Calculate for the area of the shaded portion. Take π=22/7.

Using translation concepts, we have that:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, the vertices of the pre-image are given as follows:

D(-5,2), E(1,5), F(0,-1).

The vertices of the transformed image are given by:

D'(-2, -5), E'(-5,1), F(1,0).

From this, we the rule is given by:

(x,y) -> (-y,x).

Which is equivalent to the rotation rule of a rotation of 270º clockwise.

Hence:

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Answer:

r≈0.5m

Step-by-step explanation:

she was right

Answer:

r≈0.5m

Step-by-step explanation:

Answer:

x = 0.45 (2 d.p.)

Step-by-step explanation:

Iteration is a numerical method used to approximate solutions to equations where exact solutions are difficult or impossible to obtain analytically.

It involves putting an approximate value of the solution into an iteration formula to calculate a new value based on the previous one. This process is repeated multiple times, with each iteration generating a more accurate approximation of the solution.

The iteration formula is just a rearrangement of the equation, leaving a single ‘x’ on one side.

For this problem, we have already been given the iteration formula and the starting value of x₁. However, sometimes you will need to determine the iteration formula. For example, to determine the iteration formula for x³ + 2x - 1 = 0, rearrange the equation as follows:

\(\begin{aligned}x^3+2x-1&=0\\x^3+2x&=1\\x(x^2+2)&=1\\x&=\dfrac{1}{x^2+2}\end{aligned}\)

Therefore, the iteration formula is:

\(\boxed{x_{n+1}=\dfrac{1}{{x_n}^2+2}}\)

To calculate the approximate solution to x³ + 2x - 1 = 0 using the given iteration formula, start by substituting  x₁ = 1 into the formula to find x₂:

\(x_2=\dfrac{1}{x_{1}{^2}+2}=\dfrac{1}{(1)^2+2}=\dfrac{1}{1+2}=\dfrac{1}{3}=0.3333...\)

Substitute the found value of x₂ into the formula to find the value of x₃:

\(x_3=\dfrac{1}{x_{2}{^2}+2}=\dfrac{1}{\left(\frac{1}{3}\right)^2+2}=\dfrac{1}{\frac{1}{9}+2}=\dfrac{1}{\frac{19}{9}}=\dfrac{9}{19}=0.47368...\)

Continue this way until the solutions are the same when rounded to 2 d.p:

\(x_4=0.44956...\)

\(x_5=0.45411...\)

\(x_6=0.45326...\)

\(x_7=0.45342...\)

\(x_8=0.45339...\)

\(x_9=0.45339...\)

Therefore, the approximate solution to x³ + 2x - 1 = 0 is 0.45, rounded to 2 decimal places.

Additional information

The quickest way to compute each solution (each value in the iteration sequence) is to enter the value of x₁ into the calculator and press "=" so that the value of x₁ becomes the "answer". Then type the iteration formula into the calculator, replacing xₙ with "answer":

\(\boxed{\dfrac{1}{\text{Ans}^2+2}}\)

Each time you press "=", the next value of xₙ in the sequence is computed.

To solve the triangle using the Law of Sines, we can use the following formula:

\(\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)\)

Given that \(\(\angle A = 38^\circ\), \(\angle C = 73^\circ\), and \(b = 19\),\) we can substitute these values into the formula and solve for the remaining sides \(\(a\) and \(c\).\)

\(\(\frac{a}{\sin(38^\circ)} = \frac{19}{\sin(B)}\) (1)\)

\(\(\frac{c}{\sin(73^\circ)} = \frac{19}{\sin(B)}\) (2)\)

From equation (1), we can solve for \(\(\sin(B)\):\)

\(\(\sin(B) = \frac{19}{a} \cdot \sin(38^\circ)\)\)

Substituting this value into equation (2), we can solve for \(\(c\):\)

\(\(\frac{c}{\sin(73^\circ)} = \frac{19}{\frac{19}{a} \cdot \sin(38^\circ)}\)\)

Simplifying, we get:

\(\(c = a \cdot \frac{\sin(73^\circ)}{\sin(38^\circ)}\)\)

Now we have expressions for both \(\(a\) and \(c\).\)

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The denominators of two or more fractions must have a common factor, and the calculation can be defined as follows:

              \(\to\) \(\frac{2}{3} - \frac{3}{5}\\\\\)

              \(\to\) \(\frac{10-9}{15}\\\\\)

              \(\to\) \(\frac{10}{15} - \frac{9}{15}\\\\\)

So, the common denominator value by using the 15 is equal to

 \(\to \frac{2}{3} : \frac{10}{15} : \frac{3}{5}: \frac{9}{15}\)

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Step-by-step explanation:

first your going to break down your total then since you have nine balls of yarn you going to take out the 9.45

The cost of each wool ball will be $2.14.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

Jessie bought 4 balls of wool to knit sweaters for her children and 5 balls of wool for herself. Then she spent $9.45 on knitting accessories. The total cost of the wool and the accessories was $28.71.

