A sample of 576 men 60 years of age with normal bone density, osteopenia (a low bone density which may lead to osteoporosis), and osteoporosis are randomly selected from hospital records and invited to participate in the study. Each participant's history of fracture (At least once vs. None) in the past 5 years is obtained from their medical records. What statistical test is the MOST appropriate to test whether there is a difference in history of fracture in the past 3 years between 60-year-old men with normal bone density, those with osteopenia, and those with osteoporosis?

Answer:

17

Step-by-step explanation:

A straight angle is 180

180 = 6z + 1 + 77 combine like terms

180 = 6z + 78  Subtract 78 from both sides

180 - 78 = 6z + 78 - 78

102 = 6z  Divide both sides by 6

17 = z

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

what you have to do is

hope this helps!

The opening price on the following days are,

April 28 = 20 thousand

May 2 = 50 thousand

And, the closing price on the following days are,

April 29 = 22 thousand

May 1 = 22 thousand

Given that;

The following stock bar chart depicts the market action for the Washington petroleum Corp. during the week of April 28.

Hence, By graph;

The opening price on the following days are,

April 28 = 20,000

May 2 = 50,000

And, the closing price on the following days?

April 29 = 22,000

May 1 = 22,000

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Answer:

Step-by-step explanation:

mass of the urine lol

The values of the variables, a, b, and c obtained from the equation of the circle and the coordinates of the point P are;

a) a = 2

b = -2

c = 4

The general equation of a circle is; (x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The coordinates of the radius of the circle

The specified equation of a circle is; x² + y² = 9

The coordinates of the center of the circle, is therefore, O = (0, 0)

a) The coordinates of the points P  and O indicates that the gradient of OP, obtained using the slope formula is; ((3·√3)/4 - 0)/(3/2 - 0) = ((3·√3)/4)/(3/2)

((3·√3)/4)/(3/2) = (√3)/2

The specified form of the gradient is; (√3)/a, therefore;

(√3)/a = (√3)/2

a = 2

The value of a is 2

b) The gradient of the tangent to a line that has a gradient of m is -1/m

The gradient of OP is; (√3)/2, therefore, the gradient of the tangent at P is -2/(√3)

The form of the gradient of the tangent at P is b/(√3), therefore;

-2/(√3) = b/(√3)

b = -2

The value of b is; -2

c) The coordinate of the point on the tangent, (0, (7·√3)/c) indicates

Slope of the tangent = -2/(√3)

((7·√3)/c - ((3·√3)/4))/(0 - (3/2)) = -2/(√3)

((7·√3)/c - ((3·√3)/4)) = (3/2) × 2/(√3) = √3

(7·√3)/c = √3 + ((3·√3)/4) = 7·√3/4

Therefore; c = 4

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The solution is: red<yellow<green<blue<violet are the colors.

The light spectrum contains waves with specific wavelength which can be classified into groups. Most of the groups are invisible to the eye (like infrared, microwaves, radio waves, gamma rays, etc.) however, there is one group that is known as visible light.

Visible light allows us to see colors from red all the way to violet. The colors have different frequencies and wavelengths. The wave with the highest frequency also has the highest energy (which in this case is violet). Hence, as the frequency decreases, the energy will also decrease, making violet have the highest energy, and red have the lowest energy.

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complete question:

which answer has the colors in order from the lowest energy to the highest? group of answer choices red, blue, green blue, red, green blue, green, red red, green, blue

Answer:

Step-by-step explanation:

You want the volume, cost, and weight of a concrete pipe 2 m long with an outside diameter of 40 cm, and an inside diameter of 30 cm. The cost is $135 per cubic meter, and the weight is 2430 kg per cubic meter.

The area of a circle in terms of its diameter is ...

  A = π/4·d²

The area of the end of the pipe will be the difference between the overall area (using the outside diameter) and the area of the missing center part (using the inside diameter). It is ...

