Use the z-transform to solve the following difference equation: y[n + 2] = 4y[n + 1] + 5y[n], y(0) = 1 y[1] = 2
Answers
The solution to the given difference equation with the initial conditions y[0] = 1 and y[1] = 2 is:
y[n] = -5 \((5^n) - e^{(-n)\)
The given difference equation is:
y[n + 2] = 4y[n + 1] + 5y[n]
Taking the z-transform of both sides, we get:
\(z^2 Y(z) - z y[0] - y[1] = 4 (z Y(z) - y[0]) + 5 Y(z)\)
Using the initial conditions y[0] = 1 and y[1] = 2, we can substitute these values into the equation:
\(z^2 Y(z) - z - 2 = 4z Y(z) - 4 + 5 Y(z)\)
Now, let's solve for Y(z):
\(z^2 Y(z) - 4z Y(z) - 5 Y(z) = z - 4 + 2\)
(Y(z))(z² - 4z - 5) = z - 2
Y(z) = (z - 2) / (z² - 4z - 5)
Now, we need to decompose the right side of the equation into partial fractions. To factor the denominator, we find the roots:
z² - 4z - 5 = 0
Using the quadratic formula, we get:
z = 2 ± 3
So, the roots are z = 5 and z = -1.
The partial fraction decomposition of Y(z) becomes:
Y(z) = A / (z - 5) + B / (z + 1)
To find A and B, we can multiply both sides by the common denominator:
(z - 5)(z + 1) Y(z) = A(z + 1) + B(z - 5)
Expanding and equating coefficients:
1 Y(z) = A + B
z Y(z) = A - 5B
From the first equation, Y(z) = A + B. We can substitute this into the second equation:
z (A + B) = A - 5B
Az + Bz = A - 5B
Az - A = -Bz - 5B
A(z - 1) = -B(z + 5)
A = B(z + 5) / (1 - z)
Since this equation should hold for all values of z, we equate the coefficients of z on both sides:
A = -5B
B = A / (1 - z)
Substituting A = -5B into the second equation:
B = (-5B) / (1 - z)
1 - z = -5
z = 6
Now, we have the values of A and B:
A = -5B
B = (-5B) / (1 - 6)
B = 5/5 = 1
Therefore, A = -5 and B = 1.
Now we can express Y(z) in terms of partial fractions:
Y(z) = -5 / (z - 5) + 1 / (z + 1)
Next, we need to find the inverse z-transform of Y(z).
By consulting a table of z-transform pairs or by using partial fraction decomposition, we can find the inverse z-transform of Y(z):
Y(z) = -5 / (z - 5) + 1 / (z + 1)
To find the inverse z-transform, we use the following pair from the table:
Inverse z-transform of 1 / (z - a) =\(e^{(at)\)
Inverse z-transform of -5 / (z - 5) = -5\(e^{(5t)\)
Similarly, using another pair:
Inverse z-transform of 1 / (z + a) = -\(e^{(-at)\)
We can find the inverse z-transform of the second term:
Inverse z-transform of 1 / (z + 1) = -e^(-t)
Combining these results, we have:
Y(z) = -5 / (z - 5) + 1 / (z + 1)
= -5\(e^{(5t)} - e^{(-t)\)
Therefore, the solution to the given difference equation is:
y[n] = -5 \((5^n) - e^{(-n)\)
Now, we can use the initial conditions y[0] = 1 and y[1] = 2 to find the specific values of the constants:
y[0] = -5\((5^0) - e^(0)\)= -5 - 1 = -6
y[1] = -5 \((5^1) - e^{(-1)\) = -25 - (1 / e) ≈ -25.368
Hence, the solution to the given difference equation with the initial conditions y[0] = 1 and y[1] = 2 is:
y[n] = -5 \((5^n) - e^{(-n)\)
Learn more about z- Transform here:
https://brainly.com/question/32387682
#SPJ4
Related Questions
 Ted is the manager at Baskin Robbins. He called Sugar Cone Factory and Coney Island for the dimensions of their ice cream cones. Both cones cost the same price. Sugar Cone Factory has a radius of 3 cm and a height of 10 cm. Coney Island has a cone with a diameter of 5 and a height of 14. Which cone company offers the better deal? Explain your answer.
Show work!
Which company ?
Explanation:
Answers
The comparision of the volumes is 0.61
We are given that;
Radius=3cm, height=10cm
Now,
To find the better deal, we need to compare the volumes of the cones from each company. The volume of a cone is given by the formula V = (1/3) * pi * r^2 * h, where r is the radius and h is the height. Using the given dimensions, we get:
\(V_Sugar = (1/3) * pi * 3^2 * 10 V_Sugar = 30 * pi cm^3V_Coney = (1/3) * pi * (5/2)^2 * 14 V_Coney = 49.167 * pi cm^3\)
To compare the volumes, we can divide them and see which one is larger. We get:
\(V_Sugar / V_Coney = (30 * pi cm^3) / (49.167 * pi cm^3) V_Sugar / V_Coney = 0.61\)
Since this ratio is less than 1, it means that V_Sugar is smaller than V_Coney. Therefore, Coney Island offers the better deal because their cones have a larger volume.
Therefore, by the unitary method the answer will be 0.61
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ1
three potential employees took an aptitude test. each person took a different version of the test. the scores are reported below. reyna got a score of 87 ; this version has a mean of 73 and a standard deviation of 10 . demetria got a score of 301.8 ; this version has a mean of 288 and a standard deviation of 23 . pierce got a score of 8.56 ; this version has a mean of 7.3 and a standard deviation of 0.6 . if the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?
Answers
The applicant who should be offered the job based on the aptitude test scores is Reyna. Reyna scored 87 on her version of the test, which has a mean of 73 and a standard deviation of 10.
Demetria scored 301.8 on her version of the test, which has a mean of 288 and a standard deviation of 23. Pierce scored 8.56 on his version of the test, which has a mean of 7.3 and a standard deviation of 0.6. The scores of Reyna, Demetria, and Pierce can be compared by standardizing them and calculating the z-scores. Standardizing involves subtracting the mean from the score and dividing by the standard deviation, resulting in z-scores. This can be used to compare the performance of each applicant relative to their own version of the test. Reyna's z-score is 1.37, Demetria's z-score is 0.86, and Pierce's z-score is 14.27. This shows that Reyna performed better than Demetria, and significantly better than Pierce. Reyna should therefore be offered the job based on her performance on the aptitude test.
for more suc question on deviation
https://brainly.com/question/475676
#SPJ11
22. Which measures could be the side lengths of
a right triangle?
А. 7 cm, 21 cm, 25 cm
B. 30 cm, 72 cm, 78 cm
C. 3 cm, 5 cm, 9 cm
D. 7 cm, 25 cm, 26 cm
Please Help me !!!!!!!
Answers
Answer:
b and d I think are both right but if you can only pick one go with B
The measure that could be the side lengths of a right triangle is 30 cm, 72 cm, 78 cm, the correct option is B.
What is the right triangle?A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.
We are given that;
The right triangle
Now,
We can use this equation to test each option by plugging in the values and checking if they satisfy the equation.
A. 7 cm, 21 cm, 25 cm
7^2 + 21^2 = 25^2
49 + 441 = 625
490 = 625
False
This option does not satisfy the Pythagorean theorem, so it cannot be the side lengths of a right triangle.
B. 30 cm, 72 cm, 78 cm
30^2 + 72^2 = 78^2
900 + 5184 = 6084
6084 = 6084
True
Therefore, by right angle triangle the answer will be 30 cm, 72 cm, 78 cm.
Learn more about a right angle triangle;
https://brainly.com/question/7116550
#SPJ2
This urgent can y’all please help me with this math problem I’ll mark y’all Brainlyist
Answers
Darwin is out shopping in find $50.00 scooter that was marked down by 50% how much was the item originally?
Answers
Answer:
100
Step-by-step explanation:
Because if 50 percent of x is 50 than x = 100
If the operation A be defined as x*Delta*y = x ^ 2 * y - 1 then find (x*Delta*x)/(1Delta*x)
Answers
The value of (xΔx)/(1Δ*x) or (x*Delta*x)/(1Delta*x) is (x³ - 1)/(x³ - x).
To find this value, we first need to apply operation A to the expressions xΔx and 1Δ*x:
xΔx = x² * x - 1 = x³ - 1
1Δ*x = 1² * x - 1 = x - 1
Substituting these values in the expression (xΔx)/(1Δ*x), we get:
(x³ - 1)/(x - 1)
We can simplify this expression by multiplying the numerator and denominator by (x² + x + 1), which is the factorization of x³ + 1:
(x³ - 1)/(x - 1) = [(x - 1)(x² + x + 1)]/(x - 1) = x² + x + 1. Factorization is the process of finding two or more numbers or expressions whose product is equal to the original number or expression.
Therefore, the value of (xΔx)/(1Δ*x) is x² + x + 1.
Learn more about factorization
https://brainly.com/question/18187355
#SPJ4
Complete Question:
If the operation A be defined as x*Δ*y = x² * y - 1 then find (xΔx)/(1Δ*x).
WILL MARK BRAINLIEST !!!! Which equation is an equation of a circle with a radius of 3 and its center is at (5, -2)?
(x - 5)² + (y + 2)² = 3
(x - 5)² + (y + 2)² = 9
(x + 5)² + (y – 2)² = 3
(x + 5)² + (y - 2)² = 9
Answers
Answer:
the first one
Step-by-step explanation:
Answer:
(x + 5)² + (y – 2)² = 3
Step-by-step explanation:
A 2 cm radius ball rests on a table as shown in the figure. Suppose we select the table as the reference plane, the bottom of the ball as its reference point, the y-axis along a vertical line, and the positive direction as pointing upward. What is the y-coordinate of the ball?.
Answers
the center of the ball rests on the table which implies that the y-coordinate of the center of the ball is zero since we have selected the table as the reference plane
the bottom of the ball as its reference point, the y-axis along a vertical line, and the positive direction as pointing upward can be calculated as follows:The y-coordinate of the ball = (y-coordinate of the center of the ball) - (the radius of the ball)As per the given problem, the center of the ball rests on the table which implies that the y-coordinate of the center of the ball is zero since we have selected the table as the reference plane.Hence, the y-coordinate of the ball = 0 - 2= -2Therefore, the y-coordinate of the ball is -2.
learn more about rests here;
https://brainly.com/question/29132935
#SPJ11
Please help with this question
Answers
Answer:
2nd graph from top
Step-by-step explanation:
a/ -5 ≥ 10
Multiply each side by -5, remembering to flip the inequality
a/-5 *-5 ≤ 10*-5
a ≤ -50
closed circle at -50 line going to the left
How do you find the scale factor of dilation in 7th grade?
Answers
Main answer:The basic formula for calculating the scale factor of a dilated figure is as follows: Scale factor = new shape dimension x original shape dimension
supporting answer:
Dilation is a transformation that allows you to resize an object. Dilation is a technique for making objects larger or smaller. This transformation yields an image that is identical to the original shape. However, there is a size difference in the shape.
body of the answer:
The scale factor is defined as the ratio of the new image's size to the old image's size. The dilation centre is a fixed point in the plane. The dilation transformation is defined based on the scale factor and the centre of dilation.
If the scale factor is greater than one, the image will stretch.The image shrinks if the scale factor is between 0 and 1.If the scale factor is 1, the original and produced images are congruentfinal answer: by following abouve we can find the scale factor of dilation
to learn more about scale factor of dilation from the given link
https://brainly.in/question/23453523#:~:text=Explanation%3A,point%20to%20the%20image%20point.
#SPJ4
The basic formula for calculating the scale factor of a dilated figure is as follows: Scale factor = new shape dimension x original shape dimension.
What is dilation?
Dilation is a transformation that allows you to resize an object. Dilation is a technique for making objects larger or smaller. This transformation yields an image that is identical to the original shape. However, there is a size difference in the shape.
The scale factor is defined as the ratio of the new image's size to the old image's size. The dilation center is a fixed point in the plane. The dilation transformation is defined based on the scale factor and the center of dilation.
If the scale factor is greater than one, the image will stretch.
The image shrinks if the scale factor is between 0 and 1.
If the scale factor is 1, the original and produced images are congruent
By following the above we can find the scale factor of a dilation.
To learn more about the scale factor of dilation the given link:
https://brainly.com/question/24551408
#SPJ4
If a two system of equation passes to the origin (0,0), How many solutions does it have?
A) One solution
B) infinity many solution
C) No solution
D) none of the above
Answers
Explanation
Since (0 ,0 ) is the cross point for both lines, we know 0 = 0 for any value of x, the system of equations has infinite solutions.
One solution would have the lines crossing at one coordinate
For an answer to have no solution both answers would not equal each other.
PLSSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
x=2
Step-by-step explanation:
Answer:
x=2
Step-by-step explanation:
10x -3 =17
10 * x-3 =17
10* x=17+3
10* x =20
x=20:10
x=2
The enrollment of students at a school is decreasing at a constant rate of 5 % per year what percent remains after one year
Answers
Answer: depends but just subtract 5 from the original rate
Step-by-step explanation:
example
100 to 95 to 90 to 85 to 80 and etc.
A landscaper plants 18 bushes in 3 rows.
How many bushes will he plant in 10
rows?
A 50
© 28
B 80
D 60
Answers
Answer:
D. 60
Step-by-step explanation:
in one row, 6 bushes are planted.
18/3 = 6
10*6 = 60
In one month 382 adults and 65 children stayed in a hotel. How many people are there altogether?
Answers
In one month, a total of 447 people stayed at the hotel.
In one month, a hotel had 382 adults and 65 children staying as guests.
To find out the total number of people who stayed at the hotel, we simply need to add the number of adults and children together.
In one month, a total of 447 people (382 adults and 65 children) stayed at the hotel.
Overall, this problem is a simple example of addition in action. By adding the number of adults and children together, we can determine the total number of people who stayed in the hotel.
To know more about addition, refer to the link below:
https://brainly.com/question/29464370#
#SPJ11
Someone broke into my house and didn't steal anything, does this mean even robbers think i'm poor.
Answers
Answer:
Not really,maybe he just went in to find something,just that he didn't that's why maybe he didn't steal anything
Step-by-step explanation:
Answer:
Not necessarily. The robbers might've seen something or someone in your house and ran. They also could've heard something and thought you were home. So, if a robber breaks into your house but runs almost immediately you migt want to get your house checked out. Or, the robbers did think you were poor. Sorry.
Step-by-step explanation:
If an airplane moves at a constant speed of 120 miles per hour for 3 hours. How far does it go?
Answers
Answer:
360 miles
Step-by-step explanation:
For every one hour traveled, 120 miles are covered. If there are three hours traveled, then we would have 120+120+120 (aka 120*3). At the end of the 3 hours, we will have traveled 360 miles. Thank you for choosing Southwest, enjoy your day.
Jaulas father throws Kayla a graduation party that costs $773. He pays the DJ $250, $75 for the cake, and $4 per party guest for food. How many guests were at the party?
Answers
Answer:
112 guests
Step-by-step explanation:
I. If her total cost is 773$
When Total = DJ + Cake + Guest
773 = 250 + 75 + 4(x)
773 = 325 + 4(x)
773 - 325 = 4(x)
448 = 4x
x = 448/4
x = 112
That makes guests are 112
a tank holds 4000 liters of water in which 100 grams of salt have been dissolved. saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. write initial the value problem for:
Answers
The mass of salt in the tank at time t.
dS/dt = 10 - S/400
S(0) = 100 grams
The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)
A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.
So dS/dt = S(in) - S(out)
S(in) = 1 × 10 = 10 gram/liters
S(out) = S/V × 10 = 10S/V gram/liters
V = V(0) + q(in) - q(out)
V = 4000 + 10t - 10t
V = 4000 liters
dS/dt = 10 - 10S/V
dS/dt = 10 - 10S/4000
dS/dt = 10 - S/400
Now given; S(0) = 100.
Here, p(t) = 1/400, q(t) = 10
\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)
\(\mu=e^{\int p(t)dt}\)
\(\mu=e^{\frac{t}{400}}\)
So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)
S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)
S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)
S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)
S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)
Now solving the bracket
S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)
At S(0) = 100
100 = 4000 + \(e^{\frac{-0}{400}}\) C
100 = 4000 + \(e^{0}\) C
100 = 4000 + C
Subtract 4000 on both side, we get
C = -3900
Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)
To learn more about mass of salt link is here
brainly.com/question/11192688
#SPJ4
The complete question is:
A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:
The mass of salt in the tank at time t.
dS/dt =
S(0) =
The solution is S(t) =
Michael has a bag of marbles. The frequency of selecting each color is recorded in the table below.
Outcome Frequency
Green 4
Black 6
Orange 5
Based on the given frequency, determine the experimental probability of selecting an orange marble.
0.27
0.33
0.40
0.67
Answers
The probability of selecting an orange marble is 0.33.
Option B is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
The number of times each marble is selected.
Green = 4
Black = 6
Orange = 5
Total number of times all marbles are selected.
= 4 + 6 + 5
= 15
Now,
The probability of selecting an orange marble.
= 5/15
= 1/3
= 0.33
Thus,
The probability of selecting an orange marble is 0.33.
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ1
5.Compare deductive reasoning and inductive reasoning
in the form of table and Make an example for each one.
Answers
Deductive reasoning and inductive reasoning can be compared using a table. Deductive reasoning uses general principles to derive specific conclusions, while inductive reasoning uses specific observations.
Deductive Reasoning | Inductive Reasoning
Starts with general principles | Starts with specific observations
Leads to specific conclusions | Leads to general conclusions
Based on logical inference | Based on probability and likelihood
Top-down reasoning | Bottom-up reasoning
Example of Deductive Reasoning:
Premise 1: All mammals are warm-blooded.
Premise 2: Dogs are mammals.
Conclusion: Therefore, dogs are warm-blooded.
In this example, deductive reasoning is used to apply the general principle that all mammals are warm-blooded to the specific case of dogs, leading to the conclusion that dogs are warm-blooded.
Example of Inductive Reasoning:
Observation 1: Every cat I have seen has fur.
Observation 2: Every cat my friend has seen has fur.
Observation 3: Every cat in the neighborhood has fur.
Conclusion: Therefore, all cats have fur.
In this example, inductive reasoning is used to generalize from specific observations of multiple cats to the conclusion that all cats have fur. The conclusion is based on the probability that the observed pattern holds true for all cats.
Learn more about Deductive Reasoning | Inductive Reasoning: brainly.com/question/860494
#SPJ11
Deductive reasoning and inductive reasoning can be compared using a table. Deductive reasoning uses general principles to derive specific conclusions, while inductive reasoning uses specific observations.
Deductive Reasoning | Inductive Reasoning
Starts with general principles | Starts with specific observations
Leads to specific conclusions | Leads to general conclusions
Based on logical inference | Based on probability and likelihood
Top-down reasoning | Bottom-up reasoning
Example of Deductive Reasoning:
Premise 1: All mammals are warm-blooded.
Premise 2: Dogs are mammals.
Conclusion: Therefore, dogs are warm-blooded.
In this example, deductive reasoning is used to apply the general principle that all mammals are warm-blooded to the specific case of dogs, leading to the conclusion that dogs are warm-blooded.
Example of Inductive Reasoning:
Observation 1: Every cat I have seen has fur.
Observation 2: Every cat my friend has seen has fur.
Observation 3: Every cat in the neighborhood has fur.
Conclusion: Therefore, all cats have fur.
In this example, inductive reasoning is used to generalize from specific observations of multiple cats to the conclusion that all cats have fur. The conclusion is based on the probability that the observed pattern holds true for all cats.
Learn more about Deductive Reasoning | Inductive Reasoning: brainly.com/question/860494
#SPJ11
PLEASE HELP ME RNNNNN!!!!!! I NEED THE ANSWERS
I really need help don’t answer if your not giving the correct answer don’t respond
Answers
Answer:
pretty sure its A
Step-by-step explanation:
100 points HELP (EASY)
Answers
Answer:
6 inches
Step-by-step explanation: I did the test
Answer
HEY :) do you want hep with all f them or just some of the awnsers
Step-by-step explanation:
what is the domain of the function y=6x+2
a. all real numbers greater than or equal to zero
b.all whole numbers
c.all real numbers
d.all integers
please help i will give brainly
Answers
Answer:
c
Step-by-step explanation:
y = 6x + 2 is a straight line, that is a linear function
It is valid for all real numbers , then
domain is all real numbers
The domain of the function y=6x+2 is all real numbers.
What is a function?A relation is a function if it has only One y-value for each x-value.
The domain of a function is the set of all possible input values (also known as the independent variable).
In the function y = 6x + 2, x can be any real number.
There are no restrictions or conditions on the values that x can take.
The domain of this function is all real numbers.
Hence, the domain of the function y=6x+2 is all real numbers.
To learn more on Functions click:
https://brainly.com/question/30721594
#SPJ2
If m<1 = 88 , find the m<3.
Answers
Answer:
87?
Step-by-step explanation:
slipknot is the answer to all your problems
What is the area of the shape below?
A.
886 cm2
B.
781.5 cm2
C.
1,019 cm2
D.
990.5 cm2
Answers
Area = 886cm^2
Step-by-step explanation:
34 • 16 = 544
19 • 11 = 209
25 - 11 = 14
14 • 19 = 266/2
266/2 = 133
544 + 209 + 133 = 886cm^2
if the area of a rectangle is 12n12-30n6 168n3 and the length of a rectangle is 6n3, what is the width
Answers
The width of the rectangle is 2n^9 - 5n^3 + 28.
To find the width of the rectangle, we need to use the formula for the area of a rectangle:
Area = Length x Width
We are given that the area of the rectangle is:
12n^12 - 30n^6 + 168n^3
And we know that the length of the rectangle is:
6n³
So we can plug these values into the formula and solve for the width:
Area = Length x Width
12n^12 - 30n^6 + 168n^3 = 6n^3 x Width
Dividing both sides by 6n^3:
2n^9 - 5n^3 + 28 = Width
Therefore, the width of the rectangle is 2n^9 - 5n^3 + 28.
Know more about the rectangle here:
https://brainly.com/question/25292087
#SPJ11
what was Allen's mistake
Answers
Answer: He did not both sides by 100. He did not look for the common denominator before solving.
x is actlly equal to 64
A concert venue offers tickets in 3 zones: orchestra, grand tier, and balcony. Tickets in the orchestra zone are most expensive, and tickets in the balcony zone are least expensive. Managers of the venue want to survey approximately 150 guests at an upcoming concert about their overall experience. They want to take a systematic random sample of the 3000 guests they expect to attend. Which of these strategies will accomplish their intended design?
A. Use a computer to randomly select 150 tickets and invite those guests to participate in the survey
B. Randomly select one of the first 20 guests to arrive and every 20th guest thereafter to take the survey
C. Invite the first 150 guests that arrive to participate in the survey
D. Randomly select 50 tickets from each zone and invite those guests to participate in the survey
Answers
The correct answer for the given question is option B. Randomly select one of the first 20 guests to arrive and every 20th guest thereafter to take the survey
.The strategy that will accomplish the intended design is to randomly select one of the first 20 guests to arrive and every 20th guests thereafter to take the survey.
This strategy ensures that guests are systematically selected and that the sample is randomly selected.
It also ensures that all three zones are represented in the survey.
A systematic random sample is a type of probability sampling in which the sample is selected according to a systematic process.
The sampling interval is determined by dividing the population size by the sample size.
For example, if there are 3000 guests and the desired sample size is 150, the sampling interval would be 20.
The first guest selected would be randomly chosen from the first 20 guests to arrive, and every 20th guest thereafter would be included in the sample.
The other options given in the question will not accomplish the intended design,:
A. Using a computer to randomly select 150 tickets and invite those guests to participate in the survey will not ensure that the sample is systematically selected.
B. Inviting the first 150 guests that arrive to participate in the survey will not ensure that the sample is randomly selected.
C. Randomly selecting 50 tickets from each zone and inviting those guests to participate in the survey will not ensure that the sample is systematically selected.
Know more about the survey here:
https://brainly.com/question/14610641
#SPJ11
Find equivalent expressions for 2y + 7 - 5y + 6y - 3+ y.