Trapezoid ABCD has parallel sides AB and CD, of lengths 12 and 18, respectively. Diagonals AC and BD intersect at E. Draw the line through E that is parallel to AB and CD, and let P and Q be its intersections with DA and BC, respectively. Find PQ.

C-Size of the largest particle that can be removed is a measure of air filter efficiency.

Air filter efficiency is a measure of how effectively a filter removes particles from the air. It can be measured in various ways, depending on the type of filter and the particles it is designed to remove.

A-Total volume of dirt collected - This measure does not provide information about the efficiency of the air filter, it could be a measure of how long the filter has been in use.

B-Total weight of dirt collected - This measure does not provide information about the efficiency of the air filter, it could be a measure of how long the filter has been in use.

C-Size of the largest particle that can be removed - This measure provides information about the efficiency of the air filter, because it tells us the size of the largest particle that the filter can remove. The smaller the particle size, the more efficient the filter is.

D-Total weight of the particles that can be removed - This measure does not provide information about the efficiency of the air filter, it could be a measure of how long the filter has been in use.

Air filter efficiency is usually measured by the Minimum Efficiency Reporting Value (MERV) rating, which is a standard measurement scale that ranges from 1 to 16, the higher the MERV rating, the more efficient the filter is at capturing small particles.

The length of the third side of the triangle is​ given by 2 (b + c) S /2bc2 - 1 (b + c)

To determine: the triangle's third side's length.

Since b and c are the lengths of a triangle's sides, let S be the length of the angle that bisects the given sides.

Suppose that angle A is 2α.

ABC's area is equal to (1/2) bcsin2α.

ADC's area is (1/2) bSsinα.

ADB = (1/2) cSsinα Area

Area of ABC is equal to Area of ADC plus Area of ADB.

The equation is (1/2) bcsin2α = (1/2) bSsinα + (1/2) cSsinα.

=> bcsin2α = (b + c) Ssinα

=> bc2sinαcosα =  (b + c) Ssinα

=> cosα =  (b + c) S /2bc

cos2α = 2cos²α  - 1

=> cos2α = 2  {(b + c) S /2bc}²  - 1

also cos2α =  (b² + c² - a²)/2bc

Both being equal:

(b2 + c2 - a2)/2bc = 2 (b + c) S /2bc2 - 1 (b + c)

Simplify to discover an in relation to b.

or, if available, substitute the values of b, c, and S to find a ( this side of triangle )

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A concentration of the majority of  Muslim population of the country is on one island, leading to ethnic separatism.

Ethnic Separatism is the process by which a nation or ethnic group makes efforts to become more autonomous from the central government of a state, or even secedes, when it is unhappy with any combination of social, economic, and political conditions in the nation in which it is located.

When an ethnic group actively works to assert its rights and importance, ethnic nationalism is the result. When it serves the interests of the state, governments may support ethnic nationalism as a project; however, for a variety of reasons, ethnic nationalism may also pose a threat to the state. Separatism based on ethnicity is one of these causes. Find out what ethnic separatism is, some examples of it, and more by continuing to read.

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Full question:

THE PHILIPPINES, 2010

Total Population

Roman Catholic Population

Percent Roman Catholic

Muslim Population

Percent Muslim

92 million74 million

80.6%

5.1 million

5.6%

THE PHILIPPINE ISLAND OF MINDANAO, 2010

Total Population

Roman Catholic Population

Percent Roman Catholic

Muslim Population

Percent Muslim

18 million

10.9 million

60.9%3.7 million

20.4%Source: Philippines Statistics Authority

The cultural composition of the Philippines and its constituent islands affects the political stability of the country. Which of the following patterns is best explained by the data in the tables?

