The expected number of cars in a randomly selected American household will be 1.75.
Using the probability model, if we ignore some households that own more than 5 cars. Then,
Number of cars Probability
0 0.09
1 0.36
2 0.35
3 0.13
4 0.05
5 0.02
Multiplying each possibility by its probability
∑xP(x)
= 0x0.09+1x0.36+2x0.35+3x0.13+4x0.05+5x0.02
=1.75
Probability is simply the possibility that something will happen. When we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several. The study of events that fit into a probability distribution is known as statistics. A probability model is a representation of a random occurrence in mathematics. It is defined by its sample space, occurrences, and related probabilities for each event. When choosing a sample from a population using the randomization principle, also referred to as chance or random selection, the procedure is known as probability sampling. Generally speaking, probability sampling is more challenging, expensive, and time-consuming than non-probability sampling.
Note that the full question is:
What’s the expected number of cars in a randomly selected American household?
(a) Between 0 and 5
(b) 1.00
(c) 1.75
(d) 1.84
(e) 2.00
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the line ___ from the left to ride there for the slope is ____
The line declines from the left to the right, therefore the slope is negative.
Slope = -1.
What is the Slope of a Line?The slope of the line is the rise of a line over its run, which is given as:
Slope (m) = change in y / change in x.
If a line decreases or declines from the left to the right, then the slope is said to be a negative slope.
The line in the graph shows it is a declining from the left to the right, therefore, it is a negative slope.
Slope of the line = rise/run = -4/4
= -1.
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What two numbers add up to 72?.
Answer:
-1 + 73 =72
-2 + 74 = 72
-3 + 75 = 72
A triangle on a coordinate plane is translated according to the rule tâ€"3, 5(x, y). which is another way to write this rule? (x, y) → (x â€" 3, y 5) (x, y) → (x â€" 3, y â€" 5) (x, y) → (x 3, y â€" 5) (x, y) → (x 3, y 5)
The translation rule, T₋₃,₅ (x,y) for a given triangle on the coordinate plane can be written as
(x, y) → (x – 3, y + 5)
that is x-coordinate shifts to left on x-axis and y-coordinate shifts upward on y-axis. So, the correct option is option ( A).
Translation:
Figure translation is horizontal, vertical, or both movement of the graph or figure. Figures can be moved left, right, up, or down.
Steps to Perform a Translation on the Coordinate Plane are :
Identify the vertices of the shape in the diagram.Apply horizontal translation to the x-coordinate of each vertex in the figure. If you shift the number left, you need to subtract the amount of left shift from the x coordinate. If you shift the number right, you have to add the correct amount of shift to the x coordinate.Apply vertical translation, if you are transforming a number up, you need to add the amount you are transforming to the y coordinate. If you're transforming a number down, you'll need to subtract the amount you're transforming from the y coordinate. Select the graph with correctly transformed vertices from the options given.We have given that
A triangle say ABC is translated on coordinate plane according to following rule, T₋₃,₅ (x, y)
Another way to wright this is explained below. As we know that translation is represented
Tₕ,ₖ(x,y) = (x+h, y+k) which implies that x coordinate shifts to left h point and new coordinate is x+h.
Similarly, new y corrdinate will be y+k
Now, for our point ,
T₋₃,₅ (x,y) ---shifted---> ( x-3 , y+5)
=> (x, y) → (x – 3, y + 5)
Hence , the coordinates of new trangle say A'B'C' which is translation of triangle ABC with coordinates (x,y) are ( x-3 , y+5).
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In the coordinate plane, the point X(0,2) i tranlated to the point X(1,-3). Under the ame tranlation, the point Y(-2,4) and Z(4,5) are tranlated to Y and Z , repectively. What are the coordinate of Y and Z?
The co-ordinates of point Y and Z are (-1,-1) and (5, 0).
What is co-ordinates?
In geometry, a coordinate system could be a system that uses one or additional numbers, or coordinates, to unambiguously confirm the position of the points or alternative geometric components on a manifold like Euclidean space
Main body:
According to given information:
X (0,2) is translated to the point X(1,-3).
so the translation is 1 to right and 5 below
A) y(-2,4)
as the translation is 1 to right and 5 below
hence Y is (-1,-1).
B) Z (4,5)
as the translation is 1 to right and 5 below,
Z = (5,0)
Hence, co-ordinates of point Y and Z are (-1,-1) and (5, 0).
