Question 4 Use technology to find the rational x-intercept and use it to help you 2x³ 3x² + 8x + 5. Hence, find the exact solutions of 2x3 - 3x² + 8x + 5 = 0 -​

The equation of the given circle is (x-2)² + (y+1)² = 9.

What is a Circle?

In mathematics Round and in two dimensions, a circle is a figure. The circle's center is a place inside the circle from which all points on the circle's edge are equally far.

The radius of the circle, abbreviated "r," is the distance from the center of the circle to a point on its edge. The diameter of the circle, which is the greatest chord of any circle, is equal to the circle's doubled radius.

We know that, equation of a circle is given by :

(x-h)² + (y-k)² = r²

where, (h, k) are coordinates of the center of circle.

Here, the coordinates of center of circle is (2,-1) and the radius is 3 units.

So, equation of given circle :

(x-h)² + (y-k)² = r²

(x-2)² + (y+1)² = 3²

(x-2)² + (y+1)² = 9

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Using the Law of Cosines the length of l, to the nearest 10th of a centimeter is 4.6 cm.

To find the length of side l in triangle LMN, we can use the Law of Cosines, which states that c² = a² + b² - 2ab cos(C), where c is the side opposite the angle C.

In this case, we have:

a = 5.9 cm

b = 8.7 cm

C = 163°

First, we need to convert the angle from degrees to radians by multiplying it by π/180:

C = 163° × π/180 = 2.847 radians

Now we can plug in the values into the Law of Cosines:

l² = 5.9² + 8.7² - 2(5.9)(8.7)cos(2.847)

Simplifying the right-hand side:

l² = 68.81 - 60.83 × cos(2.847)

Taking the square root of both sides:

l ≈ 4.6 cm

Therefore, the length of l to the nearest 10th of a centimeter is 4.6 cm.

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Answer:

b ≈ 2.636.

Step-by-step explanation:

First, we can simplify both sides of the equation by combining like terms:

2b + 8 - 5b + 3 = -13 + 8b - 5

-3b + 11 = 8b - 18

Next, we can isolate the variable term on one side of the equation by adding 3b to both sides:

-3b + 3b + 11 = 8b - 18 + 3b

11 = 11b - 18

Then, we can isolate the variable term again by adding 18 to both sides:

11 + 18 = 11b - 18 + 18

29 = 11b

Finally, we can solve for b by dividing both sides by 11:

29/11 = b

b ≈ 2.636

Therefore, the solution to the equation is b ≈ 2.636.

Answer:

b = 29/11

Step-by-step explanation:

2b + 8 - 5b + 3 = -13 + 8b - 5

-3b + 11 = -18 + 8b

-11b + 11 = -18

-11b = -29

b = 29/11

Answer:

First, we need to find the slope and y-intercept of the linear regression line:

Using a calculator or statistical software, we get:

Slope (b) = 0.621

Y-intercept (a) = 50.4

Therefore, the linear regression equation is:

y = 0.6x + 50.4

To find the projected test grade for a student with a homework grade of 45, we substitute x = 45 into the equation:

y = 0.6(45) + 50.4

y = 27 + 50.4

y = 77.4

Rounding to the nearest integer, the projected test grade for a student with a homework grade of 45 is 77.

Working together, Shayna and Huong can clean an attic in 6.16 hours. Had she done it alone, it would have taken Huong 11 hours. Therefore, Shayna can clean the attic alone in 80 hours.

Let's denote the amount of work to be done by x units. The work done by Shayna in one hour is y.

Shayna and Huong work together for 6.16 hours, so in one hour they do 1/6.

16 of the work together.According to the problem:

x/6.16 = 1/6.16 units per hour

Therefore, the amount of work done by Huong in one hour is (x/11).

Now, we can express the amount of work done by Shayna and Huong in one hour as:

(x/11) + y = 1/6.16

To determine the value of y, we can solve the above equation. Solving the equation:

(x/11) + y = 1/6.16y = (1/6.16) - (x/11)y = (11-6.16x)/(11 × 6.16)

So the amount of work done by Shayna in one hour is y = (11-6.16x)/(11 × 6.16).

