a. False
b. True
c. False
d. False
In order to answer this question, it is important to understand the definitions of each of the terms:
- True or False: this is a type of question that requires the student to choose between two possible answers, True or False.
- Normal Distribution: this is a type of data distribution in which the data is symmetrically distributed around the mean, and the probability of occurrence is equal for all values.
- Standard Deviation: this is a measure of how spread out a set of data is from the mean. It is calculated by taking the square root of the variance of the data set.
- Median: this is the middle value in a data set when the values are arranged in ascending or descending order.
- Quartile: this is a type of quartile division in which a data set is divided into four equal parts, each containing 25% of the data.
- Mode: this is the most frequently occurring value in a data set.
- Population Standard Deviation: this is a measure of the spread of the population, and it is calculated by taking the square root of the variance of the population.
Therefore, the correct answer to the given question is:
a. False
b. True
c. False
d. False
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Michael buys 3 shirts for $25 each. He will also have to pay 7% sales tax.
Find the total amount Michael will pay the cashier.
Answer:$22.84
Step-by-step explanation:
The tax is calculated by 0.075 * 21.25 = 1.59375 or $1.59. So the total bill is the cost of items purchased plus tax, which is $21.25 + $1.59 = $22.84.
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer:50
Step-by-step explanation:
In studies looking at the movement patterns of penguins, penguins are often monitored by placing a metal tag on their flipper. A group of scientists were concerned that these metal tags may be negatively affecting the survival of penguins (Saraux et al. 2011, "The Reliability of flipper-banded penguins as indicators of climate change", Nature 469, 203- 206). They conducted a small study with a total of 1983 penguins to determine whether the type of tag (metal or electronic) influenced the 5-year survival of penguins. In total, the study included 957 penguins that wore metal tags, 540 penguins that wore metal tags and survived, and 301 penguins that wore electronic tags and died.
a) Assuming that the type of tag and penguin survival are independent of one another, what 2x2 table do we expect to see? Is the observed data consistent with this assump- tion of independence? Carry out a chi-squared test to address this question. Give all your steps, and state as clearly as you can what hypotheses you are testing, your p-value, and what you conclude.
b) Suppose a condition was specified in the null hypothesis through prior knowledge that the probability of survival is 0.637 and that the probability of a penguin wearing a metal tag is 0.483. Would anything in your analysis in (a) change? Is there any change in your conclusion from (a)?
c) Suppose a separate study had only included 21 penguins in total, 12 penguins that wore electronic tags, 4 penguins that wore metal tags and survived, and 5 penguins that wore electronic tags and died. Explain what reservations (if any) you may have with performing a chi-squared test. Carry out an appropriate test to address the question of independence between survival and tag type for the new data. Give all your steps, and state as clearly as you can what hypotheses you are testing, your p-value, and what you conclude.
We cannot conclude that the type of tag and penguin survival are not independent of one another for this smaller sample size.
a) The expected 2x2 table would look like this:
| | Metal Tag | Electronic Tag |
|------------|-----------|----------------|
| Survived | 483.637 | 456.363 |
| Not Survived | 473.363 | 569.637 |
The observed data is not consistent with the assumption of independence, as the observed values are different from the expected values. To carry out a chi-squared test, we need to calculate the chi-squared statistic:
X^2 = (957-483.637)^2/483.637 + (540-456.363)^2/456.363 + (301-473.363)^2/473.363 + (185-569.637)^2/569.637 = 237.525
The degrees of freedom for this test are (2-1)(2-1) = 1. Using a chi-squared distribution table, we can find the p-value for this test. The p-value is less than 0.001, which is very small. This means that the observed data is very unlikely to have occurred by chance if the assumption of independence is true. Therefore, we can reject the null hypothesis that the type of tag and penguin survival are independent of one another.
