Write a function $\verb#most_common_letter(string)#$ that determines the most commonly occurring letter in the input string. (If more than one letter is tied, it doesn't matter which one you return.) You should consider upper and lower case as the same letter. For example, $\verb#most_common_letter('This is a test of the function I have written')#$ should return 't', because 't' occurs 7 times, more than any other letter -- it occurs once as 'T' and 6 times as 't'.
Answers
Answer:
I am writing a Python program:
def most_common_letter (string): #function that takes a string as argument and returns the most commonly occurring letter in string
string = string.lower() # converts the string into lower case
inp_string="".join(string.split()) #splits the string in to a list and joins the elements of the list
maximum = 0 #sets the value of maximum to 0
letter = "" #stores the most commonly occurring letter
length = len(inp_string) #returns the length of the input string
counter = 0 #counts the occurrences of the letter in the string
for i in range(0, length): # iterates through the length of string
j = 0 #initializes j to 0
char = inp_string[i] # holds letter of input string at index position i
while length > 0: # iterates until the length of string exceeds 0
if (char == inp_string[j]): # if letter in char is equal to letter at index j of the string
counter += 1 #adds 1 to the count
j += 1 #increments j by 1
length -= 1 #decrements value of length by 1
if (maximum <= counter): #if maximum value is less than counter
maximum = counter #sets the maximum number of occurrences of a letter to maximum
letter = char #sets the most occuring letter in string to letter
return letter #returns the most commonly occurring letter in the input string
#in order to check if the function works properly use following statement
print(most_common_letter("This is a test of the function I have written")) #calls most_common_letter method by passing a string to it
Step-by-step explanation:
The program works as follows:
I will explain this with the help of an example. Suppose the string is:
string = "hello worLd"
first this string is converted to lowercase using lower() method. So the string becomes:
string = "hello world"
Next the string is split into a list using split() method. The string becomes:
['hello', 'world']
Then using join() this string is joined together on the basis of "" empty space
So the string becomes
helloworld
This string is assigned to the inp_string variable. Hence
inp_string = "helloworld"
The value of maximum is initialized to 0 and variable letter is also declared
which holds the most commonly occurring letter in the inp_string
len function is used to get the length of the inp_string
counter is initializes to 0. This counts the number of times the letter occurs in a string
The for loop iterates through the inp_string
Inside the loop the statement char = inp_string[i] sets the letter at the i-th index of inp_string to char.
i is initialized to 0 so inp_string[i] is inp_string[0] which is the first element of the string i.e. "h".
The program control then moves to the while loop. As length>0 so the program moves to the body of while loop which has an if statement: if (char == inp_string[j]):
This checks if the letter stored in char is equal to the letter at j-th index of the string. Now as j is initialized to 0. So
if (char == inp_string[0]): this evaluates to true and value of counter is incremented to 1. Next value of j also incremented to 1 and length of string is decremented to 1 Hence
counter = 1
j = 1
length = 9
Next if (maximum <= counter): condition checks if value of maximum is less than or equal to counter. It is true because maximum=0 and counter =1
So maximum = counter assigns counter value to maximum and letter = char assigns char to letter which was initially empty.
maximum = 1
letter = 'h'
At occurrence each iteration each letter in a string is counted and the letter that occurs the most in the string is returned by the function. For the above example hello world, letter l appears 3 times in the string and it is the most commonly occurring letter in the input string. So letter "l" is returned by this function. Hence the output of this program is l.
Related Questions
A vector with magnitude 4 points in a direction 250 degrees counterclockwise from the positive x axis.
write the vector in component form.
Answers
The vector with a magnitude of 4 and a direction of 250 degrees counterclockwise from the positive x-axis can be written in component form as (-2.77, 3.41).
To write a vector in component form, we need to break it down into its horizontal and vertical components. Let's analyze the given vector with a magnitude of 4 and a direction of 250 degrees counterclockwise from the positive x-axis.
To find the horizontal component, we use cosine, which relates the adjacent side (horizontal) to the hypotenuse (magnitude of the vector). Since the vector is counterclockwise from the positive x-axis, its angle with the x-axis is 360 degrees - 250 degrees = 110 degrees. Applying cosine to this angle, we have:
cos(110°) = adj/hypotenuse
adj = cos(110°) * 4
Similarly, to find the vertical component, we use sine, which relates the opposite side (vertical) to the hypotenuse. Applying sine to the angle of 110 degrees, we have:
sin(110°) = opp/hypotenuse
opp = sin(110°) * 4
Now we have the horizontal and vertical components of the vector. The component form of the vector is written as (horizontal component, vertical component). Plugging in the values we found, the vector in component form is:
(cos(110°) * 4, sin(110°) * 4)
Simplifying this expression, we get the vector in component form as approximately:
(-2.77, 3.41)
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a gold, a silver, and a bronze medal are awarded in an olympic event. in how many possible ways can the medals be awarded for a 200-meter sprint in which there are 15 runners?
Answers
Answer:
There are 1320 ways in which 15 runners can be awarded for a 200-meter sprint race three different medals.
Step-by-step explanation: Whenever we are supposed to find the ways in which certain things have to be arranged, we use the concept of Permutation.
The number of possible ways to award gold, silver, and bronze medals for a 200-meter sprint with 15 runners is 2,730.
1. Select the gold medal winner: There are 15 runners, so there are 15 choices for the gold medal.
2. Select the silver medal winner: Since the gold medalist is already chosen, there are 14 remaining runners to choose from for the silver medal.
3. Select the bronze medal winner: With gold and silver medalists chosen, there are now 13 remaining runners to choose from for the bronze medal.
Multiply the number of choices together: 15 (gold) x 14 (silver) x 13 (bronze) = 2,730 possible ways to award the medals.
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A)There are twice as many students in the math club as in the telescope club. Suppose there are $x$ students in the telescope club and $y$ students who are members of both clubs. Find an expression for the total number of students who are in the math club or the telescope club (or both). Give your answer in simplest form.
b)There are twice as many students in the math club as in the telescope club. Suppose there are students in the telescope club and students who are members of both clubs. Find an expression for the total number of students who are in the math club or the telescope club but not both. Give your answer in simplest form.
Answers
The number of students in the telescope club by $x$ and the number of students in the math club by $y$.
$y=2x$Now, suppose there are $z$ students who are members of both clubs. Then the total number of students who are in the math club or the telescope club (or both) is given by:$x + y - z$ Substituting $y=2x$ in the above expression, we get:$x + 2x - z=3x - z$ Hence, the expression for the total number of students who are in the math club or the telescope club (or both) is $3x - z$.b)The number of students who are in the math club but not in the telescope club is given by:$y-z$ And the number of students who are in the telescope club but not in the math club is given by:$x-z$ Adding these two expressions, we get the total number of students who are in the math club or the telescope club but not both:$ y-z+x-z $.
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Maddie and Josh are trying to clean the roof of their house. They place the base of the ladder 3 feet away from the base of the house. Their ladder is 27 feet long. What angle does the ladder make with the ground?
Answers
Answer:
83.6 degrees
Step-by-step explanation:
intermediate models of integration are different from the enemies and allies models because
Answers
Intermediate models of integration differ from the enemies and allies models due to their approach in fostering collaboration and cooperation between different entities while maintaining a certain degree of autonomy and independence.
Intermediate models of integration, in contrast to enemies and allies models, aim to establish a framework where entities can work together while retaining their individual identities and interests. These models recognize that complete integration or isolation may not be the most optimal or feasible approaches. Instead, they emphasize the importance of collaboration and cooperation between different entities, such as organizations or countries, while respecting their autonomy.
In intermediate models of integration, entities seek to identify shared goals and interests, leading to mutually beneficial outcomes. They acknowledge the value of diversity and differences in perspectives, considering them as assets rather than obstacles. This approach encourages open communication, negotiation, and compromise to bridge gaps and find common ground. Rather than viewing other entities as adversaries or allies, the emphasis is on building relationships based on trust, transparency, and shared values.
Intermediate models of integration often involve the establishment of frameworks, agreements, or platforms that facilitate collaboration while allowing for flexibility and adaptation to changing circumstances. These models promote inclusivity, recognizing that integration can be a complex process that requires active participation from all involved entities. By combining the strengths and resources of different entities, intermediate models of integration strive to achieve collective progress and shared prosperity while acknowledging the importance of maintaining individual identities and interests.
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How to find the Sum of a Finite Arithmetic Series?
Answers
There are two formulae to find out the sum of a finite arithmetic series. Sn = n/2[2a + (n-1)d] First formula required the number of terms n, first term a and common difference d. Sn = n/2[a + l] Second formula requires first term a, number of terms n and last term l.
A series of numbers in arithmetic series is given as, a, a+d, a+2d, a+3d,.. is called an arithmetic sequence where, a is the first term and d is the common difference of this arithmetic sequence.
Sum of finite arithmetic series of n terms is given by the formula,
Sn = n/2[2a + (n-1)d]
where,
Sn is the sum of finite arithmetic series of n terms
d is common difference
a is first term
If an arithmetic sequence has a finite number of terms and l is the last term then the sum of all terms,
Sn = n/2[a + l]
Thus, the formulae to find out the sum of a finite arithmetic series is explained.
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What is 40% of 400?
1600%
Remember use benchmark percentages to partition the number line.
Example, 5%, 10%, 20%, and 25%
Answers
Answer:
idfk good luck
Step-by-step explanation:
Two angles of a quadrilateral measure 105° and 150°. The other two angles are in a ratio of 4:17. What are the measures of those two angles?
Answers
Answer:
20 degrees and 85 degrees.
Step-by-step explanation:
105 degrees+ 150 degrees is equal to 255 degrees. 360 degrees - 255 degrees is 105 degrees. To get the ratio equivalent to 105 degrees you have to multiply both sides by 5 in order to get 20 degrees, and 85 degrees. I hope this helps! :)
One-third of the students in Mrs. Hayko's class walk to school. Of the students who do not walk to school, four-fifths take the bus.
a.) What fraction of the students in Mrs. Hayko's class take the bus to school?
b.) How many students might be there in her class?
Answers
Answer:
The possible number of students in Mrs. Hayko's class is limited to 15 or 30, as higher multiples of 15 would exceed the desired class size.
Step-by-step explanation:
a)
Let 'x' be the total number of students in Mrs. Hayko's class.
One-third of the students walk to school: (1/3)x.
The remaining students who do not walk to school: (2/3)x.
Four-fifths of the non-walking students take the bus: (4/5) * (2/3)x.
Simplify to find the fraction of students taking the bus: (8/15)x.
b)
Consider different values for 'x' to find a whole number of students taking the bus.
Start with a small number, such as x = 15.
Calculate the number of students taking the bus using (8/15)x.
If the result is a whole number, it's a possible class size.
Repeat with different values of 'x' until a whole number is obtained.
The possible number of students in Mrs. Hayko's class could be 15, 30, or any other multiple of 15.
Suppose you are given the function t(x) = x^2 + 8x - 20 Explain how you would graph this function, making sure to include the following information: Coordinate(s) of the solutions/rootscoordinate of the y-intercept location of the line of symmetrycoordinate of the vertex whether the graph opens up or down and how you know
Answers
t(x) = x² + 8x - 20
Coordinate(s) of the solutions/roots
x² + 8x - 20 = 0 ==> (x -2)(x + 10) = 0
roots: x= 2 and x = -10
coordinate of the y-intercept
y-intercept is when x = 0 ==> t(x) = x² + 8x - 20 when x = 0: t(0) = -20
y-intercept: y = -20
location of the line of symmetry
x = -4
y = (x + 4)² - 36, therefore coordinates of the vertex (-4, 36) and line of symetry x = -4
coordinate of the vertex
(-4, -36)
y = (x + 4)² - 36, therefore coordinates of the vertex (-4, 36)
whether the graph opens up or down and how you know
Opens up
Because the coefficient of x² is positive
Solve for x.
(3x + 2)°
47°
Answers
So you first write the numbers into an equation:
(3x + 2) = 47
(You can remove the parentheses if you'd like.)
So first off, you'd want to isolate 'x' since that's what you're trying to figure out. In order to do that, you must subtract 2 from both sides.
This means you would do: 2 - 2 (which cancels out)
and then you would do 47 - 2, which equals 45.
After that, you should have 3x = 45
Now, divide 3 from both sides.
3x ÷ 3 (cancels out)
45 ÷ 3, which equals 15.
So you're answer is 15.
x = 15
Dendra's boat uses 3 gallons of gas in 4 hours. How many gallons of gas will she use in 15 hours?
Answers
Answer:11.25
Step-by-step explanation:because we have to find out how many gallons we have in one hour so you divide both sides by 4
4/4 is 1 hour
3/4 is 0.75 gallons then you have to multiply both sides by 15
1 hour times 15 is 15 hours
the 0.75 x 15 is 11.25
so the answer is 11.25 gallons that she uses in 15 hours
hope this helps
Solve the equation for y.-5x+2y=-10
Answers
how do you multiply add and divide fractions?
Answers
Answer:
If the denominators are not the same: First, make them the same. Then add or subtract like fractions with the same denominators.
Step-by-step explanation:
the first step when multiplying fractions is to multiply the two numerators. the second step is to multiply the two denominators. simplify the new fractions. the fractions can also be simplified before multiplying by factoring out common factors in the numerator and denominator.
to add or subtract fractions they must have the same denominator. if the denominators are already the same then it is just a matter of either adding or subtracting the numerators if the denominators are difrent then a common denominator needs to be found.
simplify.
remove all perfect squares from inside the square roots. assume x and y are positive.
√8x^3y^2
Answers
Answer:
\(2xy\sqrt{2x}\)
Step-by-step explanation:
Because this is a whole term in itself (no addition or subtraction), you can just directly find squares and factor them out. First, when looking at 8, you can factor out 4, to get 2 on the outside. Then, while looking at x cubed, you can factor out x squared, to get x on the outside, and when looking at y squared, you can just pull that outside itself, to get y. Now, we have one 2 and one x remaining, for a total of \(2xy\sqrt{2x}\)
15.5 divided by 33.17
Answers
Answer: 15.5 divided by 33.17 would be 0.46728972
Make sure you put your decimal point
The sum of twice a number and 7 is -19
Answers
Answer:
The number will be -13
Step-by-step explanation:
Let the no. be x
Its twice will be = 2x
According to the question ,
\(2x + 7 = -19\\=> 2x = -19 - 7 = -26\\=> x = \frac{- 26}{2} = - 13\)
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The value of the number is -13.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The sum of twice a number and 7 is -19.
Let the number be M.
Now,
2M + 7 = -19
We will solve for M.
2M + 7 = -19
Subtract 7 on both sides.
2M + 7 - 7 = - 19 - 7
2M = -19 - 7
2M = -26
Divide both sides by 2.
M = -26/2
M = -13
We can cross-check.
2M + 7 = -19
2 (-13) + 7 = -19
-26 + 7 = -19
-19 = -19
Proved
Thus.,
The value of the number is -13.
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Find the Coordinates of the
Ortho center
X(-1,-4) 4 (7-4) Z (7,4)
Answers
The coordinates of the orthocenter of triangle XYZ are (3,2).
Coordinate calculation.
To find the coordinates of the orthocenter of triangle XYZ, we need to find the intersection point of the altitudes.
First, we need to find the equations of the three altitudes. An altitude is perpendicular to a side and passes through the opposite vertex.
The equation of the line through X(-1,-4) and perpendicular to YZ is:
y - 4 = (4-(-4))/(7-(-1))(x-7)
y - 4 = 8/8(x-7)
y = -x + 11
The equation of the line through Y(4,7) and perpendicular to XZ is:
y - 7 = (-1/4)*(x-4)
y = (-1/4)x + 8.5
The equation of the line through Z(7,4) and perpendicular to XY is:
y - 4 = (7-(-1))/(-4-(-4))(x-7)
y - 4 = -8/10(x-7)
y = -4/5*x + 36/5
Next, we need to find the intersection points of these lines. We can solve the system of equations:
y = -x + 11
y = (-1/4)x + 8.5
y = -4/5*x + 36/5
Solving this system of equations, we get the coordinates of the orthocenter H:
H(3,2)
Therefore, the coordinates of the orthocenter of triangle XYZ are (3,2).
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Write a summary which uses textual evidence to describe how rolf carle change due to his interaction with azucena
Answers
Rolf Carle undergoes a transformation as a result of his interaction with Azucena.
In the novel or text where Rolf Carle's character is portrayed, his interaction with Azucena brings about significant changes in his life. Through their relationship, Rolf's perspective and understanding of the world begin to shift. Azucena, with her unique experiences and perspectives, challenges Rolf's preconceived notions and broadens his horizons. As Rolf spends more time with Azucena, he starts to develop a deeper sense of empathy and compassion. He becomes more aware of the struggles and injustices faced by marginalized communities, which were previously unfamiliar to him. This newfound understanding sparks a sense of activism within Rolf, and he becomes increasingly dedicated to social justice causes.
Furthermore, Rolf's relationship with Azucena helps him question his own identity and values. He begins to reevaluate his privilege and the impact it has on others. This introspection leads him to make conscious choices and take actions that align with his newfound awareness.
Overall, Rolf Carle's interaction with Azucena leads to a transformation in his character. He evolves from a person who may have been ignorant or apathetic to the plight of others into someone who is more empathetic, socially conscious, and committed to making a positive change in the world.
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Find an angle that is positive, less than 360° , and coterminal with 395° . Subtract 360° 360 ° from 395° 395 ° .
Answers
Given an angle that is positive, less than 360°, and coterminal with 395° is 35°.
Subtract 360° from 395°.
We know that 1 revolution is equal to 360°.
Therefore, a positive angle that is less than 360° and coterminal with 395° is 35°.
When an angle is less than 360° and shares the same terminal side with another angle that is less than 360°, then the angle is referred to as a coterminal angle.
In other words, the two angles have the same initial side and terminal side but can be either positive or negative.
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Factorize: p^2+2pq+q^2-1
Answers
Answer:
have a great day
god bless you
pls help <3 Triangle QRS has side lengths q = 11, r = 17, and s = 23. What is the measure of angle R
a.44.5°
b.59.3°
c.27.0°
d.108.6
Answers
Using the cosine law, the measure of angle R is calculated as approximately: a. 44.5°.
How to Use the Cosine Law to Solve a Triangle?The cosine law is expressed as follows:
cos R = [s² + q² – r²]/2sq
Given the following side lengths of triangle QRS:
Side q = 11,
Side r = 17,
Side s = 23.
Plug in the values into the cosine law formula:
cos R = [23² + 11² – 17²]/2 * 23 * 11
cos R = 361/506
Cos R = 0.7134
R = cos^(-1)(0.7134)
R ≈ 44.5°
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true or false: if v is an eigenvector corresponding to λ, then cv is also an eigenvector corresponding to the eigenvalue λ
Answers
True. If v is an eigenvector corresponding to the eigenvalue λ, then multiplying v by a scalar c, denoted as cv, will also be an eigenvector corresponding to the same eigenvalue λ.
An eigenvector represents a direction in a vector space that remains unchanged, except for scaling, when multiplied by a specific matrix. The corresponding eigenvalue determines the magnitude of the scaling. When we multiply an eigenvector v by a scalar c, the direction of the vector remains the same, and the resulting vector cv is scaled by the same factor c.
Mathematically, if Av = λv, where A is a matrix, λ is an eigenvalue, and v is the corresponding eigenvector, then it follows that A(cv) = cAv = cλv = λ(cv). This equation shows that multiplying an eigenvector v by a scalar c preserves its status as an eigenvector, corresponding to the same eigenvalue λ.
In summary, if v is an eigenvector corresponding to λ, then multiplying it by a scalar c still results in an eigenvector corresponding to the same eigenvalue λ.
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Describe each transformation from f(x)
(red) to g(x) (green) in terms of x.
Answers
A point like (2,0) that is on the red curve goes to (-2,0) on the green curve. The rule used is \((x,y) \to (-x,y)\) which describes a reflection over the y axis. The other points use this rule as well.
In other words, every x becomes -x. Whatever the sign is for x, we swap it from positive to negative or vice versa. This means g(x) = f(-x).
Express the trig ratios as fractions in simplest terms.
Answers
The trigonometric ratios for each angle are found for the given right triangle.
What is meant by trigonometric ratios?Trigonometric ratios are the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant(sec) are the six trigonometric ratios . A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle.
In this question, we are given a right triangle.
From the triangle, we can write the following.
Hypoyenuse = longest side = 48
Height = 47
Base = √95 = 9.75
With respect to angle ∠J, we can find the trigonometric ratios.
Let ∠J = Ф
sin Ф = Opposite side/ hypotenuse = 47/48 = 0.98
cos Ф = adjacent side/ hypotenuseuse = √95/48 = 0.20
tan Ф = opposite side/adjacent side = 47/√95 = 4.82
cosec Ф = 1/sinФ = 1/ 0.98 = 1.02
sec Ф = 1/cos Ф = 1/0.20 = 5
cot Ф = 1/tan Ф = 1/4.82 = 0.21
With respect to the angle ∠I, we can find the trigonometric ratios.
Let ∠I = θ
sin θ = Opposite side/ hypotenuse = √95/48 = 0.20
cos θ = adjacent side/ hypotenuseuse = 47/48 = 0.98
tan θ = opposite side/adjacent side = √95/47 = 0.21
cosec θ= 1/sinФ = 1/ 0.20 =5
sec θ = 1/cos Ф = 1/0.98 = 1.02
cot θ = 1/tan Ф = 1/0.21= 4.8
Therefore trigonometric ratios for each angle are found for the given right triangle.
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(not really a math problem) I have a 125 gallon tank, 5ft long and 6ft in circumfrence 3 inches of fuel in the tank how much gallons is that ` - `
Answers
Answer:
6.25 gallons
Step-by-step explanation:
If 125 gallon tank in equivalent to 5ft
1 foot is equal to 12inches...
5 ft ×12 =60 inches
So 125 gallon tank= 60 inches
If 60 inches = 125 gallon
3 inches = 125 × 3 / 60
= 375/60
= 6.25 gallons
pls help having trouble!
Answers
Answer:
a is 30 degrees.
Step-by-step explanation:
The degree of a triangle is 180, which means that all the degrees in any triangle will always add up to 180. Since CB and DB are congruent, the angles C and D will be the same. This means that to get the answer, just subtract the value we already have from 180 and divide the sum by 2.
\(\frac{180-120}{2} = \frac{60}{2} = 30\)
Find the shortest distance from the point P (7.-2, -3) to a point on the line given by /: (x, y, z)=(-11, 11,-61). The distance is Preview My Answers Submit Answers You have attempted this problem 0 times. You have 3 attempts remaining
Answers
The shortest distance from point P(7, -2, -3) to the line with the equation (x, y, z) = (-11, 11, -61) is approximately 14.71 units.
To find the shortest distance, we can use the formula for the distance between a point and a line in three-dimensional space. The formula is:
d = |(P - P₀) - ((P - P₀) · u)u|
where P is the point (7, -2, -3), P₀ is a point on the line (-11, 11, -61), and u is the direction vector of the line.
The direction vector u can be obtained by subtracting the coordinates of two points on the line: u = (-11, 11, -61) - P₀
Next, we calculate (P - P₀) and ((P - P₀) · u):
P - P₀ = (7, -2, -3) - (-11, 11, -61) = (18, -13, 58)
(P - P₀) · u = (18, -13, 58) · (-11, 11, -61) = -792 + (-143) + (-3548) = -4483
Now, we can substitute these values into the formula for the distance:
d = |(18, -13, 58) - (-4483)(-11, 11, -61)|
Calculating the magnitude of the expression, we find that the shortest distance is approximately 14.71 units.
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Find each side length.
у
х
45
3
Ox= 3, y = 32
Ox=3V2, y=32
x = 3/2 y=3
x = 3, y = 6/2
Answers
Given △qrs ~ △xyz, what is the value of tan(q)? three-fifths three-fourths four-fifths four-thirds
Answers
The value of tan(Q) = 3/4, given that ΔQRS ~ ΔXYZ. Computed using properties of similar triangles. Hence, the second option is the best choice.
According to the properties of similar triangle, the corresponding sides of similar triangles are in proportion.
In the question, we are given that ΔQRS ~ ΔXYZ.
By properties of similar triangles, we know that:
QR/XY = RS/YZ = SQ/ZX.
From this, we can show that:
RS/SQ = YZ/ZX ...(i).
We are asked to find the value of tan(Q).
By trigonometric ratios, we know that:
tan(Q) = Perpendicular/Base = RS/SQ.
From (i), we know that RS/SQ = YZ/ZX.
From figure, we know that YZ = 9, and ZX = 12.
Thus, YZ/ZX = 9/12 = 3/4.
Thus, tan(Q) = RS/SQ = YZ/ZX = 3/4.
Hence, the value of tan(Q) = 3/4, given that ΔQRS ~ ΔXYZ. Computed using properties of similar triangles. Hence, the second option is the best choice.
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