What is the value of M, N, P?

The probability that the average size of the fish you caught is more than 13 inches is approximately 0.0918

We can solve this problem by using the Central Limit Theorem, which states that the sample mean of a sufficiently large sample size will be normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, we are given that the population mean is 11 inches and the population standard deviation is 3 inches. We are also given that we have a sample size of 4.

First, we need to calculate the standard error of the mean (SE) using the formula

SE = σ / sqrt(n)

where σ is the population standard deviation and n is the sample size.

SE = 3 / sqrt(4) = 1.5

Next, we need to standardize the sample mean using the formula

z = (x - μ) / SE

where x is the sample mean, μ is the population mean, and SE is the standard error of the mean.

z = (13 - 11) / 1.5 = 1.33

Finally, we can use a standard normal distribution table or calculator to find the probability that a standard normal variable is greater than 1.33. The probability is approximately 0.0918.

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A) Quartile 1 (Q1): 2, Quartile 2 (Q2): 6, Quartile 3 (Q3): 7, Decile 1 (D1): 1, Decile 2 (D2): 2, Decile 3 (D3): 3, Decile 4 (D4): 7
B) Quartile 1 (Q1): 11, Quartile 2 (Q2): 14, Quartile 3 (Q3): 16, Decile 1 (D1): 11, Decile 2 (D2): 12, Decile 3 (D3): 14, Decile 4 (D4): 17
C) Quartile 1 (Q1): 77, Quartile 2 (Q2): 85, Quartile 3 (Q3): 94, Decile 1 (D1): 71, Decile 2 (D2): 81, Decile 3 (D3): 87, Decile 4 (D4): 98
D) Quartile 1 (Q1): 42, Quartile 2 (Q2): 66, Quartile 3 (Q3): 86, Decile 1 (D1): 28, Decile 2 (D2): 42, Decile 3 (D3): 57, Decile 4 (D4): 98
E) Quartile 1 (Q1): 100, Quartile 2 (Q2): 117, Quartile 3 (Q3): 133, Decile 1 (D1): 33, Decile 2 (D2): 100, Decile 3 (D3): 111, Decile 4 (D4): 147
F) Quartile 1 (Q1): 113, Quartile 2 (Q2): 126, Quartile 3 (Q3): 146, Decile 1 (D1): 110, Decile 2 (D2): 113, Decile 3 (D3): 121, Decile 4 (D4): 848

Number is a mathematical object used to count, measure, and label. It is an abstract concept that can be used in many different forms. It can be represented by symbols such as 1, 2, 3, or 4, or by words such as one, two, three, or four. It is also used to represent quantities, distances, and other measurements. Number is an important part of mathematics, and it is used in virtually every aspect of life.

A)
Quartile 1 (Q1): 2
Quartile 2 (Q2): 5
Quartile 3 (Q3): 7
Interquartile Range (IQR): 5
Decile 1 (D1): 2
Decile 2 (D2): 2.6
Decile 3 (D3): 3.4
Decile 4 (D4): 6

B)
Quartile 1 (Q1): 12
Quartile 2 (Q2): 14.5
Quartile 3 (Q3): 16
Interquartile Range (IQR): 3.5
Decile 1 (D1): 11.1
Decile 2 (D2): 12.9
Decile 3 (D3): 14.7
Decile 4 (D4): 16.4

C)
Quartile 1 (Q1): 77
Quartile 2 (Q2): 85
Quartile 3 (Q3): 92
Interquartile Range (IQR): 15
Decile 1 (D1): 77
Decile 2 (D2): 81
Decile 3 (D3): 85.8
Decile 4 (D4): 92

D)
Quartile 1 (Q1): 42
Quartile 2 (Q2): 63
Quartile 3 (Q3): 86
Interquartile Range (IQR): 44
Decile 1 (D1): 42
Decile 2 (D2): 52.8
Decile 3 (D3): 66.2
Decile 4 (D4): 86

E)
Quartile 1 (Q1): 100
Quartile 2 (Q2): 117
Quartile 3 (Q3): 133
Interquartile Range (IQR): 33
Decile 1 (D1): 100
Decile 2 (D2): 107
Decile 3 (D3): 116
Decile 4 (D4): 133

F)
Quartile 1 (Q1): 110
Quartile 2 (Q2): 121
Quartile 3 (Q3): 136
Interquartile Range (IQR): 26
Decile 1 (D1): 110
Decile 2 (D2): 113
Decile 3 (D3): 117.8
Decile 4 (D4): 136

From the calculated values above, it can be seen that the quartiles and deciles of each set of data differ. This is due to the different values of the data sets and the number of data points in each set. The quartiles and deciles show different ranges and values which indicate the spread of the data. The quartiles and deciles are an important measure of the spread of the data and can help to identify any outliers. The quartiles and deciles also help to identify any skewness in the data.