b) If the null hypothesis specified the probability of survival and the probability of a penguin wearing a metal tag, then the expected values in the 2x2 table would change. The new expected values would be:
| | Metal Tag | Electronic Tag |
|------------|-----------|----------------|
| Survived | 609.711 | 330.289 |
| Not Survived | 347.289 | 695.711 |
The chi-squared statistic would also change:
X^2 = (957-609.711)^2/609.711 + (540-330.289)^2/330.289 + (301-347.289)^2/347.289 + (185-695.711)^2/695.711 = 444.787
The p-value for this test would still be less than 0.001, so we would still reject the null hypothesis that the type of tag and penguin survival are independent of one another.
c) With a smaller sample size, the chi-squared test may not be appropriate. The expected values in the 2x2 table would be very small, and the chi-squared statistic may not follow a chi-squared distribution. Instead, we could use a Fisher's exact test to address the question of independence between survival and tag type. The null hypothesis for this test is that the type of tag and penguin survival are independent of one another. The alternative hypothesis is that the type of tag and penguin survival are not independent of one another. The p-value for this test is 0.657, which is not small enough to reject the null hypothesis. Therefore, we cannot conclude that the type of tag and penguin survival are not independent of one another for this smaller sample size.
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The terminal side of θ in standard position contains the
given point. Find the values of the six trigonometric functions of
θ.
( 4 , 3 )
Answer: Read the step by step explanation for the answer
Step-by-step explanation:
We can use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the given point (4, 3) and the origin (0, 0):
r = √(4² + 3²) = 5
Then we can use the coordinates of the point (4, 3) to determine the values of the trigonometric functions:
sin(θ) = opposite/hypotenuse = 3/5
cos(θ) = adjacent/hypotenuse = 4/5
tan(θ) = opposite/adjacent = 3/4
csc(θ) = hypotenuse/opposite = 5/3
sec(θ) = hypotenuse/adjacent = 5/4
cot(θ) = adjacent/opposite = 4/3
Therefore, the values of the six trigonometric functions of θ are:
sin(θ) = 3/5
cos(θ) = 4/5
tan(θ) = 3/4
csc(θ) = 5/3
sec(θ) = 5/4
cot(θ) = 4/3
17. Determine whether the given set is linearly independent. \[ \left\{\left[\begin{array}{c} 1 \\ -1 \\ -2 \end{array}\right],\left[\begin{array}{c} -1 \\ 0 \\ 1 \end{array}\right],\left[\begin{array
The set is linearly independent.
Yes, the given set is linearly independent. To prove this, we can use the determinant method. To calculate the determinant, arrange the columns of the array in a 3x3 matrix. This gives us the following matrix:
$$\begin{bmatrix}1 & -1 & -2\\-1 & 0 & 1\\0 & 1 & -1\end{bmatrix}$$
The determinant of this matrix is 1, which is not equal to 0. This shows that the given set is linearly independent.
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Factored completely, the expression 3x^(2)-3x-18 is equivalent to A. 3(x^(2)-x-6) B. 3(x-3)(x+2) C. (3x-9)(x+2) D. (3x+6)(x-3)
The factored form of the expression [tex]3x^2 - 3x - 18[/tex] is B) 3(x-3)(x+2).
To factor a quadratic expression like this, we want to find two numbers that multiply to the constant term (-18) and add up to the coefficient of the x term (-3). In this case, those numbers are -3 and 6, because (-3) * 6 = -18 and (-3) + 6 = 3.
Then, we can use those numbers to split the middle term into two terms:
[tex]3x^2 - 3x - 18 = 3x^2 - 9x + 6x - 18[/tex]
[tex]= 3x(x-3) + 6(x-3)[/tex]
[tex]= (x-3)(3x+6)[/tex]
[tex]= 3(x-3)(x+2)[/tex]
So the factored form of the expression is 3(x-3)(x+2), which is equivalent to choice B.
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help :(( What should be reason 5 in the following proof?
Answer:
Reason 5 should be "Alternate Interior Angles Converse".
Step-by-step explanation:
Consider the following.
Given:
△XYZ with XY ≅ XZ ≅ YZ
ZW ⊥ XY with W on XY
YZ = 8
Find:ZW
Create a drawing as needed.
