Scale model A toy manufacturer sells a 0.9-m tall model of the CN Tower. The
model casts a shadow 0.2 m long. At the same time of day, the CN Tower casts a
shadow 123.3 m long. Find the height of the CN Tower, to the nearest metre.
Include a diagram in your explanation.
Answers
The height of the CN tower found using the trigonometric function to the nearest metre is 555m.
What are the different trigonometric functions?
Trigonometric functions are used to determine the relationship between
angles and sides of a triangle.
The basic functions are sine, cosine and tangent.
sine = perpendicular/hypotenuse
cosine = base/hypotenuse
tangent = perpendicular/base
From the figure, we can see the right-angled triangles made by both the model and real CN towers.
Since the shadow is cast at the same time of the day, we can say that the angles θ and Φ formed are the same angles.
So from the figure,
tan θ = tan Φ
0.9/0.2 = h/ 123.3
h = 554.85 m
Therefore the height of the CN Tower to the nearest metre is 555m.
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Related Questions
Let N(t) represent the number of people in line at a BBQ truck, t hours after the food truck opens. Interpret each of the following statements in context.
Answers
Each of the given statements are interpreted in context below.
What is the quadratic equation?
A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where x is the variable and a, b, and c are constants. The solutions of the equation are the values of x that make the equation true.
a. N(1) = 11: This statement represents that 1 hour after the food truck opens, there are 11 people in line.
b. N(0) = N(3): This statement represents that at the time the food truck opens, the number of people in line is the same as 3 hours after the food truck opens.
c. N(4) > N(6): This statement represents that at 4 hours after the food truck opens, the number of people in line is greater than at 6 hours after the food truck opens.
d. N(R) = 34: This statement represents that the number of people in line at an unspecified time R is 34. The letter "R" can be any value for time, it is only a placeholder for any arbitrary value.
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A survey found that 12 out of every 15 people in the United States
prefer eating at a restaurant over cooking at home. If 400 people
selected eating at a restaurant on the survey, how many people
took the survey?
Answers
If 12 out of every 15 people prefer eating at a restaurant, then 12/15 of the people who took the survey chose that option. We know that 12/15 of the total number of people who took the survey is equal to 400 people, so we can set up the equation:
(12/15)x = 400
To find the total number of people who took the survey, we can solve for x by multiplying both sides of the equation by 15/12:
x = (400)(15/12)
x = 500
So, 500 people took the survey.
The scatterplot shows the number of home runs mario hits during his first four seasons on the company softball team. If his output continues to follow the linear model, approximately how many hime runs will Mario hit during his ninth season
Answers
y = 32 home runs will Mario hit during his ninth season.
Now, According to the question:
Linear models describe a continuous response variable as a function of one or more predictor variables. They can help you understand and predict the behavior of complex systems or analyze experimental, financial, and biological data. Linear regression is a statistical method used to create a linear model.
According to the graph, we have
The equation is:
y = 3x + 5
Put the value of x = 9
We get:
y = 3 × 9 + 5
y = 32
(Figure out the function of the image, and then bring the value of 'x' into it.)
Hence, y = 32 home runs will Mario hit during his ninth season.
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have been generated by a linear function?
Answers
Answer:
no.................,.............
A cruise line ship left port A and traveled 80 miles due west and then 150 miles due north at this point what is the shortest distance from the cruise to port A in miles
Answers
Answer:
170 miles
Step-by-step explanation:
Use 80 miles and 150 miles as the legs of a right triangle, and find the length of the hypotenuse using the Pythagorean theorem.
a² + b² = c²
80² + 150² = c²
6400 + 22500 = c²
c = √28900
x = 170
Answer: 170 miles
The graphs shows the speed of a car for 30 seconds. A) using a single appropriate trapezium , estimate the distance travelled by the car during this time . B) is your answer an overestimate or underestimate ?
Answers
Answer:
Step-by-step explanation:
a)
0.5 x (a + b) x h
0.5 x (5 + 30) x 30
Area = 525
b) Overestimate
Davinder earns 4.5% interest per year on the money she has saved in her bank account.