In conclusion, the quartiles and deciles of each set of data differ due to the different values and the number of data points in each set. The quartiles and deciles provide an important measure of the spread of the data, helping to identify any outliers or skewness.

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Answer:To find Angel's monthly net pay, we can use the following steps:

Calculate Angel's annual net pay:

Her net pay is 68% of her gross pay, so we can find her net pay by multiplying her gross pay by 0.68:

Net pay = Gross pay x 0.68

Net pay = $59,600 x 0.68

Net pay = $40,648

Divide Angel's annual net pay by 12 to find her monthly net pay:

Monthly net pay = Annual net pay / 12

Monthly net pay = $40,648 / 12

Monthly net pay = $3,387.33 (rounded to two decimal places)

Therefore, Angel's monthly net pay is $3,387.33.

Step-by-step explanation:

The expected value in the game of mentioned probability is $-5.26.

Expected value can be calculated by the formula -

Expected value = (probability × winning amount) + (probability × (- losing amount))

Keep the values in formula to find the expected value -

Expected value = (1/42 × 67) + (41/42 × -7)

Performing multiplication in the brackets on Right Hand Side of the equation

Expected value = 1.57 - 6.83

Performing subtraction on Right Hand Side

Expected value = $-5.26

Hence, the expected value is $-5.26.

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Answer: x=14.75

2(2x+2)=3(21)

   4x+4 = 63

       4x = 63-4

          x = 59÷4

          x = 14.75

Check:  2(2*14.75+2)=3(21)

                             63 = 63

Answer: 63

Step-by-step explanation: It's stated that it equals 3(21) and that's 63.

Pour calculer 3/11 x 4/9, on multiplie les deux nombres ensemble en multipliant les numérateurs entre eux et les dénominateurs entre eux, ce qui donne :

3/11 x 4/9 = (3 x 4) / (11 x 9)

En simplifiant cette fraction, on peut diviser le numérateur et le dénominateur par leur plus grand diviseur commun, qui est 3 :

(3 x 4) / (11 x 9) = 12 / 99

La fraction 12/99 peut être simplifiée encore plus en divisant le numérateur et le dénominateur par 3 :

12 / 99 = 4 / 33

Ainsi, la forme la plus simple de 3/11 x 4/9 est 4/33.

The value of x is 14.

What is the triangle?

A triangle is a three-sided polygon made up of three line segments that connect at three endpoints, called vertices. The study of triangles is an important part of geometry, and it has applications in various fields such as engineering, architecture, physics, and computer graphics.

The sum of the angles in a triangle is 180°, so we can set up an equation:

(4x+3) + 76 + (4x-11) = 180

Simplifying and solving for x:

8x + 68 = 180

8x = 112

x = 14

Therefore, the value of x is 14.

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The error found in the simplification of the expression is grouping of unlike terms and required equivalent expression for 6 - 2x + 5 + 4x is equal to 11 + 2x.

Expression is equals to ,

6 - 2x + 5 + 4x

His works are,

6-2x+5+4x

(6 - 2)x + (5 + 4 )x

4x + 9x

13x

Tyler's work is incorrect.

Error is need to group like terms.

He made a mistake when he combined the constants 6 and 5 without taking into account the terms with x.

The correct simplification should be,

6 - 2x + 5 + 4x

Collect like terms we have,

= (6 + 5) + (-2x + 4x)

= 11 + 2x

The final expression is 11 + 2x, not -13x as Tyler calculated.

To write an expression equivalent to 6 - 2x + 5 + 4x that only has two terms,

Combine the terms with x and the constant terms separately,

6 - 2x + 5 + 4x

= (6 + 5) + (-2x + 4x)

= 11 + 2x

An equivalent expression with only two terms would be,

11 + 2x

Therefore, the error in the expression is grouping of unlike terms and equivalent expression is 11 + 2x.

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The above question is incomplete, the complete question is:

Tyler is simplifying the expression 6 - 2x + 5 +4x.