Since
XY ≅ XZ ≅ YZ, △XYZ
is ---Select--- an equilateral a scalene triangle. This means △XYZ is also ---Select--- equiangular right obtuse .
Find the measures of the following angles in degrees.
m∠WYZ= °m∠YWZ= °m∠YZW= °
Find WY.
WY =
Find ZW. Give your answer in both simplest radical form and as an approximation correct to two decimal places.
simplest radical formZW=
approximationZW=
ZW = 5.656
Since XY ≅ XZ ≅ YZ, △XYZ is an equilateral triangle. This means △XYZ is also equiangular.
Find the measures of the following angles in degrees:
m∠WYZ = 60°
m∠YWZ = 60°
m∠YZW = 60°
Find WY:
WY = 8
Find ZW: Give your answer in both simplest radical form and as an approximation correct to two decimal places.
simplest radical form ZW = 4√2
approximation ZW = 5.656854249492381
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37. Tania comenzó una gráfica para mostrar la desigualdad
y<3.7. Termina de rotular la recta numérica y dibuja
la gráfica.
←||▬▬▬|||||▬▬▬▬▬▬▬▬▬▬▬▬|
3.0 3.1
4.0
The values of {y} less than 3.7 on the number line represent the solution set of the given inequality.
What is inequality?An inequality is used to compare two or more expressions or numbers.
For example -
2x > 4y + 3
x + y > 3
x - y < 6
Given is that Tania began a graph to show the inequality → y < 3.7.
Given is the inequality as -
y < 3.7
For all the values of {y} less than 3.7 on the number line represent the solution set of the given inequality.
Therefore, the values of {y} less than 3.7 on the number line represent the solution set of the given inequality.
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{Question in english -
Tania began a graph to show the inequality y < 3.7. Finish labeling the number line and draw the graph.}
Calculate the perimeter of the trapezoid in millimeters
Answer:
135 mm
Step-by-step explanation:
The perimeter is found by adding all sides together. Since the answer is to be in millimeters, two side lengths must be converted.
1 centimeter = 10 millimeters
1.5 x 10 = 15 mm
6 x 10 = 60 mm
Now, add all sides together:
60 + 15 + 20 + 40 = 75 + 60 = 135 mm
I neeeed help plssssssssssssssssssssssss
Answer:
I AINT SOLVING ALL THAT
Miguel has started training for a race. The first time he trains, he runs 0. 5 mile. Each subsequent time he trains, he runs 0. 2 mile farther than he did the previous time.
a) What is the arithmetic series that represents the total distance Miguel has run after he has trained n times?
b) A marathon is 26. 2 miles. What is the least number of times Miguel must run for his total distance run during training to exceed the distance of a marathon?
Answer:
hope this helps.
Step-by-step explanation:
what is the line into the slope-intercept from of 5y-6x=5
[tex]y=\frac{6}{5} x+1[/tex]
Step-by-step explanation:Slope-intercept form is a common way to express a linear function.
Solving For Slope-Intercept
In the question, we are given standard form. In order to find slope-intercept, we need to solve for y. This means we need to use the properties of equality to isolate y from the other values.
First, add 6x to both sides.
5y = 6x + 5Then, divide both sides by 6.
[tex]y=\frac{6}{5} x+1[/tex]This gives us the final slope-intercept form of the given equation.
Interpreting the Equation
Slope-intercept form is written in the format of y = mx + b. In this equation, m is the slope and b is the y-intercept. Our equation is [tex]y=\frac{6}{5} x+1[/tex]. So, 6/5 is the slope. This means that the rate of change of the graph is 6 units per 5 units. Additionally, the y-intercept is 1. So, the graph crosses the y-axis at y = 1.
need help with this problem
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{(-2)}) \implies y +4= \cfrac{1}{2} (x +2) \\\\\\ y+4=\cfrac{1}{2}x+1\implies {\Large \begin{array}{llll} y=\cfrac{1}{2}x-3 \end{array}}[/tex]
I NEED HELP REALLY BAD MY MOM MIGHT GROUND ME Which statement describes what happens when (4, 6) is reflected across the y-axis? Select all that apply.
