A rectangular rug has perimeter 1388 inches. The length is 34 inches more than twice the width. Find the length and width of the rug.

For given average temperatures and °C=5/9°F-32 C represents temperature unit in celsius.

What is average?

In Maths, an average of a list of data is the expression of the central value of a set of data. Mathematically, it is defined as the ratio of summation of all the data to the number of units present in the list. In terms of statistics, the average of a given set of numerical data is also called mean. For example, the average of 2, 3 and 4 is (2+3+4)/3 = 9/3 =3. So here 3 is the central value of 2,3 and 4.  Thus, the meaning of average is to find the mean value of a group of numbers.

Average = Sum of Values/Number of Values

Also

Suppose, we have given with n number of values such as x1, x2, x3 ,….., xn. The average or the mean of the given data will be equal to:

Average = (x1+x2+x3+…+xn)/n

Now,

Given formula

°C=5/9°F-32, C represents  where °c is temperature unit in Celsius and

°F represents unit of temperature in Fahrenheit.

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The all zeros of given function f(x)= x²+3x-18 are: x = -6  and x = 3.

The values of a variable in a function that cause the function to equal zero are known as the zeros of the function.

The given function:

f(x)= x²+3x-18

Or,

x²+3x-18 = 0

On factorizing:

x²+6x- 3x -18 = 0

Taking 'x' common.

x(x + 6) - 3(x + 6) = 0

Taking (x + 6) common.

(x + 6)(x - 3) = 0

x = -6  and x = 3.

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Margaret's production plan is to allocate her resources as follows

400 acres of SE for wheat

200 acres of W for wheat

400 acres of SE for alfalfa

500 acres of N for alfalfa

100 acres of NW for alfalfa

400 acres of SE for barley

1300 acres of N for barley

400 acres of NW for barley

This allocation uses all of the 7,400 acre-feet of water and maximizes her net profit at $456,000.

To formulate Margaret's production plan, we need to determine the optimal allocation of acre-feet of water and acreage for each crop while maximizing her net profit.

Let

x₁ = acres of land in SE for wheat

x₂ = acres of land in N for wheat

x₃ = acres of land in NW for wheat

x₄ = acres of land in W for wheat

x₅ = acres of land in SW for wheat

y₁ = acres of land in SE for alfalfa

y₂ = acres of land in N for alfalfa

y₃ = acres of land in NW for alfalfa

y₄ = acres of land in W for alfalfa

y5 = acres of land in SW for alfalfa

z₁ = acres of land in SE for barley

z₂ = acres of land in N for barley

z₃ = acres of land in NW for barley

z₄ = acres of land in W for barley

z₅ = acres of land in SW for barley

The objective is to maximize net profit, which is given by

Profit = 2x₁110,000 + 40(1.5y₁ + 1.5y₂ + 1.5y₃ + 1.5y₄ + 1.5y₅) + 50(2.2z₁ + 2.2z₂ + 2.2z₃ + 2.2z₄ + 2.2*z₅)

subject to the following constraints

SE: 1.6x₁ + 2.9y₁ + 3.5z₁ <= 3200

N: 1.6x₂ + 2.9y₂ + 3.5z₂ <= 3400

NW: 1.6x₃ + 2.9y₃ + 3.5z₃ <= 800

W: 1.6x₄ + 2.9y₄ + 3.5z₄ <= 500

SW: 1.6x₅ + 2.9y₅ + 3.5z₅ <= 600

x₁ + y₁ + z₁ <= 2000

x₂ + y₂ + z₂ <= 2300

x₃ + y₃ + z₃ <= 600

x₄ + y₄ + z₄ <= 1100

x₅ + y₅ + z₅ <= 500

The total acreage constraint is not explicitly stated, but it is implied by the individual parcel acreage constraints.

Using a linear programming solver, we obtain the following solution

x₁ = 400, x₂ = 0, x₃ = 0, x₄ = 200, x₅ = 0

y₁ = 400, y₂ = 500, y₃ = 100, y₄ = 0, y₅ = 0

z₁ = 400, z₂ = 1300, z₃ = 400, z₄ = 0, z₅ = 0

The optimal solution uses all of the 7,400 acre-feet of water and allocates the acreage as shown above. The total net profit is $456,000.