Here is His work:

6-2x+5+4x

(6 - 2)x + (5 + 4 )x

4x + 9x

13x

A. Tyler's work is incorrect. Explain his error he made

B. Write an expression equivalent to 6 - 2x + 5 +4x That only has two terms.

Radian measure of an angle is defined to be the ratio of arc length to the radius of the circle. The length of the arc if a 60 degree angle is 1.0476. Therefore, the radian of the 60 degrees angle is 1.0476.

Radian measure of an angle is defined to be the ratio of arc length to the radius of the circle.

Arc length of sector of circle = (θ/360°) × 2πr

Arc length of sector of circle = (60°/360°) × 2 × 22/7 × 1

Arc length of sector of circle = 1.0476

radian measure of angle 60° = 1.04756/1

radian measure of angle 60° = 1.04756

In conclusion, radian measure of an angle is defined to be the ratio of arc length to the radius of the circle. The length of the arc if a 60 degree angle is 1.0476. Therefore, the radian of the 60 degrees angle is 1.0476.

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The provided information in the question is insufficient to accurately determine the hours for Lisa, David, and Sarah.   To determine how many hours should be assigned to each graphic designer, we need to first understand their individual work capacity, hourly rates, or the total workload available.  

However, we can help you calculate the total cost (in dollars) based on the given information. Here's a step-by-step explanation:
Identify the number of hours worked by each designer:
  - Lisa's hours: 26
  - David's hours: 39.6
  - Sarah's hours: 16.5
Determine the hourly rate for each designer:
  Since the hourly rates are not provided in the question, we cannot proceed with this step. Please provide the hourly rates for each graphic designer to help us calculate the total cost.
Once you have the hourly rates for each designer, you can calculate the total cost using the following formula:
Total Cost = (Lisa's hours * Lisa's hourly rate) + (David's hours * David's hourly rate) + (Sarah's hours * Sarah's hourly rate)

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The height needed to reach the desired volume, 30,875.88 in³, of a rectangular prism shaped sandbox is equals to 8.4 inches.

We have a family a family is building a sandbox for their yard that is shaped like a rectangular prism. Let the dimensions of rectangular prism be l, w and h inches.

Volume of box = 30,875.88 in³

Length of box , l = 62.3 inches

Width of box, w = 59 inches

We have to determine value of h.

The volume of shape is the space covered by the shape. The volume of rectangular prism, V = l× w×h

Substitute the known values in above formula, so, 30,875.88 in³ = 62.3 × 59 in² × h

=> 30,875.88 in³ = 3,675.7 in² × h

=> h = 30,875.88 in³/3,675.7 in²

=> h = 8.4 inches

Hence, required value of height, h is 8.4 inches.

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Solomon's study on circadian rhythms in a sample of 45 pregnant women admitted to a hospital in the first 6 months of 2021 due to severe preeclampsia is an example of consecutive sampling.

Consecutive sampling, also known as continuous or complete sampling, is a non-probability sampling method.

In this approach, researchers collect data from every subject that meets the eligibility criteria within a specific time frame.

In Solomon's study, the eligibility criteria were pregnant women admitted to the hospital with severe preeclampsia during the first 6 months of 2021.

By including all eligible subjects during this period, Solomon ensured that the sample was representative of the population under study.

The consecutive sampling method has several advantages, including ease of implementation and the potential for a relatively large sample size.

Additionally, it can provide a comprehensive view of the population during the specified time frame.

However, it may be susceptible to biases if there is a change in the population over time, or if the subjects who meet the eligibility criteria within the given period are not representative of the overall population.

In summary, Solomon's study on circadian rhythms in pregnant women with severe preeclampsia used consecutive sampling, a non-probability sampling method that involves collecting data from every subject meeting the eligibility criteria within a specific time frame.

This method is straightforward to implement and can yield a large sample size, but it may be susceptible to biases if the sample is not representative of the overall population.

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Total service hours are what the y-intercept is referring to in the graph of linear equation. representing the hours Yuson left after x days.

A straight line's general equation is -

[y] = [m]x + [c]

where -

The rate at which [y] varies in respect to [x] is shown by the slope of the line, [m].

The y-intercept, or the place where the graph crosses the [y] axis, is represented by [c].

The equation of a straight line can also be written as -

Ax + By + C = 0

By = - Ax - C

y = (A/B - B/C)x - A/C

Presented is Yuson, who must perform 30 hours of volunteer work.

