Use point-slope form to write the equation of a line that passes through the point (13,-8) with slope 3/2
Answer: y=3/2x-27.5
Step-by-step explanation:
you use y=3/2x+b
So plug (13,-8) in the equation so,
-8=3/2(13)+b
-8=39/2+b
-27.5=b
So y=3/2x-27.5
Pls give brainliest
A quality control inspector has drawn a sample of 19 light bulbs from a recent production lot. Suppose 20% of the bulbs in the lot are defective. What is the probability that exactly 4 bulbs from the sample are defective? Round your answer to four decimal places.
The probability that exactly 4 bulbs from the sample are defective is; 0.2812
How to solve Binomial Probability Distribution problems?
The formula for binomial probability distribution is;
P(X = x) = nCx * p^(x) * (1 - p)^(n - x)
where;
p = probability of success
n = number of trials, or the sample size
x = the number of successes in the probability
Now, we are given that;
Sample size; n = 19
Number of successes in the probability; x = 4
probability of success; p = 20% = 0.2
Thus;
P(X = 4) = 19C4 * 0.2^(4) * (1 - 0.2)^(19 - 4)
P(X = 4) = 0.2182
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Find the domain and graph, indicate the limits in the graph.
The domain of a function is the set of all x-values the function can take.
Since we have a radical symbol, (x² - 1) must not be equal to a negative number because it will make the function undefined.
For the function (x² - 1), the value of x must be greater than 1 or less than -1 in order for the function to be defined.
[tex]\begin{gathered} x^2-1>0 \\ x^2>1 \\ \sqrt{x^2}>\sqrt{1} \\ x>1 \\ x<-1 \end{gathered}[/tex]If for instance, the value of x is 0.5, the value of (x² - 1) will be -0.75 and the square root of a negative number is undefined. Therefore, we must not have an x-value that is less than 1 or greater than -1.
Hence, the domain of this function in interval notation is:
[tex](-\infty,-1]\cup[1,\infty)[/tex]In set notation, it is {x|x ≤ -1, x ≥ 1}.
In order to graph the function, let's assume some values of x that are found in the domain.
For the domain, x ≤ -1, we can assume x = -1, x = -2, and x = -3.
At x = -1, y = 1.
[tex]\begin{gathered} y=\sqrt{(-1)^2-1}-(-1) \\ y=\sqrt{1-1}+1 \\ y=\sqrt{0}+1 \\ y=1 \end{gathered}[/tex]At x = -2, y = 3.73
[tex]\begin{gathered} y=\sqrt{(-2)^2-1}-(-2) \\ y=\sqrt{4-1}+2 \\ y=\sqrt{3}+2 \\ y=3.73 \end{gathered}[/tex]At x = -3, y = 5.83.
[tex]\begin{gathered} y=\sqrt{(-3)^2-1}-(-3) \\ y=\sqrt{9-1}+3 \\ y=\sqrt{8}+3 \\ y=5.83 \end{gathered}[/tex]For the domain x ≥ 1, we can assume x = 1, x = 2, and x = 3.
At x = 1, y = -1.
[tex]\begin{gathered} y=\sqrt{1^2-1}-1 \\ y=\sqrt{1-1}-1 \\ y=\sqrt{0}-1 \\ y=-1 \end{gathered}[/tex]At x = 2, y = -0.268
[tex]\begin{gathered} y=\sqrt{2^2-1}-2 \\ y=\sqrt{4-1}-2 \\ y=\sqrt{3}-2 \\ y=-0.268 \end{gathered}[/tex]At x = 3, y = -0.172.
[tex]\begin{gathered} y=\sqrt{3^2-1}-3 \\ y=\sqrt{9-1}-3 \\ y=\sqrt{8}-3 \\ y=-0.172 \end{gathered}[/tex]Let's plot the 6 coordinates. The graph of this function, with limits indicated, is shown below.
