Factor out the greatest common factor from the terms of the polynomial 8x4 − 12x3 + 16x.

A. 4x3(2x − 3) + 18
B. 4x(2x3 − 3x2 + 4)
C. The expression is already fully factored.
D. 8x4 − 4x(3x2 + 4)

Answer:

its not possible

Step-by-step explanation:

6=14

10 = 22

if ten is 22

how can 20 be 42

Answer:

1/6 of a mile

Step-by-step explanation:

if it is a constant pace, it must increase and decrease proportionately meaning, you divide the time by 2 so you divide the distance by 2 as well

option C is correct, [tex]f(t)=1.36^{t}[/tex] has greatest growth rate.

A relation is a function if it has only One y-value for each x-value.

Growth rates are the percent change of a variable over time

Formula for the exponential growth is,

f(x)=a(1+r/100)ⁿ

where r = rate of exponential growth

a = initial amount

n = duration or time

The greatest growth rate is in the form of percentage.

We have to check for the value which is higher in the given options.

Hence, option C is correct, [tex]f(t)=1.36^{t}[/tex] has highest growth rate.

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The given question is not complete, similar kind of question is attached below.

By the application of the exponential function to the problems we have;

1)  $16187

2) $1346

3)  6774

4) $5670

5)  $ 7233

6) 4%

We have to know that the value of the car can be obtained by the use of the function;

P = Poe^-rt

P = Value at time t

Po = initial value

r = rate of depreciation

t = time taken

P = 44,000e^-0.25*4

P = $16187

2) P= Poe^-rt

P = 1580e^-0.02 * 8

P = $1346

3) P =  Poe^rt

P = 6348e^0.013 * 5

P = 6774

4) A = P(1 + r/n)^nt

A = 5,000( 1 + 0.036/12)^12 * 3.5

A = $5670

5) A = P(1 + r/n)^nt

A = 6,013.53( 1 + 0.0185/4)^4 *10

A = $ 7233

6)  A = P(1 + r/n)^nt

6,520.02 = 4,848(1 + r/2)^6 * 2

6,520.02/ 4,848 = (1 + r/2)^6 * 2

1.34 = (1 + r/2)^12

ln 1.34 = 12ln (1 + r/2)

ln (1 + r/2) = ln 1.34/12

ln (1 + r/2) = 0.024

1 + r/2 = e^0.024

1 + r/2 = 1.02

r/2 = 1.02 - 1

r/2 = 0.02

r = 2 * 0.02

r = 0.04

r = 4%

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7 = a × 2 + b × 0 + c × 1, 7 = a × 0 + b × 4 + c × 1, 13 = a × 3 + b × 4 + c × 10 are the first vector is a linear combination of the other vectors.

In linear algebra, a linear combination is an expression formed by multiplying each element of a set of vectors by a scalar (a real or complex number) and then adding the results. The scalars are called coefficients and the vectors are called terms.

A linear combination can be written as a sum of the form:

a1 × v1 + a2 × v2 + ... + an × vn

where a1, a2, ..., an are the coefficients and v1, v2, ..., vn are the vectors. The result of the linear combination is also a vector, which can be thought of as a combination of the original vectors, weighted by the coefficients.

Linear combinations are used in many applications, including solving systems of linear equations, finding eigenvectors and eigenvalues, and representing a vector as a combination of basis vectors in a vector space.

(a) To determine whether the first vector is a linear combination of the other vectors, we can write a system of equations and solve for the coefficients. If the coefficients exist and are unique, then the first vector is a linear combination of the other vectors. If the coefficients do not exist or are not unique, then the first vector is not a linear combination of the other vectors.

-3 = a × 1 + b × 2 + c × -1

3 = a × -1 + b × 1 + c × 2

7 = a × 2 + b × 0 + c × 1

We can solve this system of equations using methods such as Gaussian elimination or matrix inversion to obtain the coefficients: a = -2, b = -1, c = 4

Therefore, the first vector is a linear combination of the other vectors.

