Write the sum using summation notation. There may be multiple representations. Use i as the index of
summation.
1/3 - 1/9 + 1/27 - 1/81 + 1/243 - 1/729

Answer:

Let's call the length of the long piece x, and the length of each shorter piece y. We can set up the following equation to represent the problem:

x + 2y = 29

Since the long piece is 1 ft longer than twice the length of each shorter piece, we can write this equation as:

x = 2y + 1

Substituting this expression for x in the first equation, we get:

2y + 1 + 2y = 29

Combining like terms on both sides, we get:

4y + 1 = 29

Subtracting 1 from both sides, we get:

4y = 28

Dividing both sides by 4, we get:

y = 7

Substituting this value for y in the expression for x, we get:

x = 2(7) + 1 = 14 + 1 = 15

Thus, the length of the long piece is 15 ft, and the length of each shorter piece is 7 ft.

The dimensions of the rectangular corral:

length = 75 ft and width = 5 ft

Let m be the length of the rectangular corral and n be the width of the rectangular corral.

The perimeter of the rectangular corral,

P = 2m + 2n

The rectangular corral split into 2 pens of the same size.

So, P = 2m + 3n

The 2 pens producing the greatest possible enclosed area given 300 feet of fencing.

300 = 2m + 3n

n = (300 - 2m)/3

Area of the rectangular corral,

A = m * n

A(n) = m * (300 - 2m)/3

A(m) = (300/3)*m - (2/3)*m

Taking derivatives on both sides of the equation:

A'(m) = 100 - (4/3)*m

for A'(m) = 0,

100 - (4/3)*m = 0

m = 100 * (3/4)

m = 75

So, n = (300 - 2(75))/3

n = 50

Therefore, the length of the rectangular corral = 75 ft and width = 5 ft

Learn more about perimeter of rectangle here:

https://brainly.com/question/29595517

#SPJ4

The number of ways in which we can select a software engineer, an administrative assistant, and a sales representative is 48.

Since we are only choosing one option from each category, the number of alternatives for each category is equal to the number of combinations for each category .

Using the equation for each pair and then adding them up,

C (n,r) = n! / (r! (n - r)! )

we get the required number of combinations as 48.

Factorial

There are n! techniques of arranging n unique things into an ordered sequence, permutations where n = r.

Combination

The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.

Permutation

The number of ways to choose a sample of r elements from a set of n distinct objects when order does matter and replacements are not allowed. When n = r this reduces to n! , a simple factorial of n.

To learn more about combinations

https://brainly.com/question/20211959

#SPJ4

162.6

+ 4.4

Separate decimals

162 + 4         =  166

0.6 + 0.4       =      1

166 + 1 = 167

162.6

Nearest ten is 160

Hope this helps

The First Derivative Test for Local Extrema is the name of the procedure when it is used to find the values of the local maximum or minimum function.

The second derivative may be used to determine the local extrema of a function under certain conditions.

A function is said to have a local (relative) extremum at a critical point if the derivative of the function changes sign near that location. At the critical point, the function has a local (relative) maximum if the derivative switches from being positive (growing function) to negative (decreasing function). The function, however, has a local (relative) minimum at the critical point if the derivative switches from negative (decreasing function) to positive (growing function). The First Derivative Test for Local Extrema is the name of the procedure when it is used to find the values of the local maximum or minimum function.

Under certain circumstances, one can utilize the second derivative to identify the local extrema of a function. A function has a local minimum at this point if it has a critical point when f′(x) = 0 and the second derivative is positive. However, if the function contains a critical point at which the second derivative is negative and f′(x) = 0, then f has a local maximum at this location. The Second Derivative Test for Local Extrema is the name of this method.

To know more about derivative tests visit: brainly.com/question/29064109

#SPJ4

Common data sources like social media comments are categorized as unstructured data. (Option 2)

Unstructured data refers to information that does not have a pre-defined data model or is not organized in a pre-defined manner. Unstructured data is a dataset that is not stored in a specific structured format and is generally text-heavy, but may contain data such as dates, numbers, and facts. Unstructured data does have an internal structure, but it is not predefined through data models. It might be human generated, or machine generated in a textual or a non-textual format. Examples of unstructured data are social media comments, blog posts, videos, and documents.

Learn more about Unstructured data:

https://brainly.com/question/28851700

#SPJ4

The minimum amount of fence that he can use is 1600 ft.

Given ;

Area of rectangular = 80,000 sq. ft

i.e.  xy = 80,000

Total fencing needed ,

      x + y + x + y + 2y = 2x + 4y

To minimize 2x + 4y, constrained to  xy = 80,000

i.e.   xy = 80,000

   ⇒  y = 80,000/x

⇒ so, s = 2x + 4 (80,000/x) to be minimized

⇒ To minimum value at ds/dx = 0

i.e.  s = 2x + 4 (80,000/x)

        = 2x + (3,20,00/x)

⇒ Now, ds/dx = 0 = 2 + (3,20,000) - [tex]\frac{1}{x^{2} }[/tex]

                              ⇒ [tex]\frac{320000}{x^{2} } = 2[/tex]

                              ⇒ [tex]x^{2} = 160000[/tex]

                              ⇒ x = 400

∴ x = 400 ft  

y = 80,000/400 = 200

∴ y = 200 ft

Total frencing is

               ⇒ 2x + 4y = 2 × 400 + 4 × 200

                                = 800  +  800

                                = 1600 ft

∴ The minimum amount of fence that he can use is 1600 ft.

Learn more about rectangle area here ;

https://brainly.com/question/25292087

#SPJ4

Answer:

£5.174

Step-by-step explanation:

Because you do 25.87 divided by 5

Answer:

  21.35 inches

Step-by-step explanation:

You want to know the circumference of a hat that has a diameter of 6.8 inches.

The circumference is given by ...

  C = πd

  C = 3.14 × 6.8 in = 21.352 in

  C ≈ 21.35 in

The distance around the hat is about 21.35 inches.

<95141404393>

The function that provides a model for the function p(t) for the population of a city is

The given problem is solved using,  f(x) = a (b)^x

the starting = a

the base = b

the exponents = x

considering the given problem

p(t) = a (b)^t

a = 1250

rate, r = 25%

r = 25 / 100

r = 0.25

for increasing rate, b = 1 + r = 1 + 0.25 = 1.25

substituting known variables

p(t) = 1250 (1.25)^t

the equation that models the population of a city is p(t) = 1250 (1.25)^t

Learn more about exponential function here:

https://brainly.com/question/29716007

#SPJ1

Answer:

Step-by-step explanation:

6-(-2^3)+-2

CA ⁻¹ is undefined because there are more columns in A ⁻¹ than there are rows in C.

A matrix is a numerical arrangement that is divided into rows and columns. Make your first introduction with matrices and learn about their dimensions and elements. A matrix is a rectangular array of integers divided into rows and columns. Matrix A, for example, contains two rows and three columns. A matrix is a rectangular organization of a collection of integers into a defined number of rows and columns. When the elements are arranged in a matrix horizontally, it forms the rows of a matrix. When the elements are arranged in a matrix vertically, it forms the columns of a matrix.

CA⁻¹ is undefined because A⁻¹ contains more columns than rows in C.

To know more about matrix,

https://brainly.com/question/29440838

#SPJ4

Answer:

3 x y (y + x)

Step-by-step explanation:

Factor the following:

(y + x)^3 - (y^3 + x^3)

Factor the sum of two cubes. y^3 + x^3 = (y + x) (y^2 - x y + x^2):

(y + x)^3 - ((y + x) (y^2 - x y + x^2))

Factor y + x out of (y + x)^3 - (y + x) (y^2 - x y + x^2), resulting in (y + x) ((y + x)^(3 - 1) - (y^2 - x y + x^2)):

(y + x) ((y + x)^(3 - 1) - (y^2 - x y + x^2))

3 - 1 = 2:

(y + x) ((y + x)^2 - (y^2 - x y + x^2))

(y + x) (y + x) = (x) (x) + (x) (y) + (y) (x) + (y) (y) = x^2 + x y + x y + y^2 = y^2 + 2 x y + x^2:

(y + x) ((y^2 + 2 x y + x^2) - (y^2 - x y + x^2))

-(y^2 - x y + x^2) = -y^2 + x y - x^2:

(y + x) (x^2 + 2 x y + y^2 + (-y^2 + x y - x^2))

Grouping like terms, y^2 - y^2 + 2 x y + x y + x^2 - x^2 = (2 x y + x y) + (y^2 - y^2) + (x^2 - x^2):

((2 x y + x y) + (y^2 - y^2) + (x^2 - x^2)) (y + x)

x y 2 + x y = x y×3:

(3 x y + (y^2 - y^2) + (x^2 - x^2)) (y + x)

y^2 - y^2 = 0:

(3 x y + (x^2 - x^2)) (y + x)

x^2 - x^2 = 0:

Answer: 3 x y (y + x)

The test is proved that hypothesis that the population mean is atleast 3-miles per gallon.

A hypothesis is the proposed explanation for any kind of  phenomenon.

So here are the values of X  BAR i=2.4. S is 1.8.

Our sample n =100.

The null hypothesis here is that mu is greater than or equal to 3.

Against the alternative hypothesis that  is less than three. Now the calculated value for the test statistic is going to be the  equal to X bar is in (-)  knots. That's 2.4 -3. divided by S over  2^2 of end. So 1.8 divided by the square root of the  100 gives us negative 3.33. So we can refer to that box of the T distribution and we are  get the value. The p value for the test is going to be less than 0.5. Therefore we have the  strong evidence that the not hypothesis is going to be the  read checked it.  So  therefore we can reject to the  null hypothesis and then it can accept the alternative by the  hypothesis that  is less than three. Where it is  here is the mean of the population, the noting the average increase per gallon.

To know more about the hypothesis click-

https://brainly.com/question/606806

#SPJ1

Answer:

  95 meters

Step-by-step explanation:

Given the dimensions of the triangles shown in the figure, you want the height of the tree.

The ratio of the height of the triangle to the base is the same for both triangles shown. That means ...

  1.9/0.75 = x/(38.25 -0.75)

where x represents the height of the tree.

Multiplying by (38.25 -0.75), we have ...

  [tex]x=\dfrac{(38.25-0.75)\cdot1.9}{0.75}=1.9\left(\dfrac{38.25}{0.75}-1\right)=95[/tex]

The height of the tree is 95 meters.

There is a non zero probability of the particle in the state of finite potential .

It is an extension of the infinite potential well, in which a particle is confined to a "box", but one which has finite potential "walls". Unlike the infinite potential well, there is a probability associated with the particle being found outside the box. The quantum mechanical interpretation is unlike the classical interpretation, where if the total energy of the particle is less than the potential energy barrier of the walls it cannot be found outside the box. In the quantum interpretation, there is a non-zero probability of the particle being outside the box even when the energy of the particle is less than the potential energy barrier of the walls (cf quantum tunnelling).

To know more about finite potential will

https://brainly.com/question/13777893

#SPJ4

Dimensions of the rectangular garden are 45 yards each and area with  the calculated dimensions are 2025 square yards.

As given in the question,

Perimeter of the rectangular garden is equal to 180 yards

Let 'x' be the length and 'y' be the width of the rectangular garden

2 ( x + y ) = 180

⇒ x + y = 90

⇒ y = 90 -x

Area of the rectangular garden 'A' = xy

⇒ A = x ( 90 - x)

⇒ A = 90x - x²

To maximize the area dA/dx = 0

dA/dx = 90 - 2x

⇒ 90 - 2x = 0

⇒ 2x = 90

⇒ x = 45 yards

⇒ y = 45 yards

Area of the rectangular garden = 45 × 45

                                                 = 2025 square yards

Therefore, the dimensions of the garden are 45 yards each and area of the rectangular garden is equal to 2025 square yards.

Learn more about area here

brainly.com/question/27683633

#SPJ4

The value of f(2) is 4.

What is a function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

The domain and range of the function are the set of values of f(x) that are produced by the values in the domain of the function, which is the set of values of x. In addition to f(x), alternative shorthand symbols for functions of the independent variable x include g(x) and P(x), especially when the nature of the function is ambiguous or uncertain.

Given function is

f(x) = x²

Putting x = 2 in the given function:

f(2) = 2²

Putting 2² = 4 in the above function:

f(2) = 4

To learn more about equation of a function, click on below link:

https://brainly.com/question/22333482

#SPJ1

Answer:

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 7.5/100

r = 0.075 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 125,000.00(1 + 0.075/12)(12)(5)

A = 125,000.00(1 + 0.00625)(60)

A = $181,661.80

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $125,000.00 at a rate of 7.5% per year compounded 12 times per year over 5 years is $181,661.80.

Answer:

Look at the sides and angles.

Step-by-step explanation:

See which sides are equal pr seem so. Use logic.

y₁ =  [1  -4  0  1] and y₂ = [5  1  -6  -1] is the orthogonal basis for w using Gram-Schmidt process.

Given,

The set;

x₁ = [1  -4  0  1]

x₂ = [7  -7  -6  1]

We have to produce the orthogonal basis for w using the Gram-Schmidt process;

Here,

y₁ = x₁ =  [1  -4  0  1]

Now,

Solve for y₂

y₂ = x₂ - [x₂y₁ / y₁y₁] y₁

That is,

y₂ = [7  -7  -6  1] - ( [7  -7  -6  1] [1  -4  0  1] / [1  -4  0  1] [1  -4  0  1] ) × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - (7 + 28 - 0 + 1) / (1 + 16 + 0 + 1) × [1  -4  0  1]

y₂ = [7  -7  -6  1]  - 36/18 × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - 2  × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - [2  8  0  2]

y₂ = [5  1  -6  -1]

That is,

The orthogonal basis for w using Gram-Schmidt process is,

y₁ =  [1  -4  0  1] and y₂ = [5  1  -6  -1]

Learn more about Gram-Schmidt process here;

https://brainly.com/question/17132977

#SPJ4

Answer:

Gary would weigh 176 ounces.

Step-by-step explanation:

One pound is sixteen ounces so just multiply sixteen and 11. ( 16 * 11 = 176 )

I hope this helped you! Have an amazing day :)

Answer: 176 ounces

Step-by-step explanation:

To convert pounds to ounces, multiply the initial value by 16. Since we have  the weight of Gary's cat as 11 pounds, their weight in ounces should be 11 * 16 = 176 ounces.

Answer:

217

Step-by-step explanation:

Answer:

Step-by-step explanation:

The probability of waiting more than 0.5 minutes to get the next inquiry call is .165 seconds.

Probability is given by the number of possible outcomes ÷ number of total outcomes

Rate of phone calls = 3.6 per minute

Total number of calls between 2:00 p.m and 4:00 p.m (120 minutes) = 3.6 × 120 = 432

Number of calls in 0.5 minutes = 3.6 × 0.5 = 1.8

The probability that the number of calls in 0.5 minutes = 1.8/432 = 1/240.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X=x) =[/tex] e^-μ *  μ^[tex]x[/tex]

                        [tex]x[/tex]!

In which

x is the number of successes

e = 2.71828 is the Euler number

μ is the mean in the given time interval.

The probability of waiting more than 0.5 minutes to get the next inquiry call is according to a Poisson process.

Each minute has 60 seconds.

Rate of phone calls = 3.6 per minute

So a rate of 1 call every 50/3 seconds.

The probability that it takes more than 0.5 minutes for the first inquiry to arrive is approximate.

Mean of 1 call every 50/3 seconds, so for 0.5 minutes, μ = 0.5*60/50/3 = 1.8.

This probability is P(X = 0).

[tex]P(X=x) =[/tex] e^-μ *  μ^[tex]x[/tex]

                        [tex]x[/tex]!

P(X=0) = e^-1.8 * 0.03^0

                      0!

= 0.165

To learn more about the probability of such problems visit: https://brainly.com/question/15520794

#SPJ4

An expression with a square root is referred to as a radical expression.

Radical simplification:

Cube root simplification:

Rational radical simplification :

                 [tex]\frac{2}{\sqrt{5} -1} \\\\=\frac{2}{\sqrt{5} -1} *\frac{\sqrt{5}+1}{\sqrt{5}+1} \\\\=\frac{2(\sqrt{5} +1) }{4} \\\\=\frac{\sqrt{5} +1 }{2}[/tex]

Exponential radical simplification :

           [tex](5^{2} )^{3} \\=(5^{2} ) (5^{2} )(5^{2} )\\=25 *25*25\\=15625[/tex]

To learn more about cube root, refer:

https://brainly.com/question/24486461

#SPJ1

Answer:

an outcome

Step-by-step explanation:

the answer is 1

Step-by-step explanation:

f(x-3.5) means f(x) is translated 3.5 units left. 3f(x) implies f(x) is vertically stretched by a factor of 3.5.

A function is a relationship between inputs where each input is related to exactly one output. Also, translation means movement on a straight line

In the cartesian plane or graph, movement in the x-axis is either to the left (negative) or right (positive).

Thus, f(x-3.5) implies f(x) is translated 3.5 units left (i.e. -3.5)

For 3.5f(x), when you multiply f(x) by 3.5, you stretch it by 3.5. Thus, f(x) is vertically stretched by a factor of 3.5

Learn more about function on:

brainly.com/question/26103899

#SPJ1