  End area = (π/4)(0.40 m)² -(π/4)(0.30 m)² = 7π/400 m² ≈ 0.05498 m²

The area of the end of the pipe is about 0.05498 m².

The volume of the pipe is the product of its base area and its length:

  V = Bh

  V = (0.05498 m²)(2 m) ≈ 0.10996 m³

The volume of the pipe is about 0.10996 m³.

At $135 per cubic meter, the cost of the concrete for the pipe is ...

  ($135/m³)(0.10996 m³) ≈ $14.84

The concrete cost for the pipe is about $14.84.

The density of 2.43 g/cm³ is equivalent to 2430 kg/m³. Since our volume is in cubic meters, we need the density to have these units.

  m = (2430 kg/m³)(0.10996 m³) ≈ 267.19 kg

The weight of the pipe is about 267 kg.

__

Additional comment

The cost is given in units of dollars per cubic meter. This suggests that it will be convenient to use meters as the unit of length. The calculations are done with 30 cm and 40 cm converted to 0.30 m and 0.40 m, respectively.

Similarly, the density is converted to units of kg per cubic meter. This facilitates finding the weight in kg from the volume in m³.

  1 g/cm³ = (0.001 kg)/(0.01 m)³ = 1000 kg/m³

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Answer:

Step-by-step explanation:

To solve this problem, we can use the fact that a regular hexagon can be divided into six equilateral triangles.The radius of the hexagon is given as 12. Let's draw a diagram to better visualize the hexagon / \ / \ / \ /_______\ B C |\ /| | \ / | | \ / | | \ / | |____D____| | / \ | | / \ | | / \ | |/_______\| E FIn the diagram above, A, B, C, D, E, and F are the vertices of the hexagon.To find the apothem of the hexagon, we need to find the height of one of the equilateral triangles. We know that the side length of each triangle is equal to the radius of the hexagon, which is 12. Using the Pythagorean theorem, we can find the height of one of the triangles/| / | h /__| b/2 (b/2)^2 + h^2 = 12^2 b^2/4 + h^2 = 144 h^2 = 144 - b^2/4Since the hexagon is regular, each side length is equal to 12. Therefore, b = 12.scssCopy codeh^2 = 144 - 12^2/4 h^2 = 144 - 36 h^2 = 108 h = sqrt(108) h = 6*sqrt(3)So the apothem of the hexagon is 6*sqrt(3).To find the area of the hexagon, we can use the formula:makefileCopy codeArea = (1/2) * apothem * perimeterThe perimeter of the hexagon is equal to six times the length of one side, which is 6*12 = 72.scssCopy codeArea = (1/2) * 6*sqrt(3) * 72 Area = 216*sqrt(3)So the area of the hexagon is 216*sqrt(3).Finally, the length of one side of the hexagon is simply equal to the radius, which is 12.

The values of the conditional probabilities are

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

Pennies = 15

Nickels = 28

Dimes = 12

Quarters = 20

So, we have the probability formula to be

P(Quarters | Not a penny) = (Quarter and not a penny)/Not a penny

This gives

P(Quarters | Not a penny) =  20/(28 + 12 + 20)

Evaluate

P(Quarters | Not a penny) =  1/3 = 0.33 = 33.33%

Next, we have

P(Dime| Not a nickel) =  12/(15 + 12 + 20)

Evaluate

P(Dime| Not a nickel) =  12/47 = 0.2553 = 25.53%

Lastly, we have

P(Not a quarter| Not a dime) =  (15 + 28)/(15 + 28 + 20)

Evaluate

P(Not a quarter| Not a dime) =  43/63 = 0.6825 = 68,25%

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This is a contradiction, which means that our initial assumption that there are n children is incorrect. Therefore, there is no solution to this problem that satisfies the given conditions.

Let's assume that there are n children in the Smith family.

