A pressure vessel has a design pressure of 50 bar. However the safety case for the chemical plant on which it is to be used requires that the pressure vessels have a 95% probability of surviving a pressure of 70 bar. Computer codes have generated an estimate of only 0.80 for the probability that any such pressure vessel, picked at random, will survive at 70 bar. However, they have also calculated that of the 20% of the pressure vessels that will not survive a pressure of 70 bar, 40% will fail under a pressure of 58 bar or less, while 80% will fail under a pressure of 65 bar or less. It is decided that an over-pressure test needs to be used to give reassurance on the behaviour of this particular pressure vessel. This test may be carried out at either 58 bar or 65 bar. The lower pressure test is considerably less difficult and cheaper to administer. (i) Suppose that you are brought in as a consultant. By calculating the probability of the pressure vessel being able to support the 70 bar maximum pressure if the over-pressure test is passed, advise on which over-pressure test should be administered.

First find height using Pythagorean theorem.

\(h^2+4^2=13^2\implies h=\sqrt{153}\approx12.37\).

Then use cone surface area formula and compute the result:

\(A=\pi r(r+\sqrt{h^2+r^2})\approx\boxed{68\pi}\mathrm{units^2}\).

Hope this helps.

Answer:

Step-by-step explanation:

period

Answer:

The whole numbers are 0 and 79.

Step-by-step explanation:

The numbers provided are as follows:

\(-2\frac{5}{6},\ -54,\ -4,\ -57,\ -89,\ 79,\ \frac{6}{9},\ \\\\-19\frac{2}{3},\ \frac{2}{4},\ 0,\ \frac{2}{7},\ -3,\ -2, -7,\ -8,\ \\\\\frac{1}{8},\ -\frac{4}{8},\ 1\frac{3}{8},\ -\frac{7}{8}\)

Whole numbers are a set of natural positive numbers and 0. This set basically consists of counting discrete numbers.

Such as: 0, 1, 2, 3, 4, 5....

From the provided set of numbers the whole numbers are:

S = {79 and 0}

Thus, the whole numbers are 0 and 79.

Answer:

it's B and C

Step-by-step explanation:

The answer closest to the margin of error is option b: 4.2%.

To determine the margin of error at the 95% confidence level for the proportion of likely voters who prefer the incumbent candidate, we can use the formula:

Margin of Error = (Z * √(p*(1-p))/√n)

Where:

Z is the Z-score corresponding to the desired confidence level (95% corresponds to approximately 1.96)

p is the proportion of voters who prefer the incumbent candidate (42% or 0.42)

n is the sample size (350)

Calculating the margin of error:

Margin of Error = (1.96 * √(0.42*(1-0.42))/√350)

Using a calculator, the closest value to the margin of error is approximately 4.2%. Therefore, the answer closest to the margin of error is option b: 4.2%.

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Answer:

£ 87.00

Step-by-step explanation:

52.20*2/3=52.20/3*2=17.4*2=34.8

52.20+34.80=87.00

The solutions for the equation \(y=-4(x-2)^2+6\) are as follows \(x = 2 + \sqrt{(6 - Y) / 4}\) or \(x = 2 - \sqrt{(6 - Y) / 4}\).

The given equation is in standard form for a quadratic equation, where the coefficient of \(x^2\) is negative. This means the graph of the equation is a downward-opening parabola, and the vertex of the parabola is (2, 6).

To solve the equation, we can first isolate the variable Y on one side:

\(Y - 6 = -4(x - 2)^2\)

Then we can divide both sides by -4:

\((Y - 6) / -4 = (x - 2)^2\)

Next, we can take the square root of both sides:

\(\sqrt{[(Y - 6) / -4] }= x - 2\)

\(\pm \sqrt{(Y - 6) / -4}= x - 2\)

So the solutions are:

\(x = 2 + \sqrt{(6 - Y) / 4}\) or \(x = 2 - \sqrt{(6 - Y) / 4}\)

These equations give the x-coordinates of the points on the graph of the equation for a given value of Y.

