Using the quadratic equation the distance of point B from the ground level is D. 3 units
What is an equation?An equation is a mathematical function that shows the relationship between two variables.
How to find the distance of point B from the level ground?Since an archway is modeled by the equation y = -2x² + 8x.
A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0.
If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, we desire to find the distance of point be from the ground. To do this , we proceed as follows.
Since we have the equations
y = -2x² + 8x and x - 2.23y + 10.34 = 0Substituting y into the second equation, we have
x - 2.23y + 10.34 = 0
x - 2.23(-2x² + 8x) + 10.34 = 0
x + 4.46x² - 17.84x + 10.34 = 0
4.46x² - 16.84x + 10.34 = 0
To find the points a and B, we solve for x where both equations intersect.
So, using the quadratic formula, we solve for x
[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex] where a = 4.46, b = -16.84 and c = 10.34
So, substituting the values of the variablers into the equation, we have that
[tex]x = \frac{-(-16.84) +/-\sqrt{(-16.84)^{2} - 4\times4.46\times10.34} }{2\times4.46}\\= \frac{16.84 +/-\sqrt{283.5856 - 184.4656} }{8.92}\\= \frac{16.84 +/-\sqrt{99.12} }{8.92}\\= \frac{16.84 +/-9.96 }{8.92}\\x = \frac{16.84 + 9.96 }{8.92} or x = \frac{16.84 - 9.96 }{8.92}\\x = \frac{26.8}{8.92} or x = \frac{6.88}{8.92}\\x = 3.004 or x = 0.771[/tex]
Since B is higher, we take the higher value x = 3.
So, the distance of point B from the ground level is D. 3 units
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Using the quadratic equation the distance of point B from the ground level is D. 3 units
What is an equation?An equation is a mathematical function that shows the relationship between two variables.
How to find the distance of point B from the level ground?Since an archway is modeled by the equation y = -2x² + 8x.
A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0.
If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, we desire to find the distance of point be from the ground. To do this , we proceed as follows.
Since we have the equations
y = -2x² + 8x and x - 2.23y + 10.34 = 0Substituting y into the second equation, we have
x - 2.23y + 10.34 = 0
x - 2.23(-2x² + 8x) + 10.34 = 0
x + 4.46x² - 17.84x + 10.34 = 0
4.46x² - 16.84x + 10.34 = 0
To find the points a and B, we solve for x where both equations intersect.
So, using the quadratic formula, we solve for x
[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex] where a = 4.46, b = -16.84 and c = 10.34
So, substituting the values of the variablers into the equation, we have that
[tex]x = \frac{-(-16.84) +/-\sqrt{(-16.84)^{2} - 4\times4.46\times10.34} }{2\times4.46}\\= \frac{16.84 +/-\sqrt{283.5856 - 184.4656} }{8.92}\\= \frac{16.84 +/-\sqrt{99.12} }{8.92}\\= \frac{16.84 +/-9.96 }{8.92}\\x = \frac{16.84 + 9.96 }{8.92} or x = \frac{16.84 - 9.96 }{8.92}\\x = \frac{26.8}{8.92} or x = \frac{6.88}{8.92}\\x = 3.004 or x = 0.771[/tex]
Since B is higher, we take the higher value x = 3.
So, the distance of point B from the ground level is D. 3 units
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Marty buys 12 ounces of granola what fraction of a pound did Marty buy?
The fraction of a pound of granola that Marty bought is 3/4 pounds.
How many pounds of granola did Marty buy?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 3/4.
The unit of conversion of ounces to pounds is :
1 pound = 16
12 ounces of granola = 12/16 pounds = 3 /4 pounds
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At a grocery store, a sign says that if you buy three bottles of water, you will pay 1/4 of the regular price per bottle. Which expression shows the amount of money saved on 3 bottles of water at the regular price of d dollars? Select three correct expressions.
Answer:
Step-by-step explanation:
the fourth one
Answer:
first three answers.
Step-by-step explanation:
each bottle is 1/4d. so all three are 3*1/4d
Jessica makes $10 an hour babysitting. She babysat 4 hours on Friday
and 7 hours on Saturday. Write an expression and use the distributive
property to find how much Jessica made.