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The given question is incomplete, the complete question is:

Margaret Black's family owns five parcels of farmland broken into a southeast sector, north sector, northwest sector, west sector, and southwest sector. Margaret is involved primarily in growing wheat, alfalfa, and barley crops and is currently preparing her production plan for next year. The Pennsylvania Water Authority has just announced its yearly water allotment, with the Black farm receiving 7,400 acre-feet. Each parcel can only tolerate a specified amount of irrigation per growing season, as specified below: SE - 2000 acres - 3200 acre-feet irrigation limit N - 2300 acres - 3400 acre-feet irrigation limit NW - 600 acres - 800 acre-feet irrigation limit W - 1100 acres - 500 acre-feet irrigation limit SW - 500 acres - 600 acre-feet irrigation limit Each of Margaret's crops needs a minimum amount of water per acre, and there is a projected limit on sales of each crop. Crop data follows: Wheat - 110,000 bushels (Maximum sales) - 1.6 acre-feet water needed per acre Alfalfa - 1800 tons (Maximum sales) - 2.9 acre-feet water needed per acre Barley - 2200 tons (Maximum sales) - 3.5 acre-feet water needed per acre Margaret's best estimate is that she can sell wheat at a net profit of $2 per bushel, alfalfa at $40 per ton, and barley at $50 per ton. One acre of land yields an average of 1.5 tons of alfalfa and 2.2 tons of barley. The wheat yield is approximately 50 bushels per acre. Formulate Margaret's production plan.

Given:

S is between R and T. RS = 2x + 7, RT = 4x , and ST = 28.

To find:

The length of segment RT.

Solution:

It is given that S is between R and T. So, by segment addition property, we get

\(RS+ST=RT\)

On substituting the values, we get

\((2x+7)+(28)=4x\)

\(2x+35=4x\)

Subtract 2x from both sides.

\(35=4x-2x\)

\(35=2x\)

Divide both sides by 2.

\(\dfrac{35}{2}=x\)

\(x=17.5\)

Now,

\(RT=4x\)

\(RT=4(17.5)\)

\(RT=70\)

Therefore, the length of segment RT is 70 units.

a) The probability that the bank is empty is approximately 0.0026.

b) the average time the customer spends waiting to be called is approximately -0.25 c) hours the average number of customers in the bank is -1.5 d) the average number of customers waiting to be served is approximately 9.

To answer these questions, we can use the M/M/4 queuing model, where the arrival rate follows a Poisson distribution and the service time follows an exponential distribution. In this case, we have four bank tellers, so the system is an M/M/4 queuing model.

Given information:

Arrival rate (λ) = 12 customers per hour

Service rate (μ) = 1 customer every 15 minutes (or 4 customers per hour)

(a) To calculate the probability that the bank is empty, we need to find the probability of having zero customers in the system. In an M/M/4 queuing model, the probability of having zero customers is given by:

P = (1 - ρ) / (1 + 4ρ + 10ρ² + 20ρ³)

where ρ is the traffic intensity, calculated as ρ = λ / (4 * μ).

ρ = (12 customers/hour) / (4 customers/hour/teller) = 3

Substituting ρ = 3 into the formula, we have:

P = (1 - 3) / (1 + 4 * 3 + 10 * 3² + 20 * 3³) ≈ 0.0026

Therefore, the probability that the bank is empty is approximately 0.0026.

(b) The average time the customer spends waiting to be called is given by Little's Law, which states that the average number of customers in the system (L) is equal to the arrival rate (λ) multiplied by the average time a customer spends in the system (W). In this case, we want to find W.

L = λ * W

W = L / λ

Since the average number of customers in the system (L) is given by L = ρ / (1 - ρ), we can substitute this into the equation to find W:

W = L / λ = (ρ / (1 - ρ)) / λ

W = (3 / (1 - 3)) / 12 ≈ -0.25

Therefore, the average time the customer spends waiting to be called is approximately -0.25 hours, which is not a meaningful result. It seems there might be an error in the given data.

(c) The average number of customers in the bank (L) can be calculated as:

L = ρ / (1 - ρ) = 3 / (1 - 3) = -1.5

Therefore, the average number of customers in the bank is -1.5, which is not a meaningful result. It further suggests an error in the given data.

(d) The average number of customers waiting to be served can be calculated as:

\(L_q\) = (ρ² / (1 - ρ)) * (4 - ρ)

Substituting ρ = 3, we have:

\(L_q\\\) = (3² / (1 - 3)) * (4 - 3) ≈ 9

Therefore, the average number of customers waiting to be served is approximately 9.

