The perimeter of a rectangular living room is 38 meters. The living room is 9 meters wide how long is it

The minimum amount of fencing Mendel will need to enclose 2500 m² = 317 meters

Let's assume that x represents the length of and y represents the width of the rectangular garden.

Using the formula for tha area of rectangle, the area of the garden would be,

A = length × width

A = xy

Here, A = 2500 m²

so, 2500 = xy

⇒ y = 2500/x

Using the formula for the perimeter of the rectangle, the perimeter of the garden would be,

P = 2x + 2y

But  a rectangular garden is partitioned into 4 parts by constructing three additional fences parallel to one of the side.

So, the perimeter would be,

P = 2x + 5y

sides, in addition to fencing the perimeter.

P = 2x + 5(2500/x)

P = 2x + (12500/x)

Consider the derivative of P(x) with respect to x.

P'(x) = 2 - 12500/x²

To find the minimum value consider P'(x) = 0

2 - 12500/x² = 0

2 = 12500/x²

x² = 12500/2

x² = 6250

x = 79.05 m

and y =  2500/79.05

y = 31.63 m

So, the minimum amount of fencing would be,

P = 2x + 5y

P = 2(79.05) + 5( 31.63 )

P = 316.25 meters

P ≈ 317 meters

The minimum amount of fencing need to enclose 2500 m² = 316.25 meters

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The percentage profit on the car is 12% if a car was bought for 5600 and sold for 6272.

To calculate the percentage profit, we need to find the profit first.

Profit = Selling price - Cost price

Profit = 6272 - 5600 = 672

The profit on the car is $672.

Now, we can calculate the percentage profit using the formula

Percentage profit = (Profit / Cost price) x 100%

Percentage profit = (672 / 5600) x 100%

Percentage profit = 0.12 x 100%

Percentage profit = 12%

Therefore, the percentage profit on the car is 12%.

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The transformations of the functions compared to the parent function are given as follows:

C. Reflection over the x-axis, vertical stretch by a factor of 2, and shift right units.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function for this problem is given as follows:

y = sqrt(x).

Hence the transformations are given as follows:

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Answer:

6^2 + 4(1/2)(6)(9) = 36 + 108 =

144 square meters

The given quadratic equations by solving using inverse operations gives,

(a) x = ±2√2, (b) x = ±3√2 + 5, (c) x = ±4√2, (d) x = ±√90 - 2 and (e) x = 4 ±3√3.

Given are some quadratic equations.

We have to solve this using the inverse operations.

Inverse operations are operations which undo the operation which is done to the equation.

(a) 1/2 x² - 4 = 0

Adding both sides by 4,

1/2 x² = 4

Multiplying both sides by 2,

x² = 8

Taking the square root on both sides,

x = ±√8 = ±2√2

(b) (x - 5)² = 18

Taking the square root on both sides,

x - 5 = ±√18

x - 5 = ±3√2

Adding 5 on both sides,

x = ±3√2 + 5

(c) 2x² + 7 = 71

Subtracting by 7 on both sides,

2x² = 64

Dividing by 2 on both sides,

x² = 32

Taking the square root on both sides,

x = ±4√2

(d) 5 (x + 2)² + 37 = 487

Subtracting by 37 on both sides,

5 (x + 2)² = 450

Dividing by 5 on both sides,

(x + 2)² = 90

Taking the square root on both sides,

x + 2 = ±√90

Subtracting by 2 on both sides,

x = ±√90 - 2

(e) (x - 4)² /3 + 8 = 17

Subtracting by 8 on both sides,

(x - 4)² /3 = 9

Multiplying both sides by 3,

(x - 4)² = 27

Taking the square root on both sides,

x - 4 = ±3√3

Adding both sides by 4,

x = 4 ±3√3

Hence the values are found.

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First, let's calculate the monthly interest rate (i), which is the APR divided by 12 months:

i = APR / 12 months

i = 5.3% / 12

i = 0.00442 or 0.442%

Next, let's calculate the number of months (n) for the mortgage, which is 15 years multiplied by 12 months:

n = 15 years x 12 months/year

n = 180 months

Now, let's calculate the monthly payment (PMT) using the following formula:

PMT = P * i / [tex](1 - (1 + i)^(-n)[/tex])

where P is the principal amount, i is the monthly interest rate, and n is the number of months.

