Answer:
Angular Displacement: 180° or π radians
Angular Velocity: 3°/sec or 0.0524 radians/sec
Angular Acceleration: 0°/sec^2 or 0 radians/sec^2
Step-by-step explanation:
I need help with this please help me
The picture of the (5, -1) beneath the same translation, in accordance with the stated statement, is (9, 6).
What does a math translation mean?Each point in a graphic is moved the same distance within the same direction using a sort of transformation known as translation.
What does math formula translation mean?Translation in mathematics is the movement of a form in any direction—left, right, up, or down—without turning. They are congruent if the translated forms appear to be of the same size as that of the original ones. They have only changed their direction or directions.
Briefing:The image of the translation is (9,-2).
The point is given as: P = (-6, -4)
The image of the point is: P' = (-2, 3)
The translation rule is calculated as:
T = x - 2 - (-6), y+3-(-4)
so, T = x + 4, y + 7
So, the image of (5, -1) is:
the Image of the translation = 5 + 4, -1 + 7
Hence, the image of the translation is (9, 6).
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Please help me with this question
Answer:
Point of intersection is (13.72, 660)
Step-by-step explanation:
You have to use your graphing tool to answer questions 2 and 3.
Then click on the point of intersection and note the coordinates.
That's it.
This can also be solved mathematically but since the question does not ask I have not given that solution process.
Graph attached
emily surveyed all the students at her school to find out if they plan to attend college. the results are shown in the two-way frequency table. emily knows that the student body at her high school is distributed as follows: freshmen: 28% sophomores: 26% juniors: 24% seniors: 22% according to the information emily has gathered, which of the following statements are true? choose all that are correct. responses more than 40% of the students at the school are freshmen or sophomores who plan to attend college. more than 40% of the students at the school are freshmen or sophomores who plan to attend college. more than 10% of the students at the school are juniors or seniors who do not plan to attend college. more than 10% of the students at the school are juniors or seniors who do not plan to attend college. if a student who plans to attend college is selected at random, the probability that he or she is a senior is 0.1804. if a student who plans to attend college is selected at random, the probability that he or she is a senior is 0.1804. if a student at the high school is selected at random, the probability that he or she is a freshman who does not plan to attend college is 0.15. if a student at the high school is selected at random, the probability that he or she is a freshman who does not plan to attend college is 0.15.
The following statements are true are more than 40% of the students at the school are freshmen or sophomores who plan to attend college.
Given :
emily surveyed all the students at her school to find out if they plan to attend college. the results are shown in the two-way frequency table. emily knows that the student body at her high school is distributed as follows: freshmen: 28 % sophomores: 26 % juniors: 24 % seniors: 22 % .
Freshmen = 0.85
sophomores = 0.80
it is clearly visible that the freshmen or sophomores is greater than the 40 % .
Hence , more than 40% of the students at the school are freshmen or sophomores who plan to attend college.
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a number has the same digit in its hundreds place and in its hundreds place. how many times greater is the value of the digit in the hundreds place than the value of the digit in the hundreds place
A number has the same digit in its hundreds place and in its hundreds place. 10,000
What is the value of the digit?Generally, Given that a number's hundreds place and its hundredths place both have the same digit, we may assume that the number is perfect.
Let's say that the digit is a 1.
Therefore, the value of the hundreds position in a number is equal to 100.
The value of the hundredth position in a number is equal to 0.01%.
The following formula may be used to determine the number of instances in which the value of the digit in the hundreds place is higher than the value of the digit in the hundredths place:
As a result, the difference between the value of the digit in the hundreds place and the value of the digit in the hundredth place is 10,000 times bigger.
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CQ
A number has the same digit in its hundreds place and its hundredths place. How many times greater is is the value of the digit in the hundreds place than the value of the digit in the hundredths place?