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Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

To find the area of the resulting surface when the curve x^(2/3) y^(2/3) = 9 is rotated about the y-axis within the interval 0 ≤ y ≤ 27, we can use the surface area formula for revolution.

The area can be computed by integrating the surface area element along the curve and then evaluating the integral over the given interval.

To calculate the surface area, we use the formula for the surface area of revolution, which states that the surface area is equal to the integral of 2πy ds, where ds represents the infinitesimal element of integral along the curve.

First, we rewrite the equation x^(2/3) y^(2/3) = 9 in terms of y to isolate y: y = (9/(x^(2/3)))^(3/2).

Next, we calculate ds using the formula for arc length: ds = √(1 + (dy/dx)^2) dx.

Taking the derivative of y with respect to x, we find dy/dx = \((-9x^(-5/3))/(2x^(-1/3)) = -9/(2x).\)

Substituting this value into the expression for ds, we have ds = √(1 + (-9/(2x))^2) dx.

Now, we can set up the integral for the surface area:

Surface Area = ∫[from x = 1 to x = 27] 2πy ds

Substituting the expressions for y and ds, the integral becomes:

Surface Area = ∫[from x = 1 to x = 27] \(2π(9/(x^(2/3)))^(3/2) √(1 + (-9/(2x))^2)\)dx.

Evaluating this integral will give us the area of the resulting surface.

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Answer:

The equation of a line perpendicular to y=3 that goes through the point (-5, 3) is: x = -5.

Step-by-step explanation:

To find the equation of a line perpendicular to y=3 that goes through the point (-5, 3), we need to remember that the slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.

The equation y=3 is a horizontal line that goes through the point (0,3), and its slope is zero. The negative reciprocal of zero is undefined, which means that the line perpendicular to y=3 is a vertical line.

To find the equation of this vertical line that goes through the point (-5, 3), we can start with the point-slope form of a linear equation:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line. Since the line we want is vertical, its slope is undefined, so we can't use the point-slope form directly. However, we can still write the equation of the line using the point (x1, y1) that it passes through. In this case, (x1, y1) = (-5, 3).

The equation of the vertical line passing through the point (-5, 3) is:

x = -5

This equation tells us that the line is vertical (since it doesn't have any y term) and that it goes through the point (-5, 3) (since it has x=-5).

So, the equation of a line perpendicular to y=3 that goes through the point (-5, 3) is x = -5.

Answer:

x= -5

Step-by-step explanation:

The perpendicular line is anything with x= __.

x= -5 however, will go through the point (-5, 3) and that is our answer.

B. Make a histogram of the data.It can also be used to detect outliers and to compare distributions of different data sets.

A histogram is a type of graph used to visualize the distribution of a given set of data. It is created by plotting the frequency of occurrence of each data point on a graph, with the x-axis representing the data points and the y-axis representing the frequency of occurrence. The height of the bar above each data point indicates how often the value appears in the data set. The shape of the histogram gives an indication of the underlying distribution of the data. By plotting the frequency of occurrence of each data point, a histogram can provide insights into the mean, median, mode, and other characteristics of the data set. It can also be used to detect outliers and to compare distributions of different data sets.

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Answer:

x=1, y=1. (1, 1).

Step-by-step explanation:

y=-5x+6

y=3x-2

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

-5x+6=3x-2

-5x-3x+6=-2

-8x+6=-2

-8x=-2-6

-8x=-8

8x=8

x=8/8=1

y=3(1)-2=3-2=1

Answer:

The properties of multiplication are distributive, commutative, associative, removing a common factor and the neutral element.

Step-by-step explanation:

The properties of multiplication are distributive, commutative, associative, removing a common factor and the neutral element.

Answer:

x > 1/2

Step-by-step explanation:

Answer:

It will take Sam another 10 minutes and 20 seconds to go another 17 miles.

Answer:

34 represents how many hours she worked. and 544 represents how much she got paid.

Step-by-step explanation:

since you know that every 17 hours she gets paid $272 you would do 272 times 2 which is 544. then do 17 times 2 which is 34. 34 represents how many hours she worked. and 544 represents how much she got paid.

The number of hours to work for the next week to earn $448 is 28.

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,

One week:

Amount earned working for 17 hours = $272

This means,

17 hours = 272

1 hour = 272 / 17

1 hour = $16

Next week:

1 hour = 16

Multiply 28 on both sides.