After [x] days, Yuson's hours of service are represented by the equation:

y = 30 - 2x

OR

y = - 2x + 30

Please see the following graph.

Therefore, the y intercept here is the total hours of service.

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The complete question and graph has been attached below.

Answer:

119

Step-by-step explanation:

divide the numbers needed until you get 119 then boom yo done brainest now!

The area of carpet the school need to order for the room, the school is designing the new classroom shown in the figure is 5 sq. cm

What is area?

Area is the region covered by the two dimensional shapes like square, rectangle, rhombus, triangle, circle etc. The area of square is given by side x side. The rectangle area is found by length times width.

Here the coordinates of the given quadrilateral are, A(2,2); B(1,4); C(3,5); D(4,3)

To identify the type of quadrilateral we need to find the distance between the points: Distance formula=[tex]\sqrt{(X-x)^{2}+(Y-y)^{2} }[/tex]

AB=[tex]\sqrt{(1-2)^{2}+(4-2)^{2} }[/tex]

   =[tex]\sqrt{5}[/tex]

BC=[tex]\sqrt{(3-1)^{2} +(5-4)^{2} }[/tex]

   =[tex]\sqrt{5}[/tex]

CD=[tex]\sqrt{(4-3)^{2} +(3-5)^{2} }[/tex]

   =[tex]\sqrt{5}[/tex]

DA=[tex]\sqrt{4-3)^{2} +(3-2)^{2} }[/tex]

    =[tex]\sqrt{5}[/tex]

As length of all sides are equal, it can be rhombus or a square.

Now length of diagonals,

AC=[tex]\sqrt{(3-2)^{2} +(5-2)^{2} }[/tex]

    =[tex]\sqrt{10}[/tex]

BD=[tex]\sqrt{(4-1)^{2} +(3-4)^{2} }[/tex]

    =[tex]\sqrt{10}[/tex]

As the length of diagonals are equal, the given quadrilateral is a square.

Area of square= side x side

                        =[tex]\sqrt{5}[/tex] x  [tex]\sqrt{5}[/tex]

                        = 5 sq. units

∴The area of carpet to be ordered is 5 sq. units

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When collecting data for research, it is important to determine the error range of the data set. In the given question, Jacob was researching the number of hours the average adult sleeps each night. He collected data from five individuals.

The data collected by Jacob is as follows:Subject 1: 6 hours of sleepSubject 2: 6.5 hours of sleepSubject 3: 6 hours of sleep Subject 4: 7.5 hours of sleepSubject 5: 5 hours of sleepWe have to find the standard error of the sample mean. The formula for the standard error of the sample mean is:Standard Error = s / sqrt (n)Where,s = the sample standard deviation,n = the sample size.

For the given data set, the sample size is 5. The sample mean can be calculated as:(6 + 6.5 + 6 + 7.5 + 5) / 5 = 6.2The sample standard deviation can be calculated as:√[((6 - 6.2)² + (6.5 - 6.2)² + (6 - 6.2)² + (7.5 - 6.2)² + (5 - 6.2)²) / 4]≈ 1.306The standard error of the sample mean can be calculated as:Standard Error = 1.306 / sqrt (5)≈ 0.58Therefore, the standard error of the sample mean is 0.58. None of the options given in the question is closest to the calculated value. Hence, none of the options is the correct answer.

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Any value of x that is less than 400 dollars will satisfy this inequality and will represent the amount of money Ron can spend on the rental car.

An inequality is a mathematical statement that compares two values or expressions using one of the inequality symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to).

The inequality that models the amount of money Ron can spend on the rental car is:

x < 400

This inequality means that the value of x (the amount of money Ron can spend) is less than 400 dollars. The symbol "<" indicates that the value of x must be less than 400, which means that Ron cannot spend more than 400 dollars on the rental car.

So, any value of x that is less than 400 dollars will satisfy this inequality and will represent the amount of money Ron can spend on the rental car. For example, if Ron decides to spend $350, then the value of x would be 350, which is less than 400 and satisfies the inequality.

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The value of the expression  |1-|2-|3-|4-|5 is 1.

We can solve this expression by working from the inside out. Starting from the innermost absolute value, we have:

|5| = 5

Next, we move outward to the next absolute value:

|4-5| = |-1| = 1

Continuing outward:

|3-1| = |2| = 2

|2-2| = |0| = 0

Finally, we have:

|1-0| = |1| = 1

Therefore, the value of the expression is 1.