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Two owner of a cattle ranch, Robert and Val, want to find the average weight for the ranch’ 200 cow. Intead of weighing all of the cow:
Robert weigh 25 cow and get an average weight of 1,550 pound (tdev = 50)
Val weigh 100 cow and get an average weight of 1,380 pound (tdev = 50)
What i Val’ margin of error, rounded to the nearet whole number? (The formula i 1. 96 (td dev) / quare root of N
Using its formula, it is found that Val's margin of error is 9.8 pounds.
What is the margin of error?
In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and research results using the margin of error.
The margin of error formula:
The margin of error is given by the following equation:
M = 1.96(s/√n)
Where,
s is the standard deviation.
n is the sample size.
Here, we have
Given
The standard deviation is 50, hence s = 50
Val weighed 100 cows, hence n = 100
By applying the margin of error formula and we get
M = 1.96(50/√100)
M = 1.96(50/10)
M = 9.8
Hence, Using its formula, it is found that Val's margin of error is 9.8 pounds.
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your online reviews have averaged 4.2 over 120 reviews. how many 5 ratings do you need to get to a 4.5 average
You already got 4.2 averaged from 120 reviews. To get a 4.5 average, you need more 72 reviews with 5 ratings.
This problem can solved using average value approach.
Average value can be calculated using:
Average = sum of data value / number of data
Let p = number of required 5 ratings to get a 4.5 average.
Then,
sum of data value = 120 x 4.2 + p x 5
number of data = 120 + p
Hence,
Average = (120 x 4.2 + p x 5) / (120 + p)
4.5 = (504 + 5p) / (120 + p)
540 + 4.5p = 504 + 5p
0.5 p = 36
p = 72
Hence, you need 72 reviews with 5 ratings.
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what would you expect to see if there was a large variance for a sample of difference scores in a repeated-measures t-test?
When there was a large variance for a sample of difference scores in a repeated-measures t-test, then there is probably not a significant difference between treatment groups and the participant's scores would be predictable.
In a repeated measures t-test, the test statistic is given by
[tex]t = \frac{d}{s_{d} / \sqrt{n} }[/tex]
Since [tex]s_{d}[/tex] = the standard deviation of difference scores is large occurs in the denominator of the test statistic.
Thus, there probably is not a significant difference between treatment groups and the participant's scores would be predictable.
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a company has given you the task to research the salary of thirty-five-year-olds in new york city. would you be more interested in looking at the mean, median, or mode?
The correct answer is median.
The salary of 35 year olds would vary greatly, with significant variations. Undoubtedly, this type of data contains outliers. Because median is unaffected by outliers in the data set, it would be appropriate for the data that included outliers.
The observations are divided into two equal portions by the median. When observations are organised in order of magnitude, it reflects the middle value for the group of observations.
When data are input in ascending order, the median value is the middle value. In other words, the observation is in the middle.
If there are an even number of observations overall, the median is calculated as the average of the middle two observations.
The median is the middle observation in the arranged data if the total number of observations is an odd number.
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The Equation P=5s represents the perimeter P of a regular pentagon with side length S. what is the perimeter of a regular pentagon with side length 3 centimeters (CM)
*constant of proportionality*
The Perimeter of the Pentagon is 15 cm
What is a Pentagon?A pentagon is a geometrical shape, which has five sides and five angles
The equation P=5s represents the perimeter P of a regular pentagon with side length s.
We are to find the perimeter of a regular pentagon with side length of 3 cm.
To find it, put s = 3 cm in the given equation.
P = 5(3) cm
P = 15 cm
Hence, the perimeter of the regular pentagon of side length 3 cm is 15 cm.
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The perimeter of a regular pentagon with side length of 3 cm is 15 cm.
How to find the perimeter of a pentagon?A pentagon is a polygon with 5 sides. A regular pentagon is a pentagon with all sides and angles equal to each other.
The Equation P = 5s represents the perimeter P of a regular pentagon with side length s.
The perimeter of a regular pentagon with side length of 3 centimetres can be calculated as follows:
P = 5s
where
P = perimeter of a pentagons = side length of the regular pentagonTherefore,
P = 5(3)
Perimeter of the regular pentagon = 15 cm.
