Answer:
[tex]X=17.9m[/tex]
Step-by-step explanation:
Length of arc [tex]L_a=24m[/tex]
Height of arc [tex]H_a=8m[/tex]
Tet the length on the ground be
[tex]2a=24\\ a=12m[/tex]
Generally the Pythagoras equation is mathematically given by
[tex]a^2=b^2+c^2[/tex]
[tex]c^2=a^2+b^2[/tex]
[tex]c^2=12^2+8^2[/tex]
[tex]c^2=144^2+64^2[/tex]
[tex]c=8.9[/tex]
Therefore the distance between he person throwing the ball and the point on the ground at which the ball first strikes X
[tex]X=2c\\X=2*8.9[/tex]
[tex]X=17.9m[/tex]
2 3X Find the solution set for each of the following equations. a 20x² + 10x -8=0 b x² − 8x + 15 = 0 3X C
The Solution set of the given quadratic equations are
1. x = 5 or x = 3
2. x= -3/2 or x = 5
What is quadratic equation?A Quadratic equation is an algebraic expression in which highest degree of the given variable is 2.
Formula used as x² +ax + b = (x + c)(x + d)
Where 'a' is the sum 'c' and 'd' and 'b' is the product of 'c' and 'd'
According to the information, Factorize all the given quadratic equations we get;
1. x² - 8x + 15 =0
Now Split middle term of quadratic equation using formula we get,
x² - 5x - 3x + 15 =0
⇒ x(x- 5) -3(x - 5) =0
⇒(x -5)(x - 3) =0
⇒ x- 5 =0 or x - 3 =0
⇒ x= 5 or x = 3
2. 20x² + 10x -8=0
Now Split middle term of quadratic equation using formula we get,
10x² + 5x - 4 = 0
⇒ 2x(x-5) +3(x-5)=0
⇒(2x+3)(x-5)=0
⇒2x+3 =0 or x-5 =0
⇒ x= -3/2 or x=5
Hence, the solution set are
1. x = 5 or x = 3
2. x= -3/2 or x = 5
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wHAT IS THE NEXT NUMBER IN THE FOLLOWING SERIES OF NUMBERS 1,4,8,13,19
Answer:
26
Step-by-step explanation:
a_n = 1/2 (n^2 + 3 n - 2) (for all terms given)
1, 4, 8, 13, 19, 26, 34, 43, 53, 64, 76, 89, 103, 118, 134, 151, 169, 188, 208, 229, ...
Answer:
26
Step-by-step explanation:
The difference between 1 and 4 is 3
The difference between 4 and 8 is 4
The difference between 8 and 13 is 5
The difference between 13 and 19 is 6
The difference between 19 and 26 is 7
Write an equation in y = mx + b form to represent this table.
Answer:
y = 3x + 2
Step-by-step explanation:
In the equation [tex]y = mx + b[/tex], m represents the slope, and b represents the y-intercept. To write the equation in this form, we must substitute m and b into this equation.
. . . . . . . . . . . Finding "b"
The y-intercept is another name for the y-value when the x- value = 0. So, we need to look at the table and find the y-value for when x = 0.
⭐ y = 2 when x = 0. Thus, b = 2.
. . . . . . . . . . . Substitute "b" into the equation
y = mx + 2
. . . . . . . . . . . One way to find "m"
m, your slope, can be found using the slope formula: [tex]m = \frac{y__2 - y__1}{x__2 - x__1}[/tex], where [tex](x__1, y__1)[/tex] and [tex](y__2, y__1)[/tex] are coordinates that you are given.
I am going to choose the coordinates (0,2) and (1,5), but you can choose any other 2 coordinates from the table.
m = (5 - 2)/(1-0)
m = 3/1
⭐ m = 3
. . . . . . . . . . . Another way to find "m"
m, your slope, can be found by substituting a coordinate that you are given into your equation with b already found.
y = mx + 2
I am going to use the coordinate (1,5), but you can choose another coordinate from the table if you'd like.