Equivalent Expression =
Evaluate =
An expression using the distributive property to find the earnings Jessica made on Friday and Saturday is 10(4 + 7).
What is distributive property?The distributive property postulates that multiplying the sum of two or more addends by a number gives the same result as multiplying each addend by the number and then adding the products together.
The distributive property helps to solve mathematical expressions written in the form of a(b + c).
The amount Jessica makes per hour babysitting = $10
The number of hours of babysitting on Friday = 4 hours
The number of hours of babysitting on Saturday = 7 hours
According to the distributive property, the results from 'a' and 'b' below are the same.
a) 10(4 + 7) = 40 + 70 = 110
b) 10(4 + 7) = 10 x 11 = 110
Thus, using the distributive property, Jessica will make $110 for babysitting on Friday and Saturday, notwithstanding whether process A or B was followed.
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A rectangle has a length of 8.2cm and a height of 42mm. The area of the rectangle is mm2
Answer: To find the area of a rectangle, you can use the formula:
Area = Length x Height
In this case, the length is given in cm and the height is given in mm. Therefore, you need to convert the length to mm before you can calculate the area.
1cm = 10mm.
So, 8.2 cm = 8.2 x 10 = 82mm
Now you can find the area of the rectangle:
Area = Length x Height = 82mm x 42mm = 3,444 mm^2
So, the area of the rectangle is 3,444 mm^2
Step-by-step explanation:
What is the answer to this?
The distance across a circle through its center
Order the correlation coefficients from least to greatest -0.50,0.60, .98,-0.10,0.68
Answer:
-0.50, -0.10, 0.60, 0.68, 0.98
A student traveled a distance of 68 miles in 136 minutes. Which graph has a slope that best represents this rate?
The given circumstance is represented by the linear equation 2y = x, and the graph is included below.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, A student traveled a distance of 68 miles in 136 minutes.
From the general formula of a linear equation:
y = mx + c
where,
m = slope
c = y-intercept
Since At 0 minutes, he started traveling so at 0 minutes total distance he traveled is 0. So the graph will pass through origin.
Thus, the y-intercept will be zero
And Slope of the graph that passes through the origin is always the ratio of the y and x values at any point of the line.
Thu, m = 68/136
m = 1/2
Therefore, a linear equation that represents the given situation is 2y = x, and the graph is attached below.
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Complete question:
USING SIMULATIONS TO CALCULATE ESTIMATED PROBABILITIES
3. A scientist wants to estimate the probability that a drought will happen in an area at least once over the next 4 years. The chances of a drought happening in a given year is 12%. She has generated 20 sets of 8 random numbers to help estimate the probability.
Part A: Before doing any calculations, use your intuition to predict the probability of a drought within the next 4 years if the probability of a drought in any one year is 12%. (1 point)
Scoring Notes: 1 point for any reasonable answer.
Part B: Which pairs of digits, starting at 00, represent a drought happening? Which pairs of digits, ending at 99, represent a drought not happening? (2 points)
Part C: Use the random numbers to estimate the probability that a drought happens at least once over the next 4 years. (7 points)
Part D: Is the probability that you calculated greater than or less than you predicted? Explain. (2 points)
Part E: If you change the pairs of digits that represent a drought happening so that they start at 10 instead of 00, does the estimated probability change? Calculate the estimated probability using the new ranges of numbers. (8 points)
Estimated probabilities are predictions made based on past data, trends, and patterns. They provide an idea of the likelihood that an event will occur in the future.
Calculate estimated probabilitiesPart A:
Answer: The probability of a drought within the next 4 years if the probability of a drought in any one year is 12% is approximately 48%.
Part B:
Answer: Pairs of digits starting at 00 and ending at 11 represent a drought happening. Pairs of digits starting at 88 and ending at 99 represent a drought not happening.
Part C:
Answer: Using the random numbers, the estimated probability that a drought happens at least once over the next 4 years is 68%.
Part D:
Answer: The probability that was calculated is greater than the probability predicted. This is because the sample size of 20 sets of 8 random numbers provided a more accurate and precise estimate than the intuition-based prediction.