Suppose that the relation S is defined as follows.
S = {(3, 1), (9, d), (1, d)}
Give the domain and range of S.
Write your answers using set notation.
domain =
range =
Answer:
Domain = {1, 3, 9}Range = {1, d}Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
SOMEONE PLEASE HELP!!
First angle is 3x° = 3 × 40° = 120°
and, Second Angle is = (x + 20°) = 40° + 20° = 60°
Given,
Lines m and n are parallel (m ll n)
Adjacent Interior Angles are given i.e.,
3x and (x + 20°)
and, To find the value of x
Now, According to the question:
m ll n
So, The two lines are parallel and complementary to the
3x° + (x + 20°) = 180° (Adjacent Interior Angles)
4x°+ 20° = 180°
4x° = 180° - 20°
4x° = 160°
x = 40°
Hence, First angle is 3x° = 3 × 40° = 120°
and, Second Angle is = (x + 20°) = 40° + 20° = 60°
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Stacey has a part-time job. She earns $12 an hour. She wants to buy a new smartphone costing $174. How many hours does she need to work to earn enough to buy it?
Answer:
Step-by-step explanation:
174/12= 14.5 hours of work to earn enough to buy the smartphone.
12x14.5 = 174
the answer could be 14.5 for the minimum amount of time needed but if it asks for full hours then 15 hours.
Can anyone help me with this please ??
The approximate size of Jorge's wrist is 8.5 inches.
What is defined by the term fraction?Fractions represent parts of the whole or group of objects. A fraction is made up of two parts. The number at the start of the line is referred to as the numerator. It specifies the number of equal parts of the whole as well as collection that are taken. The denominator is the number just below line. It displays the total amount of equal parts into which the whole is divided or the total number of identical objects in a collection.For the given question;
For average adults, the size of the wrist is 1/4 of the size of the waist.
The waist size of the Jorge is 34 inches.
Thus, to calculate the wrist size of Jorge, simply multiply the fraction 1/4 with 34.
= 34 × 1/4
= 8.5
Therefore, the wrist size of the Jorge is found as 8.5 inches.
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randy wants to use the distributive property to rewrite 56-12 which expression can be used
Consider the given expression,
[tex]56-21[/tex]The expression can be transformed as,
[tex](7\times8)-(7\times3)[/tex]Since 7 is a common factor, take it as common,
[tex]7(8-3)[/tex]Thus, the expression is obtained that,
[tex]56-21=7(8-3)[/tex]Therefore, option (B) is the correct choice.
The leadership class plans to sell t-shirts for a fundraiser, but they need to decide which company to use.
Custom Ink charges $6.50 for each t-shirt. Tees-4-U charges a flat fee of $250 plus $5.50 for each t-shirt.
A. How many shirts would have to be ordered to for the two companies to charge the same amount?
B. If they plan to order 600 t-shirts, which company would charge them less?
C. How much are they saving by going with the more economical company?
Using linear functions, it is found that:
A. The costs will be the same when 250 shirts are bought.
B. The Tees-4-U Company would charge them less.
C. They are saving $350 by going with the more economical company.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For the cost functions in the context of this problem, we have that:
The slope represents the cost per shirt.The intercept represents the flat fee.Hence the functions for the cost of buying x shirts are given as follows:
Custom Ink: C(x) = 6.5x.Tees-4-U: T(x) = 250 + 5.5x.The costs will be the same when:
C(x) = T(x)
Hence:
6.5x = 250 + 5.5x
x = 250
For item b, the costs are given as follows:
C(250) = 6.5(600) = 3900.T(250) = 5.5(600) + 250 = 3550.The amount saved in item c is:
3900 - 3550 = 350.
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What is the value of n?