-2 + 5 = 1(m) + 2 -2
⭐ 3 = m
. . . . . . . . . . . Substitute "m" into the equation
y = 3x + 2
Answer:
(0,2)
2 = b
(1,5)
5 = m + b
(2,8)
8 = m(2) + b
(3,11)
11 = m(3) + b
(4,14)
14 = m(4) + b
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-the manager of a bank record of the amount of each Time customer spent waiting in the line during peak business hours on Monday the waiting times are shown below find the mean waiting time Roger answer to one Decimal place 6.8 min 7.5 min 7.2 min brainly
Answer:
To find the mean waiting time, you need to add up all the waiting times and divide by the number of customers. In this case, the total waiting time is 6.8 + 7.5 + 7.2 = 21.5 minutes. Since there are 3 customers, the mean waiting time is 21.5 / 3 = 7.17 minutes. Rounded to one decimal place, the mean waiting time is 7.2 minutes.
Step-by-step explanation:
A triangle has its base doubled and its
height increased by 30%. By what percent
has the area of the triangle increased?
(A) 130%
(B) 160%
(C) 230%
(D) 260%
Let the base and height of triangle be b and h.
area of triangle= 1/2*base*height
Area of triangle= bh/2
Now Base is Doubled and Height increase by 30%
New base = 2b
New height = h×130/100 = 13h/10
New area = 1/2 × 2b × 13h/10
New area = 13bh/10
Area increased = New area - area
Area increased = 13bh/10 - bh/2
Area increased= 13bh-5bh/10
Area increased= 8bh/10
Area increased= 4bh/5
ratio increased in % = Area increased/ Old Area × 100
ratio increased in % = 4bh/5 ÷ bh/2 × 100
ratio increased in % = 4/bh × 2/bh × 20
ratio increased in % = 8×20
ratio increased in % = 160%
if the price of viva increases from $2.50 to $2.60 and the price of brawny is unchanged, the sales of brawny will?
The sales of Brawny will remain unchanged, as the amount of Brawny has not changed.
Price is one of the factors that influence the demand and sales of any product. Therefore, when the price of a product changes, the sales of that product may be impacted. However, when the price of one product changes, the sales of another product that has not changed in price may remain unaffected. In this case, since the price of Viva has increased from $2.50 to $2.60, while the amount of Brawny has remained unchanged, the sales of Brawny will likely remain unchanged.
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Nicholas has 5 1/2 cups of flour. One recipe for a cake he is making calls for 3 3/4 cups of flour. He also needs 8 cups of flour for a cookie recipe. How much more flour will nicholas need to make the cake and cookies?
Nicholas has a total of 5 1/2 cups + 3 3/4 cups = <<5.5+3.75=9.25>>9.25 cups of flour.
To make the cake and cookies, he needs a total of 3 3/4 cups + 8 cups = <<3.75+8=11.75>>11.75 cups of flour.
Therefore, Nicholas will need an additional 11.75 cups - 9.25 cups = <<11.75-9.25=2.5>>2.5 cups of flour to make the cake and cookies.
Savannah takes a car to a title loan business to borrow some money. Savannah is given $2,900.00. She must pay back the $2,900.00 in addition to a $1,375.00 fee in 8 months.
What simple interest rate is she
being charged?
Round to the nearest tenth of a percent and don't forget to include a percent sign, %, in your answer.
Savannah is being charged a simply interest rate of ______.
Step-by-step explanation:
To find the simple interest rate that Savannah is being charged, we can use the formula for simple interest:
I = P * r * t
where I is the total interest paid, P is the principal (the amount borrowed), r is the interest rate, and t is the time period over which the interest is paid.