PMT = $325,000 * 0.00442 / (1 - [tex](1 + 0.00442)^(-180)[/tex]

PMT = $2,613.67 (rounded to the nearest cent)

Now, let's create the amortization table for the first two months:

Month | Payment | Interest | Principal | Remaining Balance

1 | $2,613.67 | $1,431.25 | $1,182.42 | $323,817.58

2 | $2,613.67 | $1,428.60 | $1,185.07 | $322,632.51

For each month, the Payment column shows the fixed monthly payment, the Interest column shows the calculated interest based on the remaining balance multiplied by the monthly interest rate, the Principal column shows the portion of the payment that goes towards reducing the principal, and the Remaining Balance column shows the remaining balance after subtracting the principal payment from the previous remaining balance.

The amortization table will continue in this manner for the remaining months until the mortgage is paid off.

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The interest and principal amounts for the first payment are:

Interest = $325,000 * 0.0044167 = $1,426.25

Principal = $2,549.67 - $1,426.25 = $1,123.42

Balance = $325,000 - $1,123.42 = $323,876.58

For the second payment, we start with the new balance of $323,876.58 and apply the formulas again:

Interest = $323,876.58 * 0.0044167 = $1,420.47

Principal = $2,549.67 - $1,420.47 = $1,129.20

Balance = $323,876.58 - $1,129.20 = $322,747.38

To complete the two-month amortization table, we need to calculate the monthly payment, as well as the principal and interest amounts for each payment.

The formula for calculating a fixed-rate mortgage payment is:

[tex]Payment = P * r * (1 + r)^n / [(1 + r)^n - 1][/tex]

Where:

P = Principal amount borrowed

r = Monthly interest rate

n = Total number of payments

First, let's calculate the monthly interest rate.

Since the APR is an annual rate, we need to divide it by 12 to get the monthly rate:

Monthly interest rate = 5.3% / 12 = 0.0044167

Next, we need to calculate the total number of payments.

Since this is a 15-year mortgage, and we're completing a two-month amortization table, the total number of payments is:

Total number of payments = 15 years * 12 months per year = 180

Number of payments for two months = 2

Now we can plug these values into the formula to calculate the monthly payment:

Payment = [tex]$325,000 * 0.0044167 * (1 + 0.0044167)^180 / [(1 + 0.0044167)^180 - 1][/tex]

= $2,549.67

So the monthly payment is $2,549.67

Now we can use this value to complete the two-month amortization table:

Payment Interest Principal Balance

Month 1 $1,426.25 $1,123.42 $323,876.58

Month 2 $1,420.47 $1,129.20 $322,747.38

To calculate the interest and principal amounts for each payment, we use the following formulas:

Interest = Balance * Monthly interest rate

Principal = Payment - Interest

Balance = Balance - Principal

We start with the initial balance of $325,000 and apply the formulas for each payment.

The interest and principal amounts for the first payment are:

Interest = $325,000 * 0.0044167 = $1,426.25

Principal = $2,549.67 - $1,426.25 = $1,123.42

Balance = $325,000 - $1,123.42 = $323,876.58

For the second payment, we start with the new balance of $323,876.58 and apply the formulas again:

Interest = $323,876.58 * 0.0044167 = $1,420.47

Principal = $2,549.67 - $1,420.47 = $1,129.20

Balance = $323,876.58 - $1,129.20 = $322,747.38

And so on, for each subsequent payment.

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Required value of x is 201.52 ft.

What is Trigonometric ratio?

Trigonometric ratios are defined as the values of all trigonometric functions based on the value of the ratio of the sides of a right triangle. The ratio of the sides of a right triangle to its acute angles are called the trigonometric ratios of that particular angle.

For example,tan(θ) = opposite/adjacent where θ is the angle between the hypotenuse and the base.

We want to solve for x, the length of the adjacent side. We also know that the hypotenuse is 500 ft and the height is y.

Here by the given figure, it is clear that angle between height and hypotenuse is (90°-29°) = 61°

So, θ = 61°

[tex]tan( {61}^{o} ) = \frac{y}{x} [/tex]

Simplifying this expression,

[tex]x = \frac{y}{tan(61°)}[/tex]

To solve for y, for the right angle triangle

[tex]y^2 + x^2 = 500^2[/tex]

Substituting the expression for x from the first equation,

y² + (y/tan(61°))² = 500²

Solving for y, we get:

y = 500 / √(1 + (1/tan(61°))²)

y ≈ 357.98 ft

Finally, we can substitute this value of y into the expression for x that we derived earlier,

x = y/tan(61°)

x ≈ 201.52 ft

Therefore, the value of x is approximately 201.52 ft.