She starts off with £200.
How much is in her account after five years?
Just enter the value
Answers
The amount of money in Davinder's account after five years is equal to £236.
How to calculate the simple interest and future value?Mathematically, simple interest can be calculated by using this formula:
S.I = PRT or S.I = A - P
Where:
S.I represents the simple interest.P is the principal or starting amount.R is the interest rate.A is the future value.T represents the time measured in years.Substituting the given parameters into the simple interest formula, we have;
S.I = 200 × 4.5/100 × 5
S.I = 200 × 0.045 × 4
S.I = £36.
Next, we would calculate the future value as follows;
Future value, A = S.I + P
Future value, A = £36 + £200
Future value, A = £236.
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a manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 418 gram setting. is there sufficient evidence at the 0.10 level that the bags are overfilled? based on a 24 bag sample, the manufacturer decides to reject the null hypothesis. what is the conclusion?
Answers
There is sufficient evidence at 0.10 level of significance that the machine is overfilling the bags. So the option 1 is correct.
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 418 gram setting.
For the given question,
The Hypothesis for the test would be:
H(0): μ = 418
H(1): μ > 418
The fact that the null hypothesis is rejected means that there is enough data to conclude that the machine is significantly overfilling the bags at the 0.10 level of significance.
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The complete question is:
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 418 gram setting. Is there sufficient evidence at the 0.10 level that the bags are overfilled? Based on a 24 bag sample, the manufacturer decides to reject the null hypothesis. What is the conclusion?
1. There is sufficient evidence at the 0.10 level of significance that the machine is overfilling the bags.
2. There is not sufficient evidence at the 0.10 level of significance that the machine is overfilling the bags.
x≥ 0 in slope intercept form
y>4 in slope intercept form
x≤5 in slope intercept form
Please help quickly!!
Answers
The slope intercept form of the expressions are 0 ≤ x, y > 4 and 5 ≥ x
How to determine the inequalities in slope intercept form?From the question, we have the following parameters that can be used in our computation:
x≥ 0 in slope intercept formy>4 in slope intercept formx≤5 in slope intercept formThe slope intercept form of an inequality is represented as
y > mx + c
Note that the symbol > can be replaced by the appropriate inequality symbol
When the given expressions are rewritten, we have
0 ≤ x
y > 4
5 ≥ x
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Where do these two lines intercept on a graph y= -2x+9 and y=3x-6
Answers
These two lines intercept on a graph on the coordinate X(0, 1) Y(9, 7).
How to find this?The term "intercept" refers to the location where a line or curve intersects an axis on a graph. An object's x-intercept is defined as where a point crosses the x-axis. The term "y-intercept" refers to a point that crosses the y-axis. The intersection of the x-axis and the y-axis is what is meant by a line's intercept.
step1
y=-2x+9
graph the line using the slope and y intercept or two points
y=-2x+9
X(0,1) Y(9,7)
step2
y=3x-6
slope 3 y intercept (0,-6)
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events A and B in some sample sapce each have a probability 0.5 of occuring, while the probability that both occur (simultaneously) is 0.25. what is the probability that neither of A or B occurs? this is the work i did, can i please get some guidance
Answers
=============================================
Explanation:
I appreciate you showing your work so far, and your thought process.
Your steps are correct because the events [tex]A \cup B[/tex] and [tex](A \cup B)'[/tex] are complementary, aka opposite. One or the other must happen. It's like a coin flip heads vs tails.
The last thing you need to do really is simplify 1-0.5-0.5+0.25 to get the final answer 0.25
-------------------
This is what I would do as an approach.
P(A u B) = P(A) + P(B) - P(A n B)
P(A u B) = 0.5 + 0.5 - 0.25
P(A u B) = 0.75
So,
P( (A u B)' ) = 1 - P(A u B)
P( (A u B)' ) = 1 - 0.75
P( (A u B)' ) = 0.25
-------------------
Another approach:
Imagine we had 100 people.