(b) Following the same procedure, we can write a system of equations and solve for the coefficients:

-2 = a × 1 + b × 2 + c × -2

11 = a × -1 + b × 1 + c × 4

7 = a × 0 + b × 4 + c × 1

We can solve this system of equations to obtain the coefficients: a = 3, b = -2, c = 2

Therefore, the first vector is a linear combination of the other vectors.

(c) Using the same procedure, we can write a system of equations and solve for the coefficients:

2 = a × 1 + b × -1 + c × 1

7 = a × 2 + b × 2 + c × 6

13 = a × 3 + b × 4 + c × 10

We can solve this system of equations, but it will have no solution, meaning the coefficients do not exist.

Therefore, the first vector is not a linear combination of the other vectors.

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For all the given vectors the first vector is a linear combination of the other vectors.

In linear algebra, a linear combination is an expression formed by multiplying each element of a set of vectors by a scalar (a real or complex number) and then adding the results. The scalars are called coefficients and the vectors are called terms.

A linear combination can be written as a sum of the form:

a1 × v1 + a2 × v2 + ... + an × vn

where a1, a2, ..., an are the coefficients and v1, v2, ..., vn are the vectors. The result of the linear combination is also a vector, which can be thought of as a combination of the original vectors, weighted by the coefficients.

Linear combinations are used in many applications, including solving systems of linear equations, finding eigenvectors and eigenvalues, and representing a vector as a combination of basis vectors in a vector space.

(a) To determine whether the first vector is a linear combination of the other vectors, we can write a system of equations and solve for the coefficients. If the coefficients exist and are unique, then the first vector is a linear combination of the other vectors. If the coefficients do not exist or are not unique, then the first vector is not a linear combination of the other vectors.

-3 = a × 1 + b × 2 + c × -1

3 = a × -1 + b × 1 + c × 2

7 = a × 2 + b × 0 + c × 1

We can solve this system of equations using methods such as Gaussian elimination or matrix inversion to obtain the coefficients: a = -2, b = -1, c = 4

Therefore, the first vector is a linear combination of the other vectors.

(b) Following the same procedure, we can write a system of equations and solve for the coefficients:

-2 = a × 1 + b × 2 + c × -2

11 = a × -1 + b × 1 + c × 4

7 = a × 0 + b × 4 + c × 1

We can solve this system of equations to obtain the coefficients: a = 3, b = -2, c = 2

Therefore, the first vector is a linear combination of the other vectors.

(c) Using the same procedure, we can write a system of equations and solve for the coefficients:

2 = a × 1 + b × -1 + c × 1

7 = a × 2 + b × 2 + c × 6

13 = a × 3 + b × 4 + c × 10

We can solve this system of equations, but it will have no solution, meaning the coefficients do not exist.

Therefore, the first vector is not a linear combination of the other vectors.

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A fundamental identity is an equation that relates the values of the trigonometric functions for a given angle. The equation cot θ = cos θ/sinθ is an example of a fundamental identity.

This identity states that the cotangent of an angle is equal to the cosine of the angle divided by the sine of the angle. The equation sec θ = 1/cosθ is another example of a fundamental identity. This identity states that the secant of an angle is equal to the reciprocal of the cosine of the angle. The equation sec^2 + 1 = tan^2θ is also a fundamental identity. This identity states that the square of the secant of an angle plus one is equal to the square of the tangent of the angle. The equation 1 + cot^2θ = csc^2θ is not a fundamental identity. This equation states that one plus the square of the cotangent of an angle is equal to the square of the cosecant of the angle. This equation is not a fundamental identity because it does not relate the values of the trigonometric functions for a given angle.

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A. 0. 0063 is the correct answer.

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Answer:

Step-by-step explanation:

Polynomials are mathematical expressions that consist of variables raised to a power and combined with coefficients. The degree of a polynomial is the highest power of the variable in the expression. The number of terms in a polynomial is the number of separate terms that are added together to form the polynomial.