We know that the father is 48 years old, so the sum of the ages of the mother and children is:

Total age = (n + 1) * 20 (as there are n children and 1 father)

And we also know that the average age of the mother and children is 16, so we can write:

Total age / (n + 1) = 16

Combining these two equations, we get:

(n + 1) * 20 / (n + 1) = 16

Simplifying, we get:

20 = 16

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Based on the information, we can infer that the three cylinders have a similar volume. However, option 3 would be the best option for buyers.

To find the area of the cylinders we must apply the following formula:

According to the above, the area of the cylinders would be:

option 1

option 2

option 3

On the other hand, to find the volume of the cylinders we must perform the following formula:

option 1

option 2

option 3

Based on the above, we can infer that the three cylinders have a similar volume, so the amount of content would be the same in any of them. However, option 3 would be the best option for buyers because it uses fewer materials and that lowers its value.

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Step-by-step explanation:

How to solve a system of equations using substitution:

1. Choose one of the equations and solve for one of the variables in terms of the other variable.

2. Substitute the expression you found in step 1 into the other equation for the variable you solved for.

3. Solve for the remaining variable.

4. Substitute the value you found in step 3 into either of the original equations to find the value of the other variable.

5. Check your solution by plugging in the values you found in both original equations to make sure they are true.

Example:

Solve the system of equations below using substitution:

2x + y = 8

x - y = 2

1. Solve the second equation for x in terms of y:

x = y + 2

2. Substitute the expression for x from step 1 into the first equation:

2(y + 2) + y = 8

3. Simplify and solve for y:

2y + 4 + y = 8

3y = 4

y = 4/3

4. Substitute the value of y into either of the original equations to find x:

x - (4/3) = 2

x = 8/3

5. Check the solution by plugging in both values into both original equations:

2(8/3) + (4/3) = 8 (true)

(8/3) - (4/3) = 2 (true)

Therefore, the solution to the system of equations is (8/3, 4/3).

How to solve a system of equations by graphing:

1. Rewrite each equation in slope-intercept form, y = mx + b.

2. Graph each equation on the same coordinate plane.

3. Find the point of intersection of the two lines. This is the solution to the system of equations.

4. Check your solution by plugging in the values into both original equations to make sure they are true.

Example:

Solve the system of equations below by graphing:

y = 2x - 1

y = -x + 3

1. Rewrite each equation in slope-intercept form:

y = 2x - 1 is already in slope-intercept form.

y = -x + 3 can be rewritten as y = -1x + 3.

2. Graph each equation on the same coordinate plane:

The two lines intersect at the point (1, 1).

3. Check the solution by plugging in both values into both original equations:

y = 2x - 1: 1 = 2(1) - 1 (true)

y = -x + 3: 1 = -(1) + 3 (true)

Therefore, the solution to the system of equations is (1, 1).

Answer:

Substitution:

Solve one of the equations for either variable.

Substitute the expression from Step 1 into the other equation.

Solve the resulting equation.

Substitute the solution in Step 3 into one of the original equations to find the other variable.

Write the solution as an ordered pair.

Check that the ordered pair is a solution to both original equations.

Graphing:

Graph the first equation.

Graph the second equation on the same rectangular coordinate system.

Determine whether the lines intersect, are parallel, or are the same line.

Identify the solution to the system.

If the lines intersect, identify the point of intersection. Check to make sure it is a solution to both equations. This is the solution to the system.

If the lines are parallel, the system has no solution.

If the lines are the same, the system has an infinite number of solutions.

When sample observations can be paired or we have dependent samples, treating these as independent samples will reduce the power of the test.

The power of a statistical test is the probability of correctly rejecting the null hypothesis when it is false. In other words, it measures the test's ability to detect a significant effect or difference when one actually exists. When we treat dependent samples as independent, we do not take into account the relationship between the paired observations, which can lead to a loss of information and ultimately reduce the test's power.