Part E:
Answer: Yes, the estimated probability changes when the pairs of digits that represent a drought happening are changed so that they start at 10 instead of 00. Using the new ranges of numbers, the estimated probability that a drought happens at least once over the next 4 years is 64%.
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Estimated probabilities are predictions made based on past data, trends, and patterns. They provide an idea of the likelihood that an event will occur in the future.
Calculate estimated probabilitiesPredictions based on historical data, patterns, and trends are known as estimated probability. They give a sense of how likely it is that a certain occurrence will take place in the future.
Estimated probabilities calculation Part A:
If the likelihood of a drought in any given year is 12%, the likelihood that one will occur within the next four years is roughly 48%.
Part B:
Answer: The drought is represented by pairs of numerals beginning at 00 and ending at 11. A drought that is not occurring is represented by pairs of digits that begin at 88 and terminate at 99.
Part C:
According to the random numbers, there is a 68% chance that a drought will occur at least once over the next four years.
Part D:
Answer: The calculated probability is higher than the expected probability. This is due to the fact that the estimate produced by the sample size of 20 sets of 8 random numbers was more precise and accurate than the intuition-based prediction.
Part E:
Answer: When the pairs of digits that represent the occurrence of a drought are modified so that they begin at 10 instead of 00, the predicted likelihood does indeed change. According to the revised ranges of figures, there is a 64% chance that a drought will occur at least once over the next four years.
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Can someone show the steps please and thank you
y=ax+3
y=3x+5
A solution to the given system of equations include the following:
x = -2.
y = -1.
How to solve this system of equations?In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:
y = 2x + 3 .......equation 1.
y = 3x + 5 .......equation 2.
By using the substitution method to substitute equation 1 into equation 2, we have the following:
2x + 3 = 3x + 5
By re-arranging and collecting like terms, we have the following:
3x - 2x = 3 - 5
x = -2.
For the value of y, we have the following:
y = 2x + 3
y = 2(-2) + 3
y = -4 + 3
y = -1.
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Please help me out. I Need it today
The absolute values of inequality equations totally depend on the symbols.
x+1 = 3, x = 2x+1 > 3 , x > 2 x+1 < 3 , x< 2x+1 ≥ 3 , x ≥ 2 x+1 ≤ 3, x ≤ 2What is inequality?An inequality in mathematics is a relationship that compares two numbers or other mathematical expressions in unequal absolute values. By comparing the absolute valuesof two numbers on the number line, inequality is most frequently utilized. Different types of inequality are represented by a variety of different notations, including:
The symbol a b indicates that an is less than b.
A bigger value for a than a lesser value for b is indicated by the notation a > b.
a is not equal to b in either situation. These relationships are referred to be stringent inequalities since an is either strictly less than or strictly greater than b. Equivalence is not included.
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Diya earned a 36 out of a possible 80 on a test. Her teacher offered extra credit that would allow Diya to double her score. What score could she earn if she completes the extra credit?
How do I do this I am stuck on this question please and thank you
Inez finds that the area of this
figure is 9 square units. Draw unit squares to
cover this figure.
The unit square that covers the figure is attached
What is unit square?The quantity of unit squares necessary to completely cover a shape is its area.
Consequently, area is represented and measured in square units.
The attached figure shows the 9 squares that makes up the figure
Each side has 3 squares and hence
= 3 squares * 3 squares
= 9 squares
The image is attached
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The graph of (c•d)(x) is shown.
Plot a point at the ordered pair that represents (c•d)(4) on the graph of the combined function.
The ordered pair that represents (c•d)(4) on the graph of the combined function is (4, -12)
How to determine the graph of the ordered pair?From the question, we have the following parameters that can be used in our computation:
The graph
The function of the graph is a combined function (c . d)(x)
To calculate (c . d)(4), we trace the point x = 4 to the curve
So, we have
(c . d)(4) = -12
See attachment for the graph
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HELP PLEASE 100 POINT WILL GIVE BRAINLIEST
Answer:
no clue sorry I was not able to help
I need help with this question please
The probability that the mean height of a random sample of 56 ten-year-old males will be greater than 53 inches is approximately 0.9991, or 99.91% when rounded to three decimal places.
What is the central limit theorem?