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Answers in bold

\(\begin{array}{|c|c|} \cline{1-2}\text{number of rolls} & \text{number of people}\\\cline{1-2}1 & \boldsymbol{0.5}\\\cline{1-2}6 &3\\\cline{1-2}10 & \boldsymbol{5}\\\cline{1-2}16 & \boldsymbol{8}\\\cline{1-2}25 & \boldsymbol{12.5}\\\cline{1-2}n & \boldsymbol{0.5n}\\\cline{1-2}\end{array}\)

========================================================

Explanation:

The given table looks like this

\(\begin{array}{|c|c|} \cline{1-2}\text{number of rolls} & \text{number of people}\\\cline{1-2}1 & \\\cline{1-2}6 & 3\\\cline{1-2}10 & \\\cline{1-2}16 & \\\cline{1-2}25 & \\\cline{1-2}n & \\\cline{1-2}\end{array}\)

Focus on the row that has two values in it.

x = number of rolls = 6

y = number of people 3

k = constant of proportionality

y = kx

k = y/x = 3/6 = 0.5

The constant of proportionality is k = 0.5 which gives the direct variation equation of y = 0.5x

If x = 1, then y = 0.5*1 = 0.5 meaning that 1 roll feeds 0.5 people. This means we need 2 rolls to feed one person.

If x = 10, then y = 0.5x = 0.5*10 = 5 people can be fed with those 10 rolls. This process is continued until we finish filling out the table.

Answer:  \(A^{2} + B^{2}\) correct answer.

Step-by-step explanation:

What is Pythagorean Theorem?

Image result for Pythagorean theorem

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation.

                               \(A^{2} + B^{2} + C^{2}\)

The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem can be expressed as, c2 = a2 + b2; where 'c' is the hypotenuse and 'a' and 'b' are the two legs of the triangle.

So, We can write,

Consider the triangle given above:

Where “a” is the perpendicular,

“b” is the base,

“c” is the hypotenuse.

According to the definition, the Pythagoras Theorem formula is given as:

                    \(Hypotenuse^{2}\) = \(Perpendicular^{2}\) + \(Base^{2}\)

                           \(C^{2} = A^{2} + B^{2}\)

Hence,

                              \(A^{2} + B^{2}\) correct answer.

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The length of one side of the square park is approximately 26.87 meters.

To find the length of one side of the square park, we can use the Pythagorean theorem. In a square, the diagonal walkway forms a right-angled triangle with two equal sides (the sides of the square).

Let the length of one side be x meters. According to the Pythagorean theorem, the sum of the squares of the two shorter sides (x^2 and x^2) equals the square of the longest side (38^2).

x^2 + x^2 = 38^2

Combine the x^2 terms:

2x^2 = 38^2

Divide by 2:

x^2 = (38^2) / 2

Now, take the square root of both sides to find the length of one side:

x = √((38^2) / 2)

x ≈ 26.87 meters

The length of one side of the square park is approximately 26.87 meters.

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The base 10 value of the 3-digit hexadecimal number 2E5 is 741. The probability that a 3-digit hexadecimal number with repeated digits allowed contains only letters is 27/512.

a) To convert a hexadecimal number to its decimal equivalent, you can use the following formula:

(decimal value) =\((last digit) * (16^0) + (second-to-last digit) * (16^1) + (third-to-last digit) * (16^2) + ...\)

Let's apply this formula to the hexadecimal number 2E5:

(decimal value) = \((5) * (16^0) + (14) * (16^1) + (2) * (16^2)\)

= 5 + 224 + 512

= 741

Therefore, the base 10 value of the 3-digit hexadecimal number 2E5 is 741.

b) To find the probability that a 3-digit hexadecimal number with repeated digits allowed contains only letters, we need to determine the number of valid options and divide it by the total number of possible 3-digit hexadecimal numbers.

The number of valid options with only letters can be calculated by considering the following:

Therefore, the total number of valid options is 6 * 6 * 6 = 216.

The total number of possible 3-digit hexadecimal numbers can be calculated by considering that each digit can be any of the 16 possible characters (0-9, A-F), allowing repetition. So, we have 16 choices for each digit.