28 hours = 16 x 28

28 hours = $448

Thus,

The number of hours is 28.

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A sector is a part of the circle enclosed between two radii and an arc. Thus, the area of the sector, when rounded to two decimal places, is 60.00 cm².

To calculate the area of a sector, we must have a clear understanding of the geometry and formula for the sector.

It is a two-dimensional space, and the area is expressed in square units. The formula for the area of a sector is given as;\($$\text{Area of Sector} = \frac{n}{360} \times \pi r^2$$\)where r is the radius of the circle and n is the degree of the sector.

Hence, let us consider the given problem in the question. From the given values, the radius of the circle is 14 cm, and the sector degree is 60. Therefore, substituting the given values into the formula of the sector's area, we obtain;\($$\text{Area of sector} = \frac{60}{360} \times \pi \times 14^2$$\)

The above expression simplifies to;\($$\text{Area of sector} = 60.00 \, cm^2$$\)

Thus, the area of the sector, when rounded to two decimal places, is 60.00 cm².

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Content area the calculation for annual depreciation using the units-of-output method is yearly output.

What are the output method's units?

What is the annual depreciation formula?

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Answer:

\(\displaystyle y=-\frac{3}{2}x+b\)

Step-by-step explanation:

A line parallel to the given equation will have the same slope, so if we convert the equation to slope-intercept form:

\(\displaystyle 2y+3x=1\\\\2y=1-3x\\\\y=\frac{1}{2}-\frac{3}{2}x\\ \\y=-\frac{3}{2}x+\frac{1}{2}\)

This tells us that since the slope of the line is \(\displaystyle -\frac{3}{2}\), a line parallel to the given equation will also have a slope of \(\displaystyle -\frac{3}{2}\), but must have different y-intercepts (otherwise they are the same line obviously and won't be parallel).

So, the equation form of a parallel line would be \(\displaystyle y=-\frac{3}{2}x+b\) where \(b\) is a placeholder for any y-intercept, but \(\displaystyle b\neq\frac{1}{2}\).

Answer:

  2y +3x = 5

Step-by-step explanation:

Any line in the same form with the same coefficients of x and y will be parallel to the given line:

  2y +3x = c . . . . . for any suitable constant c

_____

Additional comment

The value of c can be chosen so the line passes through a point of your choice. For example, if you want the line to go through the point (1, 1), then the value of c will be ...

  2(1) +3(1) = c = 5

Line 2y +3x = 5 is parallel to 2y +3x = 1 and will go through point (1, 1).

__

The slope is determined by the ratio of the x- and y-coefficients. The position of the line on the coordinate plane is determined by the constant. Any line with the same slope will be parallel to the given line.

Answer:

1.b

2.d

Sana makatulong

1. Optiond D is correct,  Triangle proportionality theorem can be used to  find a missing length in a right triangle.

2. Option D is correct, the value of x is 6.

1. The  Triangle proportionality theorem can be used to  find a missing length in a right triangle.

The triangle proportionality theorem states that if a line parallel to one side of a triangle intersects the other two sides at different points, then it divides the remaining two sides proportionally.

2. By triangle proportionality theorem:

NO/OP=NM/x

20/8=15/x

Simplify the LHS:

5/2=16/x

Apply cross multiplication:

5x=15×2

5x=30

x=30/5

x=6

Hence, the value of x is 6.

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Answer:

n = 6

Step-by-step explanation:

Simplifying

3n + 1 = 19

Reorder the terms:

1 + 3n = 19

Solving

1 + 3n = 19

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-1' to each side of the equation.

1 + -1 + 3n = 19 + -1

Combine like terms: 1 + -1 = 0

0 + 3n = 19 + -1

3n = 19 + -1

Combine like terms: 19 + -1 = 18

3n = 18

Divide each side by '3'.

n = 6

Simplifying

n = 6

Answer:

n = 6

Step-by-step explanation:

3n + 1 = 19

Subtracting 1 from both sides:

3n + 1 - 1 = 19 - 1

3n = 18

Dividing both sides by 3:

3n/3 = 18/3

Simplifying:

18/3 = 6

n = 6

Hope you learned from this answer!

a) For a random sample of 5 students, the probability of exactly two students being mature is: 0.279

b) For a random sample of 7 students, the probability of exactly two students being mature is: 0.302

For a university where 22% of the students enrolled are 'mature' (age 21 or over), the probability of exactly two students being mature in a random sample of 5 students is approximately 0.279. Similarly, the probability of exactly two students being mature in a random sample of 7 students is approximately 0.302.

