Answers
Answer:
x=34, z=26 degrees, y=74 degrees
Step-by-step explanation:
We can find x because the triangles are equal to each other, meaning that we can set 2x-20 equal to 4x-88. When solved, x=34. This now means that the expression 2x-20 and 4x-88 both equal to 48 degrees.
Now looking at the triangle on the left, we can find the angle using supplementary angles, setting 180-154, which is 26 degrees. This means z on the triangle to the right is also 26 degrees since the triangles are equal to each other.
Because of knowing two angles, we can now find the 3rd one by adding both of them up and subtracing it from 180. That will get you 106 degrees, then using vertical angles we can find that the angle measure of 106 degrees carries over to the second triangle.
To find y now, you simply subtract 106 from 180 to get 74 degrees.
(I believe this is right, hopefully it made sense!)
Related Questions
An oil tanker is approximately 1500 feet long. How far would 8500 oil tankers span if you placed them end to end?
Answers
Answer:
12,750,000ft
Step-by-step explanation:
1,500 * 8,500 = 12,750,000
What is the sign of
−
9
⋅
(
0
−
3
)
−9⋅(
−3
0
)minus, 9, dot, left parenthesis, start fraction, 0, divided by, minus, 3, end fraction, right parenthesis?
Answers
The expression is undefined, so the sign cannot be determined.
How to determine sign for the given problem?
The following given expression can be more simplified as follows:
-9 * (0 - 3) - (9 * (-3/0))
= -9 * (-3) - 9 * undefined [Note: Division by zero is undefined]
= 27 - undefined
As anything subtracted from undefined remains undefined, the overall result is undefined.
Therefore, the sign of the expression cannot be determined.
Undefined values represent the absence of a meaningful result or outcome. In this case, the expression involves division by zero, which is undefined. As a result, any operation involving an undefined value will also be undefined, including subtraction. Thus, the overall result is undefined.
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Answer:
ITS ZEROOOO
Step-by-step explanation:
i guesses and ended up getting it right.
Rachel is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges $104 and allows unlimited mileage.
Company B has an initial fee of $65 and charges an additional $0.60 for every mile driven.
For what mileages will Company A charge less than Company B?
Use m for the number of miles driven, and solve your inequality for m.
Answers
Answer:
To find out for what mileages Company A will charge less than Company B, we need to set up an inequality using the given prices and the number of miles driven, m.
For Company A, the cost is a flat rate of $104 regardless of the number of miles driven. Therefore, the inequality is simply:
104 < 65 + 0.60m
We can simplify this inequality by subtracting 65 from both sides:
39 < 0.60m
To isolate m, we can divide both sides by 0.60:
65 < m
So, Company A will charge less than Company B for any mileage greater than 65 miles. If Rachel plans to drive more than 65 miles, she should choose Company A to save money. However, if she plans to drive less than 65 miles, Company B may be the cheaper option.
2. a college admissions director wishes to estimate the mean age of all students currently enrolled. in a random sample of 20 students, the mean age is found to be 22.9 years. from past studies, the standard deviation is known to be 1.5 years and the population is normally distributed. (a) (2 points) construct a 90% confidence interval of the population mean age. then calculate a 95% confidence interval, and a 99% confidence interval. (b) (2 point) construct a 90% confidence interval for this case, assuming that the given standard deviation of 1.5 years came from the sample instead of the population. (c) (1 point) suppose that the distribution of the population is not specified. do we have enough information to form a confidence interval in that case?
Answers
a) For a 90% confidence interval [22.25, 23.55].
For a 95% confidence interval [22.10, 23.70].
For a 99% confidence interval [21.97, 23.83].
b) For a 90% confidence interval [22.25, 23.55].
a) To construct a confidence interval for the population mean age, we can use the formula: CI = x* ± tα/2 * (σ / sqrt(n)), where x* is the sample mean age, σ is the population standard deviation, n is the sample size, and tα/2 is the critical value of the t-distribution with n-1 degrees of freedom and a given level of confidence α/2.
For a 90% confidence interval, α = 0.1 and tα/2 = 1.725, so the interval is: 22.9 ± 1.725 * (1.5 / sqrt(20)) = [22.25, 23.55].