Since Savannah must pay back the $2,900.00 principal plus a $1,375.00 fee, the total interest paid is $1,375.00. The time period is 8 months, which is equal to 8/12 = 2/3 of a year. Substituting these values into the formula and solving for r, we get:
$1,375.00 = $2,900.00 * r * (2/3)
r = $1,375.00 / ($2,900.00 * (2/3)) = 0.1429
This is the interest rate that Savannah is being charged. To express this rate as a percentage, we can multiply it by 100% to get:
r = 0.1429 * 100% = 14.3%
Therefore, Savannah is being charged a simple interest rate of approximately 14.3%.
You’re involved in the design of a new facility. It is important for people to move between work stations quickly. Based on the figure below, how many feet would a person need to walk to get from Work Station 1 to Work Station 3?
The distance from work station 1 to work station 3 is 13 feet.
How to find the side of a right triangle?The figure shows the distance between workstation. The figure represents a right angle triangle.
The distance from work station 1 to work station 3 can be calculated as follows:
using Pythagoras's theorem,
c² = a² + b²
where
c = hypotenuse sidea and b are the other legsTherefore, the distance from work station 1 to work station 3 is the hypotenuse side of the right triangle.
Hence,
5² + 12² = c²
25 + 144 = c²
c² = 169
c = √169
c = 13 ft
The distance between the work stations is 13 ft.
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Use the information below to complete the problem: p(x) = 1/(x+1) and q(x)= 1/(x-1) Perform the operation and show that it results in another rational expression. p(x) / q(x)
Answer:
p(x)/q(x) = (x+1)/(x-1)
Step-by-step explanation:
see image.
p(x)/q(x) is just dividing the two functions. So we'll put p(x) on top and q(x) on the bottom.
Now it looks like a fraction over a fraction. Use Keep-Change-Flip to simplify. Keep the top. Change the divide to times. Flip the bottom. See image.
(You can always use Keep-Change-Flip for numbers only, radicals, and algebraic expression in fraction over a fraction situations)
To multiply fractions, multiply top×top and bottom×bottom straight across.
see image.
PLEASE HELP
An equation of a line is shown. A second line is perpendicular to the given line and passes through the point (0,1).
Which is the equation of the perpendicular line?
The equation of the perpendicular line is (c) y = 2/9x - 1
How to determine the perpendicular line equation?From the question, we have the following parameters that can be used in our computation:
y + 17 = -9/2(x - 3)
Also, from the question;
We have the following points
Point = (0, -1) i.e. (x, y) = (0, -1)
The equation of a line can be represented as
y - y₁ = m(x - x₁)
Where
Slope = m
By comparing the equations, we have the following
m = -9/2
This means that the slope is -9/2
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is 2/9
The equation of the line is then calculated as
y = m(x - x₁) +y₁
Where
m = 2/9
(x₁, y₁) = (0, -1)
So, we have
y + 1 = 2/9(x - 0)
Evaluate
y = 2/9x - 1
Hence, the line has an equation of y = 2/9x - 1
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Emily go out to dinner eight times a month the average cost is $35 per meal how much does she spend each month? How much cause she save if she cut back to five times a month?
Answer:
She spend $280 a month when she goes out to eat 8 times a month.
She will save $105 a month if she cuts back to 5 times a month.
Step-by-step explanation:
35 x 8= 280
35 x 5 = 175
280 - 175 = 105
Answer:
8 * $35 per meal = $280
She spends $280 per month for 8 dinners$280 - (5 * $35)
= $280 - ($175)
= $105
Therefore, Emily will save $105 if she eats 5 times a month only.Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-The positive variables p and c change with respect to time 1. The relationship between p and c is given by the equation p^2 = (20-c)^3. At the instant when dp/dt = 41 and c = 15, what is the value of dc/dtï¼
The value of dc/dt due to changes in p and c variables is 0.364.
The positive variables p and c change with respect to time 1. The relationship between p and c is given by the equation p^2 = (20-c)^3. Now the dp/dt value is 41 and c is 15.