To find how long it would take Shayna to do it alone, we have to express the amount of work done by Shayna alone in one hour as x/h.

Using the unitary method we have:

x/h = yx/h = (11-6.16x)/(11 × 6.16)

hx = 11 × 6.16 - 6.16x

hx + 6.16x = 11 × 6.16

hx = (11 × 6.16)/0.84 = 80 hours

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When simplified, the above expression translates to = 4(x + 9) / (x + 6) where the restrictions are stated as: x ≠ -8, 4, -6.

In mathematics, restrictions refer to conditions or limitations placed on the values that a variable can take, either to ensure the validity of a mathematical expression or to satisfy a particular requirement.

With regard to the above,

We can simplify the given expression as follows:

(x^2 + 5x - 36) / (x^2 + 4x - 32) * (4x + 32) / (x + 6)

= [(x + 9)(x - 4) / (x + 8)(x - 4)] * [4(x + 8) / (x + 6)]

= (x + 9) * 4 / (x + 6)

= 4(x + 9) / (x + 6)

The restrictions on the variable are:

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Answer:

x > -6/5

Step-by-step explanation:

2 < 8 + 5x

-6 < 5x

x > -6/5

This is the correct answer, but I don't see it in the options list.

The number of pickles (p) is the dependent variable, while the number of cucumbers (c) is the independent variable.

The dependent variable is the variable that is being measured or observed and is affected by the independent variable. The independent variable is the variable that is being manipulated or changed by the researcher to determine its effect on the dependent variable.

In this scenario, the number of pickles Colette can make depends on the number of cucumbers she has. Therefore, the number of pickles (p) is the dependent variable, while the number of cucumbers (c) is the independent variable.

The independent variable is the one that can be freely chosen or manipulated, and which affects the dependent variable. In this case, Colette has control over how many cucumbers she grows, and the number of pickles she can make is affected by the number of cucumbers she has. Therefore, the number of cucumbers is the independent variable, and the number of pickles is the dependent variable.

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1) y + (1/2)x = 2

2)-59 - 153i

3)1315 - 62i

4)No real solutions

1) Equation for a line perpendicular to y=2x+3 and passing through the point (4-6)A line perpendicular to y = 2x + 3 would have a slope of -1/2 (the negative reciprocal of 2). To find the equation of the line, we use point-slope form. We substitute the point (4, -6) and the slope of -1/2:We know that the line must pass through the point (4, -6) and be perpendicular to the line y = 2x + 3, so we can write its equation in point-slope form as follows:y - (-6) = (-1/2)(x - 4)y + 6 = (-1/2)x + 2The answer is y + (1/2)x = 2.

2) Multiplying the complex numbers (11-3i)(7-12i)We will be using the FOIL method (first, outer, inner, last) for multiplying two binomials:First, we multiply 11 and 7 to get 77.Then, we multiply 11 and -12i to get -132i.Next, we multiply -3i and 7 to get -21i.Last, we multiply -3i and -12i to get 36i² (remembering that i² is equal to -1).Finally, we combine like terms:77 - 132i - 21i + 36i² = 77 - 153i - 36 = -59 - 153iThe answer is -59 - 153i.

3) Dividing complex numbers (185-72i) divided by (11+10i)To divide complex numbers, we need to multiply the numerator and denominator by the conjugate of the denominator (in which the sign of the imaginary part is changed):We multiply the numerator and denominator by the conjugate of 11 + 10i, which is 11 - 10i in this case, to eliminate the imaginary part from the denominator:(185 - 72i)(11 - 10i) = (185 × 11 - 72i × 11) - (185 × 10i + 72i × 10i) = (2035 - 792i) - (1850i + 720i²)Simplifying, we get:(2035 - 792i) - (1850i + 720i²) = (2035 - 792i) - (1850i + 720(-1)) = (2035 - 792i) - (1850i - 720) = 1315 - 62iThe answer is 1315 - 62i.