A. 100,00
B. 100
C. 1,000
D. 10,000
When an observed difference between two groups on the dependent variable is attributed to the effect of the dependent variable through statistical hypothesis testing then we know that
it is unlikely that the difference would occur by chance alone
It is true that when difference on dependent variable is attributed to effect of that variable through statistical hypothesis testing then it is unlikely that the difference would occur by chance alone
A formal assertion about the nature of a phenomenon made within the constraints of a statistical model is known as a statistical hypothesis.
Statistical hypothesis is a description of the makeup of a population. A population parameter is frequently used to express it.
There are two statistical hypotheses used in hypothesis testing. The above-described null hypothesis (H0) is the first.
If it turns out that the null hypothesis is statistically invalid, an alternative hypothesis (Ha) for each H0 will be given preference. Depending on the research hypothesis, the Ha may be directed or nondirectional.
About the statement in the question,
It is improbable that an observed difference between two groups on the dependent variable would occur by chance alone when the difference is explained by the effect of the dependent variable through statistical hypothesis testing.
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determine whether the lines are parallel, perpendicular, or neither L1: y= -2/3x-3, L2 y= -2/3x+6
The two linear equations have the same slope, -2/3, and different y-intercepts, thus, the lines are parallel.
Are the lines parallel, perpendicular or neither?A general linear equation is written as:
y = a*x +b
Where a is the slope and b is the y-intercept.
Two linear equations are parallel if both lines have the same slope and different y-intercepts.
And two lines are perpendicular if the product between the slopes is equal to -1.
In this case, we have the two linear equations:
y= -(2/3)*x - 3
y= -(2/3)*x + 6
So you can see that both linear equations have the same slope -2/3 and different y-intercepts, thus, the lines are parallel.
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The cost of three notebooks and four pencils is
$8.50. The cost of five notebooks and eight
pencils is $14.50. Determine the cost of one
notebook and the cost of one pencil.
Step-by-step explanation:
[tex]1. \: \: 3x +4 y = 8.50[/tex]
[tex]2. \: \: 5x + 8y = 14.50[/tex]
times equation 1 by 2
[tex]3. \: \: 6x + 8y = 17[/tex]
3-2 eliminates y variable
[tex]x =2.50[/tex]
[tex]y = 0.25[/tex]
Consider the vector function given below. r(t) = (9t, 4 cos(t), 4 sin(t)) (a) Find the unit tangent and unit normal vectors T(t) and N(t). T(t) N(t) = (b) Use this formula to find the curvature. k(t) = Consider the following vector function. r(t) = (2V2t, ezt, e-2t) (a) Find the unit tangent and unit normal vectors T(t) and N(t).
From the given the vector function , T(t) = (2V2, ez, -2e-2t) N(t) = (2e-2t, -2V2, ez)(b) Use this formula to find , curvature. k(t) = (2V2e-2t + 2ez) / (4V2 + e2z + 4e-4t2)
(a) To find the unit tangent and unit normal vectors, we use the following formula:
T(t) = (1/|r'(t)|) * r'(t)
N(t) = (1/|r'(t)|) * (r'(t) x r"(t))
where r'(t) is the first derivative of the vector function and r"(t) is the second derivative of the vector function.
For the given vector function, r'(t) = (9, -4sin(t), 4cos(t)).
Therefore, |r'(t)| = sqrt(81 + 16sin2(t) + 16cos2(t))
To find r"(t), we take the derivative of r'(t), which is (0, -4cos(t), -4sin(t)).
Thus, T(t) = (1/sqrt(81 + 16sin2(t) + 16cos2(t))) * (9, -4sin(t), 4cos(t))
and N(t) = (1/sqrt(81 + 16sin2(t) + 16cos2(t))) * (0, -4cos(t), -4sin(t)).
(b) To find the curvature, we use the following formula:
k(t) = |r'(t) x r"(t)| / |r'(t)|3
For the given vector function, r'(t) = (2V2, ez, -2e-2t) and r"(t) = (0, -2V2, -ez).