In summary, when we have dependent samples and treat them as independent, it will reduce the power of the test, leading to an increased chance of a Type II error. This means that we are more likely to fail to detect a true effect or difference when one actually exists. It is important to properly account for the relationship between paired observations in order to maintain the test's power and decrease the likelihood of making errors in our conclusions.

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The equation 4(x-1) + 5y = 4(-1) + 5 is transformed by moving 5 spaces right, 2 spaces down, and reflecting. The resulting equation is -4(x+6) - 5y = -44.

To move an equation 5 spaces right, we need to replace x with x-5. Then, to move it 2 spaces down, we replace y with y+2.

The equation now becomes 4(x-1-5) + 5(y+2) = 4(-1) + 5. Simplifying this, we get 4(x-6) + 5y = -16 + 5, which simplifies to 4(x-6) + 5y = -11.

To reflect the equation, we need to negate the coefficients of x and y. This gives us -4(x-6) - 5y = -11, which simplifies to -4x + 24 - 5y = -11.

Finally, we can simplify this further to get -4x - 5y = -35, or alternatively, multiply both sides by -1 to get 4x + 5y = 35.

Therefore, the new equation after the transformations is -4(x+6) - 5y = -44.

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The experimental probability of rolling a number less than 3 is given as follows:

p = 3/200.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of outcomes for this problem is given as follows:

2000.

The desired outcomes are those with a result of 1 or 2, which are numbers less than 3, hence the amount is given as follows:

16 + 14 = 30.

Hence the experimental probability is given as follows:

p = 30/2000

p = 3/200.

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Note that the equation in terms of y, volume of air in a person's lungs in mL and t, in seconds, to represent the given context is y = 800 cos (π/2 t) + 1600.

We know that

The function depicted in the graph exhibits a periodic nature, characterized by its oscillation between two extreme points.

The time period of the function is derived as T = 4 seconds,

Given that each complete oscillation occurs between one crest and the subsequent crest or from one through and the subsequent through.

The midline of this function is y = 1300 mL, which denotes its average value.

Furthermore, the amplitude of this function equals half the distance between both extreme values, equivalent to A = 800mL. Given that the function has a period of 4 seconds and that its first crest is located at (3.5, 2600), it follows that we may represent this function with an equation expressed as:

y = A Sin (2π/T ( t-  c)) + 1300

Where:

A = 800

T = 4

3.5, 2600 is a crest

Thus,

1000 = -A + 1300

A = 300

Solving for A, we get

c =3.5 - T/4 = 0.5

replacing those values, we have:

y = 800 sin (π/2 (t - 0.5)) + 1300

This can be simplified further to read

y = 800 cos (π/2 t) + 1300.

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the radius of convergence (R) is ∞, and the interval of convergence (I) is (-∞, ∞).

To find the radius of convergence (R) and the interval of convergence (I) of the series given by:

∑ 7(-1)^(n-1) n^n x^n

We can apply the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is L as n approaches infinity, then the series converges absolutely if L < 1, diverges if L > 1, and the test is inconclusive if L = 1.

Let's apply the ratio test to the given series:

L = lim(n→∞) |(7(-1)^(n-1) (n+1)^(n+1) x^(n+1)) / (7(-1)^(n) n^n x^n)|

Simplifying and canceling out common factors:

L = lim(n→∞) |(7(n+1) x) / (n^n)|

Taking the absolute value:

L = lim(n→∞) |7(n+1) x / n^n|

Now, let's evaluate the limit:

L = |7x| lim(n→∞) (n+1) / n^n

The limit can be further simplified by applying the ratio test for the sequence:

lim(n→∞) (n+1) / n^n = 0

Therefore, the limit L simplifies to:

L = |7x| * 0 = 0

Since L = 0, which is less than 1, the ratio test indicates that the series converges absolutely for all values of x. Thus, the series converges for all x.

For a series that converges for all x, the radius of convergence (R) is infinite (∞), and the interval of convergence (I) is the entire real number line (-∞, ∞).