4) Solving an equation by completing the square: y² - 6y + 19 = 5First, we isolate the y terms and move the constant to the other side:y² - 6y + 14 = 0Next, we divide both sides by the leading coefficient (1 in this case):y² - 6y = -14To complete the square, we take half the coefficient of y, square it, and add it to both sides. In this case, that's (-6/2)² = 9:y² - 6y + 9 = -5Now, we factor the left-hand side as a perfect square:(y - 3)² = -5Finally, we take the square root of both sides:(y - 3) = ±√(-5)This expression has no real solutions because the square root of a negative number is imaginary. Therefore, the answer is "No real solutions."

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If the volume of a cylinder is given, the dimensions of cylinder can be written and r = √(V/(πh)) and h = V/(πr²)

The volume of a cylinder is given, find dimensions of cylinder. To find the dimensions of a cylinder given its volume, we need to know either the radius or height. The formula for the volume of a cylinder is:

V = πr²h

where V is the volume, r is the radius, and h is the height.

If we are given the volume V, we can solve for either r or h as follows:

If we solve for the radius r:

V = πr²h

r² = V/(πh)

r = √(V/(πh))

If we solve for the height h:

V = πr²h

h = V/(πr²)

So, to find the dimensions of the cylinder, we need to know the volume V and either the radius r or height h. Once we have one of these values, we can use the equations above to find the other value and determine the dimensions of the cylinder.

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Therefοre, the sοlutiοn οf the given prοblem οf trigοnοmetry cοmes οut tο be cοt²(135-b) = 3.

Relatiοnships between cubic splines and maths variable astrοphysics is believed tο have been created when the variοus fields came tοgether. Many metric prοblems can be sοlved triangle οr the results οf their calculatiοn can indeed be determined with the help οf precise mathematical methοds. Trigοnοmetry is the study οf six basic trigοnοmetric calculatiοns. They gο by a variety οf titles and acrοnyms, including sine, deviatiοn, angle, and sο fοrth (csc).

Here,

First, we need tο find the value οf cοs(b) using the given infοrmatiοn that sin(2b) = -1/5:

=> sin(2b) = 2sin(b)cοs(b)

=> -1/5 = 2sin(b)cοs(b)

We knοw that sin^2(b) + cοs^2(b) = 1, sο we can rearrange this equatiοn tο sοlve fοr cοs(b):

=> cοs²(b) = (1 - sin²(b))

Substituting this intο the equatiοn we fοund abοve:

=> -1/5 = 2sin(b)cοs(b)

=> -1/5 = 2sin(b)√(1 - sin²(b))

Squaring bοth sides and simplifying:

=> 1/25 = 4sin²(b)(1 - sin²(b))

=> 1/25 = 4sin²(b) - 4sin²(b)

=> 4sin²(b) - 4sin²(b) + 1/25 = 0

We can sοlve fοr sin^2(b) using the quadratic fοrmula:

sin²(b) = [4 ± √(16 - 4(4)(1/25))] / (2(4))

sin²(b) = [4 ± 2/5] / 8

sin²(b) = 3/10 οr 1/20

Since sin(2b) is negative, we knοw that sin(b) is negative as well, sο sin²(b) = 3/10. Therefοre:

cοs²(b) = 1 - sin²(b) = 1 - 3/10 = 7/10

Nοw we can use the identity

=> cοt²(θ) = 1 / [tan²(θ)] tο find cοt²(135-b):

1 / [tan(135-b)] = cοt(135-b)

By applying the fοrmula tan(x) = sin(x) / cοs(x):

=> tan(135-b) Equals cοs(135-b) / sin(135-b) (135-b)

The identities sin( + 90) = cοs() and cοs( + 90) = -sin() are used tο illustrate:

=> Cοs(90-b) = sin(135-b) = sin(45 + (90-b)) = sin (b)

=> Sin(90-b) = cοs(135-b) = cοs(45 + (90-b)) = cοs (b)

Using these numbers in place οf:

=> 1/tan(135-b) = sin(b) / cοs(b) (3)

=> 1 / [tan(135-b)] = cοt(135-b) = 1 / [(-1/√(3))²] = 3

Cοnsequently, cοt2(135-b) = 3.