50 are in set A to give P(A) = 50/100 = 0.50
50 are in set B to give P(B) = 0.50
25 are in both A and B to get P(A n B) = 25/100 = 0.25
50+50-25 = 75 people are in either A, or B, or both
That leaves 100-75 = 25 in neither set
25/100 = 0.25
I recommend to draw out the Venn Diagram.
For a scale drawing bathroom, 1/6 inch represents an actual length of 1 foot. If the bathroom measures 1 1/2 inches by 2 inches in the drawing, what are it's actual dimensions (length and width)?
Answers
Answer:
12ft x 9ft
Step-by-step explanation:
1/6" equals 1' actual ==> 1"=6'actual.
1.5" = 9'
2" = 12'
By utilizing the given scale of 1/6 inch equals 1 foot, the actual length of the bathroom is calculated to be 9 feet and width is 12 feet, from the given measurements of the drawing.
Explanation:The mentioned math problem is based on scale conversion, specifically in the realm of measurement. Given that every 1/6 inch on the scale drawing equals 1 foot in reality, the first step to solving this problem is to convert the measurements of the drawing into scale inches. To convert the length of 1 1/2 inches to the actual length, multiply 1.5 by 6 (as 1 inch is 6 times of 1/6 inch). This equals to 9 feet. Similarly, for the width of 2 inches, multiply 2 by 6 to get 12 feet.
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a data analyst for a phone company is analyzing the data of 150 of their customers, which accounts for 1% of their total customers. the analyst wants to determine the average number of hours each day a customer uses their phone, for calls and for texts, during a 30-day period. based on the data, the customers averaged 0.25 hours per day per call and 1.75 hours each day for texts. construct an equation in the correct form of y
Answers
Total number of a customer uses his phone each day in hour 0.25t + 1.75
Total number of a customer uses his phone each day in hour (e) = the customer spend time in hour on calls + the customer spend time in hour on texts.
total number of a customer uses his phone each day in hour (e) = the customer spend time in hour on calls + the customer spend time in hour on texts.
the customer spend time in hour on calls = the number of calls the customer made per day (t) times the average time spent by customers per day per hour (0.25 hours)
The number of hours the customer spend on texts is given as 1.75 hours each day.
Therefore required equation is:
e = 0.25t + 1.75
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Marshall has b buttons. He gives away 13 buttons. Write an expression that shows the number of buttons Marshall
has left.
Answers
Answer:
Since Marshall gives away 13 buttons out of b buttons, it means that b is an expression of a number which is greater than 13. Therefore,the answer is b - 13.
HURRY PLEASE!!! What are the marginal
column totals?
Answers
The marginal column total for the given data is option D: 39; 16.
What is marginal total?
A set of marginal totals is produced when the cell frequencies of a (multidimensional) contingency table are added over one or more of the classifying variables. The row and column totals are the marginal totals for a two-dimensional table.
The sum of the row entries or the sum of the column entries are called the marginal totals. Marginal distributions are computed by dividing the row or column totals by the overall total.
The number of men who prefer to eat fish = 11
The number of women who prefer to eat fish = 6
The number of men who prefer to eat red meat = 28
The number of women who prefer to eat red meat = 10
So, the marginal column total for the number of men who prefer to eat fish and red meat collectively is -
11 + 28 = 39
The marginal column total for the number of women who prefer to eat fish and red meat collectively is -
6 + 10 = 16
Therefore, the marginal total is 39, 16.
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1. Amanda goes to the bookstore and buys 4 comics and 1 novel, which together cost $19. Janelle goes to the same bookstore and buys 1 comic and 2 novels for $17. How much does each comic and each novel cost? adc
Answers
Each comic costs $4.71 and each novel costs $7.29.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
Let x be the cost of one comic and y be the cost of one novel.
From Amanda's purchase, we know that:
4x + y = $19
From Janelle's purchase, we know that:
x + 2y = $17
We can use the first equation to solve for y in terms of x:
y = $19 - 4x
We can substitute this expression for y into the second equation:
x + 2($19 - 4x) = $17
x + 2$19 - 8x = $17
-7x = $17 - 2$19
-7x = -$33
x = $33/-7 = $4.71
We can use this value of x to find the value of y:
y = $19 - 4($4.71) = $7.29
Hence, each comic costs $4.71 and each novel costs $7.29.
