you want to put a fence around your vegtable garden. the garden has a square shape. you want the fence to be 1 year away from each side of thgarden. you used 56 yards of fencing. what are the dimensions of your gardenm

The shape and scale parameters have values of 4 and 2, respectively.

For Gamma distribution denoted by Gamma(k,θ) here k is the shape parameter and θ is the scale parameter.

What is shape parameter ?

A shape parameter affects the general shape of a distribution, as the name implies; they are a family of distributions with various shapes. The parameters are frequently calculated from recent data or occasionally extrapolated from historical statistical data.

What is scale parameter ?

Graphs have meaning thanks to scale settings. The scale in a typical normal model is equal to the standard deviation,. Even though the area under the graph is 1, you can't take any information from it without a scale. A standard normal distribution without any scaling parameters is shown in the top graph. 

The mean is given by the formula

Mean = kθ

And the variance is,

Variance = kθ^2

So now according to the given information we have,

θ=8

kθ^2=16

So dividing the two equations,

θ = 16/8=2

Using this in first equation,

kθ = 8

2k=8

k=4

So,

k=shape parameter=4

θ=scale parameter=2

Hence, The shape and scale parameters have values of 4 and 2, respectively.

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Based on the analysis, only statement 2 (The average length of the line will be 0.55 customers) is true.

In this scenario, we can analyze the system using queuing theory. The system follows an M/M/1 queue, where arrivals and service times are exponentially distributed.

To determine the correctness of the given statements, we can calculate the steady-state performance measures of the system.

The line will be empty 41.5% of the time:

To calculate the probability of an empty system, we use the formula: P(0) = 1 - ρ, where ρ is the traffic intensity.

The traffic intensity ρ is given by λ/μ, where λ is the arrival rate and μ is the service rate. In this case, ρ = (5/8) = 0.625. Therefore, the probability of an empty system is P(0) = 1 - 0.625 = 0.375 or 37.5%, which contradicts the given statement. So, this statement is false.

The average length of the line will be 0.55 customers:

The average number of customers in the system can be calculated using Little's Law: L = λW, where L is the average number of customers, λ is the arrival rate, and W is the average time spent in the system. The arrival rate λ = 5 customers per hour. To calculate W, we use the formula: W = 1/(μ - λ), where μ is the service rate. In this case, μ = 8 customers per hour. Plugging in the values, W = 1/(8 - 5) = 1/3 hours. Therefore, L = (5/3) * (1/3) = 5/9 ≈ 0.556 customers. This value is close to 0.55, so this statement is true.

The average time spent waiting in line will be 7.005 minutes:

The average time spent waiting in line can be calculated using the formula: Wq = Lq/λ, where Wq is the average time spent waiting in the queue and Lq is the average number of customers in the queue.

We already calculated Lq as 5/9 customers. Plugging in the values, Wq = (5/9) / 5 = 1/9 hours. Converting to minutes, Wq = (1/9) * 60 = 6.67 minutes. This value is different from 7.005 minutes, so this statement is false.

4. 5.7% of the time customers will be blocked from entering the line:

To calculate the probability of blocking, we need to find the probability that all four spaces are occupied. The probability of all spaces being occupied is given by P(block) = ρ^4, where ρ is the traffic intensity (0.625). Plugging in the values, P(block) = 0.625^4 ≈ 0.0977 or 9.77%. This value is different from 5.7%, so this statement is false.

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The volume of the tool box is 2,052 cubic inches.

To find the volume of a rectangular solid, we need to multiply its length, width, and height. In this case, the length is 19 inches, the width is 12 inches, and the height is 9 inches. So, we can use the formula:

Volume = length x width x height

Volume = 19 in. x 12 in. x 9 in.

Volume = 2,052 cubic inches

Therefore, the volume of the tool box is 2,052 cubic inches.

Conclusion: The tool box has a volume of 2,052 cubic inches, which means it can hold that much space or stuff inside it.
The volume of the toolbox is 2052 cubic inches.


To calculate the volume of a rectangular solid, you multiply the length, width, and height of the solid. In this case, the dimensions of the toolbox are 19 inches (length), 12 inches (width), and 9 inches (height).

Step 1: Multiply the length, width, and height:
Volume = Length × Width × Height

Step 2: Substitute the given dimensions:
Volume = 19 inches × 12 inches × 9 inches

Step 3: Perform the multiplication:
Volume = 2052 cubic inches

The volume of the rectangular solid toolbox with sides of 19 inches, 12 inches, and 9 inches is 2052 cubic inches.

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The value of x from the triangle inscribed in the circle which is the unknown angle is 22°

For a given triangle inscribed in a circle, it should be noted that the angle that is inscribed along the diameter of the circle will be regarded as the right angle.

This means that the angle facing the diameter line (C), i.e angle c is 90 degrees. We all know that the sum of angles in a triangle is 180 degrees. Therefore, to find the third unknown angle x, we have:

x  + 68° + 90° = 180°

x + 158° = 180°

x = 180° - 158°

x = 22°

Therefore, we can conclude that the value of x which is the unknown angle is 22°

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Answer: 96 servings.

