a norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. what is the area of the largest possible norman window with a perimeter of 30 feet?
The area of the largest possible norman window with a perimeter of 25 ft is 43.75 ft²
Let r = the semicircle's radius
h = the rectangle's radius
2r = the window's width
C = 2πr is the formula for the perimeter of a circle,
The perimeter of the semicircle =πr
The perimeter of the window is
P=πr + 2h + 2r = 25
2h + (π +2)r = 25
h = ½[25 - (π + 2)r]
h = 12.5 - (π/2 +1)r ...............(1)
The formula for the area of a circle is A= πr², so
½πr² = the perimeter of the semicircle
The area of the window is
A = ½πr² + 2rh.............. (2)
Substitute (1) with (2).
A = ½πr² + 2r[12.5 - (π/2 +1)r] = ½πr² + 25r - (π +2)r²
A = 25r - (π + 2 - π/2)r²
A = -(π/2 + 2)r² + 25r ........(3)
One way to notice the vertex is to set the first derivative equal to zero.
dA/dr =-2(π/2 + 2)r + 25 = 0
-(π + 4)r + 25 = 0
r = 25/(π + 4)
r ≈ 3.50 ft .......... (4)
Substitute (4) with (1).
h = 12.5 - (π/2 +1)(3.50) = 12.5 - (2.571× 3.50)
h = 12.5 - 9.00 = 3.50
h = 3.50 ft
Area = 1.571(3.50)² + 2×3.50×3.50 = 19.25 + 24.50
Area = 43.75 ft²
So, the area is 43.75 ft².
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Colleen and Nigel have bedrooms with the same perimeter. Nigel's bedroom has a width 34 times the width of Colleen's bedroom.
What is the length, l, of Nigel's bedroom?
Multiple choice questions.
A)
9 ft
B)
10 ft
C)
11 ft
D)
12 ft
The length of Nigel's bedroom is 11 feet while the width is 9 feet
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
For Colleen room:
length = 8 ft, width = 12 ft
Perimeter = 2(length + width)
substituting:
Perimeter = 2(8 + 12) = 2(20)
Perimeter = 40 feet
For Nigel room:
length = l ft, width = 3/4 times that of Colleen = (3/4)(12) = 9 feet
Perimeter = 2(length + width)
But Colleen and Nigel room has same perimeter
substituting:
40 = 2(l + 9)
l + 9 = 20
l = 11 feet
The length is 11 feet.
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please helppp
Examine the two news headlines from real observational studies and determine at least one plausible lurking variable that could explain the cause and effect. Remember, do not argue about the link expressed in the headline, but rather accept the association as true. Your task is to determine the other variable(s) that could be the actual cause(s).
b. “Is Gluten the Culprit in Our Fight Against Obesity?”
A plausible lurking variable that could explain the cause and effect in the headline "Is Gluten the Culprit in Our Fight Against Obesity?" is overall diet.
It's possible that individuals who consume a diet high in gluten also consume a diet high in overall calories and processed foods, leading to weight gain and obesity. This would mean that it is not specifically gluten causing the obesity, but rather a combination of factors in the individual's diet.
What is a lurking variable?A lurking variable is a variable that has a connection (e.g., may be correlated) with the response and the explanatory variable but is neither the explanatory variable nor the response variable.
Although it is not taken into account in the study, it might affect how the variables are related.
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(x² - 4)/(x² - 7x + 10)
Use interval notation to indicate where ƒ(x) is continuous.
I got (-inf,2)U(5,inf) for my answer but it says there should be something else. What am I missing?
In interval notation, the interval of continuity of f(x) is (-∞, 2) ∪ (5, +∞)
What is continuity of a function in an interval?A function is said to be continuous in an interval if all the values in the interval satisfy the function.
How to use interval notation to indicate where ƒ(x) is continuous?Since we have the function (x² - 4)/(x² - 7x + 10), we desire to find the interval in which it is continuous. So, we proceed as follows.