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To calculate the odds that the quarterback will complete the next pass he throws, we need to know the ratio of successful outcomes (pass completions) to total outcomes (all passes attempted).

The quarterback has completed 24 out of 37 passes, so the ratio of successful outcomes to total outcomes is:

24/37

To convert this to odds, we divide the ratio of successful outcomes by the ratio of unsuccessful outcomes:

24/37 ÷ 13/37

Simplifying the division gives us:

24/13

Therefore, the odds that the quarterback will complete the next pass he throws are 24 to 13, or approximately 1.85 to 1.

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The total distance that she walks over all three days is 8.5 km.

Given that:

Marcia walked 900 meters on Friday.

On Saturday, she walked 4 kilometers.

On Sunday, she walked 3 kilometers and 600 meters.

It is the measure of distance between the two points and is known as length. The length is measured in meters generally.

The total distance that she walks over all three days is given as,

⇒ 900 m + 4 km + 3 km + 600 m

⇒ 7 km + 1,500/1,000 km

⇒ 7 + 1.5

⇒ 8.5 km

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The length of the arc subtended by the angle's rays is 0.02 times the radius of the circle

To find the length of the arc subtended by the angle's rays, we need to know the angle measure. Since we know that 1/360th of the circumference is 0.04 cm long, we can find the circumference by multiplying 0.04 cm by 360, which gives us 14.4 cm.

Now, we need to find the angle measure. Since the circle is centered at the vertex of the angle, the angle measures half the arc it subtends. Thus, we can find the angle measure by dividing the circumference by 2 and then multiplying by 1/360.

Angle measure = (14.4/2) x (1/360) = 0.02 radians

Finally, we can find the length of the arc subtended by the angle's rays by multiplying the angle measure by the radius of the circle.

Length of arc = 0.02 x radius


The length of the arc subtended by the angle's rays is 0.02 times the radius of the circle. The given information of 1/360th of the circumference being 0.04 cm long helped us find the circumference and subsequently the angle measure.

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The poster width is 21.7 inches.

Given that the original print of the figure is 3.5 inches wide and 5 inches long,

Here we will use the concept of scale factors,

Scale factor is defined as the number or the conversion factor which is used to change the size of a figure without changing its shape. It is used to increase or decrease the size of an object.

The scale factor can be calculated if the dimensions of the original figure and the dimensions of the dilated (increased or decreased) figure are known.

For example, a rectangle has a length of 5 units and a width of 2 units. Now, if we increase the size of this rectangle by a scale factor of 2, the sides will become 10 units and 4 units, respectively.

Hence, we can use the scale factor to get the dimensions of the changed figures.

The scale factor (k) = ratio of the corresponding sides,

We need to find the width of the poster if it is 6.2 times wider than the photo,

So, the original width = 3.5 in

Therefore, the poster size = 3.5 x 6.2 = 21.7 inches.

Hence the poster width is 21.7 inches.

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Answer:

Dichotomous - Do you think our new line of football shoes are suitable for playing football? (Answer options: Yes Or No)

Rating Scale - On a scale from 1 to 10, how often do you purchase our brand of athletic shoes? (1 being never, 10 being extremely frequently.)

Open-Ended - Which line of our shoes do you find most suitable for playing sports, and why?

Multiple Choice - Which of the follow athletic shoes do you purchase from our company? (Basketball, baseball, football, hiking, or none of the above)

Completion - Fill in the following blank with the type of shoe that best applies to you : I purchase _____ shoes from Athletics Shoe Company.

Answer:

12.8cm

Step-by-step explanation:

radius = 0.5 X diameter

2mm = 0.2cm

volume of circular metal sheet = π r² h = π (24)² (0.2) = 115.2π cm³.

volume, V, of cylindrical bar = π r² L

L = V/(π r²)

 = 115.2π / (π (3)²)

=  115.2/ 9

= 12.8cm

Yes, the chain rule in calculus involves multiplying the derivative of the outside function by the derivative of the inside function.