A. An even dispersal of Muslims around the country, leading to assimilation

B.An even dispersal of Muslims around the country, leading to ethnic separatism

C. An even dispersal of Muslims around the country, leading to irredentism

D. A concentration of the majority of the country’s Muslim population on one island, leading to assimilation

E. A concentration of the majority of the country’s Muslim population on one island, leading to ethnic separatism

The answer in interval notation is (-∞,-6] u [4+∞)

An interval on a number line can be represented using interval notation. It is a method of representing subsets of the real number line, in other words. The numbers in between any two particular provided numbers are referred to as an interval. For instance, the interval containing 0, 5, and all values between 0 and 5 is the set of numbers x satisfying 0 x 5.

A subset of real numbers can be expressed using interval notation by the integers that bound them. Inequalities can be represented using this notation. We are aware that a range of numbers between 1 and 5 is represented by the interval 1 x 5.

Based on the numbers in the set, intervals can be categorised. Some sets have the endpoints indicated in the notation, but others may only contain them partially or not at all. There are generally three different sorts of intervals:

To represent the interval notation for various sorts of intervals, we can adhere to a set of rules and symbols. Let's examine the various symbols that can be used to represent a specific kind of interval.

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The shaded region in a standard normal distributive property corresponds to values between -1 and 1, which represent 68.27% of the area under the curve.

The shaded region in a standard normal distribution corresponds to values between -1 and 1, which represent 68.27% of the area under the curve. This is because the standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. The cumulative probability of a standard normal distribution can be found using the cumulative distribution function (CDF). The CDF of a standard normal distribution is equal to 0.6827 or 68.27%. Therefore, the shaded region in a standard normal distribution represents the cumulative probability from -1 to 1, which is equal to 0.6827 or 68.27%. This means that the shaded region corresponds to 68.27% of the area under the curve. This is important to note because it indicates that the majority of values in a standard normal distribution are located between -1 and 1.

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The complete question is

the shaded region under a normal distribution with mean 0 and standard deviation 1 (standard normal distribution) is shown. which of the following is the best choice that corresponds to the shaded region? select one Values between -1 and 1

Before any lease payments, the lease liabilities on January 1, 2021, is Liability $1,282,994.04 and Annual Deposit = $92,633.22.

Liability is a general term that describes the condition of being accountable for a good or service that is owed to another person.

For instance, a homeowner's tax responsibility may be related to the property taxes he must pay to the civil government or the income taxes he must pay to the external government.

leasing fee:A lease payment is a type of annual rent that is technically required by a contract between two parties and gives one party the right to use the other party's fixed assets, such as computers, manufacturing equipment, software, or other real estate impacts, for a predetermined period of time.

Evaluation:FVAD of $1 table or calculator function

$530,000 in future worth

n = 5

I = 5.00%

divided by 6.1533, the FV factor

Deposit each year: $92,633.22

Check out the FVAD table.

PVAD of $1 in a table or calculator function

the sum of $133,000

n = 20

I = 10.00%

9.36492 PV factor multiplied

Amount Owed $1,282,994.04

Check out the PVAD table.

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Answer:

5

Step-by-step explanation:

To find the median in a set of data, we first need to arrange the numbers in ascending order.

2,3,3,5,5,5,5,7,8

The median is the middle value of the set. Since there is an even number of data points in this set, the median is the average of the two middle values, which are 5 and 5.

So the median = (5+5)/2 = 5.

Answer:

The derivative of the function f(x) = 3x² + 2√x - 4x at x=1 is

[tex]\boxed{f'(1) = 3}[/tex]

Step-by-step explanation:

We have f(x) = 3x² + 2√x - 4x

[tex]f'(x) = \dfrac{d}{dx}\left(3x^2+2\sqrt{x}-4x\right)\\\\=\dfrac{d}{dx}\left(3x^2\right)+\dfrac{d}{dx}\left(2\sqrt{x}\right)-\dfrac{d}{dx}\left(4x\right)\\\\[/tex]

[tex]\dfrac{d}{dx}\left(3x^2\right) = 6x\\\\[/tex]