For the function f(x) = (x² - 4)/(x² - 7x + 10) to be continuous, then the denominator (x² - 7x + 10) ≠ 0
So, solving this inequality, we have
x² - 7x + 10 ≠ 0
x² - 2x - 5x + 10 ≠ 0
Factorizing, we have that
x(x - 2) - 5(x - 2) ≠ 0
(x - 2)(x - 5) ≠ 0
x - 2 ≠ 0or x - 5 ≠ 0
x ≠ 2 or x ≠ 5
Also, since the coefficient of x² is positive the function f(x) tends to ±∞.
So, the interval of continuity of f(x) is 2 < x and x > 5
So, the interval of continuity of f(x) is (-∞, 2) ∪ (5, +∞)
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The rabbit population in Butler County, which is currently at 6,004 rabbits, is increasing by 8% each year. How many rabbits will there be in 10 years?
The population of rabbits in the Butler County, where the starting rabbit population of 6,004 increases by 8% per year in 10 years is about 13,362 rabbits
What is a population?A population is the set that comprises of all individuals or items that share a common specified characteristics.
The current population of the rabbit = 6,004
The rate at which the population is increasing per year = 8%
The number of rabbits in 10 years is found using the formula for population growth as follows;
P = P₀ × e^(r·t))
Where;
P = The population or number after the time t
P₀ = The initial or starting population = 6,004 rabbits
r = The percentage growth rate = 8%
t = The time of growth = 10 years
e = Euler number
Therefore;
P₁₀ = 6,004 × e^(0.08 × 10) ≈ 13362
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As part of the study described in exercise 10, the Educational Testing Service computed the average Verbal SAT score for each state, as well as the average Math SAT score for each state. (Again, D. C. Counts as a state. ) The corre- lation between these 51 pairs of averages was 0. 97. Would the correlation between the Math SAT and the Verbal SAT computed from the data on all the individuals who took the tests-be larger than 0. 97, about 0. 97, or less than 0. 97? Explain briefly
If the data for every person who took the tests were tabulated, the correlation between the Math and Verbal SATs would be less than 0.97.
Are the SAT verbal and SAT reading the same test?
The word used to designate the SAT Reading and Writing part is an older, outmoded one. The SAT Verbal section's material is still highly significant today, though. Many of the subjects and abilities from the old SAT Verbal portion are now included in the Evidence-Based Reading and Writing section.
Here we know that the correlation between these 51 pairs of averages was 0. 97.
And as we all know that the Educational Testing Service computed the average Verbal SAT score for each state, as well as the average Math SAT score for each state.
As we know that the individual people tend to have more variation when you compare them to the average person
then if we look at the individual math and rebels course then there's probably a way more variation.
Here we know that the straight line wouldn't be there.
Then the whole thing would not be the same.
And which tells that It would be less of a correlation coefficient.
So it is less that 0.97.
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olve item carefully.
1. rm rode 4 kilometer on hi bike.hi iter matina rode 3,000 meter on her bike.who rode the farthet and how much farther did he/he ride?? anwer in term of km.
He rode 1 kilometer farther than her, which is equal to 1,000 meters.
He rode the farthest as he rode 4 kilometers and she rode 3,000 meters. To calculate how much farther he rode, we need to convert 3,000 meters into kilometers. 1 kilometer is equal to 1,000 meters. So, 3,000 meters is equal to 3 kilometers. Therefore, he rode 1 kilometer farther than her, which is equal to 1,000 meters.
To calculate the difference between the two distances, we can use the following formula:
Difference = km1 - km2
In this example, km1 is 4 kilometers and km2 is 3 kilometers.
Difference = 4 - 3
Difference = 1
Therefore, he rode 1 kilometer farther than her, which is equal to 1,000 meters.