Here are some common examples of polynomials classified by degree and number of terms:

Degree 1, one term: a linear polynomial, such as 3x + 4

Degree 2, one term: a constant polynomial, such as 25

Degree 2, two terms: a quadratic polynomial, such as 3x^2 + 4x + 5

Degree 3, three terms: a cubic polynomial, such as 2x^3 + x^2 + 4x + 7

Degree 4, four terms: a quartic polynomial, such as x^4 + 3x^3 + 4x^2 + 2x + 6

Note that a polynomial with only one term is always a constant polynomial, regardless of its degree

The relative frequencies are 0.133, 0.233, 0.167, 0.200 and 0.267

The most popular genre in your class is Romance

From the question, we have the following parameters that can be used in our computation:

C, C, R, R, D, R, H, H, C, A, A, R, A, A, A, R, R,

H, H, H, C, H, A, R, D, D, D, D, H, R

Where

Comedy (C), Horror (H), Drama (D), Action (A), Romance (R).

Using the above as a guide, we have the following:

Movie Genre Frequency

Comedy (C) 4

Horror (H) 7

Drama (D) 5

Action (A) 6

Romance (R) 8

For the relative frequencies, we have

This is the genre with the highest relative frequence

So, we have

Most popular = Romance

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[tex]w^8[/tex] is the expression using positive exponents.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

w³ x [tex]w^5[/tex]

= [tex]w^{3 + 5}[/tex]

= [tex]w^8[/tex]

Thus,

[tex]w^8[/tex] is the final expression.

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The decision rule for Fresh First Grocery Store is to sell the bread at $1.50 per loaf if they can, otherwise they will feed it to the geese.

Fresh First Grocery Store purchases bread for $1 per loaf and sells it for $1.50 per loaf. This means that for every loaf of bread they sell, they will make a profit of $0.50. The decision rule for the grocery store is to sell the bread if they can, as this will result in a profit.

However, if they are unable to sell the bread, they have decided to feed it to the geese at a local pond. This decision is likely based on the idea that it is better to give the unsold bread to the geese rather than throw it away, as it will be put to good use and not go to waste.

In conclusion, the decision rule for Fresh First Grocery Store is to sell the bread at $1.50 per loaf if they can, otherwise they will feed it to the geese. This decision takes into account both the desire to make a profit and the desire to avoid waste and put unsold bread to good use.

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The first block's acceleration is inversely proportional to its mass and directly proportional to the mass difference between the two blocks.

Without being aware of the precise values of m1, m2, and g, it is impossible to calculate the acceleration of the first block.

Newton's second rule of motion, which states that the net force on an object is equal to its mass times its acceleration, can be used to calculate the acceleration of the first block in the illustration.

Let's call the first block's acceleration "a." The difference between the tension force in the rope connecting the two blocks and the force of gravity can be used to calculate the net force exerted on the first block.

The rope's tension force is generated by:

T = m2 × g

The first block is subject to the following gravitational force:

Fg = m1 × g

The difference between these two forces is the net force exerted on the first block:

Fnet = T - Fg = (m2 - m1) × g = m2 × g - m1 × g

In light of Newton's second law, we can say:

Fnet = a × m1

(m2 - m1) × g = m1 × a

When calculating acceleration, we obtain:

a = (m2 - m1) × g / m1

As a result, the first block's acceleration is inversely proportional to its mass and directly proportional to the mass difference between the two blocks.

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Complete question -

The Expenditure incurred by the mainor school district is $60,000 & inter-period equity is not achieved.

Interperiod equity refers to a government's obligation to disclose whether current-year revenues are sufficient to pay for the services provided that year and whether or not future taxpayers will be required to shoulder the burdens for services previously provided. It also refers to whether current-year revenues are sufficient to pay for the benefits provided that year or whether current citizens deferred payments to future taxpayers.

Thus, The Expenditure incurred by the mainor school district is $60,000 & inter-period equity is not achieved.

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When graphing a function, the input values are the independent variable(s) and the output values are the dependent variable(s).

A graph is a visual representation of a function that helps to understand the relationship between the input and output values of the function. In a graph, the horizontal axis represents the input values, and the vertical axis represents the output values. Each point on the graph represents a single pair of input and output values, and the entire graph represents the entire set of input and output values of the function.