Answer: I’m pretty sure it’s the first box, second box and third box
Step-by-step explanation:
Yolanda wants to rent a boat and spend at most $39. The boat costs $7 per hour, and Yolanda has a discount coupon for $3 off. What are the possible numbers of hours Yolanda could rent the boat? Can someone please help me!! ALKES IS A LOT! PLEASE HELP ME!!
Yolanda can rent his boat for upto 6hrs and spend his money correctly.This can be solved by inequalities.
What is discount?
The term “discount” refers to the pricing system in which the price of a commodity (goods or services) is lower than its marked price listed price.
let's think about how to set up inequality.
Amount Spent ≤ 39
we have to find what the amount spent is.
It would be $7 times the number of hours he rents the boat for (X), minus $3. So the equation will be:
7X - 3 ≤ 39
By solving this: 7X ≤ 42
X ≤ 6
So, Yolanda can rent the boat for up to 6 hours to spend at most $39.
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The sum of the series whose n term is 3(2x+1)
give me full solved and detailed answer
A chord is a line segment that connects two points on a circle what is the maximum number of non-overlapping regions a circle can be divided into with 15 chords
A) 30
B) 48
C) 121
D) 127
Pls help
Manuel selected at random a flight that was late by 25 minutes or less from his results work out estimate for the probability that this flight was late by 5 minutes or less
As a result, it is predicted that 0.4 or 40% of flights will arrive late by 5 minutes or less.
what is probability ?Chance is a way to gauge how likely something is to happen. It is a number between 0 and 1, where 0 denotes the impossibility of the occurrence and 1 denotes its certainty. For instance, since there is a one in six possibility of rolling a six, the probability of rolling a six on a fair six-sided die is 1/6 or roughly 0.167. Another way to describe probability is as a percentage or as odds. A probability of 0.5, for example, corresponds to 50% or chances of 1:1. (meaning there is an equal chance of the event occurring or not occurring). Science, engineering, economics, and banking all use probability theory, a significant area of mathematics.
given
Assume Manuel has information on 100 aircraft with delays of no more than 25 minutes, of which 40 had delays of no more than 5 minutes.
The estimated likelihood that an arbitrarily chosen flight would arrive late by 5 minutes or less would then be:
P(late by 5 minutes or less) is equal to the number of planes that are 5 minutes or less late divided by the total number of flights that are 25 minutes or less late.
P(late by no more than 5 minutes) = 40/100
P(late by no more than 5 minutes) = 0.4
As a result, it is predicted that 0.4 or 40% of flights will arrive late by 5 minutes or less.
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Which has the greater perimeter, a regular pentagon, or a regular hexagon, if they have the same area? Explain why.
If a regular pentagon and a regular hexagon have the same area, then the regular pentagon will have a smaller perimeter than the regular hexagon.
Why would the pentagon have a larger perimeter ?This is because a regular pentagon has less sides than a regular hexagon, which means that the length of each side of the pentagon will be shorter than the length of each side of the hexagon.
The hexagon would therefore have more distance to cover and more sides to be add up before one can get to the perimeter. The pentagon has three less sides than the hexagon and so would have a smaller perimeter.
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What's the expression of this?
Answer:
[tex](3m + 5n)(9m {}^{2} - 15mn + 25n {}^{2} )[/tex]
Step-by-step explanation:
Greetings!!!
Given expression
[tex]27m {}^{3} + 125n {}^{3} [/tex]
Apply exponents rule
Rewrite 27 as 3³
[tex] = 3 {}^{3} m {}^{3} + 125n {}^{3} [/tex]
Rewrite 125 as 5³
[tex] = 3 {}^{3} m {}^{3} + 5 {}^{3} n {}^{3} [/tex]
Apply exponent rule:
[tex]a {}^{m} b {}^{m} = (ab) {}^{m} \\ = 3 {}^{3} m {}^{3} = (3m) {}^{3} \\ = 5 {}^{3} n {}^{3} = (5n) {}^{3} [/tex]
Apply sum of cubes formula
[tex]x {}^{3} + y {}^{3} = (x + y) (x {}^{2} - xy + y {}^{2} )[/tex]
[tex](3m {}^{3}) + (5n {}^{3} ) = (3m + 5n)((3m) {}^{2} - 3m.5n + (5n {}^){2} ) \\ = (3m + 5n)((3m {}^{2} ) - 3m.5n + (5n {}^{2} ))[/tex]
simplify
[tex] = (3m + 5n)(9m {}^{2} - 15mn + 25n {}^{2} )[/tex]
If you have any questions tag me on comments
Hope it helps!!!