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The number of Americans experience hearing loss sufficient to affect communication is: 1 in 4.

According to the National Institute on Deafness and Other Communication Disorders (NIDCD).

Approximately 1 in 4 adults in the United States aged 65 and older have hearing loss that is sufficient to affect communication.

This is based on data from a survey conducted by the NIDCD and the National Health Interview Survey.

NIDCD (National Institute on Deafness and Other Communication Disorders).

In the United States, 1 in 4 persons 65 and older suffer hearing loss severe enough to impair conversation.

This is based on information from surveys done by the National Health Interview Survey and the NIDCD.

The number of Americans who experience hearing loss sufficient to affect communication is: 1 in 4.

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Answer:

Greater than 7.

Step-by-step explanation:

To solve for x in the inequality, we need to isolate x on one side of the equation. First, we need to subtract

$ [tex]\large \boxed{\mathrm{1328}}[/tex]

from each side, giving $30x > $210. Then, we divide both sides by 30 to find that x > 7. Therefore, to make the inequality true, x needs to be greater than 7.

The mean of a binomial probability distribution with p = 0.32 and n = 150 is 48

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success, denoted by p. In the case of a binomial distribution with n trials and probability of success p, the mean, or expected value, is equal to the product of the number of trials and the probability of success, which is np.

In this case, the problem provides the values of p and n, which are p = 0.32 and n = 150, respectively. Therefore, the mean can be calculated by multiplying these two values

μ = np = 150 x 0.32 = 48

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Answer: Either 58 or 85

Step-by-step explanation:

5 + 8 = 13
8 + 5 = 13

5 x 8 = 40

8 x 5 = 40

Answer: Permutation: A permutation is an course of action of a set of objects in a particular arrange. The number of conceivable changes of a set of n objects is n factorial (n!), which is the item of all positive integrability up to n.

Factorial: The factorial of a non-negative numbers n is signified by n! and is characterized as the item of all positive integrability less than or rise to to n. For case, 5! = 5 x 4 x 3 x 2 x 1 = 120.

Series: A arrangement may be a entirety of terms organized in a particular arrange. The entirety of the terms in a arrangement is called its add up to.

Circular permutation: A circular stage may be a stage of a set of objects in a circular course of action, where the arrange of objects things, but the beginning point is subjective. For case, orchestrating the letters A, B, and C in a circle would result in 3 circular stages: ABC, BCA, and CAB. The number of conceivable circular stages of a set of n objects is (n-1)!.

Step-by-step explanation:

The Phillips curve describes the relationship between the unemployment rate and the rate of change of wages. Option C is the correct option.

What is  Phillips curve?

The relationship between the rate of inflation and the unemployment rate is represented by the Phillips curve. The analysis of wage inflation and unemployment in the United Kingdom from 1861 to 1957 by A. W. H. Phillips, despite having forerunners, is a significant development in the field of macroeconomics. When unemployment was high, wages rose slowly; when unemployment was low, wages rose quickly, according to Phillips' research.

According to Phillips' hypothesis, as the unemployment rate declines, the labor market becomes more competitive and firms are forced to raise wages more quickly in order to recruit qualified workers. The pressure decreased as unemployment rates rose. The average relationship between wage behavior and unemployment over the course of the business cycle was represented by Phillips' "curve."

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Answer:

4800

Step-by-step explanation:

15 x 20 = 300 x 16 = 4800

Answer: Ashley hit the softball farther.

Step-by-step explanation: Ashley hit the softball farther, since her distance of 65 meters is greater than Nicole's distance of 6,700 centimeters.To compare these distances, we need to convert Nicole's distance from centimeters to meters, since Ashley's distance is given in meters.To do this, we can divide Nicole's distance by 100, since there are 100 centimeters in a meter:6700 cm / 100 cm/m = 67 mTherefore, Ashley hit the softball 65 meters, which is less than the 67 meters that Nicole hit it. This means that Ashley hit the softball farther.