Let x be the cost of each wool ball. Then the equation will be

9x + 9.45 = 28.71

Simplify the equation, then we have

9x = 28.71 - 9.45

9x = 19.26

x = 19.26 / 9

x = $2.14

The cost of each wool ball will be $2.14.

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Answer:

The Original point is (1, -8)

The Final point in my graph of A is (1, -3)

Step-by-step explanation:

translate the figure 5 units up means to move the points up by 5. In my graph I've shown all the points translated 5 units up

Nominal, ordinal, interval, and ratio are measurement scales used in statistics to categorize and rank data.

Nominal, ordinal, interval, and ratio are four sorts of information estimation scales utilized in measurements.

Nominal scales are utilized to mark or classify information into particular gatherings, where each gathering is fundamentally unrelated and altogether comprehensive. Instances of ostensible information incorporate orientation, race, and occupation.

Ordinal scales include positioning information in a particular request, however the distinctions between values are not significant. Instances of ordinal information incorporate positioning motion pictures in view of their prominence or understudy execution on a test.

interval scales include positioning information in a particular request, however the distinctions between values are significant, and there is no obvious zero point. Instances of stretch information incorporate temperature, intelligence level scores, and time.

ratio scales are like span scales, however they have a genuine zero point, implying that values can be duplicated and partitioned. Instances of proportion information incorporate weight, level, and pay.

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The complete question is:

what is the nominal, ordinal, interval and ratio?

Answer:

Volume=1/3×Area of base×Height

=1/3×16×3

=16m square

Step-by-step explanation:

Different sequence of answers is  59049.

Explanation: -  

To determine the number of different sequences of answers that can be created with ten multiple-choice questions, each having three possible answers, we need to use the multiplication principle of counting. This principle states that the total number of possible outcomes of a sequence of events is the product of the number of outcomes for each event.

For the first question, there are three possible answers. For the second question, there are three possible answers, and so on for each of the ten questions. Using the multiplication principle, we can determine the total number of different sequences of answers by multiplying the number of outcomes for each question together: 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 59,049

Therefore, there are 59,049 different sequences of answers that can be created with ten multiple-choice questions, each having three possible answers.

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The inverse of the bus-admittance matrix is the bus-impedance matrix.

What is a bus-impedance matrix?

The bus impedance matrix is a square matrix that represents the electrical circuit that connects the network nodes.

The values of this matrix are the impedances of the branches that join the nodes, and they are known as self-impedance (diagonal elements) and mutual impedance (non-diagonal elements).

What is the difference between the bus impedance matrix and the bus admittance matrix?

The difference between the bus impedance matrix and the bus admittance matrix is that the bus impedance matrix has all the elements non-zero, while the bus admittance matrix has most of the elements zero.

In power systems, the bus impedance matrix is preferable over the bus admittance matrix since the former is a dense matrix while the latter is a sparse matrix.

Hence, the computational cost required for carrying out power flow analysis using the bus impedance matrix is lower as compared to the bus admittance matrix.

The Jacobian matrix is a square matrix that represents the derivatives of a vector function with respect to another vector. It is used for performing Newton Raphson power flow analysis.

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Answer:

We can use the formula for the area of a sector of a circle:

A = (θ/360) x πr^2

where A is the area of the sector, θ is the central angle of the sector in degrees, and r is the radius of the circle.

In this case, we know that the central angle of the sector is 70° and the area of the circle is 169π square inches. We can use the area of the circle to find the radius:

A = πr^2

169π = πr^2

r^2 = 169

r = 13

Now we can use the formula for the area of the sector:

A = (θ/360) x πr^2

A = (70/360) x π(13)^2

A = (7/36) x 169π

A = 29.5π square inches

Therefore, the area of the sector is approximately 29.5π square inches.

Answer:

Mean:  160

Median:  150

Mode:  none

Range:  105

Standard deviation:  35.3

Step-by-step explanation:

Given:

If each value in the data set is multiplied by a constant value, the mean, median, mode, range, and standard deviation will all be scaled by the same amount.