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3x - 4y = 6
6x - 8y = 10
The system shown has _____ solution(s).
one
infinite
no
Answer:
no solution
Step-by-step explanation:
6x - 8y = 10
Divide by 2,
6x/2 - 8y/2 = 10/2
3x - 4y = 5
3x - 4y = 6
3x - 4y = 5 = 6
But actually, 5 ≠ 6
The system shown has no solution. The answer is obtained by solving the linear equations.
What is a linear equation?
The equation with the highest degree of one is a linear equation. This demonstrates that there are no variables in a linear equation with an exponent bigger than one. Such an equation yields a straight line on the graph.
We are given 6x - 8y = 10
On dividing both sides by 2, we get
⇒6x/2 - 8y/2 = 10/2
⇒3x - 4y = 5
But, we are given that 3x - 4y = 6
This shows that 5 must be equal to 6
But, 5 ≠ 6
Hence, the system shown has no solution.
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A triangle has sides with lengths of 8 inches, 11 inches, and 13 inches. Is it a right triangle?
Yes
No
An online recruiting website offers listings for a fixed fee of $30+ $0.42 per word. Your listing has 43 words. How much
will you pay?
Answer:
You will need to pay $48.06.
Solution:
Given that,
The fixed fee of online recruiting website offers listings is $30,
and $0.42 per word.
Your listing has 43 words,
so,
No.of words*Cost per word = 43*0.42
=$18.06
Total fee for 43 listings =$30 + $18.06
=$ 48.06
Total fee for listing 43 words on an online recruiting website=$48.06
The side lengths of quadrilateral WXYZ are 8, 10, 12, and 16 units. Quadrilateral EFGH is a reduction of Quad WXYZ by a ratio of. What are the side lengths for Quad EFGH?
The side lengths for Quadrilateral EFGH are 4, 5, 6, and 8 units.
Quadrilateral EFGH is a reduction of Quad WXYZ by a ratio of 1:2. To find the side lengths for Quad EFGH, divide the side lengths of Quad WXYZ by 2. Therefore, the side lengths of Quad EFGH will be 4, 5, 6, and 8 units.
There are four sides, four vertices, and four angles in a closed quadrilateral. It is a form of polygon. Quadrilaterals' inner angles add up to 360 degrees in total. The English word quadrilateral is derived from the Latin words quadra, which means four, and latus, which means sides.
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Two stores are advertising specials on apples.
Store A
8 apples for $4.40 Store B
12 apples for $5.76
Apples are sold individually.
a) What is the cost for 1 apple at Store A?
b) What is the cost of 1 apple at Store B?
C) How much less would 30 apples cost at Store B than at Store A?
cool beans is a locally owned coffee shop that competes with two large coffee chains, planeteuro and frothies. alicia, the owner, hired two students to count the number of customers that entered each of the coffee shops to estimate what percent of people who are interested in coffee are visiting each shop. after a week, the students found the following results: 606 visited cool beans, 810 visited planeteuro, and 1,160 visited frothies. the students were surprised that cool beans had 148 visits on monday which represented 60% of all people who visited one of the three coffee shops on mondays. how many people visited one of the three coffee shops on monday?
48.15% people visited one of the three coffee shops on monday
The scholars discovered that;
518 people went to Cool Beans, 974 to Planet Euro, and 1,160 to Frothies.
Assume that x% of Monday's customers at each of the three coffee shops were x.
One hundred thirty-five people went to Cool Beans on Monday.
Of the total number of customers who went to one of the three coffee shops on Monday, 52% went to Cool Beans.
Consequently, 52/100 * x = 135
The calculation for x is (135*100)/52.
x = 260 individuals
On Monday, the following number of visitors visited either PlanetEuro or Frothies:
260-135 =125
Calculating the percentage of Monday visitors to either PlanetEuro or Frothies;
135= 52%
125=?
Cross-product as you
(125*52)/135 =48.15%
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Two trains leave Cleveland at the same time. One train travels east and the other travels west. The speed of the westbound train is 3mph
greater than the speed of the eastbound train. After 4
hours, they are 648
miles apart. Find the rate of each train. Assume that the trains travel in a straight line in directly opposite directions.
