by the distance between the start and end stations (60 meters) to find the volume of excavation:

Volume of excavation = Area of end section * Distance

Volume of excavation = 18 * 60 = 1080 cubic meters

Therefore, the volume of excavation by end area is 1080 cubic meters.

Thus,

The stationing of the end of the excavation is Station 2+080.

The volume of fill by end area method is 1440 cubic meters.

The volume of excavation by end area is 1080 cubic meters.

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The expression simplifies to one over the sum of the square root of two plus twice the square root of five plus one third times the square root of two.\($= \frac{1}{\sqrt{2}+2\sqrt{5}+\frac{1}{3\sqrt{2}}}$\)

First, we can simplify the fraction's denominator. The fraction's denominator is the sum of the square root of two, the square root of eight, the square root of two hundred, and the inverse of the square root of eighteen. We can simplify the square root of two hundred by factoring out two hundred as two times one hundred. This simplifies the square root of two hundred to ten times the square root of two. Next, we can simplify the inverse of the square root of eighteen by multiplying numerator and denominator by the inverse of the square root of eighteen, which is the square root of eighteen. This simplifies the inverse of the square root of eighteen to one. Finally, we can combine like terms in the denominator, leaving us with one over the sum of the square root of two, twice the square root of five, and one third times the square root of two.

\($\frac{1}{\sqrt{2}+\frac{1}{\sqrt{8}+\sqrt{200}+\frac{1}{\sqrt{18}}}}$\)

\($= \frac{1}{\sqrt{2}+\frac{1}{\sqrt{2}\cdot4+10\sqrt{2}+\sqrt{18}}}$\)

\($= \frac{1}{\sqrt{2}+\frac{1}{\sqrt{2}\cdot4+10\sqrt{2}+3\sqrt{2}}}$\)

\($= \frac{1}{\sqrt{2}+2\sqrt{5}+\frac{1}{3\sqrt{2}}}$\)

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Answer:

He only added Sundays run

Step-by-step explanation:

Answer:

The distance from vertex B to the midpoint of AC is 3 units

Step-by-step explanation:

we are given a triangle with vertices  A (1,-3), B (3,0) and C (5,-3).

Mid point of of AC  (x,y) =  ( 1+5/2 , -3 -3/2)

                                     = ( 6/2 , -6/2)

                                     = (3 , -3)

Distance formula = \(\sqrt{(x2 - x1)^2 + (y2 - y1)^2}\)

                              = \(\sqrt{(3-3)^2 + (0 + 3) ^2}\)

                               = \(\sqrt{(3)^2}\)

                                = 3 units

Answer:

1. City A
2. Exponential Growth
3. Linear

Step-by-step explanation:

The equation for exponential growth is f(x)=a(1+r/100)^x, where a is the initial growth/starting population, r is the growth rate, and x is the time intervals.

City A
f(x)=200(1+1.05/100)^x
Simplify:
f(x)=200(1.105)^x

City B
An increase in 20 people each year is NOT exponential but linear:
f(x)=20x+200

Now we plug in x for 1 to stand for 1 year and see which city has a greater number:
City A:
f(1)=200(1.105)^1
f(1)=200 x 1.105
f(1)=221

City B:
f(1)=20(1)+200

f(1)=20+200

f(1)=220

City A will have more people.

City A is an exponential function because there's a percent increase every year, and there will be more people every year because there are more people. This is kind of how compound interest also works

City B is a linear equation because a set number of people are added every year and doesn't change based on the amount of people already in it.

1. City B will have more population after 1 year.

In this case, we have been given of both the cities A and B with each year's growth factor and we have been told to find out, which city will have more population after 1 year. So to find out the comparison, first we need to find out the individual popoulation of both the cities after 1 year of interval.

So, population of City A after 1 year will be 200 * 1.05 = 210

Similarly,  population of City B after 1 year will be 200 + 20 = 220

It is clear that City B has more population as compared to City A.

Therefore, after 1 year City B has more population.

2. equation for City A is Exponential Growth Equation.

Exponential growth is the growth which takes place when a particular quantity increases at a constant rate over a fixed time period. It is given in the form of \(P = P_{0} * (1 + r)^t\), where P is population, \(P_{0}\) is initial population, r is the growth rate, and t is time period.

3. equation for City B is Linear Equation.

Linear equation is a representation of a straight line when graphed on paper. It has constant coefficients and variables raised to power 1. It is given in the form of \(P = P_{0} + rt\), where P is population, \(P_{0}\) is initial population, r is the growth rate, and t is time period.

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Answer: d= 120

b= 90

Step-by-step explanation:

Answer:

  B.  The function is nonlinear.

Step-by-step explanation:

A linear function graphs as a straight line. It is a polynomial function of degree 1. Any function that is not a linear function is a nonlinear function.