Differentiate the given equation to obtain the following:
2p dp/dt = 3(20-c)^2 dc/dt
Substitute the given values in the equation to obtain the following:
2p (41) = 3(20 - 15)^2 dc/dt
Simplify the equation to obtain the following:
82 = 225 dc/dt
Divide both sides of the equation by 225 to obtain the following:
dc/dt = 82/225
Simplify the equation to obtain the following:
dc/dt = 0.364
Hence, the value of dc/dt is 0.364.
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Jonas spent $134 last month eating at restaurants. He decides he needs to spend 36% less
on eating at restaurants this month. How much can he spend at restaurants this month?
Answer:
I think its $12..? if you subtract the two numbers than you should get my answer
Which graph shows an image and preimage after reflecting across y = -x ? *
Option 1
Option 2
Option 3
Option 4
The image of the correct option is attached below(image two)
What is the graph?The coordinates of the image's bottom-most vertex are (- 2, 2).
The x-coordinate and the y-coordinate switch places and become negated if you reflect over the line y = -x (the signs are changed).
As a result, following reflection, the chosen vertex's coordinates are (2, -2).
As a result, option 3's graph displays the image and preimage after reflection while taking the selected vertex into account.
Therefore Option three satisfies the solution
image of option 3 is attached below
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The complete Question was found and attached below
Which of the following is false about the central limit theorem (CLT)? O If we take more samples from the original population, the sampling distribution is more likely to be nearly normal. O If the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardless of the sample size. O As the sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless of the shape of the original population distribution. O The CLT states that the sampling distribution will be centered at the true population parameter.
Only the first statement is false. The rest are true statements about the Central Limit Theorem.
The Central Limit Theorem (CLT) is a fundamental theorem in probability and statistics which states that, given a sufficiently large sample size from a population with a given mean and standard deviation, the sampling distribution of the mean will be nearly normal, regardless of the shape of the original population distribution.
It is important to note that the first statement presented is false. Taking more samples from the population will not necessarily result in a more normal sampling distribution. The CLT does not guarantee that the sampling distribution will be normally distributed, only that it is more likely to be so as the sample size increases.
The second statement is true. If the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardless of the sample size. The third statement is also true. As the sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless of the shape of the original population distribution.
Finally, the fourth statement is also true. The CLT states that the sampling distribution will be centered at the true population parameter. This means that the mean of the sampling distribution will be equal to the mean of the population.
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could some one help me with this question please (short answers are fine)
The sum of the exterior angles of the given polygon is 360°.
What is polygon?In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words, poly which means numerous and gon means sides. To create a closed figure, a minimum of three line segments must be connected end to end.
Given that,
There is a polygon that has 4 sides.
Since, a polygon having 4 sides is called a quadrilateral, and the sum of the interior angle of the quadrilateral is 360°.
Implies that, the sum of the exterior angle of the quadrilateral will also be 360°.
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given g (x)=4x-4 solve for x when g (x)=0
Answer:
1
Step-by-step explanation:
g(x)=4x-4
g(x)=0
0=4x-4
4=4x
x=1
1. A pharmacy has determined that a healthy person should receive 70 units of proteins, 100 units of carbohydrates and 20 units of fat daily. If the store carries the six types of health food with their ingredients as shown in the table below, what blend of foods satisfies the requirements at minimum cost to the pharmacy? Make a mathematical model for the given problem.
Foods
A
20
B
30
C
Ꭰ
40
40
E
F
45
30
Protein units
Carbohydrates units
50
30
4
Cost per unit
9
235
20
11
25
10
6
50
20
Fat units
9
10
8
According to the information in the graph, the blend of foods that satisfies the requirements at the minimum cost is option A because it would be worth only 10.
How to calculate which is the cheapest blend of food option?To calculate the cheapest blend of food option, we must take into account the amounts of each element (carbohydrate, protein, fat) and identify how many units of each blend we need to cover the minimum quota.
Based on the above information, to identify the blend units we need to cover the minimum quota we must find it by multiplying each of the elements by the number of times we would need to meet the minimum requirement. Once we identify the quantities we need, we must multiply the price by the number of units we need.