Therefore, if each value in the data set is multiplied by 0.5:

Proof

Data set: {1, 2, 3, 4, 5}

\(\sf Mean\:\mu =\dfrac{\sum x_i}{n}= \dfrac{1+2+3+4+5}{5} = 3\)

\(\sf Median = 3\)

\(\sf Mode = none\)

\(\sf Range = 5-1=4\)

\(\sf Standard\:deviation\:\sigma=\sqrt{\dfrac{\sum (x_i-\mu)^2}{n}}=\sqrt{\dfrac{10}{5}}=\sqrt{2}\)

If we multiply each value by 0.5, the new data set is:

{0.5, 1, 1.5, 2, 2.5}

\(\sf Mean\:\mu =\dfrac{\sum x_i}{n}= \dfrac{0.5+1+1.5+2+2.5}{5} = 1.5\)

\(\sf Median = 1.5\)

\(\sf Mode = none\)

\(\sf Range = 2.5-0.5=2\)

\(\sf Standard\:deviation\:\sigma=\sqrt{\dfrac{\sum (x_i-\mu)^2}{n}}=\sqrt{\dfrac{2.5}{5}}=\dfrac{\sqrt{2}}{2}\)

Therefore, if each value in the data set is multiplied by 0.5, the mean, median, mode, range, and standard deviation are all scaled by the same amount.

The expression that is used to represent "the product of 3/4 and c" is 3/4c.

The term expression ins math is defined as a sentence with a minimum of two numbers or variables and at least one math operation.

Here we have given the statement "the product of 3/4 and c".

Now, we need to find the suitable expression for this one.

While we looking into the given statement we have identified that the following are presented

3/4 refers number also known as constant

c refers the variable

The term product refers the mathematical operation that has been done between number and variable.

So, as per the standard form of expression is can be written as.

=> 3/4 x c

=> 3/4 c

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The variance of the actuary's wait time is 36 / 121.

From the information, at the airport, there are three counters for checking the luggage. the employees at each counter work independently with the time for each customer modeled as an exponential distribution. the average time is one minute for one counter, two for the next, and three minutes for the third. an actuary, who is next in line, will take the next available counter,

From the complete question, the variance of the actuary's wait time will be:

= 1 / (11/6)²

= (6/11)²

= 36 / 121

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Answer:

Answer:

(x,y)=(0,-11)

Step-by-step explanation:

\(\text{The imaginary unit,}~ i = \sqrt{-1}\\\\\sqrt{-2} ~ \text{can be written as.}\\\\\sqrt{-2}\\\\=\sqrt{-1 \cdot 2}\\\\=\sqrt{-1} \sqrt{2}\\\\=i\sqrt 2\\\\=\sqrt 2 i\)

The length of side LJ in triangle JKL is approximately 12.27 centimetre .

To determine the length of side LJ in triangle JKL, we can use the concept of similarity between triangles. When two triangles are similar, their corresponding sides are proportional.

Length of side XY in triangle XYZ: 8.7

Length of side XZ in triangle XYZ: 8.2

Length of side YZ in triangle XYZ: 7.8

Length of side JK in triangle JKL: 13.05

Let's set up the proportion using the corresponding sides:

XY / JK = XZ / LJ = YZ / KL

Substituting the given values:

8.7 / 13.05 = 8.2 / LJ = 7.8 / KL

Now, we can solve for LJ:

8.2 / LJ = 8.7 / 13.05

Cross-multiplying:

8.2 * 13.05 = 8.7 * LJ

106.71 = 8.7 * LJ

Dividing both sides by 8.7:

LJ = 106.71 / 8.7

LJ ≈ 12.27

Therefore, the length of side LJ in triangle JKL is approximately 12.27cemtimetre .

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The diagram of water cycle is attached below.

The best describes the process occurring at U and X is Water changes from a liquid to a gas.

The process that occurs at the position of U and X is discussed when water transforms from a liquid to a gas. This is called Evaporation.

The following are the situations that should not be arisen at the location U and X:

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Answer:

45

Step-by-step explanation:

2x+5x=63

7x=63

x=9

number of boys =5×9=45

The value of k for a first-order reaction with a half-life of 137 minutes is approximately 5.06×10^(-3) s^(-1).

If the half-life of a first-order reaction is given as 137 minutes, we need to determine the corresponding rate constant (k) for the reaction.

In a first-order reaction, the relationship between the half-life and the rate constant is given by the equation t_1/2 = (ln(2) / k), where t_1/2 represents the half-life.