Therefore, the total number of possible 3-digit hexadecimal numbers is 16 * 16 * 16 = 4096.

The probability is then calculated as:

probability = (number of valid options) / (total number of possible options)

= 216 / 4096

To simplify the fraction, we can divide both numerator and denominator by their greatest common divisor, which in this case is 8:

probability = (216/8) / (4096/8)

= 27 / 512

Therefore, the probability that a 3-digit hexadecimal number with repeated digits allowed contains only letters is 27/512.

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For the sample of soil given a) the porosity is 100.4%; b) the specific yield is 12.2%; c) the specific retention is 14.6%; d) the void ratio is 0.5342; e) the initial moisture content is 2.3%; and f) the initial degree of saturation is 41.97%.

a) The porosity of soil can be defined as the ratio of the void space in the soil to the total volume of the soil.

The total volume of the soil = Initial volume of soil = 100 c.m³

Weight of water added to the soil = 234.6 g – 220 g = 14.6 g

Volume of water added to the soil = 14.6 c.m³

Volume of soil occupied by water = Weight of water added to the soil / Density of water = 14.6 / 1 = 14.6 c.m³

Porosity = Void volume / Total volume of soil

Void volume = Volume of water added to the soil + Volume of voids in the soil

Void volume = 14.6 + (Initial volume of soil – Volume of soil occupied by water) = 14.6 + (100 – 14.6) = 100.4 c.m³

Porosity = 100.4 / 100 = 1.004 or 100.4%

Therefore, the porosity of soil is 100.4%.

b) Specific yield can be defined as the ratio of the volume of water that can be removed from the soil due to the gravitational forces to the total volume of the soil.

Specific yield = Volume of water removed / Total volume of soil

Initially, the weight of the oven dried soil is 220 g. After allowing it to drain by gravity, the weight of soil is 222.4 g. Therefore, the weight of water that can be removed by gravity from the soil = 234.6 g – 222.4 g = 12.2 g

Volume of water that can be removed by gravity from the soil = 12.2 c.m³

Specific yield = 12.2 / 100 = 0.122 or 12.2%

Therefore, the specific yield of soil is 12.2%.

c) Specific retention can be defined as the ratio of the volume of water retained by the soil due to the capillary forces to the total volume of the soil.

Specific retention = Volume of water retained / Total volume of soil

Initially, the weight of the oven dried soil is 220 g. After adding water to the soil, the weight of soil is 234.6 g. Therefore, the weight of water retained by the soil = 234.6 g – 220 g = 14.6 g

Volume of water retained by the soil = 14.6 c.m³

Specific retention = 14.6 / 100 = 0.146 or 14.6%

Therefore, the specific retention of soil is 14.6%.

d) Void ratio can be defined as the ratio of the volume of voids in the soil to the volume of solids in the soil.

Void ratio = Volume of voids / Volume of solids

Initially, the weight of the oven dried soil is 220 g. The density of solids in the soil can be calculated as,

Density of soil solids = Weight of oven dried soil / Volume of solids

Density of soil solids = 220 / (100 – (14.6 / 1)) = 2.384 g/c.m³

Volume of voids in the soil = (Density of soil solids / Density of water) × Volume of water added

Volume of voids in the soil = (2.384 / 1) × 14.6 = 34.8256 c.m³

Volume of solids in the soil = Initial volume of soil – Volume of voids in the soil

Volume of solids in the soil = 100 – 34.8256 = 65.1744 c.m³

Void ratio = Volume of voids / Volume of solids

Void ratio = 34.8256 / 65.1744 = 0.5342

Therefore, the void ratio of soil is 0.5342.

e) Initial moisture content can be defined as the ratio of the weight of water in the soil to the weight of oven dried soil.