When graphing a function, the input values are the independent variable(s) and the output values are the dependent variable(s).

For example, in the case of a simple linear function such as y = f(x) = 5x + 4, the input value is x, and the output value is y. To create the graph of this function, you would plot a set of ordered pairs (x, y), where x is the input value and y is the corresponding output value.

Similarly, in the case of a multi-variable function such as z = f(x, y), the input values are x and y, and the output value is z. To create the graph of this function, you would plot a set of ordered triples (x, y, z), where x and y are the input values and z is the corresponding output value.

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A grasshopper starts jumping forward on the real axis, starting at 0 in the positive direction.

Her jump sizes are independent, each has exponential distribution with mean 2 units.

(a) We have to determine the probability that the number of forward jumps it takes her to jump over 9 for the first time (in forward direction), is exactly 4.

P(k = 0) = [tex]\frac{2^{0}e^{-2}}{0!}[/tex] = 0.1353

P(k = 1) = [tex]\frac{2^{1}e^{-2}}{1!}[/tex] = 0.2706

P(k = 2) = [tex]\frac{2^{2}e^{-2}}{2!}[/tex] = 0.2706

P(k = 3) = [tex]\frac{2^{3}e^{-2}}{3!}[/tex] = 0.1804

P(k = 4) = [tex]\frac{2^{4}e^{-2}}{4!}[/tex] = 0.0902

The Probability = P(k = 0) + P(k = 1) + P(k = 2) + P(k = 3) + P(k = 4)

The Probability = 0.1353 + 0.2706 + 0.2706 + 0.1804 + 0.0902

The Probability = 0.9471

(b) We have to determine the probability that the number of backward jumps N it takes her to jump over 9 for the first time (in backward direction), is exactly 4.

P(k = 0) = [tex]\frac{1^{0}e^{-1}}{0!}[/tex] = 0.3678

P(k = 1) = [tex]\frac{1^{1}e^{-1}}{1!}[/tex] = 0.3678

P(k = 2) = [tex]\frac{1^{2}e^{-1}}{2!}[/tex] = 0.1839

P(k = 3) = [tex]\frac{1^{3}e^{-1}}{3!}[/tex] = 0.0613

P(k = 4) = [tex]\frac{1^{4}e^{-1}}{4!}[/tex] = 0.015325

The Probability = P(k = 0) + P(k = 1) + P(k = 2) + P(k = 3) + P(k = 4)

The Probability = 0.3678 + 0.3678 + 0.1839 + 0.0613 + 0.015325

The Probability = 0.996125

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Answer:

(5, -2)

Step-by-step explanation:

6x + 10y = 10   You add the two equations together

-6x - 24 y = 18

       -14y = 28   Divide both sides by -14

y = -2

Substitute -2 for y into either of the two equations above or the two original equations.  I am going to choice

3x + 5y = 5

3x  + 5(-2) = 5

3x -10 = 5  Add 10 to both sides

3x - 10 + 10 = 5 + 10

3x = 15  Divide both sides by 3

x = 5

Check:

3x + 5y = 5

3(5) + 5(-2) = 5

15 - 10 = 5

5 = 5  Checks

-2x - 8y = 6

-2(5) - 8(-2) = 6

-10 + 16 = 6

6 = 6 Checks

The solution is Option B.

The probability of drawing a consonant is given by the equation P = 5/7

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability of drawing a consonant be represented as P

Now , the equation will be

The total number of letters in the word DECIMALS = 7 letters

The total number of consonants in the word DECIMALS is given by the set A = { D , C , M , L , S }

So , the number of consonants = 5 letters

And , the probability of drawing a consonant P = total number of consonants in the word DECIMALS / total number of letters in the word DECIMALS

Substituting the values in the equation , we get

The probability of drawing a consonant P = 5/7

Hence , the probability is 5/7

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The answer is the median would not change.

The median of a set of numbers is the middle value when the numbers are arranged in order. It is not affected by outliers or extreme values as much as the mean is.