[tex]\dfrac{d}{dx}\left(2\sqrt{x}\right) = 2\dfrac{d}{dx}\left(\sqrt{x}\right)\\\\=2\dfrac{d}{dx}\left(x^{\frac{1}{2}}\right)\\\\= =2\cdot \dfrac{1}{2}x^{\frac{1}{2}-1}\\\\\\=\dfrac{1}{\sqrt{x}}\\\\[/tex]

[tex]\dfrac{d}{dx}\left(4x\right)=4[/tex]

Therefore

[tex]f'(x) = 6x+\dfrac{1}{\sqrt{x}}-4\\\\f'(1) = 6(1) + \dfrac{1}{\sqrt{1}} - 4\\\\f'(x) = 6 + 1 - 4\\\\f'(x) = 3\\\\[/tex]

1) y-coordinate of the vertex of y = x^2 + 2x - 1 is -1.

2) The statement "the vertex of quadratic function f is (-b/2a, f(-b/2a))" is true.

3) The equation y = -2x^2 - 12x - 17 has a maximum.

What is Quadratic Equation?

A quadratic equation is any equation in algebra that can be rearranged in standard form as where x represents an unknown value and a, b, and c represent known numbers.

1) y = x^2 + 2x - 1 is the equation of a parabola in vertex form.

In vertex form, the equation of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

So, to find the y-coordinate of the vertex, we can substitute the values of a, h and k into the equation and get the y-coordinate.

For the equation y = x^2 + 2x - 1, the vertex is (-1, -1), where -1 is the y-coordinate.

So, the y-coordinate of the vertex of y = x^2 + 2x - 1 is -1.

2) True.

The vertex of a quadratic function f(x) = ax^2 + bx + c is the point on the parabola that represents the graph of the function where the parabola changes direction from opening upward to opening downward or vice versa.

The x-coordinate of the vertex is given by (-b/2a), and the y-coordinate is given by f(-b/2a), where a, b, and c are constants.

So, the statement "the vertex of quadratic function f is (-b/2a, f(-b/2a))" is true.

3) maximum

The equation y = -2x^2 - 12x - 17 is a quadratic function, and it is in vertex form.

The leading coefficient is -2 which is negative, so the parabola opens downward, which means the vertex of the parabola represents the maximum point of the function. Therefore, the equation y = -2x^2 - 12x - 17 has a maximum.

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Step-by-step explanation:

(b)

logx . logx = 2log x

logx = 2

so x = 100

(c)

2x + 3x= 10

5x = 10

so ×=2

The  95% confidence interval for the true average dollar loss in burglaries rounded to the nearest dollar amount is 629 to 727

The variance of  a variate X is the arithmetic mean of the squares of all the deviations of X from the arithmetic mean of the observations and it is denoted by Var(X) or σ². The spread of statistical data is measured by the standard deviation. Distribution measures the deviation of data from its mean or average position. The positive square root of the variance of a variate X is known as the standard deviation.    

Given here: Sample mean x=678, Sample size n=500, Standard deviation σ=560

Standard error=σ.x=σ/√n

                               =560/√500

                               =25.044

Now for a 95% Class interval the value of z=1.960

The margin of error, E=Z×standard error

                             =49.08624

Lower bound=628.9147

upper bound=728.0854

∴ The 95% interval for population mean = 629 to 727

Hence, The  95% confidence interval for the true average dollar loss in burglaries rounded to the nearest dollar amount is 629 to 727

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Answer:

1 tube of paint is $2.25.

Step-by-step explanation:

We can set this as an equation first. Since we know that the canvas is $6.95 and the total is $24.95, those are the values that we will work with to determine the tube price. We can set the tube price as 8x, x being the tube price, and 8 being the number of tubes Ishi plans to buy. Now, we can set an equation:

6.95 + 8x = 24.95

8x = 18

x = 18/8 (simplified is 9/4, or 2.25)

Answer:

$ 2.25

Step-by-step explanation:

A= $6.95

B= (Cost of each tube) x 8

C= $24.95

A+B = C

The slope of the graph changes from -3 to 3 and the y-intercept changes from -2 to -4.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The given equations are f(x)= -3x-2 to f(x)=3x-4.