Initial moisture content = Weight of water / Weight of oven dried soil

Initial weight of soil = 225.1 g

Weight of oven dried soil = 220 g

Therefore, the weight of water in the soil initially = 225.1 – 220 = 5.1 g

Initial moisture content = 5.1 / 220 = 0.023 or 2.3%

Therefore, the initial moisture content of soil is 2.3%.

f) Initial degree of saturation can be defined as the ratio of the volume of water in the soil to the volume of voids in the soil.

Initial degree of saturation = Volume of water / Volume of voids

Volume of water = Weight of water / Density of water

Volume of water = 14.6 / 1 = 14.6 c.m³

Volume of voids in the soil = 34.8256 c.m³

Initial degree of saturation = 14.6 / 34.8256 = 0.4197 or 41.97%

Therefore, the initial degree of saturation of soil is 41.97%.

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Answer:

6 package

Step-by-step explanation:

Given:

Amount of cheese needs = 3 KG = 3,000 gram

Assume;

1 package of cheese = 500 gram

Find:

Number of package need

Computation:

Number of package need = Amount of cheese needs / 1 package of cheese

Number of package need = 3,000 / 500

Number of package need = 6 package

Step-by-step explanation:

Therefore, 55+40+z=180

z=180-95

z=85

To get y,

z+y=180

85+y=180

y=95

The sewing kits bought by Ms, Clark is 17 in number.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,

As given in the question, Ms. Clark spent $89.85 on sewing kits that cost $5 each plus $4.85 tax on the total bill.

Let the number of sewing kits be x,
According to the question,
5x + 4.85 = 89.85
5x = 89.85 - 4.85
5x = 85
x = 17

Thus, the sewing kits bought by Ms, Clark is 17 in number.

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Answer:

3

Step-by-step explanation:

find value at  12 =12

find value at 10 =    6

 so it changes   + 6    for a change from 10 to 12

6/2 = 3  

By using area formula, we get base is \(20 m\)

What do you mean by area?

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. For instance, On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Given that:

Area of a rhombus is \(400 m^{2}\)

Height  of a rhombus is \(20 m\)

We know that,

Area of rhombus = base × height

Substituting area and height in above formula

\(400\) = base × \(20\)

∴ Base = \(\frac{400}{20}\)

           =\(20\)

Therefore, by using area formula, we get base of a rhombus is \(20 m\)

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Answer: The answer is A bc you have to multiply .57 and 18. Hope this helps

The height of each individual cracker is one-eighth inch. Then the correct option is B.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A type of cracker, rectangular in shape, is stored in a vertical column with all of the crackers stacked directly on top of each other.

Each cracker measures 2 inches in length by one and one-half inches in width.

The volume of the column is 15 inches cubed.
If there are 40 crackers in the column

The height of the cracker will be

\(\rm h = \dfrac{15}{1.5*2}\\\\h = 5\)

The height of each individual cracker will be

\(\rm h_c = \dfrac{5}{40}\\\\\\h_c = \dfrac{1}{8}\)

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Answer:

Step-by-step explanation:

is the answer

Answer:

x=5

Step-by-step explanation:

3 = 12/4

x = 20/4

x = 5

Answer:

-0.754310345

Step-by-step explanation

You do the problem noxt to the slash/ and then divide 17.5 by the sum of the right of the slash

The derivative of F(x) is \(F'(x) = x^{(1/3)\).

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.

To find the derivative of the given function F(x), we will apply the fundamental theorem of calculus and differentiate the integral with respect to x.

Let's compute F'(x):

F(x) = ∫[0 to x] \(t^{(1/3)} dt\)

To differentiate the integral with respect to x, we'll use the Leibniz integral rule:

F'(x) = d/dx ∫[0 to x] \(t^{(1/3)} dt\)

According to the Leibniz integral rule, we have to apply the chain rule to the upper limit of the integral.

\(F'(x) = x^{(1/3)} d(x)/dx - 0^{(1/3)} d(0)/dx\)   [applying the chain rule to the upper limit]

Since the upper limit of the integral is x, the derivative of x with respect to x is 1, and the derivative of 0 with respect to x is 0.

\(F'(x) = x^{(1/3)} (1) - 0^{(1/3)} (0)\)

\(F'(x) = x^{(1/3)\)

Therefore, the derivative of F(x) is \(F'(x) = x^{(1/3)\).