The central limit theorem, which states that the sample means of large samples (n > 30) from a population with any distribution approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
We can solve this problem by using the central limit theorem,
In this case, the sample size is n = 56, which is larger than 30, so we can assume that the sample means are normally distributed. The mean of the sample means is equal to the population mean, which is 55.5 inches, and the standard deviation of the sample means is equal to the population standard deviation divided by the square root of the sample size:
standard deviation = 6 / √(56) = 0.801
To find the probability that the mean height of the sample will be greater than 53 inches, we can standardize the sample mean using the standard deviation calculated above:
z = (sample mean - population mean) / (standard deviation)
= (53 - 55.5) / 0.801
= -3.12
Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is greater than -3.12:
P(Z > -3.12) = 0.9991 (rounded to four decimal places)
Therefore, the probability that the mean height of a random sample of 56 ten-year-old males will be greater than 53 inches is approximately 0.9991, or 99.91% when rounded to three decimal places.
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HELP ASAP (BRAINLIEST)
The table shows the relationship between the participants walking and running for the week's cross-country practices.
Walk (laps) 3 B 15
Run (laps) 5 10 D
Total (laps) A C 40
At this rate, how many laps will the participants walk if the total distance is 24 miles? How many miles will they run?
They will walk 7 laps and run 17 laps for a total of 24 miles.
They will walk 15 laps and run 9 laps for a total of 24 miles.
They will walk 9 laps and run 15 laps for a total of 24 miles.
They will walk 6 laps and run 18 laps for a total of 24 miles.
Option C. They will walk 9 laps and run 15 laps for a total of 24 miles.
How to calculate for the tableThe table is given as Walk (laps) 3 B 15
Run (laps) 5 10 D
Total (laps) A C 40
The total for walk and run is 3 + 5 = 8
Walk is 3
Run is 5
We are to find the laps of both categories with respect to the total distance of 24 miles
for walk = 3/8 * 24
= 9
For run we would have 5 / 8 * 24 = 15
Hence They will walk 9 laps and run 15 laps for a total of 24 miles.
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a company has offices in 3 different cities and a total of 480 workers. there are 90 workers in new york and 130 workers are in san diego. which number line represents the numbe line represents the number of workers in san diego
Using the arithmetic operation, the number of worker in San Diego is obtained as 260, and the number line which represents the same is option 1.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The number of offices are = 3
The number of workers in the company is = 480
The number of workers in New York city = 90
The number of workers in Denver city = 130
The number of workers in San Diego city = x
To find the number of workers in San Diego use the formula -
Number of workers in San Diego = Total Number of Workers - (Number of workers in New York + Number of workers in Denver)
The arithmetic operation of addition and subtraction is used.
Substitute the values into the equation -
Number of workers in San Diego = 480 - (90 + 130)
Number of workers in San Diego = 480 - 220
Number of workers in San Diego = 260
The number line which represents the number of workers in San Diego is option 1.
Therefore, the number of workers in 260.
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A company has offices in 3 different cities and a total of 480 workers. There are 90 workers in New York and 130 workers are in Denver. Which number line represents the number line represents the number of workers in San Diego?
Find the solutions to the equation:
2x² - 10x + 15 = x
5/2 and 3 are the solutions to the equation 2x² - 10x + 15 = x.
What is equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.
Here,
2x² - 10x + 15 = x
2x² - 11x + 15 = 0
2x² -6x -5x + 15 = 0
2x(x-3)-5(x-3)=0
x=5/2, 3
The solutions to the equation 2x² - 10x + 15 = x is 5/2 and 3.
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Find the domain and range of the function represented by the graph.
The function represented in Cartesian plane have the following features: Domain of function: - 4 ≤ x ≤ 2, Range of function: - 4 ≤ y ≤ 4. (Right choice: B)
How to determine the domain and range of a function
In this question we find the representation of a function on Cartesian plane. There are two important hints to answer this question:
Domain of the function is the set of x-values such that function exists. Range of the function is the set of y-values such that function exists.Then, by direct inspection we find the following results: Domain: - 4 ≤ x ≤ 2, Range: - 4 ≤ y ≤ 4.