Answer: Let x be the speed of the eastbound train.
Then the speed of the westbound train is x+3 mph.
We can set up the following equation using the distance formula (rate x time = distance)
x*4 = 648/2 + (x+3)*4
Solving for x,
x= 42
So the speed of the eastbound train is 42 mph and the speed of the westbound train is 45 mph.
Step-by-step explanation:
For each 70 mm of coloured fabric Alex uses to make his curtains, he also uses 20 cm of white fabric. Express the amount of white fabric to coloured fabric as a ratio in its simplest form.
20 : 7 is already the simplest term and there is no need to further simplify.
What is ratio?Ratio can be defined as the given value divided by total value.
When presenting a ratio as an answer:
1. It has to be in the form of integer, it cannot be in the form of fraction or decimals
2. There should be of the equivalent units.
3. It must be in its simplest form
Convert the units in cm
Coloured Fabric = 70 mm
Coloured Fabric = 70 ÷ 10 cm
Coloured Fabric = 7 cm
Find the ratio of the Colour Fabric to White Fabric:
Coloured Fabric = 7 cm
White Fabric = 20 cm
Ratio of White Fabric : Colour Fabric = 20 cm : 7 cm
Ratio of White Fabric : Colour Fabric = 20 : 7
Therefore, 20 : 7 is already the simplest term and there is no need to further simplify.
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A 32 flat screen television measures 32 inches across its diagonal. The diagonal makes a 35 degrees angle with the bottom of the television. What equation can be used to solve for the height,H, of the television screen?
The 32 inche flat screen televisions will be 19.35 inches in height based on the angle between diagonal and bottom
The diagonal, bottom and perpendicular forms
right angled triangle. The mentioned angle can be related with diagonal and height through sine function. The formula is expressed as follows -
sin theta = height ÷ diagonal
Keep the values in formula to find the value of height.
sin 35 = h/32
Rewriting the formula for h.
h = sin 35 × 32
Keep the value of sin 35 in the formula
h = 0.57 × 32
Performing multiplication on Right Hand Side of the equation
h = 18.35 inches
Hence, the TV screen is 18.35 inches high.
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A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 15 ft by 5 ft by 10 ft. If the container is entirely full and, on average, its contents weigh 0.09 pounds per cubic foot, find the total weight of the contents. Round your answer to the nearest pound if necessary.
In a case whhereby container built for transatlantic shipping is constructed in the shape of a right rectangular prism and Its dimensions are 15 ft by 5 ft by 10 ft the total weight of the contents is 68 pounds.
How can the Volume of right rectangular prism be calculated?The concept that will be usd here is rectangular prism.
Then to calculate the volume of a rectangular prism, we will need to to make the multiplication with 3 dimensions:( length×width×height).
the dimensions of the container built are 7.5 ft by 11.5 ft by 3 ft.
the container is entirely full and, on average, its contents weigh 0.15 pounds per cubic foot.
So, the volume of the container is calculated as:
The dimensions of the container built are 15 ft by 5 ft by 10 ft. since the container is entirely full , considering the average, its contents weigh 0.09 pounds per cubic foot.
we can calculate the volume of the container as:15 ft * 5 ft * 10 ft= 750ft^3
Then, the total weight of the contents can be found as :
750 ft³× 0.09 pounds per cubic foot= 67.5 pounds = 68 pounds.
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Please help with this I’ll reward you I promise
The factorized expressions are (4x - 1)(4x + 5), (2z - 7)(z + 10) and (3x - 8)(2x + 5)
The factor pairs of -80The pair factors of -80 are (-1, 80), (-2, 40), (-4, 20), (-5, 16) and (-8, 10).