The slope of the equation changes from -3 to 3 which is shown in the graph similarly the y-intercept of the graph changes from -2 to -4.

The graph of the two lines f(x)= -3x-2 and f(x)=3x-4 is attached with the answer below.

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Answer:

-9 -6

Step-by-step explanation:

The option second correctly represents a linear relationship that is also proportional.

For the stated table:

Option 1:

x y

0 2

4 4

8 6

y/x = 4/4 = 1

y/x = 6/8 = 3/4 (NOT proportionate).

Option 2:

x y

0 0

2 1

4 2

y/x = 1/2

y/x = 2/4 = 1/2 (proportionate).

Option 3:

x y

0 1

5 3

10 5

y/x = 3/5

y/x = 5/10 = 1/2 (NOT proportionate).

Option 4:

x y

0 3

3 7

6 11

y/x = 7/3

y/x = 11/6  (NOT proportionate).

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The answer is 9n²-48n+64

A Type I error would occur if the HOA falsely rejects the null hypothesis that only 45% of homeowners support the fee increase when in reality more than 45% supports the increase.

A Type I error occurs when a null hypothesis is rejected when it is actually true. In this case, the null hypothesis is that only 45% of homeowners support the fee increase. To test this hypothesis, the HOA surveys a sample of 50 homeowners and uses the results to test the hypotheses H0: p = 0.45 and Ha: p > 0.45. If the HOA finds evidence that more than 45% of homeowners support the fee increase, when in reality only 45% or less of the homeowners support the fee increase, then a Type I error has occurred. On the other hand, if the HOA does not find evidence that more than 45% of homeowners support the fee increase, when in reality more than 45% of the homeowners do support the increase, then a Type I error has also occurred. In both cases, the HOA has incorrectly rejected the null hypothesis and a Type I error has occurred.

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A vector diagram showing the vector OE denoted by a + 2b is as attached.

Vector diagrams can be used to improve visualization and understanding of the magnitude and direction of vectors, and more importantly how multiple vectors interact.

For example, if Peter is pushing a heavy container towards the west, while John is pulling it in the northwest direction, in what direction does the container actually move?

A vector diagram is what will be useful in finding the answer.

Now, we see the vectors  OC and OD denoted by a + b and a − b in the attached diagram. Now, if we want to find a + 2b, we know that a + b will be a resultant but by use of vector analysis, we can plot a + 2b as seen in the first vector diagram attached.

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Answer:

$902.36

Step-by-step explanation:

820.33 times 10% = 82.033

add 82.033 to 820.33

820.33 + 82.033 = 902.363

The range of a set of data is the difference between the highest and lowest values. In this case, the graph shows that the relative humidity changes between 30% and 80% during a 24 hour period in New York City. To find the range, we subtract the lowest value (30%) from the highest value (80%):

Range = 80 - 30 = 50%

So, the range of the relative humidity during this 24 hour period in New York City is 50%.

The range of this set of data is 30 ≤ y ≤ 80.

The correct option is 3.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given:

A meteorologist drew the accompanying graph to show the changes in relative humidity during a 24-hour period in New York City.

The graph is given in the attached image.

The function is not exceeding the value 80.

And more than the value 30.

So, the range is,

= 30 ≤ y ≤ 80.

Therefore, the range is 30 ≤ y ≤ 80.

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(x + 2)(3x + 4) on simplification we get 3x² + 10x + 8.

To ascertain whether a graph accurately depicts a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and touches it only once at any given time. If there are multiple points where the vertical line touches the graph, the graph is not a function.

Given,

(x + 2)(3x + 4)

x (3x + 4) + 2(3x +4)

3x² + 4x + 6x + 8

3x² + 10x + 8.

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After the first randomization,  μ₁ is 12.5,  is μ₂ 11.46 and μ₁-μ₂ is 1.04. After the second randomization, μ₁ is 11.36, μ₂ is 12.6 and μ₁-μ₂ is -1.24. After the third randomization, μ₁ is 11.98, μ₂ is 11.98 and μ₁-μ₂ is 0.