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According to the given information we have that (a) Linear (b) = Non-linear

(c) Linear (d) Non Linear.

What about linear graph?

A linear graph is a graph of a linear equation, which is an equation that represents a straight line when plotted on a coordinate plane. The standard form of a linear equation in two variables x and y is:

ax + by = c

where a, b, and c are constants. When this equation is graphed, it produces a straight line with a constant slope (a/b) and y-intercept (c/b). Linear graphs are used to represent relationships between two variables that change at a constant rate.

Define non linear graph:

A non-linear graph is a graph that does not represent a straight line when plotted on a coordinate plane. A non-linear graph can represent a wide variety of mathematical functions, including exponential functions, power functions, trigonometric functions, and logarithmic functions. Non-linear graphs are often used to model complex real-world phenomena that do not follow a simple linear pattern.

The shape of a non-linear graph depends on the specific equation or function being graphed, and it may have one or more curves, bends, or peaks. The slope and y-intercept of a non-linear graph are not constant and can change at different points along the curve. Non-linear graphs can be analyzed using calculus and other advanced mathematical techniques to understand the behavior and properties of the underlying function.

According to the given information:

(a) The equation given in the question follow the property of linear graph that it create a straight line in constant way .

(b) Non -linear not follow the condition.

(c) It is also linear in nature form a straight line with constant approch.

(d) The given coordinate form non-linear graph.

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Answer:

the inequality can be written as -5

Step-by-step explanation:

Endplate  area  * depth = volume

Endplate area is a composite area:

  rectangle   2x 7 = 14  cm^2

  and trapezoid area = height x average of bases = 3 x (3+7)/2 = 15  cm^2

      total endplate area = 29  cm ^2

29cm^2 * depth = volume

29 * 8 = 232 cm^3

The length of the leg of the triangle (hypotenuse, opposite side, adjacent side) are 10, 17, and 5 respectively.

To round a number to the nearest whole number, you have to look at the first digit after the decimal point. If this digit is less than 5 (1, 2, 3, 4) we don't have to do anything, but if the digit is 5 or greater (5, 6, 7, 8, 9) we must round up.

To find the length of each leg we need to consider the angle BAC.

[tex]sin60 = \frac{opposite side}{hypotenuse} =\frac{BC}{10}[/tex]

[tex]\frac{\sqrt{3} }{2} = \frac{BC}{10}\\ BC = \frac{\sqrt{3} }{2} * 10\\ BC = \sqrt{3} * 10\\ BC = 17.32 = 17[/tex]

[tex]cos60 = \frac{adjacent side}{hypotenuse} \\\frac{1}{2} = \frac{AB}{10} \\AB = \frac{1}{2} *10\\AB = 5[/tex]

Therefore the length of the leg of triangle are 17 and 5.

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Answer:

If the book was 25% off and the discounted price was $18, then 75% of the original price was $18.

In other words, 0.75 * Original Price = $18

Solving for Original Price, we get:

Original Price = $18 / 0.75

Original Price = $24

Therefore, the original price of the book was $24.

Step-by-step explanation:

The coordinates of the endpoints of the image A''B'', following the rotation and reflection transformation are are;

A''(-5, 2), and B''(1, -1)

A reflection transformation is a type of transformation that takes each point on a figure and flips or reflects it across a line known as the line of reflection to create a mirror image.

What is a rotation transformation?

A rotation transformation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees about a specified point.

The transformations in the question are a reflection and a rotation

The coordinates of the point (x, y) on the coordinate plane, following a reflection across the y-axis is; (-x, y)

The coordinate of the point (x, y) following a rotation of 90° counterclockwise about the origin is; (-y, x)

Therefore, the coordinates of the image of points A and B following a reflection across the y-axis are;

A(-2, 5) → A'(2, 5)

B(1, -1) → B'(-1, -1)

The coordinates of the image of points A' and B' following a rotation of 90° counterclockwise about the origin are;

A'(2, 5) → A''(-5, 2)

B'(-1, -1) →  B''(1, -1)

The coordinates of the endpoints of the image, A''B'' are therefore;

A''(-5, 2) and B''(1, -1)

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Marsha would earn about $35.75 more than Tamekia if they each work 22 hours.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can include numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division.

To estimate the difference in earnings between Tamekia and Marsha, we can find the average hourly rates for each and use them to calculate an approximate earnings difference.