For a 95% confidence interval, α = 0.05 and tα/2 = 2.093, so the interval is: 22.9 ± 2.093 * (1.5 / sqrt(20)) = [22.10, 23.70].
For a 99% confidence interval, α = 0.01 and tα/2 = 2.861, so the interval is: 22.9 ± 2.861 * (1.5 / sqrt(20)) = [21.97, 23.83].
b) If the given standard deviation of 1.5 years came from the sample instead of the population, we need to use a t-distribution with n-1 degrees of freedom to construct the interval. The formula is the same as before, but we replace σ with s, the sample standard deviation.
For a 90% confidence interval, the critical value is still 1.725, so the interval is: 22.9 ± 1.725 * (1.5 / sqrt(20)) = [22.25, 23.55].
c) If the distribution of the population is not specified, we can still form a confidence interval if we have a large enough sample size (typically, n >= 30) due to the central limit theorem. In this case, we have n = 20, so we may not have enough information to form a confidence interval if we cannot assume the population is normally distributed.
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from a population of 600 elements, a sample of 100 elements is selected. it is known that the variance of the population is 900. find the approximate standard error of the mean.
Answers
The approximate standard error of the mean is 3.
Here is how to find the approximate standard error of the mean from a population of 600 elements, where a sample of 100 elements is selected, and it is known that the variance of the population is 900.
Determine the sample size n, which is 100
Find the population variance, which is 900.
Compute the population standard deviation, which is the square root of the variance, as follows:
σ = √900σ
= 30
Compute the standard error of the mean as follows:
SEM = σ/√nSEM
= 30/√100SEM
= 3
The standard error of the mean (SEM) can be calculated using the formula:
SEM = σ / √n
where σ represents the population standard deviation, and n represents the sample size. In this case, we know that the population variance is 900.
To find the standard deviation, take the square root of the variance:
σ = √900 = 30
Now, we can plug in the values into the formula:
SEM = 30 / √100
SEM = 30 / 10
SEM = 3
The approximate standard error of the mean for this sample is 3.
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Which answer choice below is closest to the length of segment DE?
Answers
Answer:
15.71
Step-by-step explanation:
Triangle ABC and triangle ADE are similar triangles so we can find the length of DE using similarity ratio.
[tex] \frac{14}{22} = \frac{10}{de} [/tex]
Cross multiply fractions14×DE = 220
Divide both sides by 14DE = 15.71 approximately.
the product of twice a number and four
Answers
The product of twice a number and four is 8 times the number.
What is product of a number?The product means a number that you get by multiplying two or more other numbers together.
Equation:The product of twice a number and four can be represented algebraically as:
4(2x)
where x is the number we are referring to.
Simplifying the expression, we get:
4(2x) = 8x
Therefore, the product of twice a number and four is 8 times the number.
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explain how to take a systematic sample of 100 companies from the 1,803 companies that are members of an industry trade association. state important numerical values used in the process.
Answers
To take a systematic sample of 100 companies from a population of 1,803 companies, determine the sampling interval (k) which is N/n, choose a random starting point between 1 and k, and select every kth company until 100 companies are sampled.
To take a systematic sample of 100 companies from the 1,803 companies that are members of an industry trade association, follow these steps
Determine the sampling interval (k), which is the number of companies in the population divided by the desired sample size. In this case, k = 1803/100 = 18.03. Round this number up or down to the nearest whole number based on your sampling preferences.
Choose a random starting point between 1 and k. For example, you could randomly select a number between 1 and 18.
From the starting point, select every kth company in the list of members until you have 100 companies. For example, if the starting point is 4, you would select companies 4, 22, 40, 58, 76, 94, 112, and so on until you reach 100 companies.
Important numerical values used in this process are:
Population size (N) = 1,803 companies
Desired sample size (n) = 100 companies
Sampling interval (k) = N/n = 1803/100 = 18.03
Random starting point (any number between 1 and k, depending on sampling preference)
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Graph the inverse of the provided graph on the accompanying set of axes. You must
plot at least 5 points.
*Click the graph to make a point. Click it again to erase.
Answers
The inverse of the provided graph is shown in the image attached below.