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a) The minimum number of wins he needs is 15. b) The standard deviation of X is σ = sqrt(Var(X)) ≈ 3.641. c) Standard normal table ≈ 0.411.

In part (a), we can use the formula for a binomial distribution to find the minimum number of wins Sam needs to break even. Let X be the number of wins in 520 spins, then X ~ Bin(520, 1/38). To break even, Sam needs to win at least $520, which means he needs at least m wins where 35m ≥ 520, or m ≥ 14.86. Since m must be an integer, the minimum number of wins he needs is 15.

In part (b), we can use the mean and variance of a binomial distribution to find the mean and standard deviation of X. The mean of X is E(X) = np = 520*(1/38) ≈ 13.684, and the variance of X is Var(X) = np(1-p) = 520*(1/38)*(37/38) ≈ 13.255. Therefore, the standard deviation of X is σ = sqrt(Var(X)) ≈ 3.641.

In part (c), we can use the Normal approximation to the binomial with the continuity correction to find P(X ≥ 15). Using the continuity correction, we can convert the discrete probability P(X ≥ 15) to a continuous probability P(X > 14.5). Standardizing X, we get Z = (14.5 - 13.684) / 3.641 ≈ 0.224. Using a standard normal table, we can find that P(Z > 0.224) ≈ 0.411. Therefore, P(X > 14.5) ≈ 0.411.

This answer is closer to the exact probability of 0.396 than the previous estimate of 0.10 too large, but it still overestimates the probability slightly. This could be due to the fact that the Normal approximation to the binomial assumes a continuous distribution, while the binomial distribution is discrete. Nonetheless, the Normal approximation with continuity correction is a useful tool for approximating probabilities in situations where the sample size is large.

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Answer:

look above

Step-by-step explanation:

hope it helps

's' and 't' represent free parameters that can take on any real values.

In the given system of equations:

x1 - x2 + 4x3 = -4

6x1 - 5x2 + 7x3 = -5

3x1 - 39x3 = 45

To solve this system, we can use the method of Gaussian elimination or matrix operations. Let's use Gaussian elimination:

Step 1: Write the augmented matrix for the system:

[1 -1 4 | -4]

[6 -5 7 | -5]

[3 0 -39 | 45]

Step 2: Perform row operations to transform the matrix into row-echelon form:

R2 = R2 - 6R1

R3 = R3 - 3R1

The updated matrix becomes:

[1 -1 4 | -4]

[0 1 -17 | 19]

[0 3 -51 | 57]

Step 3: Perform additional row operations to further simplify the matrix:

R3 = R3 - 3R2

The updated matrix becomes:

[1 -1 4 | -4]

[0 1 -17 | 19]

[0 0 0 | 0]

Step 4: Write the system of equations corresponding to the row-echelon form:

x1 - x2 + 4x3 = -4

x2 - 17x3 = 19

0 = 0

Step 5: Express the variables in terms of a parameter:

x1 = s

x2 = 19 + 17s

x3 = t

where s and t are parameters.

Therefore, the solution to the system is:

[x1] = [s]

[x2] = [19 + 17s]

[x3] = [t]

In the provided solution format:

[x1] = [s] []

[x2] = [19 + 17s] + s []

[x3] = [t] [__]

Here, 's' and 't' represent free parameters that can take on any real values.

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a. To provide $10,100 in four years at an interest rate of 4%, you would need to set aside $8,702.53 today.

This can be calculated using the formula for the future value of a single sum of money:

Future Value = Present Value * (1 + Interest Rate)^Number of Periods

In this case, the future value is $10,100, the interest rate is 4%, and the number of periods is four years. Rearranging the formula to solve for the present value, we have:

Present Value = Future Value / (1 + Interest Rate)^Number of Periods

Substituting the given values, we get:

Present Value = $10,100 / (1 + 0.04)^4 = $8,702.53

Therefore, you would need to set aside $8,702.53 today to provide $10,100 in four years.

b. To cover the school fees of $10,000 a year for the next five years at an interest rate of 7%, you would need to set aside $41,289.28 today.