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Complete question:

Solve for b in cot²(135-b) if sin²b = -1/5

Answer:A

Step-by-step explanation:

Answer:y=4-X

Step-by-step explanation:

the 4 comes before the variable because you are subtracting the 4 by the variable.

The equation that represents the given graph is

f(x) = 1/(x - 1) - 2

The graph of a rational function

A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational

function if, it can be represented as f (x) = p (x)/q (x), where p (x) and q (x) are polynomials such that q (x) ≠ 0.

To write the equation that represents this function, we need to identify the key features of the graph.

The graph is a hyperbola with the vertical asymptote x = 1 and the horizontal asymptote y = -2.

The graph passes through the point (0, -1).

Therefore, the general form of the equation that represents the given graph isf(x) = A/(x - 1) - 2

Since the horizontal asymptote is y = -2, A = -2.

Therefore, the equation that represents the given graph is f(x) = 1/(x - 1) - 2.

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Option (a) is correct i.e., the questions are acceptable because the researcher is studying the relationship   between age and preferred dress style.

Age is any person time he live till time calculated. Use age we solve different math problems.

Like calculate the age of a person or what was his age 5 year ago.

If the age is given in the form of a ratio, for example, a:g, then the age shall be considered as g h and a h. If you are assuming   the current age to be h, then n times the current   age will be (h × n) years. If you are   assuming the current age to be h, then 1/n of the age shall   be equal to ( h / n)  years.

Option (a) is correct i.e., the questions are acceptable because the researcher is studying the relationship   between age and preferred dress style.

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The researcher is investigating the association between age and favourite dress style, thus the questions are appropriate. The assertion is true.

Days are calculated as the difference between both the current day and the person's birth day. Age is calculated as follows: aged = (years x 365) + (months x 31) + days. The person's age is expressed in days. For the age in years, divide the figure by 365.

Age is determined by comparing a person's birthdate to the day on which age must be determined. The age of a person is determined by subtracting the provided date from the individual's birthdate. Provided date minus birthdate equals age of a person.

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Answer:

Below

Step-by-step explanation:

Domain    'x' can be any value except 10 <====which would make the denominator = 0 which is not allowed

   (-∞, 10 )  U (10 , +∞)

Range :   horizontal asymptote    the degree of the numerator and the denominator is the same : 1     so the horizontal asymptote will be

          3 / -1 = -3    ( The coefficients of 'x' in the num and den)

   the vertical asymptote occurs at x = 10 ...then the value of y goes to + inf

        so range is   ( -3, +∞)

Inverse Does exist , switch x's and y's in the original equation

   x = (3y+1) / (10-y)     now solve for   y

     and you will get  f^-1 (x) = (10x-4) / (x+3)

Here is graph of f(x) , f^-1(x)   and  x=y :

x + 4y = -52.

The point-slope form of the equation of a line passing through the point (x1, y1) with slope m is:y - y1 = m(x - x1)Here, the point (x1, y1) = (18, -17) and the slope m = -1/4Therefore, the equation of the line in point-slope form is:y + 17 = (-1/4)(x - 18)Expanding the equation:4(y + 17) = -x + 18 => 4y + 70 = -x + 18 => x + 4y = -52The required equation of the line is x + 4y = -52.

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Answer:

the answer is in the image above

The derivative of y = tan(x) is sec²(x).

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

y=tanx

dy/dx = dy/dx = cos x.cos x - sin x(-sin x) / cos² x

⇒ dy/dx = (cos² x + sin² x) / cos² x

⇒ dy/dx = 1 / cos²x

⇒ dy/dx = sec²(x)

Thus, the derivative of y = tan(x) is sec²(x).

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The surface area of the cylinder is 3,428 square centimeter, the curved surface area of the cylinder is 2,198 square centimeter and the volume of the cylinder is 15,386 cubic centimeter.

What is area and volume?

A flat, two-dimensional object's area is the space it takes up in a plane. A three-dimensional object's volume is the area it takes up in space.