Randomization is the process of placing a group of objects, persons, etc. in an unpredictable, illogical, or random order. The sum of all observations in a data set divided by the total number of observations is the data set's mean. The subtraction of two variables is the result of subtracting the means of the two variables. Each randomization in this problem consists of two sets of five observations.

For the first randomization:

μ₁=  [tex]\frac{13.6+12.1+15.9+11.2+9.7}{5}[/tex] = 12.5            [ μ₁ = Group A      

μ₂=[tex]\frac{9.2+8.2+11.5+13.8+14.6}{5}[/tex] = 11.46                μ₂ = Group B]

μ₁-μ₂ = 1.04

Similarly solve for the second and third randomizations

The complete question is:

A random number generator assigned each pepper to one of two groups. The weights of the peppers in each group, given three randomizations, appear in the tables.

First randomization

group a

13.6

12.1

15.9

11.2

9.7

group b

9.2

8.2

11.5

13.8

14.6

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Answer:

Ali's mark= 40

Ahmad's mark= 85

Step-by-step explanation:

Let x be Ali's mark and y be Ahmad's mark.

y=2x+5

x+y=125

x+2x+5=125

3x=120

x=40

y=85

The Area and perimeter of the triangle is given by 75m² and 33.02 m respectively.

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, a² + b² = c².

Given here: A right triangular garden with base 10m and  height 15 m

We know the area of a triangle is given by A=1/2×b×h where b=base and h=height. And the perimeter of a triangle is given by sum of all sides.

Thus Area of triangular Garden =1/2×10×15

                                                    =75 m²

And the perimeter the triangle is given by=10+15+[tex]\sqrt{10^2+15^2}[/tex]

                                                                      =10+15+18.02

                                                                      =33.02 m

Hence, The Area and perimeter of the triangle is given by 75m² and 33.02 m respectively.

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The largest possible value for the probability of A4 is 0.2000

Since A1, A2, A3, and A4 are events from a common sample space, the sum of their probabilities must be less than or equal to 1.

So, the sum of the probabilities of the events can be expressed as:

P(A1) + P(A2) + P(A3) + P(A4) = 1

From the question, we have

P(A1) = P(A2) = P(A3) = 0.3

Also, we have that

Al and A2 occur simultaneously with a probability of 0.1

This means that the initial equation becomes

P(A1) + P(A2) - P(A1 and A2) + P(A3) + P(A4) = 1

Where

P(A1 and A2) = 0.2

So, we have

0.3 + 0.3 - 0.1 + 0.3 + P(A4) = 1

Evaluate the like terms

P(A4) = 0.2

Hence, the probability is 0.2

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the annual expenditure of the US federal government is 4 trillion dollars and dollar bill is 0.001m then, the length of four trillion dollars would be 4×[tex]10^{9}[/tex] m

Government spending or expenditure includes all government

consumption, investment, and transfer payments. In national income accounting, the acquisition by governments of goods and services for current use, to directly satisfy the individual or collective needs of the community, is classed as government final consumption expenditure.

Since we have given that annual expenditure = 4 trillion dollars,

1 dollar bill = 0.0001m

so, the thickness would be.

[tex]4*10^{12} *0.001\\\\=4*10^{12}*10^{-3}\\\\=4*10^{9}[/tex]

the length of 4 trillion dollars would be. 4×[tex]10^{9}[/tex]

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He used [tex]$=1 \frac{7}{8} \mathrm{lb}$[/tex] . An algebraic equation, often known as a polynomial equation

Determine the number of pounds used

To solve this, we simply multiply the fraction of tomato used by the total;

[tex]Used $=$ Fraction $*$ Total[/tex]

Used[tex]=\frac{5}{8} * 3 l b$[/tex]

Used[tex]=\frac{5 * 3}{8} l b$[/tex]