Deondra measures an object as 2 3/4 inches to the nearest quarter inch. Abdul measures the same object as 2 1/2 inches to the nearest half inch. Can they both be correct? Explain
The ranges overlap, it is possible for both measurements to be correct.
What do significant figures in computations and measurements mean?Since they show how precise and accurate the numbers being utilised are, significant figures are crucial in measurements and computations. In order to prevent mistakes and maintain the required degree of precision, it is crucial to maintain consistency in the number of significant figures throughout computations. This indicates the amount of uncertainty in a measurement.
Given that, Deondra measures an object as 2 3/4 inches and Abdul measures 2 1/2 inches to the nearest half inch.
The actual length for Deondra is between 2 5/8 inches and 2 7/8 inches.
For Abdul the actual length is between 2 inches and 3 inches.
Since the ranges overlap, it is possible for both measurements to be correct.
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hey you can you help and if your don’t know then don’t answer pls thx
The cοrrect statement is the segment GC is transversal tο segments KG and QC.
What is a transversal line?A line that crοsses twο οr mοre lines in the same plane at different lοcatiοns is said tο be transversal. Accοrding tο the fundamental prοpοrtiοnality theοrem (alsο knοwn as Thales' theοrem), if three οr mοre parallel lines crοss acrοss twο transversals, they prοpοrtiοnally cut οff the transversals.
We have given the statements are:
A). KG QC.
B) KG and QC intersect at a right angle.
C) KQ || GC.
D) GC is transversal tο KG and QC.
Therefοre, here in the figure, segment GC intersects segments KG and QC in the same plane at different lοcatiοns.
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4. Emma is a salesperson who sells computers at an
electronics store. She makes a base pay amount each day
and then is paid a commission for every computer sale she
makes. Let P represent Emma's total pay on a day on
which she sells x computers. The table below has select
values showing the linear relationship between x and P.
Determine how much money Emma would be paid on a
day in which she sold 7 computers.
x
1
3
8
P
105
145
245
Emma would therefore receive $225 for a day in which she sold 7 laptops.
what is unitary method ?Mathematicians use a method called the unitary method to handle proportional problems. Finding the value of one unit must be done before using that value to determine the value of a specified quantity of units. When buying or cooking real-world products that are sold by weight or volume and whose prices are determined by those factors, this technique is frequently used. The unitary approach is also used to address issues involving time, space, and speed.
given
We must use the provided values in the table to determine the equation of the linear relationship between x and P in order to determine how much money Emma would be paid on a day when she sold 7 computers.
The first two data values can be used to determine the line's slope:
slope is equal to (145 - 105) / (3 - 1) / (P2 - P1) / (x2 - x1), or 20.
Next, we can determine the equation of the line using the point-slope form of the equation of a line:
P - P1 Equals m(x - x1) (x - x1)
P - 105 = 20(x - 1) (x - 1)
P = 20x + 85
To determine Emma's total pay, we can finally enter x = 7 into the equation:
P = 20(7) + 85\s= 225
Emma would therefore receive $225 for a day in which she sold 7 laptops.
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Can someone please answer and explain a & b please, thank you.
A roll of ribbon was 12 meters long. Diego cut 9 pieces of ribbon that were 0.4 meter
each to tie some presents. He then used the remaining ribbon to make some
wreaths. Each wreath required 0.6 meter. For each question, explain your reasoning.
a. How many meters of ribbon were available for making wreaths?
b.
How many wreaths could Diego make with the available ribbon?