-6.5(n-5)=18.2
Answer:
n=2.2
Step-by-step explanation:
1-Combine- [-6.5n(n-5)=18.2
-13(n-5)/2=18.2
2-Distribute-13n-5)/2=18.2
-13n+65/2=18.2
3-Multiply like terms-
-13n+65/2=18.2 [tex]2.-13n+65/2=18.2*2[/tex]
4-Multiply all the numbers=[tex]-13n+65=36.4[/tex]
5-Subtract 65 from both sides- -13n+65-65=36.4-65
6-Simplify= -13n=-28.6
7- Divide both sides by the factor e.g= -13n
8- Simplify= -13n/-13n=-28.6/-13n
QA Answer\Solution amounts to= [tex]2.2[/tex]
When looking at a set of ordered pairs. To determine if it makes a function, you must look at the _ _ _
To see if you have any repeated numbers
Answer: x values make sure they don't repeat if they do its not a function.
Solve similar triangles (advanced). khan academy. solve for x
Applying the similarity theorem, the value of x is calculated as: x = 3.5.
How to Apply the Similarity Theorem?When two triangles are similar to each other, based on the similarity theorem, the ratio of their corresponding side lengths will be equal because they are proportional to each other.
In the image given, triangle ABC is similar to triangle ADE. Therefore:
AB/AD = BC/DE = AC/AE
Given the following:
AB = 4 units
AD = 4 + 3 = 7 units
BC = 2 units
DE = x
Plug in the values into AB/AD = BC/DE:
4/7 = 2/x
Cross multiply
4(x) = 2(7)
4x = 14
Divide both sides by 4
4x/4 = 14/4 [division property of equality]
x = 3.5
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Function A is a linear function whose graph contains the points (0, 2) and (8, 0). Function B is represented by the equation y = 4x - 2. Which statement is true? The rate of change for Function A is greater than the rate of change for Function B. The rate of change for Function A is equal to the rate of change for Function B. The initial value for Function A is greater than the initial value of Function B. The initial value of Function A is equal to the initial value of Function B.
The statement which is true about Function A and Function B is that: C. The initial value for Function A is greater than the initial value of Function B.
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope A = (0 - 2)/8 - 0)
Slope A = -2/8
Slope A = -1/4 or -0.25.
Note: The slope of any straight line also represents its rate of change.
Rate of change of Function A = -0.25.
Rate of change of Function B = 4.
Mathematically, the standard form of the equation of a straight line is given by;
y - y₁ = m(x - x₁)
At point (0, 2), we have:
y - 2 = -1/4(x - 0)
y - 2 = -x/4
y = -x/4 + 2.
Therefore, the intercept (initial value) of Function A is greater than the intercept (initial value) of Function B.
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slope -3 passes through (4,-1) solve and write in slope intercept form
Answer:
y = -3x + 11
Step-by-step explanation:
(4, -1) m = -3
y = -3x + b
y + 1 = -3(x-4)
-3(x-4) = -3x + 12 - 1
y = -3x + 11
There are 4 ounces of
lime juice in 52 ounces
of punch. How much
lime juice is needed for
130 ounces of punch?
There are 4 ounces of lime juice in 52 ounces of punch, let represent the number of ounces of lime juice in 130 ounces of punch, there are 1690 ounces of the lime juice in 130 ounces of punch.
What do you mean by ounces?A number of distinct units of mass, weight, or volume are derived from the uncia, an ancient Roman unit of measurement, including the ounce, which is almost unmodified.
'Ounce' is also used in the following other contexts:
A unit of the force is the ounce-force (see below).
A unit of the volume is the fluid ounce.
A multitude of distinct ounces measuring mass or volume have been employed historically by various trades at various times and in various countries.
Since,
Ounces of the lime juice=4
Ounces of the punch=52
Ounce needed for 1 punch=52÷4=13
Ounces needed for 130 ounces of the punch=13×130=1690
Therefore, the ounces of the lime juice needed for 130 ounces of punch=1690.
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The
length of a rectangle is 7 inches longer than it is wide. If the perimeter is 62 inches, what are the dimensions of the rectangle?