If the number 1772 was accidentally changed to 1972, this would increase the value of the number and it would become an outlier in the set. To calculate the median, we need to arrange the numbers in order. The new set would be:

1362 1439 1460 1614 1666 1867 1972

The median of this set is 1614, which is the middle value. As you can see, the change from 1772 to 1972 did not affect the median.

Therefore, the answer is the median would not change.

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The answer is the median would not change.

The median of a set of numbers is the middle value when the numbers are arranged in order. It is not affected by outliers or extreme values as much as the mean is.

If the number 1772 was accidentally changed to 1972, this would increase the value of the number and it would become an outlier in the set. To calculate the median, we need to arrange the numbers in order. The new set would be:

1362 1439 1460 1614 1666 1867 1972

The median of this set is 1614, which is the middle value. As you can see, the change from 1772 to 1972 did not affect the median.

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In statistics the sampling method is collecting data based on sample of people who represent a population, whereas the census method involves studying each and every member of the population.

What is statistics?

The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.

The differences between census and sampling method is -

The investigator gathers data using the census method, which asks questions about every component of the population.

The investigator gathers data using the sampling method by selecting a sample of the objects that represent the entire population.

The Census Method of Collecting Data is appropriate when the area under inquiry is rather small. The sampling method is preferred when the investigation region is large.

The Census Method requires more time to gather data. The sampling method requires less time to gather data.

Generally speaking, the Census Method is more accurate than the Sampling Method. This accuracy can be attributed to the Census Method's inclusion of a study of every component of the population. The sampling approach has a lower level of accuracy because it examines a smaller sample of the population. However, since there are fewer elements in the sampling method, errors are simple to find and eliminate. Consequently, if that's the case, the sampling method gives more accuracy than census method.

Therefore, the differences for census and sampling method are pointed out.

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What is the difference between census method and sampling method in statistics?

On solving the exponential function y = 49 (0.81)⁹, the number of Bison left after 9 years is obtained as 7.35 million.

What is an exponential function?

The formula for an exponential function is f(x) = aˣ, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The number of Bison that roamed were a = 49 million

The survival rate dropped to b = 0.81.

The time period is t = 9 years

The exponential function is -

y = abˣ

Substitute the values into the equation -

y = 49 (0.81)⁹

y = 49 × 0.1500

y = 7.35

Therefore, the number of Bison left is 7.35 million.

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Answer: there is no answer

Step-by-step explanation: if the whole sentence is letters it is not answerable

Analyzing a function's graph will reveal if it is linear or not. When a linear function is graphed, it produces a straight line. In contrast to a linear function, a nonlinear function has some kind of curve.

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The values of x and y in the triangle are 2√30 and 2√21

The value of y

From the question, we have the following parameters that can be used in our computation:

y : 6 = 14 : y

Express as fraction

y/6 = y/14

So, we have

y^2 = 14 * 6

Evaluate

y = 2√21

For the value of x

Here, we have

x^2 = y^2 + 6^2

So, we have

x^2 = (14 * 6) + 6^2

Evaluate

x^2 = 120

So, we have

x = 2√30

Hence, the values are 2√21 and 2√30

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Answer:

A= 1, B= 2, C= 3 D= 2

Step-by-step explanation:

The required coordinate of the point on the segment from (3,4) to (9,1)  is (7 , 7/3) which partitioned the segment into a ratio of 2 to 1.

The coordinates of the point on the directed line segment from (3,4) to (9,1)  that partitions the segment into a ratio of 2 to 1

Section formula.

x = mx₂ + nx₁ / m + n   ; y = my₂ + ny₁ / m + n

Where, m = 2 and n = 1
Substitute the value in the above equation,
x = 2 × 9 + 1 × 3 / 2 + 1 ; y = 3 × 1 + 1 × 4 / 2 +1
x = 21 / 3                     ; y = 7/3

x = 7                            ; y = 7/3

Thus, the required coordinate of the point on the segment from (3,4) to (9,1)  is (7 , 7/3) which partitioned the segment into a ratio of 2 to 1.

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The opposite side of a triangle is divided into two segments by the angle bisector theorem that are proportional to the other two sides of the triangle.