For Tamekia:

The hourly rate is between $6.00 and $6.25.

The average hourly rate is approximately $(6.00 + 6.25) / 2 = $6.125.

For Marsha:

The hourly rate is between $7.50 and $8.00.

The average hourly rate is approximately $(7.50 + 8.00) / 2 = $7.75.

If they each work 22 hours, Tamekia would earn approximately $6.125 x 22 = $134.75, and Marsha would earn approximately $7.75 x 22 = $170.50.

The difference in earnings between Marsha and Tamekia would be approximately $170.50 - $134.75 = $35.75.

Therefore, Marsha would earn about $35.75 more than Tamekia if they each work 22 hours.

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first off, something noteworthy is that we have two angles of 60°, that means that the angle atop is also 60°, so we really have an equilateral triangle, with an altitude or height as shown above, so

[tex]\textit{height of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2}~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ h=4\sqrt{15} \end{cases}\implies 4\sqrt{15}=\cfrac{s\sqrt{3}}{2}\implies 8\sqrt{15}=s\sqrt{3} \\\\\\ \cfrac{8\sqrt{15}}{\sqrt{3}}=s\implies \cfrac{8\sqrt{2\cdot 3}}{\sqrt{3}}=s\implies \cfrac{8\sqrt{2}\cdot \sqrt{3}}{\sqrt{3}}=s\implies 8\sqrt{2}=s \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{ \textit{\LARGE perimeter} }{8\sqrt{2}~~ + ~~8\sqrt{2}~~ + ~~8\sqrt{2}}\implies 24\sqrt{2}[/tex]

The likelihood that there are 1 man and 2 girls are selected is approximately 0.4357. We can use the following formula for the chance of an occurrence to determine the probability that one male and two female candidates are chosen:

P(event) equals (number of possible outcomes for the event) / (total number of possible outcomes) Out of a total of 25 pupils, the programme is choosing 1 male and 2 female participants. 

Using the combination formula, we can first determine the overall number of events that are possible: nCr equals n and (r! * (n-r)!) where r is the number of students being chosen, and n is the overall number of students (25). (3). Therefore, there are a total of the following outcomes: 25C3 = 25! / (3! * (25-3)!) = 25! / (3! * 22!) = 2300

Next, we need to determine how many different methods there are to choose 1 guy and 2 females. Utilizing the product law of chance, we can accomplish this: The number of methods is equal to the sum of the ways to select one man and two females. 

There are 11 methods to choose one guy out of 11, and there are 91 ways to choose two females out of 14. The overall number of options for choosing one man and two females is thus: 11 * 91 = 1001

Finally, we can enter these numbers into the likelihood of the occurrence formula as follows: P(1 man, 2 women) = 1001/2300 = 0.4357

Consequently, the likelihood that there are 1 man and 2 girls are selected is approximately 0.4357.

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Answer:

Let's start by finding out how long it takes Jim to fold the washing in minutes. Since there are 60 minutes in an hour, Jim takes 60 minutes to fold the washing. Sara can do the same job in half the time, so she takes 30 minutes to fold the washing. To find out how long it would take them to fold the washing together, we can use the formula: Time = (Work) / (Rate) In this case, the "work" is folding the washing, and the "rate" is how long it takes each person to do the work. We can add their rates together to get the combined rate: Combined rate = Jim's rate + Sara's rate Combined rate = 1/60 + 1/30 To add these fractions, we need to find a common denominator, which is 60:

Constructing the foci of an ellipse using a compass works because the intersection of the arcs drawn with the compass is a point that is equidistant to the endpoints of the major or minor axis, which are precisely the foci of the ellipse.

Draw the major and minor axes of the ellipse.

Place the compass on one end of the major axis, and set the width of the compass to half the length of the major axis.

Draw an arc that intersects both the major and minor axes.

Repeat step 2 and 3 with the other end of the major axis.

The intersection of the two arcs is one of the foci of the ellipse.

To find the other focus, repeat the above steps using the minor axis instead of the major axis.

Now, let's justify why this method works. Recall that an ellipse is defined as the set of all points such that the sum of their distances to the foci is constant. This means that the foci play a fundamental role in defining the shape of the ellipse.

When we draw the arcs using the compass, we are essentially finding all the points that are equidistant to the two endpoints of the major or minor axis. The intersection of these arcs is a point that is equidistant to both endpoints of the major or minor axis, which means it lies on the ellipse.

Learn more about foci here

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