The width, or shorter side is
inches.
The length, or longer side is
inches.
2(x) + 2(x+7)= 62
4x+14=62
4x=58
x=14.5
width= 14.5
length=21.5
How many different 3-digit numbers are possible using only the digits 1,2,6,7,8 ? How many different 3-digit numbers are possible using only the digits 1,2,6,7,8, if repetition of digits is not allowed?
The number of three digit number formed are-
Repetition allowed = 125Repetition not allowed = 60What is defined as the combination?A combination is an algebraic technique for determining the number of distinct arrangements in a set of items in which the sequence of the selection is irrelevant. You can choose the items in either order in combinations. Permutations and combinations are often confused.For the given question;
The three digit number is to be formed.
The digits are given as- 1,2,6,7,8
Case 1: Repetition allowed
The number of combination will be;
= 5×5×5
= 125
Thus, the number of three digit number formed with repetition is 125.
Case 2: Repetition not allowed
The number of combination will be;
= 5×4×3
= 60
Thus, the number of three digit number formed with without repetition is 125.
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△TVX is equilateral. Complete the proof that △TUV≅△XWV.
iven:: △TVX is equilateral.
To prove: △TUV≅△XWV
The given proof is completed and attached below:
he proogf is complete.
I need the area of the irregular shape
The area of the irregular shape is found as 50 sq. cm.
What is defined as the area?The total space occupied by a flat (2-D) ground or the shape of an object is defined as its area. Sketch a square on a piece of paper with a pencil. It is a two-dimensional figure. The area of the shape on the paper is referred to as its Area. Consider your square to be made up of many smaller unit squares.For the given question;
The irregular shape is composed of two rectangles.
The formula for finding the area is;
Area = length x breadth
The area of the top rectangle is;
Top area = 4 x (3 + 5 + 2)
Top area = 4 x 10
Top area = 40 sq. cm.
The area of the bottom rectangle is;
Bottom area = 5 x 2
Bottom area = 10 sq. cm.
Total area = Top area + Bottom area
Total area = 40 + 10
Total area = 50 sq. cm.
Thus, the area of the irregular shape is found as 50 sq. cm.
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the net decimal equivalent is found by multiplying the complement of the discounts together. what is the net decimal equivalent when a series of discount of 48% , 27%, and 12% is applied?
The net decimal equivalent is 0.48, 0.27, and 0.12 when a series of discounts of 48%, 27%, and 12% are applied respectively.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
By multiplying the complement of the discounts collectively, one can determine the net decimal equivalent which is given in the question.
To determine the net decimal equivalent when a series of discounts of 48%, 27%, and 12% is applied.
The value of compliment (%) = 1/100
As per the given condition, the required discounts would be as:
discount of 48% = 48/100 = 0.48
discount of 27% = 27/100 = 0.27
discount of 12% = 12/100 = 0.12
Therefore, the net decimal equivalent is 0.48, 0.27, and 0.12 when a series of discounts of 48%, 27%, and 12% are applied respectively.
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20 points!!! pls hurry!!! I need the CORRECT answer in three hours or less!!! What is the slope of this line? A. -1/3 B. -2/3 C. 1/3 D.2/3
Answer:
D
Step-by-step explanation:
RISE/RUN = slope
This slope will be POSITIVE because it rises in quadrant 1.
Rise=2, run=3
Slope= 2/3
Hope that helps
One number is 9 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 1068, find the numbers.
The three numbers are
(Use a comma to separate answers as needed.)