__

The function given is a polynomial function of degree 2. (Its highest-degree term is x^2, which has an exponent of 2.)

Since the degree is not 1, the function is nonlinear.

_____

Additional comment

A polynomial function will never be "linear at some points and nonlinear at other points." Such a description might apply to a piecewise-defined function.

Answer:

C (ignore this it asked for 24 characters)

Answer:

There is no error, Amad is correct.

Step-by-step explanation:

Khan Academy Checked.

Amad had done no error. His conclusion is true.

Two triangles are said to be congruent if their sides are equal in length, the angles are of equal measure, and they can be superimposed on each other.

For example,

In the figure given above, Δ ABC and Δ PQR are congruent triangles. This means that the corresponding angles and corresponding sides in both the triangles are equal.

Sides: AB = PQ, BC = QR and AC = PR;

Angles: ∠A = ∠P, ∠B = ∠Q, and ∠C = ∠R.

Therefore, Δ ABC ≅ Δ PQR

The following are the congruence theorems or the triangle congruence criteria that help to prove the congruence of triangles.

As, from the given cases the prediction of congruency of two triangles is correct. There is no error he made.

Hence, Amad had not made any error.

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Answer:

Step-by-step explanation:

thanks For Answering For My Subscribe

Answer: If n>1, then any positive number raised to the power of n will always be greater than 1. Therefore, any number greater than 1 raised to the power of n, such as 2^n, 3^n, etc., will also always be greater than 1.

Step-by-step explanation:

Answer:

Yes and no (YES: can be a triangle, but NOT a right angle triangle)

Step-by-step explanation:

Notice 8^2+11^2=185

while 17^2=289

Notice Pythagoras do apply for every right triangle. since 185 is not 289. is not a right triangle. But it can be a triangle (just not a right angle triangle)

Based on the data above, The five-number summary is 0.00, 0.17, 0.5, 1.43, 292.00.

The following data represent the dividend yields (in percent) of a random sample of 26 publicly traded des.

The following data represents the dividend yields (in percent) of a random sample of 26 publicly traded des:

0.5 0.8 1.75 0.04 0.18 0.35 3.69 0 0.95 0 0.17 1.83 1.33 0 0.54 1.14 0.41 159 21 2.41 292 3.18 3.03 1.43 0.58 0.13 0 0.19

Here, the five-number summary is given by:

Minimum value = 0.00

First Quartile (Q1) = 0.17

Median (Q2) = 0.5

Third Quartile (Q3) = 1.43

Maximum value = 292.00

Therefore, the five-number summary is 0.00, 0.17, 0.5, 1.43, 292.00.

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Say it is two o'clock, draw an imaginary line between the hour hand and twelve o'clock to create the north-south line. You know the sun rises in the east and sets in the west so this will tell you which way is north and which way south. If you are in the Southern Hemisphere then it will be the other way round.

Let the original value be x.

After the first year, the value will decrease 50%, so, it will be 0.5x.

By the end of the second year, it will decrease other 8%, 0.08.

so:

0.5x*(1-0.08) = 0.46x

And by the end of the third year, will decrease 8% again, so:

0.46*(1-0.08) = 0.4232x

The price will be 42.32% of the original value.

Answer:

4

Step-by-step explanation:

Answer: 4

Step-by-step explanation: Same thing as 8 / 0.5

Answer:

y=x-6

Step-by-step explanation:

The value of the given differentiation f'(1).f'(1)=1024/1089 if f(x)+x²[f(x)]⁴=18.

To ascertain the instantaneous rate of change of a function dependent on one of its variables, differentiation is applied. The most common example is velocity, which is the rate at which a distance changes with respect to time.

The derivative of a function of a real variable in mathematics is used to assess a function's sensitivity to change with respect to a change in its argument. The derivative is a key mathematics tool.

The slope of the tangent line to the graph of a single-variable function at a specific input value is referred to as the derivative if the function exists at that point. The tangent line is the most accurate linear approximation of the function close to that input value.

Given,

f(x)+x²[f(x)]⁴=18

Now, by differentiating on both sides, we get:

f'(x)+2x[f(x)]⁴+4x²[f(x)]³f'(x)=0

f'(x)[1+4x²[f(x)]³]=-2x[f(x)]⁴

f'(x)= (-2x[f(x)]⁴)/[1+4x²[f(x)]³]

Given,

f(1)=2

Let x=1 then,

f'(1)=(-2(1)[f(1)]⁴)/[1+4x²[f(1)]³]

f'(1)=(-2×2⁴)/(1+4×2³)

f'(1)=-32/33

f'(1).f'(1)=(-32/33)(-32/33)

=1024/1089

Therefore, the value of the given differentiation f'(1).f'(1)=1024/1089 if f(x)+x²[f(x)]⁴=18.

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Answer:

ok if its wrong then dont ask on period

Step-by-step explanation: