The length of a rectangle is four times its width. If the perimeter of the rectangle is 180 ft, find its area

Answer: [tex]x=2\sqrt{5}[/tex]

Step-by-step explanation:

Detailed explanation is attached below.

We can integrate this S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx over the given interval (1.1 to 4.4) to find the surface area.

We can evaluate the integral using numerical methods or a calculator to find the final answer.

We have,

To find the surface area of the revolution about the x-axis of the function f(x) = 5√x over the interval (1.1 to 4.4), we can use the formula for the surface area of revolution:

S = ∫(a to b) 2πy√(1 + (f'(x))²) dx

In this case,

f(x) = 5√x, so f'(x) = (d/dx)(5√x) = 5/(2√x).

Let's calculate the surface area:

S = ∫(1.1 to 4.4) 2π(5√x)√(1 + (5/(2√x)²) dx

Simplifying the expression inside the integral:

S = ∫(1.1 to 4.4) x 2π(5√x)√(1 + 25/(4x)) dx

Next, we can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.

To find the surface area of revolution about the x-axis of the function

f(x) = 5√x over the interval (1.1 to 4.4), we need to evaluate the integral:

S = ∫(1.1 to 4.4) 2π(5√x)√(1 + 25/(4x)) dx

Let's calculate the integral:

S = 2π ∫(1.1 to 4.4) (5√x)√(1 + 25/(4x)) dx

To simplify the calculation, let's simplify the expression inside the integral first:

S = 2π ∫(1.1 to 4.4) (5√x)√((4x + 25)/(4x)) dx

Next, we can distribute the square root and simplify further:

S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx

Thus,

We can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.

We can evaluate the integral using numerical methods or a calculator to find the final answer.

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Answer:

42

Step-by-step explanation:

Rectangle: A = 6 x 5 = 30

Triangle: A = 1/2(6 x 4) = 12

Area of figure: 30 + 12 = 42

Answer:Peggy will spend approximately $363.52 constructing the pond and patio in her backyard. The correct answer is not provided among the options given (A, B, C).

Step-by-step explanation:

To calculate the cost of constructing the pond and patio in Peggy's backyard, we need to determine the areas of the pond and patio and then multiply them by their respective costs per square foot.

From the given scale, we can convert the dimensions of the pond and patio from centimeters to feet. According to the scale, 1 cm represents 5 ft.

Patio dimensions:

Width: 2 cm (2 cm * 5 ft/cm = 10 ft)

Length: 2 cm (2 cm * 5 ft/cm = 10 ft)

Area of patio = Width * Length = 10 ft * 10 ft = 100 ft²

Pond dimensions:

Width: 4 cm (4 cm * 5 ft/cm = 20 ft)

Length: 4 cm (4 cm * 5 ft/cm = 20 ft)

Area of pond = π * (Width/2)² = π * (20 ft/2)² = π * 10 ft² ≈ 31.42 ft²

Cost calculation:

Cost of pond = Area of pond * Cost per square foot = 31.42 ft² * $6/ft² = $188.52

Cost of patio = Area of patio * Cost per square foot = 100 ft² * $1.75/ft² = $175.00

Total cost = Cost of pond + Cost of patio = $188.52 + $175.00 = $363.52

This problem is relatively simple. Before we begin, it might be beneficial to imagine the graph as a vertical number line. Imagining it this way makes it easy to count the units between them and gives you the answer: [tex]$\boxed{4}$[/tex].

Here's a slightly more advanced way to think about it:

The example question tells us to subtract the distance between the two points. The formula for this is [tex]\sqrt{\big{(}(x_{2}-x_{1})+(y_{2}-y_{1})\big{)}^2[/tex], but for this question, let's say that it is [tex]\sqrt{(y_{2}-y_{1})^2[/tex], or, to simplify it even more, [tex]$|y_{2}-y_{1}|$[/tex]. Now that we know the formula, we can substitute our y-values into the last formula and solve. Let's say that Point C is our first point and Point D is our second.

[tex]\big{|}(-8)-(-4)\big{|} = \big{|}-8+4\big{|} = \big{|}-4\big{|} = \boxed{4}[/tex] , so [tex]$4\text{ units}$[/tex] is our answer.

Disclaimer: Neither of the last two formulas I provided is the actual formula, just a version of the Distance Formula that might be easier to understand. The first formula is the actual thing, but you will encounter this in math later in life, probably around 8th or 9th grade.

The solution to the problem at hand i.e. to draw a horizontal line segment, OM, of any length, the longer the better using ruler, protractor, compass and coloured pencils

are as follows:

Step 1: Take a ruler and align it with a sheet of paper and draw a line. This line can be of any length, although longer lines are preferred.

Step 2: The line is now OM; we must now label its endpoints. Label the leftmost point O, and the rightmost point M.

Step 3: The coloured pencils are used to add decorations to the line. To add decorations, use coloured pencils to make patterns and stripes along the length of the line. This is entirely optional and based on personal preference.

Step 4: To ensure that the line is perfectly horizontal, the protractor should be used. Place the protractor on the line and make sure the zero-degree angle is at O. The line will be horizontal if it is parallel to the baseline of the paper.

Step 5: Using a compass, measure the length of OM to ensure that it is of the desired length.

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The remainder of the polynomial division [tex]\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)}[/tex] is 2y²

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

[tex]\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)}[/tex]

When the numerator is expanded, we have

[tex]\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = \frac{(y - 1)(y^3 + 1) + 2y^2}{y^3 + 1}[/tex]

Split the expanded expression

[tex]\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = \frac{(y - 1)(y^3 + 1)}{y^3 + 1} + \frac{2y^2}{y^3 + 1}[/tex]

Evaluate

[tex]\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = y - 1 + \frac{2y^2}{y^3 + 1}[/tex]

From the above, we have

Quotient = y - 1

Remainder = 2y²

Hence, the remainder of the polynomial division is 2y²

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Answer:

correct answer is 650ml

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

The value of the expression 226²⁸ ● (25)⁶ is approximately [tex]4.1406562 \times 10^{119.[/tex]

To evaluate the expression 226²⁸ ● (25)⁶, we can follow the order of operations (also known as PEMDAS/BODMAS) which states that we should perform any calculations inside parentheses, then evaluate any exponents, and finally perform any multiplications or divisions from left to right.

Let's break down the expression :

Evaluate the exponent (25)⁶

[tex](25)^{6} = 25^{(6\times 1)} = 25^6 = 244,140,625[/tex]

Substitute the value into the expression:

226²⁸ ● 244,140,25.

Evaluate the exponent 226²⁸

[tex]226^{28} = 226^{(2\times28) = 226^{56 \\[/tex]

Now, calculating [tex]226^{56}[/tex] might not be feasible manually due to the large exponent.

However, we can use a calculator or a computer program to obtain the result.

[tex]226^{56} \approx 1.6951718 \times 10^{112[/tex]

Substitute the value back into the expression:

[tex]1.6951718 \times 10^{112[/tex] ● 244,140,625

Perform the multiplication:

[tex]1.6951718 \times 10^{112}\times 244,140,625 \approx 4.1406562 \times 10^{119[/tex] .

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Given statement solution is :- On average, she spent approximately $115 per visit.

To calculate the total amount spent on the visits, we need to add up the co-payments and the cost of the shots.

Co-payments:

The co-pay for each visit is $25, and you visited the doctor 3 times a week for 8 weeks within 2 months. So the total co-payment is:

3 visits/week * $25/visit * 8 weeks = $600.

Shots:

You received the shot 2 times out of each visit, and you visited the doctor 3 times a week for 8 weeks within 2 months. So the total cost of the shots is:

2 shots/visit * $135/shot * 8 weeks = $2,160.

Total amount spent:

Co-payments + Shots = $600 + $2,160 = $2,760.

Therefore, the total amount spent for the visits and shots over 2 months is $2,760.

Trivia Answer:

To find out the average amount spent per visit, we can divide the total amount spent by the total number of visits. In this case, the total amount spent is $2,760, and the total number of visits is 3 visits/week * 8 weeks = 24 visits.

Average spent per visit = Total amount spent / Total number of visits

Average spent per visit = $2,760 / 24 visits

Average spent per visit ≈ $115.

Therefore, on average, you spent approximately $115 per visit.

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Answer:

A

Step-by-step explanation:

To simplify the expression 3 11 5 ÷ 3 − 9 5, let's break it down step by step:

First, let's simplify the division 3 11 5 ÷ 3:

3 11 5 ÷ 3 = (3 × 115) ÷ 3 = 345 ÷ 3 = 115.

Next, let's subtract 9 5 from the result we obtained:

115 - 9 5 = 115 - (9 × 5) = 115 - 45 = 70.

Therefore, the simplified expression is 70.

The correct answer is A. 70.

The square root of the number 32 and the values of the perfect squares before and after 32 indicates;

5 < √(32) < 6

The square root of a number can be calculated by using the following methods; 1. Estimation, 2. Longhand method, 3. Calculator, and 4. Newton method.

The square root of 32 is; √(32) ≈ 5.66

Therefore, the value of the square root of 32 is between 5 and 6, and we get;

The square root of 32 is between the square root of 25 = 5², and the square root of 36 = 6², and the completed inequality can be expressed in the form;

5 < √(32) < 6

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a) The value of fraction is,

⇒ 2 / 3

b) The value of fraction is,

⇒ 1 / 3

c) There are 24 hours in a day.

Now, We can simplify all the fraction as,

a) To find fraction of an hour is 40 minutes,

Since, 1 hour = 60 minutes

Hence,

⇒ 40 / 60

⇒ 4 / 6

⇒ 2 / 3

b) Since, 1 day = 24 hours

Hence, we get;

⇒ 8 / 24

⇒ 1 / 3

c) We know that,

⇒ 1 day = 24 hours

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The amount natalya will spend constructing the patio with concrete and brick is $4320, the correct option is D.

We are given that;

The concrete portion of the patio cost=$3 per square

To construct and the brick portion of the patio cost= $6 per square

Now,

The area of a rectangle is given by length times width. The concrete portion of the patio is a rectangle with length 6 cm and width 3 cm. Using the scale, we can convert these to feet:

6 cm = 6 x 4 ft = 24 ft 3 cm = 3 x 4 ft = 12 ft

Therefore, the area of the concrete portion is:

24 ft x 12 ft = 288 ft^2

The brick portion of the patio consists of two identical rectangles with lenth 3 cm and width 6 cm. Using the scale, we can convert these to feet:

3 cm = 3 x 4 ft = 12 ft 6 cm = 6 x 4 ft = 24 ft

Therefore, the area of one brick rectangle is:

12 ft x 24 ft = 288 ft^2

Since there are two brick rectangles, the total area of the brick portion is:

2 x 288 ft^2 = 576 ft^2

Now we can multiply the areas by their costs per square foot to get the costs of each portion:

Concrete cost = $3 x 288 ft^2 = $864 Brick cost = $6 x 576 ft^2 = $3456

The total cost of constructing the patio is the sum of the costs of each portion:

Total cost = $864 + $3456 = $4320

Therefore, by area the answer will be $4320.

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Manuel received $187.50, and George received $562.50 for the job.

Let's break down the information provided:

The job paid a total of $750.

George received $3 for every $2 that Manuel received.

To determine the amounts George and Manuel received, we can set up a ratio based on their earnings.

Let's assume Manuel's earnings as the base amount:

George's earnings : Manuel's earnings = $3 : $2

We can set up the following equation to solve for Manuel's earnings:

(Manuel's earnings / Manuel's earnings) = ($2 / $2)

Since the ratio is equivalent, we can say:

George's earnings / Manuel's earnings = $3 / $2

To find the amount each person received, we'll assign a variable to Manuel's earnings. Let's call it "x."

Therefore, George's earnings can be represented as "3x."

According to the given information, their total earnings should sum up to $750:

x + 3x = $750

Combining like terms, we have:

4x = $750

To solve for x, we divide both sides by 4:

x = $750 / 4

x = $187.50

Now, we can determine the amounts each person received:

Manuel's earnings = x = $187.50

George's earnings = 3x = 3 * $187.50 = $562.50

Therefore, Manuel received $187.50, and George received $562.50 for the job.

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The item most likely to weigh 2 kilograms is a roast chicken.

The size, breed, and any other ingredients or stuffing used can all affect the weight of a roast chicken. Weights of roast chickens can range from petite ones weighing less than 1 kilogram to larger ones weighing more than 2 kilograms.

The other things that we have there would either weigh less than 2 Kg such as a tea bag or much more than 2 Kg such as a horse. The egg and the tea a very light and would be less than 2 Kg in weight while the bag and the horse would be above 2 Kg in weight.

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The number of students taking all three languages would be 1 student. The number of students taking none of the languages are 32.

The total number of students taking each language is given so the number of people taking these languages are:

15 + 14 - X + X = 30

X = 1

So, there is 1 student taking all three languages.

For the students taking none of these languages:

Total students - students taking at least one language = students taking none of these languages.

= 100 (total students) - (53 ( taking only one language ) + 14 ( taking Arabic and Bulgarian ) + X (taking all three languages))

= 100 - 53 - 14 - 1

= 32 students

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Collecting the like terms in the expression 5z - 7 - 13z + 35 gives -8z + 28

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

5z - 7 - 13z + 35

Consider an expression given as

Ax + Bx

Where A and B are constants and x is a variable

The terms Ax and Bx are like terms

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

5z - 7 - 13z + 35 = 5z - 13z - 7 + 35

Evaluate the like terms

5z - 7 - 13z + 35 = -8z + 28

Hence, collecting the like terms gives -8z + 28

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Answer:

18+x = -40

Step-by-step explanation:

The sum of 18 and a number x is translated to "18+x"
Equals means "="
Negative forty is "-40"
Put them all in order and you get 18+x = -40

Answer:

x=2

Step-by-step explanation:

I don’t really have an explanation, it was all mental math

Answer:

Step-by-step explanation:

[tex]\sf 2(4-x)-3(x+3)=-11[/tex]

Expand:-

Now, add 1 to both sides:-

Divide both sides by -5:-

Therefore, the value of x is 2!

- - - - - - - - - - - - - - - - - - - - - -

Hope this helps!

The discounted price of the item would be Rs. 23,940.

To calculate the discounted price of an item, you can use the following formula:

Discounted Price = Original Price - (Original Price * Discount Percentage)

Given that the original price (MP) is Rs. 26,600 and the discount is 10%, we can calculate the discounted price as follows:

Discounted Price = Rs. 26,600 - (Rs. 26,600 x 0.10)

Discounted Price = Rs. 26,600 - Rs. 2,660

Discounted Price = Rs. 23,940

Therefore, with a 10% discount, the discounted price of the item would be Rs. 23,940.

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Answer:

60 degrees

Step-by-step explanation:

To convert radians to degrees, multiply by 180/pi

pi/3 * 180/pi = 180/3 = 60 degrees

Step-by-step explanation:

3 radians =

171.887 degrees

 AreaData Transfer RateDigital StorageEnergyFrequencyFuel EconomyLengthMassPlane AnglePressureSpeedTemperatureTimeVolume 

  ArcsecondDegreeGradianMilliradianMinute of arcRadian 

  ArcsecondDegreeGradianMilliradianMinute of arcRadian 

Formula

3rad × 180/π = 171.887°

Answer:        -0.7

Step-by-step explanation:

Given statement solution is :- The volume of the resulting part is approximately 267 cubic inches.

To find the volume of the resulting part, we need to calculate the volume of the larger cone and subtract the volume of the smaller cone.

The formula for the volume of a cone is given by:

V = (1/3) * π * [tex]r^2[/tex] * h

where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the cone's base, and h is the height of the cone.

For the larger cone:

Radius (r) = 5 inches

Height (h) = 12 inches

V_large_cone = (1/3) * π * [tex](5^2)[/tex] * 12

V_large_cone = (1/3) * π * 25 * 12

V_large_cone = (1/3) * π * 300

V_large_cone = 100π

For the smaller cone:

Radius (r) = 3 inches

Height (h) = 5 inches

V_small_cone = (1/3) * π * [tex](3^2)[/tex] * 5

V_small_cone = (1/3) * π * 9 * 5

V_small_cone = (1/3) * π * 45

V_small_cone = 15π

Therefore, the volume of the resulting part is:

V_resulting_part = V_large_cone - V_small_cone

V_resulting_part = 100π - 15π

V_resulting_part = 85π

Now, we can approximate the value of π as 3.14159:

V_resulting_part ≈ 85 * 3.14159

V_resulting_part ≈ 267.10715

Rounded to the nearest whole number, the volume of the resulting part is approximately 267 cubic inches.

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One main disadvantage of piece rate or commission pay is low quality.

Piece rate or commision pay involves paying workers based on coverage or performance. This way the company is able to cut short excess salary especially for low performing workers.

However, a notable disadvantage of piece-rate pay is that it can lead to employees sacrificing quality for quantity. When employees are paid based on the number of units they produce, they may be tempted to produce low-quality products in order to meet their quotas. This can damage the company's reputation and lead to customer dissatisfaction.

Therefore, piece rate pay will often lead to quality reduction.

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The term 9b represents the cost to rent a bike.

We have,

               Rentals

Bike                            $9/h

Electric scooter          $10/h

Kayak                          $18/h

Canoe                         $20/h

Paddleboard               $22/h

Helmet                        Add $6

Here, the term 9b represents the cost to rent a bike.

In the provided rental options, the cost of renting a bike is $9 per hour.

The term "9b" indicates that the cost is calculated by multiplying the hourly rate of $9 with the number of hours (b) the bike is rented for.

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Answer:

i want to say it is 50[tex]\pi[/tex] square yards but i'm not entirely positive let me double check and i'll submit another answer

Step-by-step explanation:

although i can't promise this is correct, i can try my best to explain how i got to the answer i did in case that might help you determine if you want to use it.

formula for finding the area of a circle sector is (theta/360) x [tex]\pi[/tex][tex]r^{2}[/tex]

if you insert these things, it's just simplifying the problem after that.

we know what theta is (80 degrees) since the subtended angle is the same as the measure of the arc because it is a central angle, and those always correspond with each other. and we also know our radius because it connects the center of the circle to the outer edge. it is 15 yards.

so then we have (80/360) x [tex]\pi\\[/tex] x (15)^2

essentially, what you're going to do is break down the problem from there. simplify 80/360 to 2/9 and multiply it by pi and then by 15 squared (which is 225).

you will get 450[tex]\pi[/tex]/9 which, when simplified, is 50[tex]\pi[/tex]

i really hope this helps you at some sort of capacity.

The sign of -xy cannot be determined without knowing the signs of x and y. It can be positive, negative, or zero.

The signs of x and y influence the sign of -xy. A positive result is produced when multiplying two numbers with the same sign (both positive or both negative), while a negative result is produced when multiplying two numbers with opposite signs (one positive and the other negative). Their product is 0 when either one or both of the values are zero.

Therefore, depending on the signs of x and y, the sign of -xy can be positive, negative, or zero.

-xy is negative if x and y are both positive.

-xy is positive if x and y are both negative.

Regardless of the sign of the other number, if either x or y is zero, then -xy is also zero.

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