What is an inverse function?In Mathematics and Geometry, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value). By critically observing the graph, we can logically deduce the following points;
Vertex (h, k) = (-4, 6)
y-intercept (x, y) = (0, 8)
y-intercept (x, y) = (0, 4)
Point (x, y) = (5, 9)
Point (x, y) = (5, 3)
By swapping both the input value (x-value) and output value (y-value), we have:
Vertex (h, k) = (6, -4)
x-intercept (x, y) = (8, 0)
x-intercept (x, y) = (4, 0)
Point (x, y) = (9, 5)
Point (x, y) = (3, 5)
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algebra 1 mid term help!!
Answers
Answer:
Yes,
Step-by-step explanation:
Because no x- Values repeat.
a sum of 8000 is compounded annually for 3 years if the rate of interest in 10% per annum for the first year 12% per annum for the second year and 15% per annum for the third year then what is the amount at the end of 3rd years?
Answers
Answer:
the amount at the end of the third year is A3 = $11,330.40.
Step-by-step explanation:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
For the first year, the interest rate is 10%, so we have:
A1 = 8000(1 + 0.1/1)^(1*1)
A1 = 8800
After the first year, the principal becomes 8800. For the second year, the interest rate is 12%, so we have:
A2 = 8800(1 + 0.12/1)^(1*1)
A2 = 9856
After the second year, the principal becomes 9856. For the third year, the interest rate is 15%, so we have:
A3 = 9856(1 + 0.15/1)^(1*1)
A3 = 11330.4
Therefore, the amount at the end of the third year is A3 = $11,330.40.
In summary, the initial amount of $8,000 is compounded annually for three years at different interest rates. By using the formula for compound interest, we find that the amount at the end of the third year is $11,330.40.
HELP ASAP A hockey season ticket holder pays $136.98 for her tickets plus $2.50 for a program each game. A second person pays $17.72 for a ticket to every game, but doesn't buy programs. In how many games will they have paid the same amount?
Answers
Therefore, they will have paid the same amount after attending 9 games.
What is equation?An equation is a mathematical statement that expresses the equality between two expressions or values. It consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, as well as other mathematical functions. An equation typically includes an equal sign (=) that indicates that the two sides of the equation are equal in value.
Here,
Let's start by setting up an equation to represent the total cost for each person after attending a certain number of games:
For the season ticket holder: Total Cost = 136.98 + 2.5x, where x is the number of games attended
For the second person: Total Cost = 17.72x
To find the number of games at which they will have paid the same amount, we can set the two equations equal to each other and solve for x:
136.98 + 2.5x = 17.72x
136.98 = 15.22x
x = 9
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example: marlon jogs two miles to the park in 25 minutes, turns around, and takes another 55 minutes to walk the same path back to his house. what is the average speed of the round-trip?
Answers
The average speed of the round-trip for same path back to his house is given by 3 miles per hour.
The mean value of a body's speed over a period of time is its average speed. As a moving body's speed is not constant over time and fluctuates, the average speed formula is required. The values of total time and total distance travelled may be employed even when the speed varies, and with the aid of the average speed formula, we can identify a single number that sums up the whole motion.
So the average speed is simply: [tex]\frac{distance}{time}[/tex]
In case, the total time = 25 minutes + 55 minutes
which is a total of 80 minutes, or 1.33 hours.
The total distance traveled is two miles + two miles, since he jogged two miles to the park, and then he turns around and walks the same path.
So in total he traveled 4 miles.
Plugging this in to the formula gives you the equation:
[tex]v = \frac{d}{t} \\= \frac{4\ miles}{4/3 \ hour} \\= \frac{4 \ miles}{1} * \frac{3}{4} hours\\= 3mph[/tex]
Therefore, average speed of the round-trip is 3 mph.
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State what each variable may be so that the equation is true. You must have at least one negative number. Explain how you chose the values for a and b. 2^a • 2^b = 2^0
Answers
Answer:
[tex] {2}^{a} \times {2}^{b} = {2}^{a + b} = {2}^{0} [/tex]
From this, a + b = 0, meaning a and b are additive inverses of each other.
As an example, let a = 1, so b = -1.
Find the probability of exactly three successes in eight trials of a binomial experiment in which the probability of success is 45%.
Answers
The probability of exactly three successes in eight trials is approximately 26.61%
To find the probability of exactly three successes in eight trials of a binomial experiment with a success probability of 45%, use the binomial probability formula:
P(x) = C(n, x) * [tex]p^x[/tex] * [tex](1-p)^{(n-x)}[/tex]
where n is the number of trials, x is the number of successes, p is the probability of success, and C(n, x) is the combination function representing the number of ways to choose x successes from n trials.
In this case, n = 8, x = 3, and p = 0.45.
Calculate the probability:
P(3) = C(8, 3) * [tex]0.45^3[/tex] * [tex](1-0.45)^{(8-3)}[/tex]
P(3) = 56 * 0.091125 * 0.1721865
P(3) ≈ 0.2661
So, the probability of exactly three successes in eight trials is approximately 26.61%.
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Hello everyone, can you help me please?
-where n is an integer,
-Which of the following is the result of the process?
Answers
Answer:
A) -1
Step-by-step explanation:
[tex] \dfrac{i^{2n - 3} \times i^{3n - 1}}{i^{5n - 2}} = [/tex]
[tex] = i^{2n - 3 + 3n - 1 - (5n - 2)} [/tex]
[tex] = i^{2n - 3 + 3n - 1 - 5n + 2} [/tex]
[tex] = i^{-2} [/tex]
[tex] = \dfrac{1}{i^2} [/tex]
[tex] = \dfrac{1}{-1} [/tex]
[tex] = -1 [/tex]
Nolan is trying to pick out an outfit for the first day of school. He can choose from 6 pairs of pants, 3 t-shirts, 3 sweaters or hoodies, and 5 pairs of shoes. How many different outfits does Nolan have to choose from?
Answers
Nolan has 270 different outfits to choose from.
What is permutation?
Ways" or permutation refers to the number of different possible outcomes or arrangements in a situation. For example, if you have 3 different shirts and 4 different pants, there are 12 ways (3 x 4) to choose one shirt and one pant. The concept of "ways" is often used in combinatorics, which is the branch of mathematics that deals with counting and arranging objects.
To find the total number of different outfits that Nolan can choose from, we need to multiply the number of options for each clothing item:
Total number of outfits = number of pants x number of t-shirts x number of sweaters or hoodies x number of shoes
Total number of outfits = 6 x 3 x 3 x 5 = 270
Therefore, Nolan has 270 different outfits to choose from.
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Arianna measured a boarding school and made a scale drawing. The scale of the drawing
was 3 millimeters = 9 meters. What is the scale factor of the drawing?
() Simplify your answer and write it as a fraction.
Videa
Answers
Answer:
The scale factor would be 3,000
Step-by-step explanation:
3(3000) = 9000 millimeters
9000 x [tex]\frac{1}{1000}[/tex] = 9 to convert to meters
Helping in the name of Jesus.
preform the indicated operation
(1)/(x^(2)-6x)=(x)/(x^(2)-36)+2
solve for x
[ sorry if im missing anything ]
Answers
The solutions to the equation are x = -11/3 and x = 6.
Describe Equation?In mathematics, an equation is a statement that two expressions are equal. It consists of two sides separated by an equal sign (=). The expression on the left side of the equal sign is usually called the left-hand side (LHS), while the expression on the right side is called the right-hand side (RHS).
Equations can take many different forms and can involve various types of functions and operators, such as addition, subtraction, multiplication, division, exponentiation, logarithms, trigonometric functions, and more. They can also involve one or more variables, which can be solved for to obtain a specific value or range of values that make the equation true. Equations are used extensively in mathematics, science, engineering, economics, and many other fields.
To solve the equation for x, we can start by simplifying both sides of the equation and bringing all the terms to one side:
(1)/(x²-6x) - (x)/(x²-36) = 2
We can simplify the left side of the equation by finding a common denominator:
[(1)(x-6) - (x)(x+6)] / [(x-6)(x+6)] = 2
Expanding the numerator and simplifying, we get:
(-x² + 7x - 6) / [(x-6)(x+6)] = 2
Multiplying both sides by the denominator, we get:
-x² + 7x - 6 = 2(x-6)(x+6)
Expanding the right side, we get:
-x² + 7x - 6 = 2(x² - 36)
Simplifying and rearranging, we get:
3x² - 7x - 66 = 0
We can solve this quadratic equation by factoring or using the quadratic formula:
3x² - 7x - 66 = (3x + 11)(x - 6) = 0
So either 3x + 11 = 0 or x - 6 = 0:
3x + 11 = 0 => x = -11/3
x - 6 = 0 => x = 6
Therefore, the solutions to the equation are x = -11/3 and x = 6.
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Quick for 100 points and 5 stars please help!!
For a certain video game, the number of points awarded to the player is proportional to the amount of time the game is played. For every 1 minute of play, the game awards one half point, and for every 7 minutes of play, the game awards three and one half points.
Part A: Find the constant of proportionality. Show every step of your work. (4 points)
Part B: Write an equation that represents the relationship. Show every step of your work. (2 points)
Part C: Describe how you would graph the relationship. Use complete sentences. (4 points)
Part D: How many points are awarded for 18 minutes of play? (2 points)
Answers
Step-by-step explanation:
Please find the attached pics for answers.
Maths. Please help me as best as you can.
Answers
Answer:
Step-by-step explanation:
She is traveling via Bootle.
Crosby to Bootle is 4 miles.
Bootle to Speke is 12 miles.
That is 16 miles each way.
16 times 2 = 32 miles per day
5 times 32 for the work week.
5 times 32 = 160 miles per week
Suppose you purchased a house for $250,000, and three years later it is valued at $280,00. How much equity do you have in the house?
Show your work
Answers
According to the given data the equity in the house is $30,000.
What is meant by equity?Equity is the difference between the current market value of the property and the outstanding mortgage balance on the property.
According to the given information:If you purchased the house for $250,000 and it is now valued at $280,000, your equity in the house can be calculated as follows:
Equity = Current market value - Outstanding mortgage balance
Assuming you took out a mortgage for the full purchase price of the house and haven't made any extra payments, your outstanding mortgage balance would be the same as the original mortgage amount, which is $250,000. Therefore, your equity in the house would be:
Equity = $280,000 - $250,000
Equity = $30,000
So, your equity in the house is $30,000.
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Find the area of the parallelogram. 8 cm 9 cm 24 cm
Answers
Answer:
we know the area of the parallelogram is given by a=b×h
There is a screenshot below showing my question. Please help asap, will name branliest plus its 10 points :)
Answers
Answer:
h = 9km
Step-by-step explanation:
area of a trapezoid= ½ x (a+b) x h
117 = (2+2+11 +11) / 2 x h
h = 117 / 26÷2
h = 9km
Jay is planting a maximum of 60 bulbs of lilies and tulips in her garden. She wants to plant
at least twice as many tulips (x) as lilies (y). Tulip bulbs cost 1.60 each and lily bulbs cost
$1.25 each. How many bulbs of each should Jay purchase to minimize her costs? (Solution
should contain object function, constraints, and graph).
Answers
The minimum cost occurs when Jay plants 30 tulip bulbs and 15 lily bulbs, and the minimum cost is $67.50.
Let x be the number of tulip bulbs that Jay plants, and let y be the number of lily bulbs that Jay plants.
Since Jay wants to plant at least twice as many tulips as lilies, we have the constraint:
x ≥ 2y
Also, the total number of bulbs that Jay plants cannot exceed 60, so we have the constraint:
x + y ≤ 60
We want to minimize the total cost of the bulbs that Jay purchases, which is given by the object function:
C = 1.6x + 1.25y
To solve this problem, we can use linear programming. First, we graph the two constraints on a coordinate plane:
The shaded region represents the feasible region, which is the region that satisfies both constraints. The vertices of the feasible region are (0, 0), (40, 20), (60, 0), and (30, 15).
Next, we evaluate the object function at each vertex to find the minimum value. We have:
C(0, 0) = 0
C(40, 20) = 1.6(40) + 1.25(20) = 92
C(60, 0) = 1.6(60) + 1.25(0) = 96
C(30, 15) = 1.6(30) + 1.25(15) = 67.5
Therefore, the minimum cost occurs when Jay plants 30 tulip bulbs and 15 lily bulbs, and the minimum cost is $67.50.
Graphically, we can see that the optimal solution occurs at the intersection of the two constraints, which is the point (30, 15). This is where the slope of the object function is equal to the slope of the feasible region, which indicates that the object function is optimized at this point.
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Mack, Nina, Samuel, and Tara play a board game. Each of them is equally likely to go first in the game. Also, each of them is equally likely to win the game. Winning the game is independent of going first. What is the probability Samuel goes first and wins the game?
A0
B0.0625
C0.25
D0.5
Answers
The probability that Samuel goes first and wins the game is 1/16 (0.0625). The Option B is correct.
What is the probability in this case?The probability that Samuel goes first is 1/4, since there are four players and each is equally likely to go first.
The probability that Samuel wins the game, given that he is playing, is also 1/4, since each player is equally likely to win and there are four players in total.
To find the probability that Samuel goes first and wins the game, we need to multiply these two probabilities:
P(Samuel goes first and wins) = P(Samuel goes first) x P(Samuel wins | Samuel is playing)
= (1/4) x (1/4)
= 1/16
= 0.0625
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1) Evaluate. Help me plsss
Answers
The logarithm expression is approximately 4.6.
How to evaluate the expression with which logarithmic identity?To evaluate 9㏒₉⁵ - ㏒₃3⁵, we can use the logarithmic property that states:
㏒ₐ(b^c) = c x ㏒ₐ(b)
Using this property, we can simplify the expression as follows:
9㏒₉⁵ - ㏒₃3⁵
= ㏒₉(95^9) - ㏒₃(35)
= ㏒₉(1423892081) - ㏒₃(35)
We can evaluate these logarithmic terms using the change of base formula, which states:
㏒ₐ(b) = log(b) / log(a)
Using this formula, we get:
㏒₉(1423892081) = 8.032
㏒₃(35) = 3.432
Substituting these values back into the expression, we get:
9㏒₉⁵ - ㏒₃3⁵ = 8.032 - 3.432
= 4.6
The above answer is in response to the question below;
Evaluate
9㏒₉⁵ - ㏒₃3⁵
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m∠CBD=6x+27 ∘ so you have to find C B D with this
Answers
For the given triangle, m∠CBD = 63 degrees.
What is triangle?
A triangle is a two-dimensional geometric shape with three sides and three angles. It is one of the basic shapes in geometry and is formed by connecting three non-collinear points with line segments.
In a triangle, the sum of the angles is always 180 degrees.
So, we can write:
m∠ABD = m∠ABC + m∠CBD
Substituting the given values, we get:
96 = (7x - 9) + (6x + 27)
Simplifying the equation:
96 = 13x + 18
Subtracting 18 from both sides:
78 = 13x
Dividing by 13:
x = 6
Therefore:
m∠ABD = 96 degrees
m∠CBD = 6x + 27 = 6(6) + 27 = 63 degrees
m∠ABC = 7x - 9 = 7(6) - 9 = 33 degrees
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30 points to whoever solves
Answers
Answer:
Step-by-step explanation:
its a 12/14 probabiloty or a 92.5%
Step-by-step explanation:
I'll try:
7 boys choose 5 = 7! / (5!2!) = 21 ways
4 girls choose 2 = 4 ! / (2! 2!) = 6 ways
6 x 21 = 126 ways to choose 5 boys and 2 girls
11 cats total choose 7 = 11! /( 7! 4!) = 330 ways to choose 7 cats
126 of these will be 5 boys and 2 girls
126 out of 330 = 126/330 = .382
a botanist wants to create an srs of size 10 from 60 plants that are arranged in an array of 10 rows of 6 plants each. she numbers the plants in each row from one to six. for each of the 10 rows, she rolls a six-sided number cube and selects the plant corresponding to the number rolled. which statements are true? check all that apply. the sample is a random sample. the sample is an srs. the sample is not a random sample. there are restrictions placed on the sample. each plant has an equal chance of being selected
Answers
The statements: the sample is random, the sample is an srs, and restrictions are placed on the sample, each plant has an equal chance of being selected are true.
Each tree has an equal chance of being selected.
This sample is a simple random sample (SRS) because each tree has an equal chance of being selected and the selection of each tree is independent of the others.
Restrictions are imposed on the sample because the botanist selects only one plant from each row, based on a specific criterion (roll a cube).
Hence the following statements are true by probability
The sample is random.
The template is an SRS.
Restrictions are imposed on the sample.
Each tree has an equal chance of being selected.
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