We know that

Curved surface area = 2πrh

So, using this we get

⇒Curved surface area = 2 × 3.14 × 14 ×25

⇒Curved surface area = 2,198 square centimeter

Similarly,

Total surface area = 2πr (r + h)

So, using this we get

⇒Total surface area = 2 × 3.14 × 14 (14 + 25)

⇒Total surface area = 2 × 3.14 × 14 (39)

⇒Total surface area = 3,428 square centimeter

Similarly,

Volume = π[tex]r^{2} h[/tex]

So, using this we get

⇒Volume = 3.14 × [tex]14^{2}[/tex] × 25

⇒Volume = 15,386 cubic centimeter

Hence, the area and volume of the cylinder have been obtained.

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Answer:

7 times 5 = 35

Step-by-step explanation:

the nth term of the sequence is (16n²2 - 29n + 15)/(90n).

How to find?

To find the nth term of this sequence, we can use the formula:

an = a1 + (n-1)d

where a1 is the first term, d is the common difference, and n is the term number.

In this sequence, we can see that the common difference is not constant. However, we can still find a pattern:

a1 = 1/3

a2 - a1 = 2/5 - 1/3 = 1/15

a3 - a2 = 3/7 - 2/5 = 1/35

a4 - a3 = 4/9 - 3/7 = 1/63

We can see that the common difference is decreasing by a factor of 5 with each term. So the next difference would be 1/63× 1/5 = 1/315.

Using this pattern, we can find the nth term as:

an = 1/3 + (n-1)(1/15 - (n-2)(1/315))

Simplifying this expression, we get:

an = (16n²2 - 29n + 15)/(90n)

So the nth term of the sequence is (16n²2 - 29n + 15)/(90n).

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The selling price of the house was approximately $1.918 or rounded to the nearest dollar, $19,180.

We can start by setting up an equation to represent the problem. We know that the commission Bea earned is equal to 6100 of the selling price, which can be expressed as:

commission = 6100 × selling price

We also know that the commission Bea earned was $11,700, so we can substitute that into the equation:

11,700 = 6100 × selling price

Now we can solve for the selling price by dividing both sides by 6100:

selling price = 11,700 ÷ 6100

simplifying:

selling price = 1.918

Therefore, the selling price of the house was approximately $1.918 or rounded to the nearest dollar, $19,180.

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The solution to the inequality 5x - 6 <4 + 6x is x > -10

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

5x - 6 <4 + 6x

Subtract -6 from both sides of the inequality expression

So, we have the following representation

5x < 10 + 6x

Subtract 6x from both sides of the inequality expression

So, we have the following representation

-x < 10

Divide by -1

x > -10

So, the solution is x > -10

The graph of the inequality is added as an attachment

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The owners need to deposit in an account paying 0. 65% compounded quarterly so that they will have $120,000 in 270 days is $119,262.94

To calculate the amount the owners need to deposit today, we can use the formula for compound interest:

A = [tex]P(1 + r/n)^{(nt)}[/tex]

where:

A is the future value of the investment

P is the principal amount (the amount to be deposited)

r is the annual interest rate (0.65%)

n is the number of times the interest is compounded per year (4 for quarterly)

t is the time in years (270 days/365 = 0.7397 years)

Substituting the values given into the formula, we get:

$120,000 = [tex]P(1 + 0.0065/4)^{4\times0.7397}[/tex]

$120,000 = [tex]P(1.001625)^{2.9588}[/tex]

$120,000 = P(1.004845)

P = $120,000/1.004845

P = $119,262.94

Therefore, the owners need to deposit $119,262.94 in an account paying 0.65% compounded quarterly so that they will have $120,000 in 270 days.

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The number of weeks until Riley and Amari would have earned the same, would be 10 weeks.

Variables:

Let x be the number of weeks they work.

Let y be their total earnings in dollars.

System of equations:

For Riley: y = 5x

For Amari: y = 20 + 3x

Setting the two expressions for y equal to each other, we get:

5x = 20 + 3x

5x - 3 x = 20

x = 20 / 2

x = 10 weeks

Therefore, their earnings will be the same after 10 weeks of work.