Step-by-step explanation:
There are 16 cups in 1 gallon, so 3 gallons of punch would be equal to:

3 gallons x 16 cups/gallon = 48 cups

If each serving size is 1/2 cup, then the number of servings in 3 gallons of punch would be:

48 cups / (1/2 cup/serving) = 96 servings

Therefore, 3 gallons of punch would provide 96 servings, assuming each serving size is 1/2 cup.

Answer: 7x + 6

Step-by-step explanation:

Combine like terms:

(2x + 5x) + (16 - 10)

Answer:

soln

2x + 16 + 5x – 10

8(x+2) + 5(x + 2)

8+2 (x+2)

10 (x + 2 )

The image of (5,−4) after a dilation by a scale factor of 4 centered at the origin is (20,−16)

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

Point = (5,−4)

Scale factor of 4 centered at the origin

The image after a dilation centered at the origin is

Image = Point  * Scale factor

Substitute the known values in the above equation, so, we have the following representation

image = (5,−4) * 4

Evaluate

image = (20,−16)

Hence, the image after a dilation centered at the origin is (20,−16)

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Answer: 28 inches

Step-by-step explanation:

Since their areas are the same their perimeter would be the same too. So plug 8 in for the length, for the formula of perimeter( 2(L+W) ) which would be 2(8+6) and you get 28

Answer: \(\displaystyle 2x^4 + 9x^3-8x^2+9x -13\)

Step-by-step explanation:

     Given:

\(\displaystyle (2x^4 + 9x^3 -8)-(8x^2-9x+5)\)

     Subtract the second term:

\(\displaystyle (2x^4 + 9x^3 -8)-8x^2+9x-5\)

     Reorder by the power's degree:

\(\displaystyle 2x^4 + 9x^3-8x^2+9x -8-5\)

     Combine like terms:

\(\displaystyle 2x^4 + 9x^3-8x^2+9x -13\)

Answer:

\(g=\frac{9}{2}, \\x=-6\)

Step-by-step explanation:

Answer:

The Vet saw most of the Cats (2/4 or 1/2)

Step-by-step explanation:

We know some information...

2/8 = Rabbits, 1/2 = Cats, 1/4 = Dogs.

Total there is 1 Whole of Animals, or 4/4.

Let's make their denominators the same to understand easier.

2/8 is nothing but 1/4

And 1/2 is nothing but 2/4

So the Values are 1/4(rabbits), 1/4 Dogs, and 2/4 Cats.

We know that 1/4 (Rabbits) and another 1/4(Dogs) is the same value,

So 1/4 (Rabbit or Dog) < 2/4 (Cat)

This means the Vet Saw most of the Cats or more cats than any other animal

Answer:0.41

Step-by-step explanation:

When computing the area of a circle, the mathematical constant pi () is required. Pi is the circumference-to-diameter ratio of a circle and is approximately equal to 3.14159.

The area of a circle is calculated by multiplying pi by the radius squared (r2). To estimate the area of a circle, utilize pi in the calculation since it is a vital aspect of the relationship between the circumference and diameter of a circle.

Pi is not required when determining the area of a square, rectangle, or cube since the formulas for these shapes are different.

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The question is -

The mathematical constant pi is needed when calculating the area of a _.

a. circle

b. square

c. rectangle

d. cube

Answer:

x = 19°

Step-by-step explanation:

Given that < (6x + 1)° + < (3x + 8)° are supplementary angles whose sum = 180°

6x + 1 + 3x + 8 = 180°

Add common terms:

9x + 9 = 180°

Subtract 9 from both sides:

9x + 9 - 9 = 180° - 9

9x = 171°

Divide both sides by 9 to solve for x:

\(\frac{9x}{9} = \frac{171}{9}\)

x = 19°

Answer:

Let's start by rearranging this polynomial.

x^3 - 2x^2 + x - 2

x^3 + x - 2x^2 - 2

Now, factor out the common terms in the first two terms, and the second t wo terms. So we have: x(x^2 + 1) - 2(x^2 +1)

Apply the distributive property, and you have: (x-2)(x^2+1), which can't be factored further.

There's definitely something wrong with the answer choices here, or the problem itself.

Hopefully this helps!

The complete factorization of the polynomial is,

⇒ (x + i) (x - i) (x - 2)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The polynomial is,

⇒ x³ - 2x² + x - 2

Now, We can factor the polynomials as;

The polynomial is,

⇒ x³ - 2x² + x - 2

⇒ x² (x - 2) + 1 (x - 2)

⇒ (x² + 1) (x - 2)

⇒ (x + i) (x - i) (x - 2)

Therefore, The complete factorization of the polynomial is,

⇒ (x + i) (x - i) (x - 2)

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To find the probability that exactly k out of the next n months have sales greater than 100, you can use the binomial probability formula:

P(k successes in n trials) = (n choose k) * p^k * (1-p)^(n-k)

where p is the probability of success in a single trial, and n choose k is the binomial coefficient, which is equal to n!/(k! * (n-k)!).