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The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 9 above 80 to 89, at 9 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Flower Town.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Desert Landing is skewed
IQR, because Desert Landing is symmetric
Range, because Flower Town is skewed
Range, because Flower Town is symmetric
Answers
Range, because it measures the distinction between the highest and lowest values in a dataset, providing a clear estimate of variability for both sets of data. It is unaffected by skewness or symmetry, making it a useful measure of variability for comparing the temperature consistency of Desert Landing and Flower Town.
What is meant by histogram?A histogram is a rough illustration of how numerical values are distributed. Karl Pearson coined the phrase at the beginning.
A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data points over a range of successive numerical intervals of equal width. The independent variable and dependent variable are plotted along the horizontal axis and the vertical axis, respectively, in the most typical type of histogram.
A common tool for graphing is the histogram. It is employed to summarise continuous or discrete data that is measured on an interval scale. It is frequently used to provide a convenient manner of illustration for the main characteristics of the data distribution.
Therefore, the correct answer is both option c) and d) Range, because Flower Town is skewed and symmetric.
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Answer:
The correct answer is:
Range, because Flower Town is symmetric
How to do this question? I don't really know what the lines next to 2t are, or are they just brackets?
Answers
Answer:
- 14
Step-by-step explanation:
the bars around 2t , indicate the absolute value of 2t
the absolute value function always gives a positive value , that is
| - a | = | a | = a
so for example
| - 4 | = | 4 | = 4
given
[tex]\frac{2}{3}[/tex] p - | 2t | - s² ( substitute values for p, t and s into the expression )
= [tex]\frac{2}{3}[/tex] × 12 - | 2(- 3) | - (- 4)²
= 2 × 4 - | - 6 | - 16
= 8 - 6 - 16
= 2 - 16
= - 14
Which expression represents the correct form for the quotient and remainder, written as partial fractions, of
8x²³-21²-67x-24?
2x²-x-21
Answers
The quotient and remainder, when written as partial fractions, of 8x²³-21²-67x-24 is represented by 2x²-x-21.
Which expression represents the correct form for the quotient and remainder?(8x³-21²-67x-24) = (2x²-x-21) + (6x¹-42)
This is done by dividing 8x²³-21²-67x-24 by 2x² and using long division to find the remainder.
The result of the division is a quotient of 4x²-33x+12 and a remainder of 2x²-x-21.
The remainder is the expression which represents the quotient and remainder, written as partial fractions, of 8x²³-21²-67x-24.To illustrate this further, we can break down the long division process into steps. First, divide 2x² into 8x²³.The result is 4x².
Then, subtract 4x² from 8x²³ to get the remainder of 4x³.
Next, divide 4x² into 21².
The result is 33x.
Then, subtract 33x from 4x³ to get the remainder of 4x²-33x.
Finally, divide 4x²-33x into 67x.
The result is 12. Subtract 12 from 4x²-33x to get the remainder of 2x²-x-21.This remainder is the expression which represents the quotient and remainder, written as partial fractions, of 8x²³-21²-67x-24.To learn more about partial fractions refer to:
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Jayden needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 3. 75 hours and charged him $60 for parts. The total was $528. 75. Write and solve an equation which can be used to determine xx, the cost of the labor per hour
Answers
The required equation is x × 3 = 528.75 - 60.
The cost of the labor per hour is $156.25
How do equations work?
The definition of an equation is a mathematical statement with at least two terms that contain variables or equal numbers.
Let x be the cost of the labor per hour.
We know that
x × 3 = labor cost
60 + x × 3 = total cost
We also know that the total cost is $528.75
So we can write the equation:
60 + x × 3 = 528.75
Solving for x:
x × 3 = 528.75 - 60
x × 3 = 468.75
x = 468.75/3
x = 156.25
Therefore, the cost of the labor per hour is $156.25
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Use a model to solve t+4=5.
Answers
The model to solve t + 4 = 5 is that John hast number of oranges and got 4 more making 5 oranges.
How to explain the model?A mathematical model is an abstract, mathematically based description of a physical system. Mathematical modeling is the process of creating a mathematical model.
To make a prediction or offer insight, mathematical modeling is the process of creating a mathematical representation of a real-world scenario.
The equation t + 4 = 5 can be solved by subtracting 4 from both sides of the equation:
t + 4 = 5
t = 5 - 4
t = 1
So t = 1 is the solution to the equation
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A bullet shot straight up is s feet above the
ground after seconds, where f(1) = -16t² + 256t. Find the height of the bullet 3 seconds after it is shot.
Answers
The height of the bullet after 3 second is 640m
What is motion under gravity?Motion under gravity refers to the movement of an object whose vertical motion is affected by the presence of gravity. The force that attracts objects downwards is gravity. In fact, gravity works towards the centre of the Earth.
When an object is thrown up, the height of the object is calculated as h = v²/2g
where v is the velocity and g is the acceleration due to gravity.
v = -16t²+ 256(t)
when t = 3s
v = -16( 3)²+ 256
v = -144+256
v = 112m/s
therefore the height attained by the bullet =
h = 112²/2×9.8
h = 640m
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How do you solve the equations that is listed to the right? (8x-9)-(3x-1)
Answers
Answer: The answer is 5x-8.
Step-by-step explanation: The equation we have is (8x-9)-(3x-1). The first step is to write the equation as shown:
8x-9-(3x-1)
After that step, next is to apply the distributive law:
8x-9-3x+1
Then, group/combine like terms:
8x-3x-9+1
Then adding similar elements:
5x-9+1
And finally, solving:
5x-8
can someone help me with this question?
Answers
The final balace in Tracy's bank account is $ 361.80.
How to follow transactions in a bank account
In this question we must pay attention to every movement in a bank account and determine final balance within. The hint is having an active reading in the meaning of translating every Tracy's movement in additions and subtractions, First, we translate very sentence into numbers and signs:
Tracy's checking account: + $ 300.00
Tracy bought new sneakers: - $ 63.00
Tracy deposited a paycheck: + $ 43.25
Tracy wrote a check: - $ 17.75
Tracy wrote a check: - $ 9.45
Tracy made a withdrawal at her bank: - $ 20.00
Tracy deposited a paycheck: + $ 43.25
Tracy wrote a check: - $ 18.00
Tracy made a withdrawal at another bank: - $ 20.00 - $ 1.50
Tracy deposited her birthday money: + $ 125.00
Second, calculate the final balance in Tracy's account:
x = 300.00 - 63.00 + 43.25 - 17.75 - 9.45 - 20.00 + 43.25 - 18.00 - 20.00 - 1.50 + 125.00
x = 361.80
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A net of a rectangular pyramid is shown. The rectangular base has length 25 ft and width 22 ft. The net of the pyramid has length 74.8 ft and width 70.4 ft. Find the surface area of the pyramid.
Answers
The surface area of the pyramid is 1702.8 ft².
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
Rectangular pyramid has a rectangular base and four triangular faces.
Net of the pyramid is shown below.
Area of the rectangular base = 25 × 22 = 550 ft²
Now we have to find the area of four triangular faces.
Area of a triangle = [tex]\frac{1}{2}[/tex] × base × height
Heights of the triangle BCX and ADZ can be found as below :
Combined height of both triangles = 74.8 - 25 = 49.8
Height of each triangle = 49.8 / 2 = 24.9 ft
Area of triangles BCX and ADZ = 2 × ( [tex]\frac{1}{2}[/tex] × base × height)
= Base × height
= 22 × 24.9
= 547.8 ft²
Similarly,
Combined height of triangles ABW and CDY = 70.4 - 22 = 48.4
Height of each triangle = 48.4 / 2 = 24.2 ft
Area of triangles ABW and CDY = Base × height
= 25 × 24.2
= 605 ft²
Total surface area of the pyramid = 550 ft² + 547.8 ft² + 605 ft²
= 1702.8 ft²
Hence 1702.8 ft² is the total surface area of the pyramid.