The chain rule is a fundamental concept in calculus that allows us to find the derivative of a composite function. When a function is composed of two or more functions nested inside each other, the chain rule enables us to differentiate the composite function by taking into account the derivatives of the individual functions.

Mathematically, if we have a composite function f(g(x)), where g(x) represents the inside function and f(u) represents the outside function, the chain rule states that the derivative of the composite function is given by the product of the derivative of the outside function f'(u) and the derivative of the inside function g'(x). In other words, it is the prime of the outside function multiplied by the prime of the inside function.

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Answer:

gradient = [tex]\frac{1}{2}[/tex] , y- intercept = - [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope ( gradient) and c the y- intercept )

given

x - 2y = 3 ( subtract x from both sides )

- 2y = - x + 3 ( divide through by - 2 )

y = [tex]\frac{-1}{-2}[/tex] x + [tex]\frac{3}{-2}[/tex] = [tex]\frac{1}{2}[/tex] x - [tex]\frac{3}{2}[/tex] ← in slope- intercept form

with gradient m = [tex]\frac{1}{2}[/tex] and y- intercept c = - [tex]\frac{3}{2}[/tex]

Answer:

Step-by-step explanation:

Answer:

-----------------

Multiply both the numerator and denominator by √2 to rationalize the denominator.

Distribute and simplify:

Answer:

[tex]\sqrt{2} +3\sqrt{3}[/tex]

Step-by-step explanation:

To solve this you have to rationalize the denominator. That is, you have to multiply both numerator and denominator by √2.

Let us do it now.

[tex]\sf \dfrac{2+3\sqrt{6} }{\sqrt{2} } \\\\\sf \dfrac{\sqrt{2}* (2+3\sqrt{6} )}{\sqrt{2} *\sqrt{2} }\\\\\sf \dfrac{2\sqrt{2} +3\sqrt{6}\sqrt{2} }{\sqrt{2*2} }\\\\\sf \dfrac{2\sqrt{2} +3\sqrt{12}}{\sqrt{4} }\\\\\sf \dfrac{2\sqrt{2} +3*2\sqrt{3} }{2} }\\\\\sf \dfrac{2\sqrt{2} +6\sqrt{3} }{2} }\\\\\sf \dfrac{2\sqrt{2}} {2}+\dfrac{6\sqrt{3} }{2} \\\\\sqrt{2} +3\sqrt{3}[/tex]

It is most important to have a random sample in inferential statistics, particularly in making statistical inferences about a population based on the sample data.

Random sampling is a critical component of inferential statistics because it helps to ensure that the sample is representative of the population. When a sample is randomly selected, each member of the population has an equal chance of being included in the sample, which reduces the risk of bias in the results. Without a random sample, the results of statistical analyses may not be accurate or generalizable to the population, and the conclusions drawn from the data may be flawed or misleading.

Therefore, random sampling is crucial in making valid statistical inferences about a population.

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Answer:

- 0.75x - 6y
- 2¼x + ¼y

Step-by-step explanation:

They are asking you to simplify as much as possible.

The interquartile range of the two data sets are:

Band members = $100.

Choir members = $150.

The difference between the median amounts raised by this group is

A statement that is best supported by the random samples is: A. the amounts raised by band members are more varied than the amounts raised by choir members.

In Mathematics and Statistics, the interquartile range (IQR) of a data set is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):

Interquartile range (IQR) of band members = Q₃ - Q₁

Interquartile range (IQR) of band members = 250 - 150

Interquartile range (IQR) of band members = $100.

For the choir members, we have;

Interquartile range (IQR) of choir members = 400 - 250

Interquartile range (IQR) of choir members = $150.

Median of band members = $200.

Median of choir members = $350.

Therefore, the median difference can be calculated as follows;

median difference = 350 - 200 = $150

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