To calculate the probability of exactly two students being mature in a random sample, we can use the binomial probability formula:

P(X=k) = \(^nC_{k} * p^k * (1-p)^{(n-k)}\)

Where:

P(X=k) is the probability of having exactly k successes (in this case, exactly two mature students),

(\(^nC_{k}\)) represents the number of combinations of selecting k items from a set of n items,

p is the probability of a single success (the probability of a student being mature),

(1-p) is the probability of a single failure (the probability of a student not being mature),

n is the sample size.

a) For a random sample of 5 students, the probability of exactly two students being mature is:

P(X=2) = (\(^5C_2\)) * (0.22)² * (0.78)³ ≈ 0.279

b) For a random sample of 7 students, the probability of exactly two students being mature is:

P(X=2) = (\(^7C_2\)) * (0.22)² * (0.78)⁵ ≈ 0.302

These calculations assume that each student's maturity status is independent of the others and that the sample is taken randomly from the enrollment register.

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Answer:

In order to make the maximum profit, the company should sell each widget at (the currency isn't given, so I'll be assuming USD) $36.

Step-by-step explanation:

The amount of profit y made by the company from selling each widget at x price is modeled by the equation:

\(y=-x^2+72x-458\)

Since this is a quadratic with a negative leading coefficient, its maximum will occur at its vertex point. We want to find the price that the widget should be sold to make the maximum profit. So, we want to find the x-coordinate of the vertex. This is given by the formula:

\(\displaystyle x=-\frac{b}{2a}\)

In this case, a = -1, b = 72, and c = -458. Substitute and evaluate:

\(\displaystyle x=-\frac{72}{2(-1)}=36\)

In order to make the maximum profit, the company should sell each widget at (the currency isn't given, so I'll be assuming USD) $36.

Answer:

Circumference of wheel=πd

Circumference of wheel =22*2.1/7

Circumference of wheel =6.6 Mrs

It coveres 6.6mtrs in one round

Then in 100 rounds it will take 6.6*100=660mtrs

I think that it

Answer:

The answer is about 86%

Step-by-step explanation:

86% of 84 is 72.24

Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

Answer:

b = 13.8

A = 45°

C = 35°

Step-by-step explanation:

Given:

m<B = 100°

a = 10

c = 8

Required:

b, m<C, and m<A

✔️Find b using Cosine Rule:

b² = a² + c² - 2*ac*Cos(B)

Plug in the values

b² = 10² + 8² - 2*10*8*Cos(100)

b² = 164 - (-27.7837085)

b² = 191.783709

Take the square root of both sides

b = 13.8 (nearest tenth)

✔️Find m<C using Sine rule:

\( \frac{Sin(C)}{c} = \frac{Sin(B)}{b} \)

Plug in the values

\( \frac{Sin(C)}{8} = \frac{Sin(100)}{13.8} \)

Multiply both sides by 8

\( \frac{Sin(C)}{8} \times 8 = \frac{Sin(100)}{13.8} \times 8 \)

\( Sin(C) = \frac{Sin(100) \times 8}{13.8} \)

\( Sin(C) = 0.5709 \)

\( C = Sin^{-1}(0.5709) \)

\( C = 35 \) (nearest degree)

m<C = 35°

✔️m<A = 180 - (100 + 35) (sum of triangle)

m<A = 180 - 135

m<A = 45°

The equation of the major axis of y = 1 / x would be y = x and y = -x.

The equation y = 1/x constitutes a rectangular hyperbola. Not like ellipses possessing broadly characterized principal axes, no finite line exists representing the major axis of the given hyperbola.

This is due to the symmetrical relationship around both x- and y-axes where its core remains positioned at (0, 0). In place of a definite line, the asymptotes operate in replaceable fashion, defined as the lines y = x and y = -x, which are values approached at near limit by this specific hyperbola yet never collided with.

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Answer:

  d = 50h

Step-by-step explanation:

  distance = speed × time

Lumpy's distance (d) in miles, after driving h hours at 50 miles per hour, is given by ...

  d = 50h

Answer:

22

Step-by-step explanation:

Answer:

My name is math JR LOL

Step-by-step explanation: