A. The total value of the loan with quarterly compounded interest is $52,400.
B. The total value of the loan with monthly compounded interest is $52,010.04
How did we get the values?Part A: Total value of the loan with the quarterly compounded interest
To find the total value of the loan, we'll use the formula for compound interest:
A = P * (1 + r/n)^(nt)
Where:
A = final amount (loan + interest)
P = principal amount (initial loan) = $20,000
r = interest rate = 7% = 0.07
n = number of times compounded per year = 4 (quarterly)
t = number of years = 10
Plugging in the values, we get:
A = $20,000 * (1 + 0.07/4)^(4 * 10)
A = $20,000 * (1.0175)^40
A = $20,000 * 2.620075
A = $52,401.51
Rounding to the nearest hundred, the total value of the loan with quarterly compounded interest is $52,400.
Part B: Total value of the loan with the monthly compounded interest
To find the total value of the loan with monthly compounded interest, we'll use the same formula with a different value of n:
A = P * (1 + r/n)^(nt)
Where:
n = number of times compounded per year = 12 (monthly)
Plugging in the values, we get:
A = $20,000 * (1 + 0.07/12)^(12 * 10)
A = $20,000 * (1.005833)^120
A = $20,000 * 2.600502
A = $52,010.04
Rounding to the nearest hundredth, the total value of the loan with monthly compounded interest is $52,010.04
The difference between the two loans is $52,401.51 - $52,010.04 = $391.47
The difference between the two loans is due to the higher frequency of compounding in the monthly compounded interest loan. The interest is compounded more times per year, so the interest is accumulating on the interest more quickly, leading to a higher overall interest charge.
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if you wanted to visualize the change in the mean test score for the same exam over multiple semesters which visualizations might be used? a. bar chart b. pie chart c. histogram d. line chart
if you wanted to visualize the change in the mean test score for the same exam over multiple semesters line chart will be used.
A line chart connects a number of data points with a continuous line to graphically depict the historical price movement of an item. The simplest sort of chart used in finance, it often merely shows the closing prices of a security over time.
A line chart, also known as a line graph or a line plot, uses a line to link a group of data points. This type of graph uses sequential values to show trends. The x-axis (horizontal axis) often shows a succession of numbers in consecutive order.
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What is a in this question
The value of the segment a for the similar triangles is equal to 6.
How to calculate for a for the similar trianglesThe triangles MNO and YXO are similar, this implies that the length OX of the smaller triangle is similar to the length ON of the larger triangle
and the length OY of the smaller triangle is similar to the length OM of the larger triangle
so;
a/(a + 18) = 4/(4 + 12)
16a = 4(a + 18) {cross multiplication}
16a = 4a + 72
16a - 4a = 72 {collect like terms}
12a = 72
a = 72/12 {divide through by 12}
a = 6.
Therefore, the value of the segment a for the similar triangles is equal to 6.
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[tex]}\frac{4}{x-2} =14[/tex]
What is the proportion of this
the proportionality ratio of the given Data is solved below.
AB/ DF = AC/EGAD/BD = AE/CEAC/CG = AB/BFDE/FG = AD/A to FWhat is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc. If a defensive action against an unfair attack results in destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given a figure where Two lines are intersecting three individual parallel lines.
Since Proportionality in Lengths is When quantities have the same relative size. In other words, they have the same ratio.
thus,
as we can observe the proportionality ratio for the given figures:
AB/ DF = AC/EGAD/BD = AE/CEAC/CG = AB/BFDE/FG = AD/A to FTherefore, the proportionality ratio of the given Data is solved above.
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Write the equation for a parabola that has x− intercepts (5,0) and (−6,0) and y− intercept (0,−1).
The equation for a parabola that has x-intercepts (5,0) and (6,0) and y-intercept (0,1) is: [tex]y =[/tex] [tex]a(x + 0.5)^2 - 1[/tex]
The equation of a parabola can be found by using the vertex form of a parabolic equation, which is given by:[tex]y = a(x - h)^2 + k[/tex], where (h, k) is the vertex of the parabola. In this case, the x-intercepts (5, 0) and (-6, 0) can be used to find the value of h, which is the midpoint between the x-intercepts and is equal to (-6 + 5) / 2 = -0.5.
The y-intercept (0, -1) can be used to find the value of k. So, the equation is:[tex]y = a(x + 0.5)^2 - 1[/tex], where a is a constant that can be determined by substituting the vertex coordinates (h, k) into the equation.
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19. Describe the graph of a proportional relationship.
The graph of a proportional relationship can be described as a graph that always starts at point zero and is always a straight line graph.
What is a straight line graph?A straight line graph is defined as the type of graph that is also called a linear graph which shows a relationship between two or more quantities that uses a graphical form of representation.
There are some characteristics that shows that a graph is of proportional relationship which include the following:
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Write \frac{\sqrt[4]{v^{9}}}{\sqrt[3]{v^{4}}}
3
v
4
4
v
9
as a single radical using the smallest possible root.
Answer:
[tex]\mbox {\large \boxed{\sqrt[12]{v^{11} }}}\\[/tex]
Step-by-step explanation:
[tex]\textrm{We are asked to simplify\:$\dfrac{\sqrt[4]{v^9}}{\sqrt[3]{v^4}}$}[/tex]
Using the fact that [tex]\sqrt[n]{x} = n^{{1/n}}[/tex]
[tex]\mbox{\large {\sqrt[4]{v^9}} =\left(v^9)^{1/4} = v^{9/4}}\\\\[/tex]
[tex]\mbox{\large {\sqrt[3]{v^4}}} = (v^4)^{1/3} = v^{4/3}}[/tex]
[tex]\mbox{\large $\dfrac{\sqrt[4]{v^9}}{\sqrt[3]{v^4}}$}[/tex] [tex]= \mbox{\large \dfrac{v^{9/4}}{v^{4/3}}}[/tex]
Using the fact that [tex]\dfrac{x^a}{x^b} = x^{a-b}[/tex]
[tex]\mbox{\large \dfrac{v^{9/4}}{v^{4/3}} = v^{9/4 - 4/3}}[/tex]
[tex]\dfrac{9}{4} - \dfrac{4}{3} = \dfrac{9 \cdot 3 - 4 \cdot 4}{12} = \dfrac{27-16}{12} = \dfrac{11}{12}[/tex]
[tex]\mbox{\large \dfrac{v^{9/4}}{v^{4/3}} = v^{9/4 - 4/3}= v^{11/12} } = \sqrt[12]{v^{11} }}[/tex]
Answer
[tex]\mbox {\large \boxed{\sqrt[12]{v^{11} }}}\\[/tex]
Rewrite the sentences below, focusing on spelling, capitalization, and
punctuation.
The Panthers soccer team dose not like to loze becuse they alwayz try
to be there best. one day they were embarased when all there shirts
were so loos they started to fall off during a game. Guess who did not
win that day.
(10 errors)
Answer:
The Panthers soccer team does not like to lose because they always try to be their best. One day, they were embarrassed when all their shirts were so loose they started to fall off during a game. Guess who did not win that day?
You have a 10% sugar salutation and a 30% sugar salutation and you need a 25% sugar salutation how many cups of each salution do you need to get 8 cup of 25% sugar salution let x represent numbernof cups of 10% and y represent numberbof cups 30% sugar salution what eqution represent the total valume
2 cups of 10% sugar solution and 6 cups of 30% sugar solution.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements
Let,
x = number of cups of the 10% solution
y = number of cups of the 30% solution
As this is the whole amount we need, the two mixtures sum up to 8 cups. Consequently, the first equation is just x + y = 8
Solve for y to get y = 8-x. We'll use this equation later.
The second equation is a bit more tricky.
0.10x = amount of pure sugar from just the 10% batch
0.30y = amount of pure sugar from just the 30% batch
0.10x+0.30y = total amount of pure sugar from both batches
25% of 8 = 0.25×8 = 2 = total amount of pure sugar required
0.10x+0.30y = 2 is the second equation
Apply substitution to solve for x and y
0.10x+0.30y = 2 ..... start with the second equation
0.10x+0.30(8-x) = 2 ....... plugin y = 8 - x
0.10x + 2.4 - 0.30x = 2 ..... distribute
- 0.20x + 2.4 = 2 - 0.20x = 2-2.4 ....... subtract 2.4 from both sides
-0.20x = - 0.4
x = -0.4/(-0.20)
x = 2
Now that we know the value of x, we can find y.
y = 8 - x
y = 8 - 2 ... plug in x = 2
y = 6
So we need 2 cups of the 10% solution and 6 cups of the 30% solution.
As a check,
x + y = 2 + 6 = 8 works out
0.10x + 0.30y = 0.102 + 0.306 = 0.2 + 1.8 = 2 works out as well
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Find the first 3 iterates of the function f(x)=-2x + 3 when x0=0
Accordingly, x0 = 0, x1 = 3, x2 = 0, and x3 = 3 are the first three iterations of f ( x) = -2x + 3 when x0 = 0.
Is iterate the same as loop?A loop is described as a section of code that runs repeatedly. The procedure in which a code fragment is run just once is referred to as iteration. One iteration is the single time a loop is run. A loop may run through numerous iterations.
x1 = f(x0) = f(0) = -2 * 0 + 3 = 3
x2 = f(x1) = f(3) = -2 * 3 + 3 = 0
x3 = f(x2) = f(0) = -2 * 0 + 3 = 3
So the first 3 iterates of the function f(x) = -2x + 3 when x0 = 0 are:
x0 = 0, x1 = 3, x2 = 0, x3 = 3
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A veterinarian has 100 feet of fencing and wishes to construct six dog kennels by first building a fence around a rectangular region, and then subdividing that region into six smaller rectangles by placing five fences parallel to one of the sides. What dimensions of the region will maximize total area?
The dimensions of the rectangular region that will maximize the total area are 20ft x 50ft.
The goal is to find the dimensions of a rectangle that will maximize the total area when it is divided into 6 smaller rectangles.
Let the length of the rectangle be x and the width be y.
The total length of the fencing used to enclose the rectangle is 100 feet, so 2x + 2y = 100.
To divide the rectangle into 6 smaller rectangles, we need 5 partitions,
so we have x/6 = y, or y = x/6.
Substituting y = x/6 into 2x + 2y = 100 gives 2x + 2x/3 = 100, or x/3 = 50.
Solving for x, we find x = 150.
Then y = x/6 = 150/6 = 25.
The maximum area of the rectangle is 150 * 25 = 3750 square feet.
To maximize the area of the rectangular region, the width and length should be in the ratio of 1:2. This allows the rectangular region to be split into six smaller rectangles of equal area by placing five fences parallel to the width.
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Select the correct answer from each drop-down menu. The general form of the equation of a circle is x2 + y2 + 42x + 38y − 47 = 0. The equation of this circle in standard form is . The center of the circle is at the point , and its radius is units. The general form of the equation of a circle that has the same radius as the above circle is .
The equation of this circle in standard form is (x + 21)² + (y + 19)² = 849.
The center of the circle is at the point (-21, -19), and its radius is √849 units.
The general form of the equation of a circle that has the same radius as the above circle is x² + y² - 50x - 30y + 1 = 0.
What is the equation of a circle?In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.In order to transform the general form of the equation of a circle to a standard form, you can either make use of completing the square method or convert the equation x² + y² + Dx + Ey + F = 0 to x² + y² + (-2h)x + (-2k)y + (h² + k² - r²) = 0.
By using the following expression x² + y² + (-2h)x + (-2k)y + (h²+k²-r²) = 0, we would determine the center (h, k) and radius of this circle as follows;
-2h = 42
h = 42/2
h = -21
-2k = 38
k = 38
k = -19
For the radius (r), we have:
-47 = h² + k² - r²
-47 = (-21)² + (-19)² - r²
r² = 849
Radius, r = √849
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Help pls I really need help
The functions for this problem are classified as follows:
a) q(x) is an odd function.
b) r(x) is an even function.
What are even and odd functions?In even functions, we have that the statement f(x) = f(-x) is true for all values of x. -> meaning that r(x) is an even function.In odd functions, we have that the statement f(-x) = -f(x) is true for all values of x. 0> meaning that q(x) is an odd function.If none of the above statements are true for all values of x, the function is neither even nor odd.More can be learned about odd and even functions at https://brainly.com/question/2284364
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in 2015, the college board sat mathematics score of high school seniors, which follow an approximately normal distribution, has a mean of 511 and a standard deviation of 120^2.
The probability that a randomly chosen high school student who took the SAT in 2015 will have a mathematics SAT score of more than 700 points is 5.8%.
The distributed samples can be solved using the z-score formula:
We can set with mean and standard deviation, the z-score of a measure X is given by:
[tex]Z=\frac{X-u}{sd}[/tex]
The Z-score defines how many standard deviations will be measured from the mean. After finding the Z-score, we should see the z-score table and find the p-value included with this z-score.
This p-value is the probability of the value measuring smaller than X, that is, the percentile of X. by Subtracting 1 from the p-value, we get the probability of the value of the measure is greater than X.
In this problem, we have that:
u=511 sd=120.
This is 1 subtracted by the value of Z when X = 700.
[tex]Z=\frac{X-u}{sd}\\\\Z=\frac{700-511}{120}[/tex]
Z=1.575.
Z=1.575 has a p-value of 0.942
1 - 0.942 = 0.058.
5.8% probability that a randomly chosen high school student who took the SAT in 2015 will have a mathematics SAT score of more than 700 points.
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Zeg has $9.20 left on a gift card to the candy store. He has the following items in his shopping basket: 2 giant lollipops, 3 popcorn balls, 1 candy bar, and 5 candy sticks. Zeg wants to buy two more items. Which of the following combinations of items can he buy? Select all that apply.
The combinations of items he can buy are:
1 popcorn balls and 1 candy stick.
2 candy sticks
How to determine the combinations of items he can buy?Zeg has $9.20 left
First, calculate the price of items in his shopping basket:
2 giant lollipops = 2 * $1.75 = $3.5
3 popcorn balls = 3 * $0.5 = $1.5
1 candy bar = 1 * $0.99 = $0.99
5 candy sticks = 5 * $0.45 = $2.25
Total price = $3.5 + $1.5 + $0.99 + $2.25 = $8.24
Amount left = $9.20 - $8.24 = $0.96
Since the price of 1 popcorn balls and 1 candy stick = $0.5 + $0.45 = $0.95
Also, 2 candy sticks = 2 * $0.45 = $0.90.
Notice that these two are still within $0.96 we have left
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Solve the system of equations using elimination.
−2x + 3y = 15x + y = 10
A (2, 8)
B (3, 7)
C (6, 9)
D (9, 11)
The solution of the linear equations −2x + 3y = 15 and x + y = 10 will be (3. 7). Then the correct option is B.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The system of linear equations is given below.
−2x + 3y = 15 ....1
x + y = 10
2x + 2y = 20 ...2
Add equations 1 and 2, then we have
5y = 35
y = 7
Then the value of the variable 'x' is given as,
x + 7 = 10
x = 3
The solution of the linear equations −2x + 3y = 15 and x + y = 10 will be (3. 7). Then the correct option is B.
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the student conuncil iis selling t-shirtsto raise awareneess for the local animal shelter.for each t-shirt they sell, they will donate $5.00
The student council is selling t-shirts to increase awareness for the local animal shelter. For each t-shirt they sell, they will donate $5.00 to the shelter.
This means that the amount of money the student council will donate to the shelter will be directly proportional to the number of t-shirts they sell. The more t-shirts they sell, the more money they will donate to the shelter.
By selling t-shirts, they are taking a proactive step to help raise awareness and support for the local animal shelter.
Directly proportional: as one amount increases, another amount increases at the same rate. The symbol for "directly proportional" is ∝
(Do not confuse it with the symbol for infinity ∞)
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For the following type of data set, would you be more interested in looking at the mean, median, or mode? State your reasoning. The price of cars on a car lot Answer First, select the correct measure of center and then select the justification for your choice Correct measure of center O mean O median O mode Justification O The prices of cars are quantitative data with no outliers. O The prices of cars are quantitative data with outliers. O The prices of cars are qualitative data.
Yes, we would be more intrigued by looking so at mean, median, or mode for the below type of data set.
Explain the term center measurement?A value known as a measure of central tendency (measure of center) aims to characterize a set of data by pinpointing the set's geographic center. The mean, median, and mode are well-known central tendency measures.Choose the proper center measurement first, and then decide how to support your decision.
Correct center measurement
median, mean.modeJustification:
Car prices are quantitative data that don't include any outliers.Outliers exist in quantitative data about car pricing.Car costs are an example of qualitative data.To know more about the center measurement, here
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The correct question is-
For the following type of data set, would you be more interested in looking at the mean, median, or mode? State your reasoning.
The price of cars on a car lot-
What is the product of 2.8\times 10^32.8×10
3
and 9.7 \times 10^39.7×10
3
expressed in scientific notation?
The product of two numbers 2.8 × 10³ and 9.7 × 10³ can be represented in scientific notation as, 2.716 x 10⁷
What is the scientific notation of a number?The standard form for a number is a method by which we write number in a format like b×10ˣ. The value of b should be in between 0 to 10.
Given that,
The numbers,
2.8 × 10³
And 9.7 × 10³
the product in scientific notation = ?
the product in scientific notation = 2.8 × 10³ x 9.7 × 10³
It is known that,
if same numbers are in multiplication form,
their powers can be added
the product in scientific notation = 27.16 x 10³⁺³
= 27.16 x 10⁶
It can be further written as,
multiplied and divide by 10
the product in scientific notation = 27.16 x 10⁶x10/10
= 2.716 x 10⁷
Hence, the product is 2.716 x 10⁷
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fill in the blank. a simple linear regression equation relates r and w as follows: the explanatory variable is___, and the dependent variable is___. the slope parameter is___, and the intercept parameter is___. when w is zero, r equals___. for each one unit increase in w, the change in r is___units.
w, r, the coefficient of w, the constant term in the equation, the intercept parameter, equal to the slope parameter in units are ans of fill in the blank respectively.
A simple linear regression equation is used to model the relationship between two variables, where one variable is the independent or explanatory variable and the other is the dependent or response variable. The equation has the form:
y = β0 + β1x,
where y is the dependent variable, x is the explanatory variable, β0 is the intercept parameter, and β1 is the slope parameter. The intercept parameter represents the value of y when x is zero, and the slope parameter represents the change in y for each one-unit change in x. In this problem, the explanatory variable is w, and the dependent variable is r. The slope and intercept parameters need to be estimated from the data to obtain the regression equation. The equation can be used to make predictions about the response variable given a certain value of the explanatory variable.
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You make $29/hour, work 40 hours/week, 50 weeks a year. You save 12% of your
GROSS Your employer matches your savings up to 6%. Your spouse ALSO
contributes $150/month to your retirement fund.
Your average return over 50 years of work is 6.7%. How much will you have
accumulated once you retire in 50 years?
A vacant lot is being converted into a community garden. The garden and a walkway around its perimeter have an area of 550 square feet. Find the width of the walkway if the garden measures 12 feet wide by 15 feet long.
Answer:
The width of the walkway is 5ft long
Graph the function.
f(x)=√x+4
State four points on the graph of the function: the leftmost point and three additional points.
Answer: The function f(x) = √x + 4 describes a radical function that maps a real number x to its square root, shifted to the right by 4 units. The graph of this function is an upward-opening parabola that intersects the x-axis at x = -4.
Here are four points on the graph of the function:
The leftmost point: (0, 4)
An additional point to the right of the leftmost point: (1, 4.5)
Another additional point: (2, 5)
The third additional point: (9, 5.5)
Note: The values of x used in these examples are arbitrary and can be any real numbers. These points are only intended to give you an idea of what the graph of the function might look like
Step-by-step explanation:
The functions f(x)=−3/4x+2 1/4 and g(x)=(1/2)^x+1 are shown in the graph. What are the solutions to −3/4x+2 1/4=(1/2)^x+1? Select each correct answer.
−1
1
0
1
2
3
The solutions to the equations -³/₄x + 2¹/₄ = (¹/₂)ˣ + 1 are; -1 and 1
How to find the solution to simultaneous equations?The functions are given as:
f(x) = -³/₄x + 2¹/₄
g(x) = (¹/₂)ˣ + 1
The solution to these two simultaneous equations will be the point where they both intersect each other.
From attached graph, both functions intersect at at two coordinates that have their x-coordinates as x = -1 and x = 1
This means that- 1 and 1 represent the solutions to f(x) = g(x) or
-³/₄x + 2¹/₄ = (¹/₂)ˣ + 1
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when 2610 11.7 0.22 are added, the answer to the correct number of decimal places is . group of answer choices 2621.9 2600 2620 2621.92 2621
Answer: 2621.92
Step-by-step explanation:
The addition of the numbers 2610 and 11.7 and 0.22 is 2621.92.
Hence the correct option is given by (D).
Addition is a mathematical operation to sum up between two or more than two mathematical quantities or numbers specially.
Here given the numbers are 2610 and 11.7 and 0.22.
So the addition of the numbers 11.7 and 0.22 is given by,
= 11.7 + 0.22
= 11.92
So the sum of 2610, 11.7 and 0.22 is given by,
= 2610 + 11.7 + 0.22
= 2610 + 11.92
= 2621.92
Hence the correct option is given by (D).
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Which equation represents the same relationship?
X
5
7
9
11
13
y
13
17
21
25
29
The linear function that represents the relationship is given as follows:
y = 2x + 3.
How to obtain the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.From the table, when x increases by 2, y increases by 4, hence the slope m is found as follows:
m = 4/2
m = 2.
Hence:
y = 2x + b
When x = 5, y = 13, hence the intercept b is obtained as follows:
13 = 2(5) + b
b = 3.
Meaning that the function is given as follows:
y = 2x + 3.
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Please help me answer this :)
extra points
The required complete table for the given function f(x) = 2x - 1 is given as,
x = 1 0 -1 2
f(x) = 1 -1 -3 3
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Given function,
f(x) = 2x - 1
To complete the table,
Put x = 1
f(1) = 2(1) - 1
f(1) = 1
Similarly
f(0) = -1
f(-1) = -3
f(2) = 3
Thus, the required complete table for the given function f(x) = 2x - 1 is given as,
x = 1 0 -1 2
f(x) = 1 -1 -3 3
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Suppose X,Y and Z are three different random variables. Let X obey a Bernoulli Distribution. The probability distribution function is. c is a constant here.
Let Y obey the Standard Normal (Gaussian) Distribution, which can be written as Y N(0,1). X and Y are independent. Meanwhile, let Z = XY.
Calculate the covariance of Y and Z (Cov(Y, Z)) and determine whether values of c would affect the correlation.
The value of c does not affect the covariance of Y and Z.
How did we arrive at this assertion?The covariance of Y and Z can be calculated as Cov(Y, Z) = E[YZ] - E[Y]E[Z]. Since X is Bernoulli with parameter p and E[X] = p, we have E[Z] = pE[Y]. Hence,
Cov(Y, Z) = E[YZ] - E[Y]E[Z]
= E[YXY] - pE[Y]^2
= pE[Y^2 X] - pE[Y]^2
= p(E[Y^2]E[X] + Var[Y]p) - pE[Y]^2
= p(1 * p + 1 * p^2) - p^2
= p - p^2
It can be seen that the value of c does not affect the covariance of Y and Z.
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positive continous random variable with disbution and density we define in class the expected value to be prove, that given this definition:
Continuous random variable is a random variable that can take on a continuum of worth. In alternative words, a random variable is said to be continuous if it supposes a value that falls between a particular interval.
A continuous random variable can be described as a random variable that can take on an infinite number of possible values. Due to this, the probability that a continuous random variable will take on a fixed value is 0.
The probability density function of a continuous random variable can be explained as a function that gives the probability that the value of the random variable will drop between a range of values. Let X be the continuous random variable, then the formula for the pdf, f(x).
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Find the probability of randomly entering each room.
P(A) = 11/18
P(B) = 5/18
P(C) = 1/9
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Explanation:
Check out the diagram below. I have marked your given diagram with fractions. The red fractions 1/3, 1/3, and 1/3 are probabilities that correspond to picking the left-most set of 3 branches. Each has 1/3 chance of randomly being selected. This assumes any of the branches are equally likely.
The blue fractions 1/2 and 1/3 are the probabilities for the next set of sub-branches. For instance, the upper pair of branches each have probability 1/2 of being randomly selected, since we have two of them.
The green fractions are the result of multiplying the red and blue fractions along a particular pathway. Eg: The upper-most pathway has (1/3)*(1/2) = 1/6
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The diagram below shows that:
The green fractions 1/6, 1/9, and 1/3 correspond to room A. So 1/6+1/9+1/3 = 3/18+2/18+6/18 = 11/8 is the probability of landing in room A. Therefore, P(A) = 11/18The green fractions 1/6 and 1/9 correspond to room B. We have P(B) = 1/6+1/9 = 3/18+2/18 = 5/18 as the probability of ending in room B.Lastly, P(C) = 1/9 as there's only one fraction in green corresponding to room C.In summary
P(A) = 11/18P(B) = 5/18P(C) = 1/9Side notes:
The probabilities P(A), P(B), and P(C) add to 1.Each probability is in the interval [tex]0 \le P(X) \le 1[/tex]1/9 = 2/18