We can also solve the system of equations graphically by plotting the two equations and finding the point of intersection. The point of intersection is (10,50). Therefore, their earnings will be the same after 10 weeks of work and their total earnings will be $50.

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The question, when translated to English is:
Riley and Amari earn weekly chore allowances for the summer, Riley is paid $5 a week and Amari is paid $20 at the beginning of the summer and then earns $3 a week.

When will their earnings be the same?

Answer:

Nobody ever said having faith would be easy, but it will be worth it and here is why.

He knows better than we do. God knows everything we are going through at this very moment and everything we will go through in the future. ...

All Things Are Possible With God.

He Is Worthy Of Our Trust.

He Knows What He Is Doing.

He is the creator of the universe

he exited before the heavens and earth

He is our father and the father of our ancestors

He has performed many miracles

He is the God who answers all prayers if you believe.

He is the one who stands by you in any situation, in good times and bad

He is a merciful, understandable and dependable God

What he says he'll do, that is what he'll do

The value of f(15) is approximately 346.42.

An exponential function is a mathematical function of the form f(x) = abˣ, where a and b are constant and b is greater than zero and not equal to 1. An example is f(x) = 2ˣ

We can use the properties of exponential functions to find the value of f(15). Since f(x) is an exponential function, we can write it in the form:

f(x) = a × bˣ

f(4.5) = 16 = a × b⁴.5

f(9.5) = 60 = a × b⁹.5

Dividing second equation by first equation gives:

f(9.5)/f(4.5) = (a × b⁹.5)/(a × b⁴.5) = b⁵

Substituting the given values, we get:

60/16 = b⁵

b = (60/16)¹/⁵

b ≈ 1.46

Substituting b into the first equation gives:

16 = a × 1.46⁴.5

a ≈ 0.30

Therefore, the exponential function is:

f(x) = 0.30 × 1.46ˣ

To find f(15), we can substitute x = 15 into the function:

f(15) = 0.30 × 1.46¹⁵

f(15) ≈ 346.42

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Claude will need approximately 1202.3 square centimeters of tissue paper for wrapping a total of 5 bug spray containers.

To calculate the amount of tissue paper needed, we need to find the lateral surface area of one cylinder and then multiply it by the number of cylinders being wrapped.

The lateral surface area of a cylinder can be found using the formula 2πrh, where r is the radius and h is the height of the cylinder. In this case, r = 3 cm and h = 12.7 cm.

Lateral surface area of one cylinder = 2π(3 cm)(12.7 cm) = 239.38 cm² (rounded to two decimal places)

Since Claude is wrapping 5 bug spray containers, we need to multiply the lateral surface area of one cylinder by 5:

Therefore, Claude will need approximately 1202.3 square centimeters of tissue paper.

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the sample is drawn without replacement from a class of 9 females and 18 males, so the number of males selected follows a hypergeometric distribution.

3. False: The percentage distribution can be constructed from the frequency distribution directly. A frequency distribution is a summary of the number of times each score occurs in a set of data. It shows the distribution of scores into classes or groups of equal size. It is useful in understanding the pattern of data. A percentage distribution is a distribution of data as a percentage of the total data. This distribution is constructed by dividing the frequency of each class by the total frequency and multiplying by 100.7. True: The coefficient of variation is a measure of relative variation. The coefficient of variation is a ratio of the standard deviation to the mean of the distribution expressed as a percentage. It is used to compare the variability of two or more sets of data with different means. The formula for coefficient of variation is given as CV= (standard deviation/mean) *100.9. True: The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a hypergeometric distribution. A hypergeometric distribution is a probability distribution used to calculate the probability of obtaining a specific number of successes in a fixed number of draws from a finite population. It is used to find the probability of obtaining a certain number of successes in a sample without replacement from a finite population with a specified number of successes and failures. In this case, the sample is drawn without replacement from a class of 9 females and 18 males, so the number of males selected follows a hypergeometric distribution.

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