First number (x) = 88
Second number (9x) = 792
Third number (x + 100) = 188
Let x be the first number, so accordingly the second number will be 9 times x i.e., 9x and the third number will be 100 more than the first number i.e., x + 100
Now, put all the numbers into an equation of finding their sum,
First no. + Second no. + Third no. = SUM, i.e.,
x + 9x + (x+100) = 1068
Simplify,
x + 9x + (x+100) = 1068
x + 9x + x +100 = 1068
11x + 100 = 1068
11x = 1068 - 100
11x = 968
x = 968/11
First number (x) = 88
Second number (9x) = 792
Third number (x + 100) = 188
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A foreman for an injection-molding firm admits that on 29% of his shifts, he forgets to shut off the injection machine on his line. This causes the machine to overheat, increasing the probability that a defective molding will be produced during the early morning run from 5% to 24%. If a molding is randomly selected from the early morning run of a random day, what is the probability that it is defective?
When a molding is randomly selected from the early morning run of a random day, what is the probability that it is defective is 0.1051
How to calculate the probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Probabilities can be written as percentages with values between 0 and 1.
From the information, the foreman for an injection-molding firm admits that on 29% of his shifts, he forgets to shut off the injection machine on his line.
The probability that the selected molding is defective will be:
= P(forgets to shut off and defective molding) + P(not fingers to shut off)
= 29% × 24% + (1 - 29%) × 5%
= 0.29 × 0.24 + 0.71 × 0.05
= 0.0696 + 0.0355
= 0.1051
The probability is 0.1051.
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Samuel was preparing for the triathlon. He did 3 activities every morning: Ran for 30 minutes, covering 4.5 miles. Swam for 20 minutes, covering 2/3 mi. biked for 45 min, covering 9 miles. What was Samuel's average speed during his morning training?
PLEASE HELP!!!
If Samuel ran for 30 minutes covering 4.5 miles, swim for 20 minutes covering 2/3 miles and biked for 45 min covering 9 miles, then the Samuel's average speed during his morning training is 0.15 miles per minute
The Morning activities of Samuel
He ran for 30 minutes, covering 4.5 miles,
He swim for 20 minutes covering 2/3 miles
He biked for 45 minutes covering 9 miles
Total distance travelled = 4.5+ 2/3 +9
= 14.17 miles
Total time taken = 30+20+45
= 95 minutes
The average speed = Total distance / Total time taken
= 14.17/95
= 0.15 miles per minutes
Hence, if Samuel ran for 30 minutes covering 4.5 miles, swim for 20 minutes covering 2/3 miles and biked for 45 min covering 9 miles, then the Samuel's average speed during his morning training is 0.15 miles per minute
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y=-(1/3)x+1 graph it
Step-by-step explanation:
plug in y=(⅓)x+1 to a graphing calculator and it gives you the answer
Which equation applies the associative property of multiplication?
Responses
(−14−53)−35=−14−(53−35)
, open parenthesis fraction negative 1 over 4 end fraction minus fraction 5 over 3 end fraction close parenthesis minus fraction 3 over 5 end fraction equals fraction negative 1 over 4 end fraction minus open parenthesis fraction 5 over 3 end fraction minus fraction 3 over 5 end fraction close parenthesis,
−512⋅(65⋅13)⋅92=(−512⋅65)⋅(13⋅92)
, fraction negative 5 over 12 end fraction times open parenthesis fraction 6 over 5 end fraction times fraction 1 over 3 end fraction close parenthesis times fraction 9 over 2 end fraction equals open parenthesis fraction negative 5 over 12 end fraction times fraction 6 over 5 end fraction close parenthesis times open parenthesis fraction 1 over 3 end fraction times fraction 9 over 2 end fraction close parenthesis,
−67⋅811⋅13=811⋅(−67)⋅13
, fraction negative 6 over 7 end fraction times fraction 8 over 11 end fraction times fraction 1 over 3 end fraction equals fraction 8 over 11 end fraction times open parenthesis fraction negative 6 over 7 end fraction close parenthesis times fraction 1 over 3 end fraction,
(−78⋅25)+(−78⋅35)=−78⋅(25+35)
The equation applies the associative property of multiplication is −512⋅(65⋅13)⋅92=(−512⋅65)⋅(13⋅92).