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how do you solve -2x=8
Answer:
All you have to do is divide by -2 on both sides. You're trying to get x by itself, so divide by a number by cancels itself out. Don't forget the negative sign as well, or else you'll be left with -x instead of just x. A positive number divided by a negative number will become negative.
-2x=8
x=-4
to see if the cartons have a significantly different mean weight from 46 pounds, what would the value of the z-test statistic be? answer choices are rounded to the hundredths place.
The value of the z-test statistic = 1.16667
When told the question that a random number of samples is tested
z test statistic formula = x - x bar(x with bar above it) /Standard error
From the question
x = raw score = 46 pounds
x bar (x with bar above it)= sample mean = 45.5 pounds
Standard Error = σ/√n
Standard deviation = σ = 3
n = random number of samples = 49
z = 46 - 45.5/3/√49
z = 0.5/ 3/7
z =0.5/ 0.4285714286
z = 1.16667
Therefore, the value of the z-test statistic = 1.16667
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Which of the following are multiplied by the monthly interest rate when calculating finance charges? Select all that apply.
adjusted balance
daily balance
transaction
previous balance
average daily balance
When calculating the finance charges, the monthly interest rate (MPR) is multiplied by the D. average daily balance.
How is the finance charge for credit cards determined?The finance charge refers to the interest and other fees a borrower pays on a credit card.
To compute the finance charge, the annual percentage rate (APR) or the monthly percentage rate (MPR) is multiplied by the balance owed.
The balance commonly used for this calculation is the average daily balance.
Thus, Option D is multiplied by the MPR to compute the finance charges.
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Please answer this question for me
The student is trying to construct a bisector of a given Angle i.e. A.
what is a bisector?
In Geometry, a “Bisector” is a line that divides the line into two different or equal parts. It is applied to the line segments and angles. A line that passes through the midpoint of the line segment is known as the line segment bisector, whereas the line that passes through the apex of an angle is known as the angle bisector. The bisector of a segment always contains the midpoint of the segment. There are two types of bisectors based on what geometrical shape it bisects.
Line Segment Bisector (Perpendicular Bisector Theorem)
Angle Bisector (Triangle Bisector Theorem)
Now,
As we can see from the figure given that the bisector is dividing the angle in two equal segments.
Hence,
The student is trying to construct a bisector of a given Angle.
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Water leaks from a tank at the rate of r(t) gallons per hour. The rate decreased as time passed, and values of the rate at two-hour time intervals are shown in the table below. The total amount of water that leaked out is evaluated by a Riemann sum. Find the upper estimate (left end-points of each rectangle) for the total amount of water that leaked out by using five rectangles.
Give your answer with one decimal place
t(hr) r(t) (gal/hr)
0 10.7
2 8.6
4 6.6
6 5.2
8 5.0
10 4.5
The upper estimate (left end-points of each rectangle) for the total amount of water that leaked out by using five rectangles is 72.2 gallons.
R(t) gallons per hour of water leak from a tank. The values of the rate at two-hour intervals are shown in the table below. As time went on, the rate decreased. A Riemann sum is used to determine the overall volume of water that has leaked out.
An integral representation of the rate function would be the amount of water. Estimation with the Riemann sum and left endpoints:
F(x) ≅ ∑f(xi-1)Δx where Δx=10/5 = 2 for this case and i = 1 to 5
W = (10.7 + 8.6 + 6.6 + 5.2 + 5.0)2
= 36.1•2
= 72.2 gallons
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d 8, write the equation of the plane passing through p with normal vector n in (a) normal form and (b) general form.
The equation of the plane passing through point P with normal vector n A(x-2) + B(y-3) + C(z-4) = 0
(a) Normal Form:
The equation of the plane passing through point P with normal vector n can be written in normal form as:
n • (r - p) = 0
where r is a position vector in three-dimensional space and n is the normal vector of the plane.
Given n = (1,2,3) and p = (2,3,4).
Therefore, n • (r - p) = (1,2,3) • (r - (2,3,4)) = r1 + 2r2 + 3r3 -2 - 3 - 4 = 0
=> r1 + 2r2 + 3r3 - 8 = 0
=> Plane equation in normal form: 1x + 2y + 3z - 8 = 0
(b) General Form:
The equation of the plane passing through point P with normal vector n can also be written in general form as:
A(x-x0) + B(y-y0) + C(z-z0) = 0
where A, B and C are the components of the normal vector n and (x0,y0,z0) are the coordinates of the point p.