Plugging in the given half-life value of 137 minutes, we can rearrange the equation to solve for the rate constant (k). Taking the natural logarithm of both sides, we have ln(2) / t_1/2 = k.

Substituting the value for t_1/2 as 137 minutes, we can calculate the rate constant.

Performing the calculation, we find that the rate constant (k) is approximately 5.06×10^(-3) s^(-1).

Therefore, the correct option is 5.06×10^(-3) s^(-1) as the value of k for the first-order reaction with a half-life of 137 minutes.

It's important to note that the rate constant represents the rate at which the reaction occurs, and in this case, it corresponds to the specific reaction with the given half-life.

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Answer:

Vertex for 8: (-1,-1) Aos for 8: -1

Vertex for 9 (5,0) Aos: 5

I’m not sure about the solution because I’m not sure what you mean by solutions. So sorry!!! :-(

The third term a₃ of the sequence is 15

The definition of the function is given as

a₁= 13

aₙ₊₁ = aₙ + 1

The above definitions imply that we simply add 1 to the previous term to get the current term

Ssing the above as a guide,

so, we have the following representation

a₂ = 13 + 1

a₂ = 14

Also, we have

a₃ = 14 + 1

a₃ = 15

Hence, the value of a₃  is 15

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M = A + |B| is the function's highest possible value. When sin or cos x equals 1, this maximum value is reached. m = A |B| is the function's lowest possible value. If either cos x or sin x is equal to 1, this minimum will be reached.

Example :

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Answer:

The first/top option

Step-by-step explanation:

First, we can find the inequality that the line is representing. X is the number of hours she has already done, and she has five hours more to do to fulfill the 12 or more hours of required service. The inequality would be x+5≥12.

The minimum that X has to be is 7 because any value lower than 7 would make the inequality false[ ex. 6 + 5 ≠ 12 ]. The arrow would be pointing to the right, because 7 is the minimum value, not the max, so any value higher than 7 would still make the inequality true. Lastly, the circle would be filled, because 7 is included in the set of values that make the inequality true[ 7 + 5 = 12 ].

So, the answer would be the first option.

Answer:

Step-by-step explanation:

As per definition of the function, every x- value (input) has exactly one corresponding y-value (output)

We can see on the table:

Two same input values with different outputs.

So this not a function

A Poisson random variable represents the number of occurrences of an event in a fixed interval of time or space. It is a discrete random variable, which means that it can only take on integer values, starting from zero. Therefore, the smallest numerical value that a Poisson random variable can be is zero.

This means that there is a possibility that the event will not occur at all during the given interval. For example, if we are counting the number of customers who visit a store in an hour, it is possible that no customers show up during that hour, resulting in a Poisson random variable of zero.

However, the probability of this occurring depends on the average rate of the event occurring, which is denoted by the parameter λ in the Poisson distribution. The larger the value of λ, the smaller the probability of a Poisson random variable being zero.

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In a boxplot, potential outliers are data points that are more than 1.5 Interquartile Ranges (IQRs) from the edges of the box. A boxplot visually represents the distribution of a dataset, with the box containing the middle 50% of the data and the edges representing the lower and upper quartiles.

To answer your question, potential outliers in a boxplot are points that are more than 1.5 times the interquartile range (IQR) away from the edges of the box. The IQR is the difference between the third quartile (75th percentile) and the first quartile (25th percentile) of the data. The box in a boxplot represents the IQR, with the median (50th percentile) marked by a line inside the box. The whiskers of the boxplot extend to the minimum and maximum values that fall within 1.5 times the IQR from the edges of the box. Any points outside this range are considered potential outliers and are plotted as individual points beyond the whiskers. However, it is important to note that potential outliers do not necessarily indicate errors or incorrect data, and further investigation may be needed to determine their validity. Overall, boxplots are a useful tool for visualizing the spread and distribution of numerical data.

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\(\text{To get the total surface area, all we have to do is multiply } 18 \text{ by } 12, \text{which gets us}\)\($18\cdot12 = \boxed{216\text{ ft}^2}\).

\(\text{So, our answer is } \boxed{216\text{ ft}^2}.\)

Larry needs 216 square feet of carpeting for her rectangular living room.

To find the amount of carpeting Larry needs, we need to calculate the area of her rectangular living room. The area of a rectangle can be found by multiplying its length by its width. In this case, the length of the living room is 18 feet and the width is 12 feet.

So, the area of the living room is:

Area = Length * Width

Area = 18 feet * 12 feet

Area = 216 square feet

Therefore, Larry needs 216 square feet of carpeting for her living room.

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