An angle bisector divides the opposite side of a triangle into two portions that are proportional to the other two sides, according to the angle bisector theorem.

According to the angle bisector theorem, the opposing side of a triangle is divided into two segments that are proportional to the other two sides of the triangle. A ray known as an angle bisector divides a given angle into two angles of the same size.

In order to solve proofs and find the appropriate portions of similar triangles, bisectors are crucial tools. A triangle's opposite side will be divided proportionally if one of the angle bisectors—there are three, one for each vertex—is drawn in.

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Given: A boat is located 324 feet from the base of the cliff.

The distance from the top of the cliff to the boat is 81 more than twice the height of the cliff, or 2h + 81.

We want to find: The height of the cliff, h.

Equations:

h + (2h + 81) = 324 (The height of the cliff plus the distance from the top of the cliff to the boat is equal to 324 feet)

3h + 81 = 324 (Expanding the left side of equation 1)

3h = 243 (Subtracting 81 from both sides of equation 2)

h = 81 (Dividing both sides of equation 3 by 3)

Therefore, the height of the cliff, h, is 81 feet.

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The area of the region outside the doghouse that skipper can reach is 3(pi)^2 yards.

This problem is based on the area of sectors. Now, we know that a sector is a pie-shaped part of a circle made of the arc along with its two radii.

The image which correctly explains the situation in the problem is attached.

From the figure, we can see that the spot can be located anywhere in the two sectors of 120  and  60 degrees each respectively. Now, these radii are respectively of 2 and 1 yards.

Area of one sector of 120 degrees = 120/360 π (2)^2 since radius is 2 yards.

So, area of two sectors is 2 x  120/360 π (2)^2 = 8π /3 square yards.

Similarly, Area of the two 60 degrees sectors is -

2 x  60/360 π (2)^2 = π /3 sq. yards.

Therefore , the total area that the skipper can reach outside the doghouse is given by the sum of all the four sectors i.e. π /3 + 8π /3 =

3π square yards.

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The area of the region outside the doghouse that the skipper can reach is [tex]3\pi ^2[/tex] yards.

This problem is based on the area of sectors. Now, we know that a sector is a pie-shaped part of a circle made of an arc along with its two radii.

The image which correctly explains the situation in the problem is attached.

From the figure, we can see that the spot can be located anywhere in the two sectors of 120  and  60 degrees each respectively. Now, these radii are respectively 2 and 1 yards.

Area of one sector of 120 degrees [tex]=\frac{(\pi*2^2*120) }{360}[/tex] since the radius is 2 yards.

So, the area of the two sectors is [tex]\frac{(2*120*2^2*\pi )}{360}=\frac{8\pi }{3}[/tex] square yards.

Similarly, the Area of the two 60 degrees sectors is -

[tex]\frac{(2*60*\pi *2^2)}{360} =\frac{\pi }{3}[/tex] sq. yards.

Therefore, the total area that the skipper can reach outside the doghouse is given by the sum of all the four sectors i.e. [tex]\frac{\pi }{3} +\frac{8\pi }{3} =3\pi[/tex]square yards.

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The Average Value of f(x) = (sin x)4^(cos x) for the closed interval 0≤ x≤π/2   is (B) 6/(πln(4))   .

The average value of a function over a closed interval can be found by calculating its definite integral over the interval and dividing by the length of the interval.

The function is : f(x) = (sin x)4^(cos x)  ;

Substituting the values :

we get ;

Average Value is = (1/π/2) × [tex]\int\limits^\frac{\pi }{2} _0[/tex] (sin x)4^(cos x) dx  .

On Simplifying ,

we get ;

Average Value is = [(-2/π)/ln(4) ] (1 - 4)

⇒ 6/(πln(4))

Therefore ,  the average value of the function over the interval 0≤ x≤π/2 is 6/(πln(4)).

What is the average value of f(x) = (sin x)4^(cos x) for the closed interval 0≤ x≤π/2 ?

(A) 3/ln(4)

(B) 6/(πln(4))

(C) 4/ln(4)

D) 8/(πln(4))

(E) 3π/(2ln(4))

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