Given n = (1,2,3) and p = (2,3,4).
Therefore, A(x-2) + B(y-3) + C(z-4) = 0
=> 1(x-2) + 2(y-3) + 3(z-4) = 0
=> Plane equation in general form: x - 2y + 3z - 8 = 0
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Provide complete question here:Write the equation of the plane passing through p with normal vector n in (a) normal form and (b) general form.
3. One hundred million copper atoms are arranged in a line. Which is a reasonable estimate for the length of this line?
O
1 nanometer
1 kilometer
1 meter
1 centimeter
Answer:
D. I centimeter
Step-by-step explanation:
Since it is only 0.128 nm wide
0.128 nm x 100,000,000 =
1.28 centi meters
Answer:
D) 1 centimeter
Step-by-step explanation:
The SI base unit for length is meters (m).
The radius of a copper atom is 128 pm.
Picometer (pm) is a unit of length equal to 1 × 10⁻¹² meters.
Therefore, the radius of a copper atom in the SI base unit for length is:
[tex]\implies \sf 128 \times 10^{-12} = 1.28 \times 10^{-10}\;m[/tex]
One hundred million = 100,000,000 = 1 × 10⁸
Therefore, the length of a line of one hundred million copper atoms in meters is:
[tex]\implies \sf 1 \times 10^{8} \times 1.28 \times 10^{-10}[/tex]
[tex]\implies \sf 1.28 \times 10^{-10} \times 10^{8}[/tex]
[tex]\implies \sf 1.28 \times 10^{-10+8}[/tex]
[tex]\implies \sf 1.28 \times 10^{-2}\;\;m[/tex]
Centimeter (cm) is a unit of length equal to 1 × 10⁻² meters.
To convert meters to centimeters, divide by 1 × 10⁻²:
[tex]\implies \sf \dfrac{1.28 \times 10^{-2}}{1 \times 10^{-2}}=1.28\;cm[/tex]
Therefore, a reasonable estimate for the length of one hundred million copper atoms arranged in a line is 1 centimeter.
Question content area top Part 1 Compare A and B in three ways, where A=52093 is the number of deaths due to a deadly disease in the United States in 2005 and B=17821 is the number of deaths due to the same disease in the United States in 2009.
In the below we have compared deaths in A and B in terms of ratio, percentage and in terms of proportion.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
The first comparison is in terms of rato.
The ratio of deaths due to a deadly disease in the United States at A and B is A : B = 17821 : 52093.
The second comparison in terms of percentage,
The percentage of people died in A is (52093/17821)×100 = 292.31% more than people died in B.
The third comparison is in terms of fractions.
The fraction of people died in A is (52093/17821) = 2.92 times more than people died in B.
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The area of a circle is 4/pi cm. What is the circumference in centimeters express your answers in terms of pi
Answer:
4 cm.
Step-by-step explanation:
Area = pi r^2, so:
pi r^2 = 4 / pi
(pi)^2 r^2 = 4
r^2 = 4/ (pi^2)
r = 2/pi
Therefore, the circumference
= 2 pi r
= 2* pi * 2/pi
= 4
Provide an appropriate response. From a group of 496 students, every 49th student starting with the 3rd student is selected. Identify the type of sampling used in this example, Select one: A. Cluster sampling B. Systematic random sampling C. Stratified sampling D. Simple random sampling
Systematic random sampling is used when selecting every nth item from a list of items. In this example, every 49th student starting with the 3rd student is selected.
Option B. Systematic random samplingSystematic Random Sampling of 496 StudentsIn systematic random sampling, a list of items is created and every nth item is selected for the sample. This technique is useful when selecting a representative sample from a large population of items. In the example given, 496 students were listed and every 49th student starting from the 3rd student was selected. This is a systematic random sampling technique because the items were selected in a systematic and random fashion. The selection of every 49th student starting from the 3rd student ensures that the sample is representative of the population while also randomizing it so that all students have an equal chance of being selected.
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