Therefore, k(t) = |(2V2, ez, -2e-2t) x (0, -2V2, -ez)| / |(2V2, ez, -2e-2t)|3
= (2V2e-2t + 2ez) / (4V2 + e2z + 4e-4t2)
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Find the angle round to the nearest degree. please help.
63 degrees is the angle.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given triangle is a right angle triangle.
The opposite side length is 85 and the adjacent side is 38.
Opposite side=85
Adjacent side=38.
Calculate Opposite/Adjacent
= 85/38= 2.236
Which is tanθ=2.236
Now tan inverse on both the sides
θ=tan⁻¹2.236
θ=tan⁻¹2
θ=63 degrees.
Hence, the angle is 63 degrees.
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Find the x and y intercepts of the line: 3x - 4y = -24
Answer:
x- intercept = - 8 , y- intercept = 6
Step-by-step explanation:
to find the x- intercept let y = 0 in the equation and solve for x
3x - 4(0) = - 24
3x = - 24 ( divide both sides by 3 )
x = - 8 ← x- intercept
to find the y- intercept let x = 0 in the equation and solve for y
3(0) - 4y = - 24
- 4y = - 24 ( divide both sides by - 4 )
y = 6 ← y- intercept
City A is located in a valley 15 meters below sea level, and City B is located *
43 meters above sea level. What is the difference, in meters, between the
elevations of these two cities? Remember, difference means subtract (and
you will need to SCO).
Answer:
To find the difference between the elevations of City A and City B, we need to subtract the elevation of City A from the elevation of City B. Since City A is located 15 meters below sea level, and City B is located 43 meters above sea level, the difference between their elevations is $43 - (-15) = 43 + 15 = 58 meters. Therefore, the difference between the elevations of City A and City B is 58 meters.
Solve the following system of equations graphically on the set of axes below.
y=- 5/2 x-6
x - y= -1
Plot two lines by clicking the graph.
Click a line to delete it.
We have drawn the graph, and point (-2, -1) satisfies both equations and lies on the graph of the system.
What is the system of equations?
A system of equations is a set of two or more equations that are solved simultaneously. In other words, a system of equations is a group of equations that are related to each other and must be considered together in order to find a solution.
The given equations are
y = -5/2x -6
x - y = 1
To find the points of these equations on the graph, we need to solve the system of equations formed by the two given equations.
After solving these equations, we get the point (-2, -1).
Hence, we have drawn the graph, and point (-2, -1) satisfies both equations and lies on the graph of the system.
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8w-16 how do i answer this
The factor of the expression 8w - 16 will be 8 and (w - 2).
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
A frequency table displays a sequence of scores in either increasing or decreasing order together with their occurrences as a way to compactly organize raw data.
The expression is given below.
⇒ 8w - 16
The factor of each term in the expression, then we have
8w = 8 x w
16 = 8 x 2
Then the expression is written as,
⇒ 8w - 16
⇒ 8 × w - 8 × 2
⇒ 8 × (w - 2)
⇒ 8(w - 2)
The component of the articulation 8w - 16 will be 8 and (w - 2).
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your goal is to generate a simple math quiz with a number of equations that will be determined by the user. you will prompt the user for an answer to each equation and display whether they answered it correctly or incorrectly. at the end of the math quiz, you will display the number of total equations that they answered correct out of how many were given
The statement of the problem has already made a lot of decisions for us. We are told to use three global variables of type int[]. The variables must be static, and I have chosen to make them private, so the declarations become:
private static int[] firstNumbers; // The first numbers in all ten questions.
private static int[] secondNumbers; // The second numbers in all ten questions.
private static int[] user answers; // The user's answers to the ten questions.
Note that these declarations are not in any subroutine. These statements only create variables, not arrays. We still need to create three arrays of length 10. The arrays can be created using the new operator. This initialization could in fact be combined with the declaration of the variables:
private static int[] firstNumbers = new int[10];
private static int[] secondNumbers = new int[10];
private static int[] userAnswers = new int[10];
Another possibility would be to create the three arrays at the beginning of the main() routine. In fact, I chose to create them in the subroutines where they are first used.
The program has three stages -- create the problems, administer the quiz, and grade the quiz -- and we are told to write a subroutine to do each stage. The main program simply has to call the subroutines:
public static void main(String[] args) {
createQuiz();
administerQuiz();
gradeQuiz();
}
This is an example of using subroutines to break up a large task into several simpler subtasks, so that programming each subtask becomes a separate problem. The subroutines are short and not too hard to write. Looking at administerQuiz() as an example, note that the user's answers have to be stored in the array, the user answers so that they can be used when grading the quiz. I create the array itself before asking any questions and then store the user's responses in the array as they are read by the user. On the other hand, the arrays that hold the numbers that occur in the questions have already been created and filled before administerQuiz() is called. Here's the subroutine:
private static void administerQuiz() {
userAnswers = new int[10];
for (int i = 0; i < 10; i++) {
int questionNum = i + 1;
System.out.printf("Question %2d: What is %2d + %2d ? ",
questionNum, firstNumbers[i], secondNumbers[i]);
userAnswers[i] = TextIO.getlnInt();
}
}
A couple notes about the output: I wanted to number the questions 1, 2, ..., 10, but the elements of the arrays are numbered 0, 1, ..., 9. This means that the question number that I output has to be one more than the array index. Also, all the numbers that occur in my program are either one or two digits. By allowing exactly two digits for each number in the output, I can get everything to line up neatly. Here's the I/O for a sample run of the program:
Welcome to the addition quiz!
Question 1: What is 40 + 14 ? 54
Question 2: What is 18 + 38 ? 46
Question 3: What is 21 + 31 ? 52
Question 4: What is 18 + 36 ? 54
Question 5: What is 43 + 12 ? 55
Question 6: What is 21 + 17 ? 38
Question 7: What is 33 + 25 ? 58
Question 8: What is 39 + 21 ? 70
Question 9: What is 1 + 25 ? 26
Question 10: What is 39 + 26 ? 65
Here are the correct answers:
Question 1: 40 + 14 = 54. You were CORRECT.
Question 2: 18 + 38 = 56. You said 46, which is INCORRECT.
Question 3: 21 + 31 = 52. You were CORRECT.
Question 4: 18 + 36 = 54. You were CORRECT.
Question 5: 43 + 12 = 55. You were CORRECT.
Question 6: 21 + 17 = 38. You were CORRECT.
Question 7: 33 + 25 = 58. You were CORRECT.
Question 8: 39 + 21 = 60. You said 70, which is INCORRECT.
Question 9: 1 + 25 = 26. You were CORRECT.
Question 10: 39 + 26 = 65. You were CORRECT.
You got 8 questions correct.
Your grade on the quiz is 80.
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LAST QUESTION PLEASE HELP ASAP I HAVE 5 MINS!!!
Answer:
Step-by-step explanation:
When any value of x, other than 0, is multiplied by itself the result will ALWAYS be a POSITIVE value. Therefore, equations in the form x square =p, where p is GREATER THAN 0, will have 2 SOLUTIONS.
What values of x make the two expressions below equal?
(x-1)(x-6)_
4(x-1)
x-6
4
A. All real numbers except 1
B. All real numbers except 6
C. All real numbers
D. All real numbers except 1 and 6
All the real numbers except 1 make the two expressions equal. Then the correct option is A.
What is an equivalent expression?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expressions are given below.
[(x - 1)(x - 6)] / [4(x - 1)] and (x - 6) / 4
Simplify the expression [(x - 1)(x - 6)] / [4(x - 1)], then we have
⇒ [(x - 1)(x - 6)] / [4(x - 1)]
⇒ (x - 6) / 4
But at x = 1, the expression [(x - 1)(x - 6)] / [4(x - 1)] is not defined.
All the real numbers except 1 make the two expressions equal. Then the correct option is A.
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A scientist began measuring the temperature of a solution when it was 100 °F. The temperature of the solution
decreased at a constant rate of 1.5 °F per hour.
Which function can be used to find y, the temperature of the solution in degrees Fahrenheit after x hours?
Ay 1.5x - 100
By 1.5x + 100
y 100x1.5
Oy - 100x + 1.5
Conditional problems are problems that involve one or more conditions that must be met in order for a certain action to be taken or a certain result to be obtained. The temperature of the solution in degrees Fahrenheit after x hours, is y = 1.5x - 100.
The required details for Conditional problems in given paragraph
This function models the temperature of the solution as it decreases at a constant rate of 1.5 °F per hour. The initial temperature of the solution is 100 °F, and the temperature decreases by 1.5 °F for each hour that passes. Therefore, the temperature of the solution after x hours can be found by subtracting 1.5x degrees from the initial temperature of 100 degrees.
For example, if we plug in x = 2 into the function, we get y = 1.5 * 2 - 100 = 3 - 100 = -97, which means that the temperature of the solution after 2 hours is -97 °F.
The other options listed are not correct because they do not correctly model the temperature of the solution as it decreases at a constant rate of 1.5 °F per hour. Option A is incorrect because it adds 1.5x degrees to the initial temperature, rather than subtracting it. Option B is incorrect because it adds 100 degrees to the temperature, rather than subtracting it. Option C is incorrect because it multiplies the initial temperature by 1.5x, rather than subtracting 1.5x degrees from it. Option D is incorrect because it adds 1.5 to the temperature, rather than subtracting 1.5x degrees from it.
what are conditional problems?
Conditional problems are often expressed using words like "if," "then," or "when." For example, a conditional problem might involve finding the value of a variable x if it satisfies a certain condition, such as "If x is greater than 5, then x is even." In this case, the problem specifies that x must be greater than 5 in order for it to be even.
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if you apply demorgan's theorem to the expression overbar(overbar((overbar(a) overbar(b))) (overbar(c d))), you get:
Applying DeMorgan's theorem to the expression overbar(overbar((overbar(a) overbar(b))) (overbar(c d))) results in (a b) + (c + d).
DeMorgan's theorem states that when two terms are combined with an AND operator (such as overbar(a) overbar(b)), the result is the two terms combined with an OR operator (such as a + b).
Similarly, when two terms are combined with an OR operator (such as overbar(c d)), the result is the two terms combined with an AND operator (such as c overbar(d)). Applying this theorem to the expression above results in (a b) + (c + d).
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You are making several purchases from the I.B. Electric electronics store. You can buy from this store online or in a physical store. You have a coupon for 10% off that can only be used in the physical store and a $5.00 off coupon that can only be used online. The sales tax of 5% only applies to the physical store. Shipping for the online store is a flat rate of $6.99. Using this information and the information below, which way would you save the most money?
15% discount; 6% sales tax in-store. Online retailer: $5 discount; $8.99 for delivery.
Which way would you save the most money?$5 off offer that can only be used online and a physical shop. Only the actual store is subject to the 5% sales tax. The online retailer charges a fixed $6.99 shipping fee.
Let's say the entire amount spent was $100.
In a physical store, 100 times 15% equals 15 off.
100 - 15 = 85 is the item's reduced cost.
85 x 6% is 5.1 sales tax.
85 + 5.1 = 90.10 as a whole price
Internet shop:
Discounted cost of item: 100 - 5 = 95
95 plus 8.99 is 103.99 in total.
15% discount; 6% sales tax in-store.
Online retailer: $5 discount; $8.99 for delivery.
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consider all postive interges that are multiples of 20 and that are less than or equal to 300. what fraction of those interges are multple of 15
Answer:
1/3
Step-by-step explanation:
Every third multiple of 20 is a multiple of 15.
Can anyone help me ASAP?
- At a bake sale, the Math Club raised $225 by selling 300 baked goods. If the amount
raised varies directly with the baked goods sold, how much money will be raised for
selling 450 baked goods?