The factor pairs with a sum of 16The pair factors of -80 in this category is
(-4, 20)
This is so because
-4 + 20 = 16
Factor the expressionWe have
16x^2 + 16x - 5
So, we have
16x^2 + 20x - 4x - 5
Factorize
4x(4x + 5) -1(4x + 5)
So, we have
(4x - 1)(4x + 5)
For the other expressions, we have
2z^2 + 13z - 70
2z^2 + 20z -7z - 70
So, we have
(2z - 7)(z + 10)
6x^2 - x - 40
6x^2 + 15x -16x - 40
So, we have
(3x - 8)(2x + 5)
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Someone help me do further maths ‘transformations of graphs and functions’ question
Answer:
see attached
Step-by-step explanation:
just draw a narrower one, about 1/2 of the x value.
Which expressions are equivalent to -56Z +28?
An expression that is equivalent to -56Z +28 can be -23z + 10 - 33z + 18
How to calculate the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
In this case, an expression that is equivalent to -56Z +28 can be:.
-23z + 10 - 33z + 18
= -23z - 33z + 10 + 18
= -56z + 28
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Help Me Please!!!!!
Homework!
A graph of the inequality w ≤ 200 is shown in the image attached below.
How to graph the inequality?In this scenario, we would solve the given inequality by making "w" the subject of formula as follows;
w/-10 ≤ -20
By multiplying both sides of the inequality by -10, we have the following:
-10 × w/-10 ≤ -20 × -10
w ≤ 200
Next, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Additionally, the circle is closed because of the less than or equal to (≤) symbol.
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The ordered pair (a, b)(a,b)left parenthesis, a, comma, b, right parenthesis gives the location of point P on the coordinate plane. The values of a and b have the same sign. Neither a nor b is 0. Where could point P be located on the coordinate plane?
Point P cannot be located on either the x-axis or y-axis, as neither a nor b is 0.
The coordinate system's two axes, the x-axis and the y-axis, constitute a region called a quadrant.
If both a and b have the same sign, point P could be located in one of the four quadrants:
For First quadrant (a > 0, b > 0)
For Second quadrant (a < 0, b > 0)
For Third quadrant (a < 0, b < 0)
For Fourth quadrant (a > 0, b < 0)
Hence, Point P cannot be located on either the x-axis or y-axis, as neither a nor b is 0.
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A. 60 degrees
B. 150 degrees
C. 120 degrees
D. 240 degrees
Answer:
D
Step-by-step explanation:
How many different roots does the polynomial function,
y = (x − 2)(x + 3)² have?
-
A. 1
B. 3
C. 2
D. 4
The polynomial function is the product of two different linear factors, (x-2) and (x+3)^2, which means that we have two different roots, x=2 and x=-3
What are the roots the given polynomial function have?A polynomial function is a function that can be written as constants and n is the degree of the polynomial. The polynomial function y = (x − 2)(x + 3)² is a quadratic function because it has an [tex]x^{2}[/tex] term.
The roots of a polynomial function are the values of x that make the function equal to zero. In other words, they are the solutions to the equation y = 0.
The polynomial function y = (x − 2)(x + 3)² can be factored as (x-2)(x+3)(x+3), which means that we have three different linear factors, (x-2), (x+3), and (x+3) . Each linear factor corresponds to one root of the polynomial.
So the polynomial function y = (x − 2)(x + 3)² has 2 distinct roots. The correct answer is C.
Alternatively, we can also see that the polynomial function is the product of two different linear factors, (x-2) and [tex](x+3)^{2}[/tex], which means that we have two different roots, x=2 and x=-3.
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What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer? What is the answer?
Assuming the interest is compounded monthly, the interest rate that would be required in order for Joshua to end up with $1,500 is 2.26%.
How to calculate the interest rate?Mathematically, compound interest can be calculated by using this formula:
A(t) = P(1 + r/n)^{nt}
Where:
A represents the future value.n represents the number of times compounded.P represents the principal.r represents the interest rate.T represents the time measured in years.Substituting the given parameters into the compound interest formula, we have;
1,500 = 1,000(1 + r/12)^{12 × 18}
1.5 = (1 + r/12)^{216}
Taking the 216th root of both sides of the equation, we have:
1.00187891623 = 1 + 0.083333333r
0.083333333r = 1.00187891623 - 1
0.083333333r = 0.00187891623
r = 0.00187891623/0.083333333
r = 2.26
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Answer:
the interest rate that would be required in order for Joshua to end up with $1,500 is 2.26%.