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ten observations were selected from each of three populations, and an analysis of variance was performed on the data. the following are part of the results. source of variation sum of squares degrees of freedom mean square f between treatments 82.4 within treatments (error) 158.4 total
The MS error in the variance is 5.867 using ANOVA
What is Analysis of Variances(ANOVA )?
ANOVA is a statistical method for determining if the effects of different independent variables on a given dependent variable differ or correlate. ANOVA can be used in finance in a variety of ways, such as to forecast price changes in securities by first identifying the variables that affect stock variations. This study can be a useful tool for understanding how a securities or market index will behave in certain scenarios.
Treatment = k-1=2 The degree of freedom
N-k=30-3=27 for the error degrees of freedom
N-1 = 29 degrees of freedom in total.
MS Therapy = (SS Therapy /df Therapy)
82.4/2 = 41.2
MS error = (SS error/df error)
158.4/27 = 5.867
Hence the MS error in the variance is 5.867
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What does find the mean of these numbers mean?.
The mean of the numbers means that it is average of the given numbers.
According to the question,
We have the following information:
Mean of the numbers
We know that the mean of a given data set means that we add all the numbers in data set and divide the obtained result by the total numbers.
For example, we have a following data set:
2,5 and 8
Total numbers in the set = 3
Now, the mean of these numbers will be:
Mean = (2+5+8)/3
Mean = 15/3
Mean of the numbers = 5
So, in other words, it can be expressed as the average of the numbers.
Hence, the mean of the numbers means that it is average of the given numbers.
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How do you solve an equation in slope intercept form without graphing?.
To solve a system of linear equations without graphing, you can use the substitution method.
How do you solve a system of equations without graphing?
To solve a system of linear equations without graphing, you can use the substitution method. This method works by solving one of the linear equations for one of the variables, then substituting this value for the same variable in the other linear equation and solving for the other variable.
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the results of a recent poll on the preference of shoppers regarding two products are shown below. product shoppers surveyed shoppers favoring this product a 800 560 b 900 549 find the point estimate for the difference between the two population proportions in favor of this product.
The point estimator for the difference between two populations proportion in favor of this product is 0.09.
In the given question, the results of a recent poll on the preference of shoppers regarding two products are shown below.
Product Shoppers Surveyed Shoppers Favoring this Product a 800 560
b 900 549
We have to find the point estimate for the difference between the two population proportions in favor of this product.
n(1)=800, x(1)=560
n(2)=900, x(2)=549
P(1)=x(1)/n(1)
P(1)=0.7
P(2)=x(2)/n(2)
P(2)=0.61
The point estimator for the difference between two populations proportion in favor of this product is
P(1) - P(2)=0.7-0.61
P(1) - P(2)=0.09
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If you have more than one quadratic predictor in your model, you can test them all at the same time using the partial F-test. True False
If you have more than one quadratic predictor in your model, you can test them all at the same time using the partial F-test. This statement is True.
What is partial F-test?
A partial F-test is used to determine whether or not there is a statistically significant difference between a regression model and some nested version of the same model.
A nested model is simply one that contains a subset of the predictor variables in the overall regression model.
Partial F-test is a statistical analysis used in multivariate linear regression to determine independent variables are to be considered when fitting a multivariate linear regression mode.
This is necessary because if too many variables are considered, then the model would be too complex. On the other hand, if too few variables are used, then we may get a very weak fit.
Hence if you have more than one quadratic predictor in your model, you can test them all at the same time using the partial F-test.
The given statement is true.
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Which inequality is true?.
Inequality is use when we are not sure about the exact date of a given sample.
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
For example:
If the cost of a Jersy = $40
Cost of Hat = $15
The softball team has a total of $1,200 to spend.
Let x equal the number of jerseys the team orders and y equal the number of hats the team orders.
So the total money will be spent within the budget will be
40*x + 15*y ≤ $1200
Hence, the inequality model will be 40*x + 15*y ≤ $1200.
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a swimming pool is circular with a 30-ft diameter. the depth is constant along east-west lines and increases linearly from 4 ft at the south end to 9 ft at the north end. find the volume of water in the pool. (round your answer to the nearest whole number.)
This circular swimming pool has 4595 ft³ of water in it.
Define the term circular volume?The formula V=r² can be used to determine a cylinder's volume (h). Determining the area of both the circular bottom shape then multiplying it by the height is all that's required to calculate a cylinder's volume.According to what is said, the depth grows linearly from 2 feet at the south end to 7 feet at the north end and remains constant along east-west lines.
The given data in the question-
Diameter of circular swimming Pool; d = 30 ft
Radius r = d/2 = 30/2 = 15 ft
The average depth is given as;
avg (h) = (4 + 9)/2
avg (h) = 6.5 ft
Formula for circular area is;
A = πr²
Put the values;
A = π × 15²
A = 225π
Formula for circular volume is;
Volume = Area × depth
Volume = 225π × 6.5
Volume = 4594.57 ft³
Rounding to a whole number;
Volume = 4595 ft³
Thus, this circular swimming pool has 4595 ft³ of water in it.
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Which one of the following statements is true regarding Statistical Plans?
Select one:
A. Transaction-based plans better support the business need for data.
B. Summary-based plans provide the most accurate data for actuarial-related purposes.
C. Transaction-based plans collect loss data only when a claim is closed.
D. Summary-based plans do not provide enough detail for regulatory reporting purposes.
A. Transaction-based plans better support the business need for data.
The true statement regarding statistical plan is Transaction-based plans better support the business need for data
What is statistical plan?The term statistical plan refers to the document that a statistical organization uses to specify the data items that must be provided to the organization as well as the format in which the data must be reported.
The statistical analysis plan SAP includes information on the scope, population definitions, and methodology of planned analyses. The SAP should be built before any such data analysis because it is essential for directing them.
Hence The statement that transaction-based plans better meet the business demand for data is true with relation to statistical plans.
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you are to use the erdpml: a diver exits the water at 1:30 p.m. after a dive to 63 feet for 35 minutes. he reenters the water at 2:20 p.m. for a dive to 55 feet for 25 minutes. how soon could the diver reenter the water for a dive to 50 feet for 38 minutes?
After 33 minutes the diver reenter the water for a dive to 50 feet for 38 minutes.
What is eRDPML?
The Electronic Recreational Dive Planner Multi Level, or simply eRDPml, is a novel programme created by PADI to help you correctly plan your dives. FOR MANY. An electronic version of the PADI dive tables may be more convenient for certain divers than having to recall how to use them.
If a diver exits the water at 1:30 pm after a 35-minute dive to 19 metres utilising the eRDPML, he will be in pressure group P.
At 2:20 PM, he returns to the ocean. His surface interval is 50 minutes, according to this. A diver in pressure group P switches to pressure group G after 50 minutes.
He will then be in pressure group S if he stays at 17 metres for another 25 minutes. Go to the Surface Interval Mode to find out how long must be spent above the surface before the third dive.
After the second dive, join the pressure group S and start the third dive at a depth of -15 metres for 38 minutes.
33 minutes are determined to be the necessary surface interval. A 33 minute surface interval after the second dive places the diver in pressure group K before the third dive, completing the dive profile.
Hence, after 33 minutes the diver reenter the water for a dive to 50 feet for 38 minutes.
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which types of measurement are used to group respondents or objects into groups or categories and are thus referred to as categorical measures?
The answer to the given question is nominal and ordinal measurements. These two type measurements are used to group respondents or objects into groups or categories and also considered as categorical measures.
What is nominal measurement?Nominal measurement is the least accurate and informative, because it only names the characteristic or identity which we are interested. In nominal variables, the numerical values just "name" the attribute differently. Thus, numerical value is simply a label.
What is ordinal measurement?Ordinal measurement reports the ranking and ordering of the data without chartering the degree of variation. Ordinal measurement includes statistical data type in which variables are in order or rank but without a degree of difference between categories. The ordinal measurement includes qualitative data. This measurement places variables in order or rank, and only allowing to measure the value as higher or lower in measurement.
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Mariam is going to invest $3,000 and leave it in an account for 13 years. Assuming the interest is compounded monthly, what interest rate, to the nearest hundredth of a percent, would be required in order for Mariam to end up with $6,200?
The interest rate that would be earned each month on the amount invested is 0.47%.
What is the interest rate?When the money invested in an account earns a compound interest, it means that both the amount invested and the interest that has already being earned increases 12 times in a year. When an investment earns at a compound interest, it grows exponentially.
The formula that can be used to determine the interest rate is :
Interest rate = [(future value / amount invested)^(1/n)] - 1
Where n is the number of periods
Number of periods = number of years x compounding period
Number of periods = 13 x 12 = 156
Number of periods = [(6200 / 3000)^(1/156) ] - 1 = 0.47%
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Solve the system by elimination. Check your solution x+2y=7 / 13-5y=x
Answer:
x = 3
y = 2
Step-by-step explanation:
x + 2y = 7 and
13 - 5y = x
transfer x to the left side and 13 to the right side of the equation for the second equation:
-x - 5y = -13 now find the sum of both equations:
x + 2y - x - 5y = 7 - 13 add/subtract like terms
-3y = -6 divide both sides by -3
y = 2
To find the value of x replace y with 2:
x + 2*2 = 7
x + 4 = 7 subtract 4 from both sides
x = 3
when reading a table for bivariate analysis that displays percentages of some attributes, what is the rule of thumb for reading the table?
Bivariate table is that which shows the relationship between two variables. The rule of thumb... if the table is scaled down by percentage, read the whole thing. If the table is percentages, read it down.
Bivariate table:
A table that depicts the relationship between two variables by showing the distribution of one variable over the categories of a second variable.
Bivariate Table Primary Purpose:
A bivariate table shows the distribution of one variable over the categories of another variable.
Finally, we mentioned that univariate data can be displayed in many different ways, such as bar charts and box plots. Bivariate data, on the other hand, are usually displayed in scatter plot.
Rule of thumb:
Bivariate analysis results can be represented in form of a two-column data table.
A rule of thumb when reading spreadsheets created by others is then spreadsheet is percentage down, read the whole thing. If the table is percentages, read it down.
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What are 10 multiples of 3?.
The 10 multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 when we can just write the table of 3 all terms.
Given that,
We have to find the 10 multiples of 3.
We know that,
What is multiple?We can find the multiples of a number by counting the digits. A multiple in mathematics refers to the outcome or output of multiplying two numbers together.
The Least Common Multiple is the smallest common multiple of two or more numbers (Least Common Multiple).
The 10 multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.
Therefore, The 10 multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 when we can just write the table of 3 all terms.
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Kevin had 55 ¼ boxe of admiion form in inventory a month ago. Now he ha 27 5/8 boxe left. How many boxe have been ued?
Boxes used in one month is 221/8 as fraction.
What is mixed fraction?
A fraction portrayed with its quotient and remainder may be a mixed fraction. as an example, two 1/3 may be a mixed fraction, wherever two is that the quotient, one is that the remainder. So, a mixed fraction may be a combination of a full range and a correct fraction.
Main body:
Initial boxes with kevin = 55 1/4
converting mixed fraction in simple fraction = 55[tex]\frac{1}{4}[/tex]
= 221/4
Total boxes left = 27[tex]\frac{5}{8}[/tex]
converting it ,
=27 [tex]\frac{5}{8}[/tex] = (27*8+5)/8
=221/8
Total boxes used = 221/4 - 221/8
taking L.C.M , we get
=442-221/8
= 221/8
Hence total boxes used = 221/8
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What foods have the most pesticides?.
Strawberries, apples, cherries, spinach, nectarines, and grape samples were positive for residues of two or more pesticides in more than 90% of the cases. The most pesticides were found in kale, collard, mustard greens, spicy peppers, and bell peppers totaling 103 and 101 pesticides, respectively.
According to the Environmental Working Group's 2022 Shoppers Guide to Pesticides in Vegetables, strawberries and spinach continue to have the highest pesticide levels of any product categories.
According to the EWG, more than 70% of non-organic vegetables contained pesticide residue. Nearly all the produce had pesticide residue levels below limits set by U.S. regulators.
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FILL IN THE BLANK. to test if there is a difference in two population means, a ___should be used. anova one sample t test two sample t test none of the above
To test if there is a difference in two population means, a difference in sample mean should be used , the correct option is (b) .
In the question ,
we have to find the what is used to test whether their is a difference in two population means or not .
For each hypothesis problem, there is test statistic .
This test statistic is compared to the critical value to make the decision about the hypothesis.
Hence choosing the appropriate test statistics matters a lot.
Here two samples are there. It is clearly given for which we have to test the hypothesis that is sample means .
Hence, we can say that the test statistic is, the difference in sample mean .
Therefore , the difference in sample mean is used to test if there is a difference in two population means .
The given question is incomplete , the complete question is
To test if there is a difference in two population means, a ___ should be used.
(a) alpha
(b) the difference in sample means
(c) the degrees of freedom
(d) the difference in the population means
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A pool has some initial amount of water in it. Then it starts being filled so the water level rises at a rate of .6 cm/min After 20 min, the water level is 220 cm. Graph the relationship between the pool's water level (in cm) and time (in min).
The relationship that represents the given function is y = 0.6x + 208 and the graph is attached below.
The water level rises at the rate of 0.6 cm/min .
After 20 minutes the water level is 220 cm
let the initial water level be a.
∴ 220 = a + 0.6×20
or, 220 = a + 12
or, a = 208 cm
therefore the initial water level is at 208 cm.
Now we will find the relationship.
Let the water level is y and the level rises at the rate of 0.6 cm /min .
The require function will be :
y = 0.6x + 208
The graph of the function is attached .
The set of all pairings (x, f (x)) that singularly represent a function is known as the graph of both the function, which is a common technique for illuminating the function.
When the domain and/or the codomain are sets of real values, each such pair can be thought of as the Cartesian coordinates of a point in the plane.
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What is the solution to the system of equations y 1. 5x 4 y =- X?.
The solution of the given equations y=1.5x-4 and y=-4 is given by the coordinates (x,y) as (0, -4)
Illustrate System Of Equations.
A system of equations is two or more equations that contain the same variables. A solutions to a system of equations are the point where the lines intersect. There are four methods to solving systems of equations: graphing, substitution, elimination and matrices.
[tex]y=1.5x-4 , y=-4[/tex]
Substitute the value of y as - 4
-4=1.5x-4
Solving for x, by transposing the terms we get
1.5x = - 4 + 4
1.5x = 0
x = 0
Therefore, the solution is (0, -4).
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which sampling method is conducted when every 50th person registered to vote in a given state is selected from list of voters
Cluster Sampling method , is the required method .
Because the population is split into two separate groups in two different ways.
In a given problem, a survey says that a sample is selected by dividing the population into the gifts of votes, and we need to figure out how to sample. This is called cluster sampling. Analysts are run using a sample her cluster.
Cluster Sampling Method:
In cluster sampling, researchers divide the population into smaller groups called clusters. Then randomly select from these clusters to form a sample. Cluster sampling is a probabilistic sampling technique commonly used to study large populations, especially those that are geographically dispersed.
How to cluster the samples
Define the population Divide thesamples into clusters Randomly select clusters to use as samples Collect data from the samplesTo learn more about Cluster Sampling, refer:
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Create all of the possible arrays for modeling a rectangular quilt with the 24 paper squares. write an equation to accompany each array. you can use the attached pre-made quilt squares by cutting and pasting them, or you can draw the arrays with your own designs on a separate sheet of paper.
The array formulas are (r³ - 3) × 1 = 24, (r² + 3) × 2 = 24, (r² - 1 ) × 3 = 24, (r² - 3 ) × 4 = 24, (r) × 8 = 24, (r - 1 ) × 12 = 24, and (r - 2) × 12 = 24 where, r = 3.
The array can be taken as rows.
If we take the first side as the length denoted by L and the second side as the width indicated by W.
Then the area can be given as;
Area = length * width
Area = L * W
The total area of the quilt is 24 squares which can be obtained as;
24 × 1 = 24
All squares are arranged in a single row.
(r³ - 3) × 1 = 24
12 × 2 = 24
12 squares arranged in 2 rows.
(r² + 3) × 2 = 24
8 × 3 = 24
8 squares arranged in 3 rows.
(r² - 1 ) × 3 = 24
6 × 4 = 24
6 squares arranged in 4 rows.
(r² - 3 ) × 4 = 24
3 × 8 = 24
3 squares arranged in 8 rows.
(r) × 8 = 24
2 × 12 = 24
2 squares arranged in 12 rows.
(r - 1 ) × 12 = 24
1 × 24 = 24
1 square arranged in 24 rows.
(r - 2) × 12 = 24
In all of the above r = 3.
Thus, the array formulas are (r³ - 3) × 1 = 24, (r² + 3) × 2 = 24, (r² - 1 ) × 3 = 24, (r² - 3 ) × 4 = 24, (r) × 8 = 24, (r - 1 ) × 12 = 24, and (r - 2) × 12 = 24 where, r = 3.
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