Following the previous procedure, we can identify that the best option would be blend A because we must buy it 5 times to cover the minimum requirements. Additionally, its value would be 10, while the others would have a higher value.
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1. Norah uses an ounce of butter to bake 13 cookies. How many cookies can she bake with 89 ounces of butter?
Answer:
1157
Step-by-step explanation:
You multiply 13 and 89
Answer:
1,157 cookies
Step-by-step explanation:
[tex]\frac{cookies}{butter}[/tex] = [tex]\frac{cookies}{butter\\}[/tex]
[tex]\frac{13}{1}[/tex] = [tex]\frac{x}{89}[/tex] You need to multiply 1 by 89 to get 89, so multiply 13 by 89 and you get 1157 cookies.
There are 640 acres in 1 square mile. The area of a forest is increasing at a rate of 1 acre per decade. Which of the following is closest to the rate at which the area of the forest is increasing, in square kilometers per decade? (Use 1 kilometer=0.62mile.)
A.0.0006
B.0.0010
C.0.0025
D.0.0041
The rate at which the area of the forest is increasing, in square kilometers per decade, is 0.0041.
What does the rate of change mean?
How quickly one variable changes in relation to another is known as the rate of change. Speed is an example of a "rate of change." Speed is defined as the rate at which the distance to an object varies in relation to the time spent.
It is given that there are 640 acres in 1 square mile which can also be written as 640 acres= 1[tex]mi^2[/tex].
The area of forest is increasing at a rate of 1 acre/decade.
It is given that 1 km= 0.62mi
By squaring on both sides we will get 1 [tex]km^2[/tex] = 0.3844 [tex]mi^2[/tex].
The rate at which the area of forests is increasing in square kilometers per decade is
[tex]\frac{1acre}{decade} *\frac{1mi^2}{640acre} *\frac{1km^2}{0.3844mi^2} =0.00406478\frac{km^2}{decade}[/tex] .
Therefore the closest value is [tex]0.0041[/tex].
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How many meters per second are in 37 miles per hour? Round to one
decimal.
Answer:
16.5 m/s
Step-by-step explanation:
Solve the system by graphing ツ= 3x ツ = -3x + 6
Answer:
(1, 3)
Step-by-step explanation:
Using a graphing website like Desmos or a graphing calculator, we can figure out the solution: (1, 3)
Match the following graph with the name of the graph
Absolute value: C
Quadratic: D
Constant: A
Square root: E
Linear: B
There are the equations for the graphs on the bottom:
y=2 is constant because the y value never changes
y=x is linear because the y value changes at a constant rate
y= |x| is absolute value because |x| is the absolute value of x
y=x^2 is quadratic because quadratic functions have a degree of 2
y=sqrt(x) is a square root because y= square root of x
i am very confused on this question
It will take kangaroo 7.5 minutes to travel 5 kilometers.
The kangaroo will travel 1.33 kilometers in 2 minutes.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Kangaroo hopes 2 kilometers in 3 minutes.
To find the time taken by kangaroo to travel 5 kilometers,
Use ratio property,
2 kilometers = 3 minutes,
1 kilometer = 3/2 minutes
5 kilometer 15/2 minutes.
In 15/2 or 4.5 minutes, kangaroo will travel 5 kilometers.
The distance travelled by kangaroo in 2 minutes,
In 3 minutes = 2 kilometers covered
in 1 minute = 2/3 kilometers covered
in 2 minutes = 4/3 kilometers will be covered.
So in 2 minutes the kangaroo will cover 4/3 or 1.33 kilometers.
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Suppose y varies directly with x, and y=10 when x =-3. What direct variation equation relates x and y? What is the value of y when x =-1?
The relation between 'x' and 'y' will be y = -(3/10)x. Then the value of the variable 'y' at x = -1 will be 3/10.
What are ratio and proportion?A proportion is a gathering of consecutively requested numbers an and b communicated as a/b, where b is never equivalent to nothing. At the point when two items are equivalent, a proclamation is supposed to correspond.