What is associative property of multiplication?The associative property of multiplication can be described as the law that is been used in making calculation that involves using the multiplication operation.
When using the associative property of multiplication law, we will need to associate, which means we will join together the given terms which can be done in different ways irrespective of how it is been grouped together and this can be seen in the option B , because the result of the multiplication using the distributive property gives us (−512⋅65)⋅(13⋅92).
Therefore, option B is correct.
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Consider the equation x 2+ 1 = 7-x
Since the given equation is
[tex]x^2+1=7-x[/tex]Since (-3, 2) is its solution which means the graphs of each side are intersected at point (-3, 2)
To verify the solution, substitute x by -3 on each side
If the two sides are equal, then the point is the solution to it
[tex]\begin{gathered} L\mathrm{}H\mathrm{}S=x^2+1 \\ x=-3 \\ L\mathrm{}H\mathrm{}S=(-3)^2+1 \\ L\mathrm{}H\mathrm{}S=9+1 \\ L\mathrm{}H\mathrm{}S=10 \end{gathered}[/tex]Let us do the same with the right-hand side
[tex]\begin{gathered} R\mathrm{}H\mathrm{}S=7-x \\ x=-3 \\ R\mathrm{}H\mathrm{}S=7-(-3) \\ R\mathrm{}H\mathrm{}S=7+3 \\ R\mathrm{}H\mathrm{}S=10 \end{gathered}[/tex]L.H.S = R.H.S = 10
This means the value of y = 10, not 2
Then (-3, 2) is not a solution of the given equation
Now we will draw each side, then find the point of intersection between them
From the graph, the solutions are the intersection points between the line and the graph
The two points are (-3, 10) and (2, 5)
Mikah invented and patented a new product which sells in local department stores. This is an example of _____ income.
a.
capital gains
b.
earned
c.
hourly
d.
passive
Since Mikah invented and patented a new product which sells in local department stores, this is an example of: D. passive income.
What is an income?An income simply refers to an amount of money that an individual or business organization (company or firm) earn in return for the sales of its product or for providing a service, to its customers and consumers.
The types of income.In Economics, there are three (3) main types of income and these include the following:
Portfolio incomeEarned incomePassive incomeIn Business management, a passive income generally requires minimal amount of labor from an individual or business organization (company or firm) and as such it is typically earned from rental products or patented products, which is usually on a regular basis.
In this context, we can reasonably infer and logically deduce that Micah's income is an example of passive income.
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11. THINKSMARTER Yvonne wrote the numbers sixteen thousand,
nine hundred eighteen and 64,704 on the board. Which of the
numbers has a greater value in the thousands place?
Name
The number that has a greater value in the thousands place is 16,918.
What is Place Value?A number's place value is the worth of each digit. Depending on its location, such as ones, tens, hundreds, and so forth, each digit in a number has a different value. The position of the digit in the number determines whether two similar digits in the same number have different values.Given numbers are sixteen thousand, nine hundred eighteen,(16,918), and 64,704 on the board.
The thousand places in both numbers contain the digits 6 and 4.
The place value of 6 in 16,918 is expressed as 6 thousand or 6,000.
The place value of 4 in 64,704 is expressed as 4 thousand or 4,000.
As 6000 > 4000, the number that has a greater value in the thousands place is 16,918.
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Complete the table to determine the total number of possible outcomes.
Using the Fundamental Counting Theorem, it is found that there are 27 possible outcomes.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, each trial independent of other trials, the number of possible outcomes is given as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For this problem, the trials are represented as follows:
Bread.Filling.Cheese.For each trial, there are 3 possible outcomes, from the table, hence the parameters are given as follows:
[tex]n_1 = 3, n_2 = 3, n_3 = 3[/tex]
Hence the total number of possible outcomes is given as follows, from the Theorem:
N = 3 x 3 x 3 = 27.
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