Step-by-step explanation:
Select the correct answer. Sides of three square rooms measure 13 feet each, and sides of two square rooms measure 15 feet each. Which expression shows the total area of these five rooms? A. (3 × 13^2) + (2 × 15^2) B. (2 × 13^3) + (2 × 15^2) C. (3 × 15^2) + (2 × 13^2) D. (3 × 13^2) × (2 × 15^2)
The correct answer i.e. the total area is A. (3 × 13^2) + (2 × 15^2).
What is the area formula?The edge of a shape's area is measured. You must divide the length and breadth of a rectangles or square in order to determine its area. A is x times y in size.
How do you calculate a square's area?The area of a square is composed of (Side) (Side) square units. Once the diagonally, d, is known, the surface of a square is equal to d22 square units. For instance, 8 8, or 64 sq ft is the size of a cube with sides that are each 8 feet long (ft2).
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Which polynomial is NOT equivalent to (5x – 2)(-2x + 4)?
The polynomial which is not equivalent to (5x – 2)(-2x + 4) is -10x + 20x + 4x – 8 and is therefore denoted as option A.
What is a Polynomial?This is referred to as a type of algebraic expression in which the exponents of all variables should be a whole number.
(5x – 2)(-2x + 4) when expanded will give:
-10x² + 20x + 4x – 8 which can be rewritten as the following below:
-8 + 24x – 10x² -10x² + 24x – 8This is therefore the reason why -10x + 20x + 4x – 8 was chosen as the correct choice.
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The options are:
A) -10x + 20x + 4x – 8
B) 4x + 20x – 10x2 – 8
C) -8 + 24x – 10x2
D) -10x2 + 24x – 8
I really need help on this question
Answer: NOT Parallel because 98 /= 82 (Alternate angles are equal)
the difference between a positive number X and 3 is 21 what is a number stepsssss
Answer:
Solution:
Let another number be x.
Then positive number = 5x
According to the question,
5
�
+
21
=
2
(
�
+
21
)
5x+21=2(x+21)
⇒
5
�
+
21
=
2
�
+
42
⇒5x+21=2x+42
⇒
5
�
−
2
�
=
42
−
21
⇒5x−2x=42−21
⇒
3
�
=
21
⇒3x=21
⇒
�
=
21
3
=
7
⇒x=
3
21
=7
Hence another number = 7 and positive number = 7 x 5 = 35.
the subjects in this dataset answered a call for volunteers to participate in this study. assuming every subject who volunteered has a recorded response for every variable, what type of bias could possible result from this sampling design?
The individuals in this dataset consented to participate in this study after receiving a request for volunteers. This sampling design may be biased in favor of volunteers, given that every volunteer has recorded responses for each variable.
At any point during the trial—from recruitment to retention to follow-up—volunteer bias may manifest itself. Volunteers and the target community differ not only in terms of sociodemographic characteristics but also in terms of views about the experiment and the institutions involved.
Volunteer bias may also be related to the illnesses or conditions being investigated, as volunteers may be less likely to volunteer for research on illnesses or behaviors that are viewed as less acceptable by society, such as ailments linked to drug usage.
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After being asked for volunteers, the people in this dataset agreed to take part in the study. Given that each volunteer has recorded responses for each variable, this sample design may be skewed in favour of the volunteers.
Volunteer bias may appear at any time during the experiment, from recruitment to retention to follow-up. The target community and volunteers have different sociodemographic features, as well as different perspectives on the experiment and the participating institutions.
As volunteers may be less likely to volunteer for research on illnesses or behaviours that are perceived as less acceptable by society, such as conditions associated to drug use, bias may also be related to the illnesses or conditions being examined.
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