To use this formula, you first need to determine the values of p and n. The value of p is the probability that a single month's sales will be greater than 100. To find this probability, you need to know the mean and standard deviation of the normal distribution representing the monthly sales.

Once you have the values of p and n, you can plug them into the formula and compute the probability of exactly k successes in n trials.

For example, suppose the mean monthly sales are 80 and the standard deviation is 20. This means that the normal distribution representing the monthly sales has a mean of 80 and a standard deviation of 20. To find the probability that a single month's sales will be greater than 100, you can use the standard normal distribution table or a calculator to find the area under the curve of the standard normal distribution that is greater than 100. Suppose the result is 0.15. This means that the probability of a single month's sales being greater than 100 is 0.15.

Now suppose you want to find the probability that exactly 2 out of the next 3 months will have sales greater than 100. In this case, p is 0.15, k is 2, and n is 3. Plugging these values into the formula gives:

P(2 successes in 3 trials) = (3 choose 2) * 0.15^2 * (1-0.15)^(3-2)

= 3 * 0.15^2 * 0.85

= 0.3483

This is the probability that exactly 2 out of the next 3 months will have sales greater than 100.

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15^2 = x^2 + 11^2

225 = x^2 + 121

Subtract both sides 121

225 - 121 = x^2 + 121 - 121

104 = x^2

x = √104

x = √4 × 26

x = √4 × √26

x = 2 × √26

x = 2 √26

If the width of the swimming pool is 90 feet and length is 30 feet, then the total tiles required to cover the swimming pool are:Each tile is square with 1 foot width and length.

Area of 1 tile = 1 × 1 = 1 square feet

Total number of tiles required = Area of pool / Area of 1 tile = 90 × 30 / 1 = 2700 tiles

Hence, 2700 tiles are required to surround the pool.

The diameter of a $1 coin is 26.5 mm. The formula for the area of the circle is:Area of circle = πr², where r is the radius of the circle.

So, we need to find the radius of the coin first:Diameter = 26.5 mm

So, the radius = Diameter/2= 26.5/2 = 13.25 mm

Now, we can find the area of one side of the coin by substituting the value of the radius in the formula of area of circle.

Area of one side of the coin = πr²= 3.14 × 13.25²≈ 553.73 sq.mm

Therefore, the area of one side of the coin is approximately 553.73 sq.mm.

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Answer:The answer is C

Step-by-step explanation:

The values of h(t) when t=4 and 5 should be 0

Answer: c

Step-by-step explanation:

Answer:

The number of large size candles sells are 12 and the number of small size candles are 5 .

Step-by-step explanation:

As given Sia sells large candles for $3 each and small candles for $2 each.She sold 17 candles for $46.00.Let us assume that the large size candle sells are x .Let us assume that the small size candle sells are y.             Equation becomes

x + y = 17

3x + 2y = 46

Multiply x + y = 17 by 3 and subtracted from 3x + 2y = 46 .

3x - 3x + 2y - 3y = 46 - 51

-y = - 5

y = 5

Put in the equation x + y = 17 .

x + 5 = 17

x = 17 - 5

x = 12

Therefore the number of large size candles sells are 12 and the number of small size candles are 5

Answer:

i would help but i can't understand that im sry

Step-by-step explanation:

3. /9.49 thanks

Answer:

4. search it you can find it

Answer:

1= 4/7 of the fruit are apples 2 = the ratio of apples to oranges is 4 to 3 3= the ratio of oranges to apples 3 to 4

Answer:

-1 is the answer god luck

Answer:

x(x+1)(x−1)

Step-by-step explanation:

Answer: HCF of 30,36 and 84 is 6

so, by cutting equal lenghts of wire by 6 metres we get 30/6,36/6,84/6=5,6 and 14.

the least number of pieces obtained is 25 by adding 5, 6 and 14.

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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The total current is given by ITotal = 0.2605 - j0.7635A2.

Calculation of total current:

According to the given circuit, resistance of the circuit = R = 100 Ω

Inductance of the circuit = L = 500 mH = 0.5 H

Capacitance of the circuit = C = 3.00 μF = 3.00 x 10^-6 F

Frequency of the circuit = f = 65.0 Hz

Voltage of the circuit = V = 120 V

Reactance of the circuit can be calculated as follows:

Xl = 2πfL = 2 x 3.14 x 65.0 x 0.5 = 204.2 Ω

Capacitive reactance can be calculated as:

Xc = 1/(2πfC) = 1/(2 x 3.14 x 65 x 3.00 x 10^-6) = 498.9 Ω

Total impedance can be calculated as:

Z = R + j(Xl - Xc)Z = R + j(204.2 - 498.9)

Z = 100 - j294.7

The total current is given by the ratio of the voltage and the total impedance:

ITotal = V/ZITotal = 120/(100 - j294.7)

ITotal = 0.2605 - j0.7635A2.

Total current obtained was ITotal = 0.2605 - j0.7635 A

Hence the results are identical.

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