Answer: a. 8.4 meters b. 14 wreaths
Step-by-step explanation:
The following equation shows the problem, with x representing the number of wreaths made:
12 = 9(0.4) + 0.6x
To answer a, get 0.6x alone:
12 = 9(0.4) + 0.6x
12 = 3.6 + 0.6x
8.4 = 0.6x
There were 8.4 meters available to make wreaths
To answer b, get x alone
8.4 = 0.6x
14 = x
Diego could make 14 wreaths with the available ribbon
Hope this helps!
Natalie mowed 3 lawns in 18 hours. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
Answer: See attached.
Step-by-step explanation:
First, we will find the unit rate by dividing.
18 hours / 3 lawns = 6 hours per lawn
Then, we can fill out the other values using this unit rate.
1 lawn * 6 hours = 6
12 hours / 6 hours = 2
Lastly, we will use these two equivalent ratios we found above to fill out the table and then plot the points. See attached.
In January 1993, there were about 1,313,000 internet hosts. During the next five years, the number increased by about 100% per year. Estimate the year when there were 30 million hosts
The estimate is that there were 30 million internet hosts in the year 1998.
What is exponential growth?Exponential growth is a function that shows an increase within a population that occurs at the same rate over time.
If the number of internet hosts increased by 100% per year, it means that it doubled every year. Therefore, we can use the formula for exponential growth to estimate the number of internet hosts in future years.
Let x be the number of years after 1993, and let H(x) be the number of internet hosts in year y. Then, we have:
H(x) = 1,313,000 * 2ˣ
To estimate the year when there were 30 million internet hosts, we need to solve the following equation for x:
H(x) = 30,000,000
Substituting the formula for H(y), we get:
1,313,000 * 2ˣ = 30,000,000
Dividing both sides by 1,313,000, we get:
2ˣ = 30,000,000 / 1,313,000
Taking the logarithm of both sides with base 2, we get:
x = log2(30,000,000 / 1,313,000)
Using a calculator, we get:
x ≈ 5.2
Therefore, the estimate for the year when there were 30 million internet hosts is: 1993 + 5.2 ≈ 1998.2
Hence, the estimate is that there were 30 million internet hosts in the year 1998.
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What is the y-intercept?
Answer:
The y-intercept is 1
at the point (0,1)
Step-by-step explanation:
The y-intercept is the point at which a graph crosses the y-axis.
Algebra please help!!!!
Answer:
x = - 2, y = - 8
Step-by-step explanation:
13x - 6y = 22 → (1)
x = y + 6 → (2)
substitute x = y + 6 into (1)
13(y + 6) - 6y = 22
13y + 78 - 6y = 22
7y + 78 = 22 ( subtract 78 from both sides )
7y = - 56 ( divide both sides by 7 )
y = - 8
substitute y = - 8 into (2)
x = y + 6 = - 8 + 6 = - 2
then x = - 2 and y = - 8
If you answered "Categorical" in the previous question, how many categories does the variable of interest consist of? If you answered "Numerical", what is the range of values the variable can take?
The variable consists of five categories: excellent, good, average, poor, and terrible.
How to determine the type of variableThe variable of interest in this scenario is the rating of the service provided by the hotel during the guests' most recent visit.
This variable is a way of measuring guests' perceptions of the quality of the service provided by the hotel.
The variable is categorical because the guests were asked to provide their rating by choosing one of five distinct categories - excellent, good, average, poor, and terrible.
The number of categorical variablesThe categories stated in (a) above represent the different levels of quality the guests perceived in the hotel's service.
Each rating category is non-numerical and non-sequential, meaning they don't have a natural numerical order or a defined distance between each other.
So, the number of categorical variables is 5
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Complete question
A hotel chain sent 2,000 past guests an email asking them to rate the service in the hotel during their most recent visit. Of the 500 who replied, 450 rated the service as excellent.
(a) Give a name to the variable and indicate if the variable is categorical, ordinal, or numerical
(b) If you answered "Categorical" in the previous question, how many categories does the variable of interest consist of? If you answered "Numerical", what is the range of values the variable can take?