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there i 2 worker, one can make a houe in 2 day the other one can make houe in 3 day, if they work together how much day it take them to make a houe
Answers
The time taken by both the workers working together, which is 2 days.
The time taken to build a house by two workers working together can be calculated using the formula T = (1/W1 + 1/W2)^-1, where W1 and W2 are the working speeds of each worker. In this case, W1 = 2 days and W2 = 3 days. So, the time taken to build a house by both workers together is calculated as follows:
T = (1/2 + 1/3)^-1 = (3/6)^-1 = 6/3 = 2 days
Therefore, both the workers working together will take 2 days to build a house. This is because when two workers work together, the total work done in a given time is equal to the sum of the work done by each worker separately in that given time. In this case, both the workers will take 2 days and 3 days respectively to build the house when working separately, so when they work together the total work done in a given time will be 5 days. This is equal to the time taken by both the workers working together, which is 2 days.
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The track team is hosting a bake sale to earn money for new uniforms. They are selling 3 different types of pies:
Apple, Pumpkin, & Key Lime.
They arrange the pies on 2 tables, with all the apple pies on one table and all the pumpkin & key lime pies on the other. Both tables have the exact same number of pies. There are twice as many pumpkin pies as key lime. There are 5 more apple than pumpkin pies.
Write & Solve a System of Equations to determine how many PUMPKIN pies they are selling.
Answers
Here is one possible system of equations to represent the information provided:
The system of equationsLet x be the number of apple pies, y be the number of pumpkin pies, and z be the number of key lime pies.
The number of apple pies is the same as the number of pumpkin and key lime pies combined, since both tables have the same number of pies: x = y + z
There are twice as many pumpkin pies as key lime pies: y = 2z
There are 5 more apple pies than pumpkin pies: x = y + 5
Solving for y in the second equation, we have: y = 2z
Substituting that into the first equation we have: x = 2z + z = 3z + 5
Substituting that into the third equation we have: x = y + 5 = 2z + 5
So we have a system of equations:
x = 3z + 5y = 2zNow we can solve for any of the variables. Let's find the number of PUMPKIN pies
y = 2z
We can substitute in any value of z to get y.
For example, if we let z=5, we can find that
y=2(5)=10 pumpkin pies
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what is right! its either a or c
Answers
Answer: I believe it is A
Ned help PLEASE…………………
Answers
Answer:
0.82
Step-by-step explanation:
A： area =2( 0.8*0.6*+0.6*1+0.8*1) =2(0.48+0.6+0.8)=2*1.88 =3.76
B：area = 2(1.4*0.5+0.5*1.2+1.4+1.2) =2(0.7+0.6+1.68)=2*2.98=5.96
total 9.72
cost = $6.79* 9.72/80 =$0.82
What equation should i us
Answers
Answer: C
Step-by-step explanation:
The length of the PR would be 82.
Option (A) is correct.
What is an expression?
An expression is a combination of numbers, variables, and mathematical operations that represents a value or a computation. Expressions can be simple or complex and can include constants, variables, and various mathematical operations such as addition, subtraction, multiplication, and division. Expressions are often used to represent mathematical operations in algebraic, trigonometric, and calculus problems. They can be evaluated to find a numerical value or simplified to reveal underlying mathematical relationships.
In the given figure, the length of both line segments is equal, hence
PR = 10x + 842
PQ + QR = 10x + 842
8x + 678 + 12 = 10x + 842
First we can subtract 12 from both sides of the equation:
8x + 678 = 10x + 830
Then we can subtract 8x from both sides of the equation:
678 = 2x + 830
Then we can subtract 830 from both sides of the equation:
-152 = 2x
Then we can divide both sides of the equation by 2:
x = -76
So PR = 8x + 678 + 12
PR = 8(-76) + 678 + 12
PR = -608 + 678 + 12
PR = -608 + 690
PR = 82
Hence, the length of the PR would be 82.
Option (A) is correct.
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