Record your answer on the answer document.
5x3
The amount of money for selling 450 baked goods will be
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
At a bake sale, the Math Club raised $225 by selling 300 baked goods.
And, The amount raised varies directly with the baked goods sold.
Now,
Let the amount of money for selling 450 baked goods = x
Since, At a bake sale, the Math Club raised $225 by selling 300 baked goods.
And, The amount raised varies directly with the baked goods sold.
Hence, By definition of proportion we get;
⇒ $225/300 = x / 450
⇒ x = 225 × 450 / 300
⇒ x = $337.5
Thus, The amount of money for selling 450 baked goods = $337.5
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Dan has a jar full of quarters and dimes. He has 21 more dimes than he has quarters. Overall, Dan has 67 coins. How many of each coin does Dan have?
Answer:
Dan has 42 quarters and 25 dimes.
Step-by-step explanation:
which are prime polynomials
-12f+21
f-36
-3f-23
5f+10
Answer:
f - 36
-3f - 23
are your prime polynomials.
Let U = {−8, −7, −6, −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, 6, 7, 8}, A = {−7, −4, −2, −1, 1, 4, 8}, B = {−7, −6, −3, −2, −1, 3}, and C = {−4, 0, 2, 4, 7}. Use the roster method to write the set. Enter EMPTY or ∅ for the empty set.) (a) Find B' (b) Find A' ∪ (B ∩ C).
After solving the following sets in roster form we get B' = {-8,-5,-4,0,1,2,4,5,6,7,8} and
A' U (B ^ C) = {-8, -6, -5 , -4 , 0 , 2, 3, 5, 6 ,7 }
What are sets and roster form?
Either elements or members of a set are terms used to describe the objects that make up a set. A set's components are denoted by curly brackets enclosing them and commas separating them. The sign "" is used to indicate that an element is part of a set. 2 A in the previous illustration. The symbol "" is used to designate an element that is not a part of a set. Here, 3 ∉ A.
The roster notation, in which the components of the sets are contained in curly brackets and separated by commas, is the most popular way to express sets. Set B, for instance, which is made up of the first five even integers, is equal to 2, 4, 6, 8, and 10. The order of the set's components in a roster form is irrelevant; for instance, the first five even integers can equally be described as 2, 6, 8, 10, 4. Additionally, if a set has an infinite number of items, the endless list is defined by adding a string of dots to the end of the final element. For instance, the representation of infinite sets is X = 1, 2, 3, 4, 5,..., where X is the set of natural numbers.
Please see the examples below for a summary of the roster form's notation.
Set A = 1, 2, 3, 4, and 5 in the finite roster notation of sets (The first five natural numbers)
Sets in Infinite Roster Notation: Set B = {5, 10, 15, 20 ....} (The multiples of 5) (The multiples of 5)
a) B' = U - B = {-8,-5,-4,0,1,2,4,5,6,7,8}
b) A' U (B ^ C)
A' = U - A = {-8, -6, -5 , -4 , 0 , 2, 3, 5, 6 ,7 }
B intersection C = ∅
A' U (B ^ C) = A' = {-8, -6, -5 , -4 , 0 , 2, 3, 5, 6 ,7 }
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In what ways did WWII-era policies deliver prosperity to white veterans and their families while preventing the same for Americans and veterans of color?
The WW2 era helped tp deliver several prosperity to the whites in the forms of college education funding, It gave them unemployment insurances in the nation and also helped them with housing benefits.
How did WW2 help the US?This bill, commonly known as the G.I. Bill, was passed by President Franklin D. Roosevelt on June 22, 1944, and it gave World War II veterans money for housing, unemployment insurance, and college tuition. Millions of WWII and post-World War II military veterans now have access to higher education.
It made it possible for hundreds of thousands of men and women to pursue higher education, many of whom would not have been able to do so without its assistance. Although it left many minority veterans behind, the bill also contributed to the growth of the middle class in America.
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Write as a single fraction in its simplest form.
[tex] \frac{ {x}^{2} - 3x}{ {x}^{2} - 9 } [/tex]
Answer:
[tex]\frac{x}{x+3}[/tex]
Step-by-step explanation:
[tex]\frac{x(x-3)}{(x+3)(x-3)}[/tex]
[tex]\frac{x}{x+3}[/tex]
The area of a rectangle is given by the function A(x) = 2x3 + 6x2 + 5x + 15. If the length is defined by x + 3, what is the width of the rectangle?
Answer:
2x² +5
Step-by-step explanation:
You want the width of a rectangle with a length of x+3 and an area of A(x) = 2x³ +6x² +5x +15.
AreaThe area is the product of length and width, so the width will be ...
A = LW
W = A/L = (2x³ +6x² +5x +15)/(x +3)
The cubic expression can be factored by grouping, so we have ...
Area = (2x³ +6x²) +(5x +15)
= 2x²(x +3) +5(x +3)
= (2x² +5)(x +3)
Then the width is ...
[tex]\text{width}=\dfrac{(x+3)(2x^2+5)}{x+3}=\boxed{2x^2+5}[/tex]
The width of the rectangle is 2x² +5.
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An alternative sampling method would be to select a stratified random sample of eight apartments, where the
strata are apartments with children and apartments with no children. A stratified random sample of size eight
might include two randomly selected apartments with children and six randomly selected apartments with no
children. In the context of this situation, give one statistical advantage of selecting such a stratified sample as
opposed to a cluster sample of eight apartments using the floors as clusters.The amount of carpet wear could be different for apartments with and without children.
2. The stratified random sample ensures that some apartments with children will be selected.
(a) There are 36 ways to select 8 apartments randomly by cluster sampling method.
(b) Throughout this process, we obtain floors 3, 4, 6, or 3, 6, which do not have sample flats with children, and as a result, the sample will not accurately reflect the population.
(a) Given the building has 9 floors which are taken as N=9 clusters.
Each floor has 4 apartments.
It is to select 8 apartments by cluster sampling method.
That is to select a sample of size any n=2 floors(clusters) by cluster sampling method out of the population of N=9 clusters.
By simple random sampling without replacement, there are NCn = 9C2 =36 ways to select 2 clusters.
Hence, there are 36 ways to select 8 apartments randomly by cluster sampling method.
(b) The main benefit of stratified sampling over cluster sampling is that the sample obtained using this method will unquestionably include representations of both features, i.e., apartments with and without children as a full representative of the population.
In contrast, there is no guarantee that the sample of flats with and without children from the cluster sampling approach will accurately reflect both qualities. Sometimes throughout this process, we obtain floors 3, 4, 6, or 3, 6, which do not have sample flats with children, and as a result, the sample will not accurately reflect the population.
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The right question is given beow:
Express the following fraction in simplest form, only using positive exponents.
\frac{3a^9r^{-3}}{-4(a^2)^{-1}}
−4(a
2
)
−1
3a
9
r
−3
The simplified expression of the fraction in its simplest form is -12a¹¹r⁻³
How to express the fraction expression in its simplest form?From the question, we have the following parameters that can be used in our computation:
\frac{3a^9r^{-3}}{-4(a^2)^{-1}}
Rewrite the above expression properly
So, we have the following representation
3a⁹r⁻³/(-4a²)⁻¹
Evaluate the expression in bracket
So, we have the following representation
3a⁹r⁻³/(-4a²)⁻¹ = 3a⁹r⁻³ * (-4a²)
Remove the brackets
This gives
3a⁹r⁻³/(-4a²)⁻¹ = 3a⁹r⁻³ * -4a²
Evaluate the products
So, we have the following representation
3a⁹r⁻³/(-4a²)⁻¹ = -12a¹¹r⁻³
Hence, the the fraction expression in its simplest form is -12a¹¹r⁻³
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