This can be calculated using the formula for the present value of a series of future cash flows:

Present Value = Cash Flow / (1 + Interest Rate)^Period

In this case, the cash flow is $10,000 per year, the interest rate is 7%, and the number of periods is five years. We need to calculate the present value of each cash flow and then sum them up. The formula becomes:

Present Value = $10,000 / (1 + 0.07)^1 + $10,000 / (1 + 0.07)^2 + $10,000 / (1 + 0.07)^3 + $10,000 / (1 + 0.07)^4 + $10,000 / (1 + 0.07)^5

Evaluating this expression, we get:

Present Value = $10,000 / 1.07^1 + $10,000 / 1.07^2 + $10,000 / 1.07^3 + $10,000 / 1.07^4 + $10,000 / 1.07^5 = $41,289.28

Therefore, you would need to set aside $41,289.28 today to cover the school fees of $10,000 a year for the next five years.

c. After paying the school fees of $10,000 a year for five years, and assuming the initial investment of $50,000 at an interest rate of 7%, the remaining amount would be $32,619.46.

We can calculate the remaining amount by subtracting the present value of the school fees from the initial investment. Using the same formula as in part b

Remaining Amount = Initial Investment - (Cash Flow / (1 + Interest Rate)^Period + Cash Flow / (1 + Interest Rate)^(Period-1) + ... + Cash Flow / (1 + Interest Rate)^1)

Substituting the values, we have:

Remaining Amount = $50,000 - ($10,000 / (1 + 0.07)^1 + $10,000 / (1 + 0.07)^2 + $10,000 / (1 + 0.07)^3 + $10,000 / (1 + 0.07)^4 + $10,000 / (1 + 0.07)^5)

Calculating the expression, we get:

Remaining Amount = $50,000 - ($10,000 / 1.07^1 + $10,000 / 1.07^2 + $10,000 / 1.07^3 + $10,000 / 1.07^4 + $10,000 / 1.07^5) = $32,619.46

Therefore, after paying the school fees for five years, $32,619.46 would remain from the initial investment of $50,000 at a 7% interest rate.

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The area of the rectangular parking lot is 929.03 square meters.

Use the formula for the area of a rectangle to calculate the area of the rectangular parking lot, which is given as:

Area = length × width

We know that the parking lot is 67.5 ft wide and 148 ft long, the area can be calculated as follows:

Area = 67.5 ft × 148 f

t= 9990 sq. ft

However, the question asks for the area in square meters, so we need to convert square feet to square meters. 1 square foot is equal to 0.092903 square meters, so we can use this conversion factor to convert square feet to square meters.

Area in square meters = Area in square feet × 0.092903

= 9990 sq. ft × 0.092903

= 929.03 sq meters

Therefore, the area is 929.03 square meters.

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Answer:

B

Step-by-step explanation:

your welcome

Answer:

90 degrees.

Step-by-step explanation:

They right ray point is on the 90 degree number and left ray is on zero so we find the difference.

90-0=90

so it measures 90 degrees.

Answer:

<ba=180 <bc=90

Step-by-step explanation:

Answer:

36 tiles

Step-by-step explanation:

Because the room is square, the numbers of tiles along the edge of the room were multiplied by the same number, meaning that:

81 = x²

So to find x, we must square root both sides of the equation:

\(\sqrt{81} = \sqrt{x^2}\)

x = 9

So the length of one side is 9 tiles. Now to calculate the circumference, as each side of a square is the same length, we can multiply this number by 4:

9 * 4 = 36

So there are 36 tiles along the edge of the room.

Hope this helps!

The regression equation of the data values is y = 0.3x^2 - 2.8x +4.2

Using a technology such as a graphing calculator, we simply input the data values in the graphing calculator and then wait for the result.

The x coordinates must be entered into the x values and the y coordinates must be entered into the y values

Using a graphing technology, the regression equation of the data values is y = 0.3x^2 - 2.8x +4.2

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