Used = 15/8 lb

Convert to mixed number

Used [tex]$=1 \frac{7}{8} \mathrm{lb}$[/tex]

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Answer:

[tex]\displaystyle{f'(x)=\dfrac{9}{4}x\left(8x^4+x^2-1\right)^{\frac{1}{8}}(16x^2+1)}[/tex]

Step-by-step explanation:

Given the function [tex]\displaystyle{f(x)=\sqrt[8]{\left(8x^4+x^2-1\right)^9}}[/tex]. We can rewrite the function in exponential form as [tex]\displaystyle{f(x)=\left(8x^4+x^2-1\right)^{\frac{9}{8}}}[/tex]. Here, we have to know the power rules and the chain rule:

[tex]\displaystyle{f(x) = u^n \to f'(x) = nu^{n-1} \cdot \dfrac{du}{dx}}[/tex]

Therefore, from the above formula, we will have:

[tex]\displaystyle{f'(x)=\dfrac{9}{8}\left(8x^4+x^2-1\right)^{\frac{9}{8}-1} \cdot \dfrac{d}{dx}\left(8x^4+x^2-1\right)}\\\\\displaystyle{f'(x)=\dfrac{9}{8}\left(8x^4+x^2-1\right)^{\frac{9}{8}-\frac{8}{8}} \cdot \dfrac{d}{dx}\left(8x^4+x^2-1\right)}\\\\\displaystyle{f'(x)=\dfrac{9}{8}\left(8x^4+x^2-1\right)^{\frac{1}{8}} \cdot \dfrac{d}{dx}\left(8x^4+x^2-1\right)}[/tex]

Next, we derive the function 8x⁴ + x² - 1 by applying the power rules:

[tex]\displaystyle{f(x) = x^n \to f'(x) = nx^{n-1} \cdot \dfrac{dx}{dx} \to f'(x)=nx^{n-1}}[/tex]

Also, deriving any constants will result in 0 always.

Therefore:

[tex]\displaystyle{\dfrac{d}{dx}\left(8x^4+x^2-1\right)} = 4\cdot 8 x^{4-1} + 2\cdot x^{2-1} - 0}\\\\\displaystyle{\dfrac{d}{dx}\left(8x^4+x^2-1\right)} = 32x^3 + 2x}[/tex]

Thus, we will have:

[tex]\displaystyle{f'(x)=\dfrac{9}{8}\left(8x^4+x^2-1\right)^{\frac{1}{8}} \cdot (32x^3+2x)}\\\\\displaystyle{f'(x)=\dfrac{9}{8}\left(8x^4+x^2-1\right)^{\frac{1}{8}} \cdot 2x(16x^2+1)}\\\\\displaystyle{f'(x)=\dfrac{9}{4}x\left(8x^4+x^2-1\right)^{\frac{1}{8}}(16x^2+1)}[/tex]

Therefore, the derivative is:

[tex]\displaystyle{f'(x)=\dfrac{9}{4}x\left(8x^4+x^2-1\right)^{\frac{1}{8}}(16x^2+1)}[/tex]

or you can rewrite in the form of surd as:

[tex]\displaystyle{f'(x)=\dfrac{9}{4}x(16x^2+1)\sqrt[8]{8x^4+x^2-1}}[/tex]

The obtained Z score for the following blood pressures =-2

Enter data in Excel work sheet and use the formulae

=VAR(A1:A6)  and =VAR(B1:B6)  to get the variance

Variance for

Men aged 20-29=42.97

Men aged 60-69=211.77

The variance is substantiaaly larger for the set of blood pressures of men aged 60-69

Enter the data in Excel worksheet and use =AVERAGE(A1:A15) to find mean and calculate is the mean

Mean=15833.33 and is to calculated for finding relative position

Z=38-(27*10)=-232Z=262.7-(200*57)=-11,137.3

Hence 262.7 has higher relative position

=[48-70]/11=-2

Z score=-2

The calculated Z score for the subsequent blood pressures is therefore = -2.

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