The variable 'y' is directly proportional to the 'x'. Then the equation is given as,
y ∝ x
y = kx
At x = - 3 and y = 10, then the value of the constant 'k' is calculated as,
-3 = k(10)
k = - 3/10
Then the equation is written as,
y = -(3/10)x
At x = - 1, then the value of the variable 'y' is calculated as,
y = - (3/10) (-1)
y = 3/10
The connection between 'x' and 'y' can't avoid being y = - (3/10)x. Then, at that point, the worth of the variable 'y' at x = - 1 will be 3/10.
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Using circles to model the ratios, divide both circles into
equal parts.
For the ratio 2 to 7,
parts should be shaded.
For the ratio 5:7,
parts should be shaded.
The ratio 2 to 7 is
the ratio 5:7.
By using circle model the images are attached below:
What is a circle model?A circle with a diameter of one has n firms distributed uniformly around it. In light of this, every company's distance from each of its closest neighbors is 1/n.
We must first create two circles in order to compare the ratios of 2 to 7 and 5:7 using a circle model.
Then, we must divide each circle into seven pieces.
We must shade 2 of the circle's total 7 portions in order to maintain the 2:7 ratio.
We must shade 5 of the circle's total 7 portions in order to maintain the 5:7 ratio.
As a result, the first circle symbolizes a 2:7 ratio, while the second circle a 5:7 ratio.
By using circle model the images are attached below:
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Answer: using circles to model the ratios, divide both circles into
7
equal parts.
For the ratio 2 to 7,
2
parts should be shaded.
For the ratio 5:7,
5
parts should be shaded.
The ratio 2 to 7 is
less than
the ratio 5:7
What is the greatest common factor of 18 and 27
Answer:
Step-by-step explanation.
The HCF of 18 and 27 is 9
Which statements about the opposite of −12 are true?
Select each correct answer.
Responses
The opposite of −12 is −112.
The opposite of , negative 12, is , negative fraction 1 over 12, .
−12 and its opposite are located the same distance from zero on a number line.
negative 12, and its opposite are located the same distance from zero on a number line.
−12 and its opposite are on located on the same side of zero on a number line.
negative 12, and its opposite are on located on the same side of zero on a number line.
The opposite of the opposite of −12 is −12.?
According to Integers and number line the correct statements are given below
what is Integers and number line?
Including zero, integers are a range of positive and negative numbers. The definition of an integer on a number line is an image of an integer on a number line. We can do several arithmetic operations using integers on a number line.
solution:
The opposite of the opposite of -12 is -12
The opposite of -12 is 12, and the opposite of 12 is -12.
−12 and its opposite are located the same distance from zero on a number line.
negative 12, and its opposite are located the same distance from zero on a number line.
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question 11 options: in a random sample of 64 orders from on online retailer the proportion of orders made by women is 86%. construct a 95% confidence interval for the true population proportion of online orders made by women. round answers to 3 decimal places, i.e., .xxx. do not put as a percent. do not include leading or ending zeros. lower limit
The Lower limit is 0.745 and the Upper limit is 0.976.
In data, an easy random sample is a subset of people (a pattern) chosen from a larger set (a population) wherein a subset of individuals are selected randomly, all with identical possibilities. it is a system of choosing a pattern in a random manner. In SRS, each subset of okay individuals has the identical chance of being chosen for the sample as every other subset of okay individuals. An easy random pattern is an independent sampling approach. simple random sampling is a fundamental sort of sampling and may be an element of other extra complicated sampling strategies.
In statistics, an easy random pattern is a subset of individuals (a pattern) selected from a bigger set (a population) in which a subset of individuals are chosen randomly, all with identical chances. it's far a manner of choosing a pattern in a random way. In a random sample, every subset of okay people has the identical possibility of being chosen for the pattern as any other subset of okay individuals. An easy random pattern is an impartial sampling approach. simple random sampling is a fundamental type of sampling and can be an issue of other extra complex sampling strategies.
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