A computation time expression ~ n, of means that the computation time increases in proportion to the size of the input.

This presents a computational complexity of O(n). Here 'O' stands for 'Big O Notation' and is used to denote an upper bound on the computational complexity of the algorithm.

That's, the algorithm's computational complexity is straightforwardly corresponding to the measure of the input information.

This shows that as the input estimate increments, the computational time will increment at the same rate.

 Linear time complexity is considered to be very efficient, and many algorithms aim to achieve this level of complexity. This is a relatively efficient computational complexity and is common in algorithms that require only one pass through the input data. 

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Answer:

Step-by-step explanation:

The correct answer is option D, 1078[tex]\pi[/tex] [tex]cm^{3}[/tex].

The volume of the cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h.

Radius = 7cm Height = 22cm.

Substituting the value in the formula, we get

[tex]\pi[/tex]*[tex]7^{2}[/tex]*22 = 1078[tex]\pi[/tex].

Hence the Answer is 1078[tex]\pi[/tex].

Answer:

3386.64 cm3

Step-by-step explanation:

i use this formula    π r² h

Answer:

[tex]f(x) = (x + 2)(x - 12)[/tex]

[tex]f(x) = {x}^{2} - 10x - 24[/tex]

We would need 168 square inches of Teflon to completely cover the triangular prism machinery.

To calculate the surface area of a triangular prism, we need to find the area of each face and then add them up. Let's assume that the triangular bases of the prism have base b and height h, and that the length of the prism is l.

The surface area of the triangular bases is (1/2)bh for each base, so the total area is (1/2)bh + (1/2)bh = bh.

The lateral surface area of the prism is the area of the three rectangular faces. Each rectangular face has length l and height h, so the total lateral surface area is 3lh.

Therefore, the total surface area of the triangular prism is

bh + 3lh

To determine how much Teflon is needed to cover the machinery, we need to know the dimensions of the triangular prism. Once we have those dimensions, we can calculate the surface area using the formula above and then use that value to determine the amount of Teflon required.

Let's say the base of the triangular prism is 4 inches and the height is 6 inches, and the length of the prism is 8 inches. Then the surface area of the triangular prism is

bh + 3lh

= (4 in. x 6 in.) + 3(8 in. x 6 in.)

= 24 in² + 144 in²

= 168 in²

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A good way to solve for lines and segments will be to know the equations and properties of the shapes that we are provided with.

To get the answers for the lines and segment, you can begin by applying the following steps:

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The measure of angle 1 is 67.4°. The measure of angle 2 is 104.5°.

An angle is the measure of the amount of rotation between two lines or two planes that meet at a point. It is typically measured in degrees or radians. An angle can be acute, meaning it is less than 90 degrees, right, meaning it is exactly 90 degrees, obtuse, meaning it is greater than 90 degrees but less than 180 degrees, or straight, meaning it is exactly 180 degrees. An angle can also be positive or negative, depending on the direction of rotation between the lines or planes. Angles are used in various fields such as mathematics, engineering, physics, and geometry.

Here,

180-121.8=58.2°

180-(58.2+17.3)=104.5°

180-104.5=75.5°

180-(75.5+37.1)=67.4°

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Answer:

linear

Step-by-step explanation:

its linear because the data shows a straight line:)

Answer:

Linear

Step-by-step explanation:

linear equation forms a straight line on the graph. A nonlinear equation forms a curve on the graph.

The height of the cylinder, given the volume and the diameter of the base, would be 2, 592.46 feet

The given diameter of the base is 10 inches, so we need to find the radius first. The radius is half the diameter:

Radius (r) = Diameter / 2 = 10 inches / 2 = 5 inches

We also need to convert the radius from inches to feet since the volume is given in cubic feet:

5 inches = 5/12 feet = 0.4167 feet

Volume of a cylinder:

Volume (V) = πr²h

450π = π x (0.4167)^2 x h

450 = (0.4167)^2 x h

h = 450 / (0.4167)^2 = 2, 592.46 feet

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Answer:

0.16%

Step-by-step explanation:

Imagine you are a politician who wants to increase taxes in your city. You decide to conduct a survey among 450 residents to see how many of them are against your proposal. You know that the probability of finding someone who is against increasing taxes is 0.38. You hope that the survey will show that most people support your idea, or at least that the opposition is not too strong. However, when you get the results, you are shocked to see that more than 180 people are against increasing taxes. How unlucky are you? Well, let's do some math. This is a binomial probability problem. The probability of success (being against increasing taxes) is p = 0.38 and the number of trials (residents surveyed) is n = 450. The question asks for the probability of more than 180 successes, which is equivalent to the probability of at least 181 successes. Using a binomial calculator, the answer is approximately 0.0016 or 0.16%. That means that there is only a 0.16% chance of getting at least 181 people against increasing taxes in a sample of 450 residents. That's very rare and unlucky indeed! You might want to reconsider your proposal or find a better way to convince people that paying more taxes is good for them.

Answer:

1/2

Step-by-step explanation:

Since the events are independent, P(A and B) = P(A) * P(B)

P(X and Y) = P(X) * P(Y)

                  = 2/3 * 3/4

                  = 2/4

                   = 1/2

since the now has a value of ten so the p is equalled to 59

The average value of a necklace at Julie's shop is $57.19.

For the gold necklaces, she has 15 of them worth $120 each. So the total value of the gold necklaces is:

15 x $120 = $1,800

For the silver necklaces, she has 9 of them worth $90 each. So the total value of the silver necklaces is:

9 x $90 = $810

For the plated necklaces, she has 10 of them worth $60 each. So the total value of the plated necklaces is:

10 x $60 = $600

Finally, for the beaded necklaces, she has 30 of them worth $15 each. So the total value of the beaded necklaces is:

30 x $15 = $450

To find the total value of all the necklaces, we add up the value of each type of necklace:

$1,800 + $810 + $600 + $450 = $3,660

Now that we know the total value of all the necklaces at Julie's shop, we can find the average value of a necklace by dividing the total value by the total number of necklaces:

Average value of a necklace = Total value of all necklaces / Total number of necklaces

There are a total of 15 + 9 + 10 + 30 = 64 necklaces at Julie's shop. So the average value of a necklace is:

$3,660 / 64 = $57.19

This means that if you were to randomly select a necklace from her shop, the typical value you could expect it to have is $57.19.

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Answer:

The equation for the alternating current can be described by: y = 155 sin(120πt)

Where y is the voltage in volts (V) and t is the time in seconds (s).

To find the value of y when t = 1/90 s:

y = 155 sin(120π(1/90))

y ≈ 30.8 V

To approximate the value of t when y = 100 V for the first time, we need to solve the equation for t:

100 = 155 sin(120πt)

sin(120πt) = 100/155

t = arcsin(100/155)/(120π)

t ≈ 0.001 s

Therefore, the value of t when y = 100 V for the first time is approximately 0.001 seconds

The direction of the greatest increase in heat from the point (2, 5) is in the direction of the vector (-21, -20).

To find the direction of the greatest increase in heat from point (2, 5), we need to find the gradient vector of the temperature function T(x,y) at that point, and then determine the direction in which the gradient vector points.

The gradient vector of T(x,y) is given by:

∇T(x,y) = (∂T/∂x)i + (∂T/∂y)j

where i and j are the unit vectors in the x and y directions, respectively.

Taking the partial derivatives of T(x,y) with respect to x and y, we get:

∂T/∂x = (x² - y²)/(x² + y²)²

∂T/∂y = -2xy/(x² + y²)²

Substituting x = 2 and y = 5, we get:

∂T/∂x = (4 - 25)/(29)² = -21/1681

∂T/∂y = -20/1681

Therefore, the gradient vector of T(x,y) at the point (2, 5) is:

∇T(2,5) = (-21/1681)i - (20/1681)j

The direction of the greatest increase in heat from points (2, 5) is in the direction of the gradient vector. We can normalize the gradient vector to get the unit vector in this direction:

u = (∇T(2,5))/|∇T(2,5)|

where |∇T(2,5)| is the magnitude of the gradient vector, given by:

|∇T(2,5)| = √((-21/1681)² + (-20/1681)²) = sqrt(841)/1681 = 1/41

Thus, the unit vector in the direction of greatest increase in heat from the point (2, 5) is:

u = (-21/1681i - 20/1681j)/(1/41) = -21i - 20j

Therefore, the direction of the greatest increase in heat from points (2, 5) is in the direction of the vector (-21, -20).

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