The ticket price that maximizes profit is $2.90.
What is profit and how is it related to revenue and cost?
In business and economics, profit is the amount of money earned after all expenses and costs have been deducted from revenue. Profit is a key metric used to measure the financial success of a company or enterprise. It is calculated as follows:
Profit = Revenue - Cost
Revenue is the total income earned from the sale of goods or services, while cost is the total expense incurred to produce and sell those goods or services. Profit is an important measure of financial performance because it reflects how efficiently a company is using its resources to generate income.
Finding the price that maximizes profit:
We need to find the value of x that corresponds to the maximum value of the revenue function R(x). The price of the tickets can then be determined by adding the value of x to the initial price of $2.
Using the revenue function [tex]R(x)=-30(x-6)^2+320[/tex], we can find the value of x that maximizes the revenue as follows:
Take the derivative of R(x) with respect to x:
[tex]R'(x) = -60(x-6)[/tex]
Set the derivative equal to zero and solve for x:
[tex]R'(x) = 0[/tex]
[tex]-60(x-6) = 0[/tex]
[tex]x = 6[/tex]
Determine the second derivative of R(x) to check that x = 6 corresponds to a maximum:
[tex]R''(x) = -60[/tex]
Since R''(x) is negative, this confirms that x = 6 corresponds to a maximum.
Calculate the corresponding revenue at x = 6:
[tex]R(6) = -30(6-6)^2 + 320[/tex]
[tex]R(6) = 320[/tex]
Determine the ticket price by adding the value of x to the initial price of $2:
Ticket price = $2 + $0.15(x)
Ticket price = $2 + $0.15(6)
Ticket price = $2.90
Therefore, the ticket price that maximizes profit is $2.90.
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A well of 3 cm diameter is dug to a depth of 14 m. Akind of embankment is made by spreading the soil out of it evenly around the well, forming a circular platform (ring) 4m wide. Find the height of this embankment
The height of the embankment will be 1.125. As the embankment is in cylinder shape shown in figure.
The shape of the well will be cylindrical as shown in the figure below in the image section.
Given that :
Depth (h1) of well = 14m
Radius (r1) of the circular end of well = 3/2 m Width of embankment = 4 m
From the figure, it can be observed that our embankment will be in a cylindrical shape having outer radius, (r2) = 4 + 3/2 = 11/2m
Let the height of the embankment be h2 .
Volume of soil dug from well = Volume of earth used to form the embankment
⇒ π × r1² ×h1 = π × (r2-r1)² ×h2
⇒ π × (3/2)² × 14 = π ×[(11/2)² - (3/2)² × h2]
⇒ 9/4 × 14 = 112/4 × h2
⇒ h2 = 9/8
⇒ h2 = 1.115 m
Therefore the height of the embankment will be 1.125m.
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the capacity of a dump truck is listed by the manufacturer as 10 yd3. a construction site requires the removal of 170 m3 of dirt, and the contractor has three identical trucks. how many trips will each need to make?
Trips will each need to make 6 trips.
Given
Capacity = 10yd³
Dirts = 170 m³
Trucks = 4
Required
Count the trips made by each truck.
To determine how much dirt is in each truck, divide the amount of soil by 4.
Each Truck = 170/4 m³
Each Truck = 42.5 m³
Divide the portion of each truck by capacity of each truck to get the number of trip
Trip = Each Truck / 10yd³
Convert m³ to yd³
Trip = 55.587875/10
Trip = 5.5587875
Approximate:
Trip = 6
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the probability of getting heads on a fair coin is 0.50. the probability of getting tails is also 0.50. if you toss the coin three times and get heads all three times, what is the probability of getting tails on the next toss?
The probability of getting tails on the next toss is 0.5 as the coin is a fair coin and doesn't remember the past results.
The probability of getting heads on a fair coin is 0.50.
The probability of getting tails is also 0.50.
If you toss the coin three times and get heads all three times,
The probability of getting tails on the next toss:The probability of getting tails on the next toss is 0.5 as the coin is a fair coin and doesn't remember the past results.
The term 'fair coin' mean:A fair coin is a coin where each of the two faces has the same probability of landing on any coin toss. That is, a fair coin will land on tails and heads equally often.
In other words, the probability of getting heads and tails is 0.5.
The possible outcomes of flipping a fair coin:There are only two possible outcomes of flipping a fair coin.
The two outcomes are heads or tails:The probability of each outcome is 0.5.
This is because a fair coin has two equally likely outcomes.
The probability of getting heads on any flip is 0.5.
The same goes for the probability of getting tails on any flip.
This implies that the probability of flipping a fair coin three times and obtaining three heads is
(0.5 x 0.5 x 0.5) = 0.125
Similarly, the probability of flipping a fair coin three times and obtaining three tails is also 0.125.
As each flip is independent, the outcome of the preceding flips does not affect the next flip, and the probability of getting tails on the next toss is 0.5.
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Please solve with workings out
Answer:
1500 g
Step-by-step explanation:
part a) is correct
part b)
The ratio of syrup to oats for one flapjack is 1:4
That means for each g of syrup you will require 4 g of oats
For 12 flapjacks you require 250 g
Therefore quantity of oats needed for 12 flapjacks = 250 x 4 = 1000 g
If you were to make 18 flapjacks then you would need 18/12 x quantity needed for 12 flapjacks
18/12 = 3/2 (dividing numerator and denominator by 6)
Quantity of oats needed for 18 flapjacks
= 18/12 x 1000
= 3/ 2 x 1000
= 3 x 500
= 1500 g
is there a significant difference in the mean amount of e. coli bacteria detected by the two methods for this type of beef? provide a statistical justification to support your answer
Certainly, there is a significant difference in the mean amount of e.coli bacteria detected by the two methods for this type of beef. This can be supported statistically by conducting a hypothesis test.
The null hypothesis ([tex]H_0[/tex]) is that there is no significant difference in the mean amount of E. coli bacteria detected by the two methods. The alternative hypothesis ([tex]H_a[/tex]) is that there is a significant difference in the mean amount of e.coli bacteria detected by the two methods.
The two-sample t-test can be used to test the hypothesis. The t-test compares the means of two independent groups and determines whether they are significantly different. The t-test assumes that the two samples are normally distributed and have equal variances.
If the sample sizes are large, then the t-test can still be used even if the samples are not normally distributed.
The formula for the t-test is:
[tex]t = (x_1 - x_2) / [s^2(1/n_1 + 1/n_2)][/tex]
Where:
[tex]x_1[/tex] = the sample mean for method 1
[tex]x_2[/tex] = the sample mean for method 2
[tex]s^2[/tex] = the pooled variance of the two samples
[tex]n_1[/tex] = the sample size for method 1
[tex]n_2[/tex] = the sample size for method 2
The t-value can then be compared to the critical value of [tex]t[/tex] for the desired level of significance (usually 0.05).
If the t-value is greater than the critical value of [tex]t[/tex], then the null hypothesis can be rejected and it can be concluded that there is a significant difference in the mean amount of E. coli bacteria detected by the two methods.
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w(x)= -5(x-8)(x+4)
What is the maximum height that the stone will reach?
Answer:
(2, 180)
Step-by-step explanation:
w(x)=-5x^2+20x+160
a=-5 b=20
x=-20/2x(-5)
x=2
w(2)=180
2, 180
circle project represented in a graph
1. Draw a point at (1,-2).
2. Draw a long radius of 8 units.
3.Using a compass, draw a circle with your point from step one as its center and the point from step two as the side.
4.Using a protractor, draw a 70 degree arc
5. draw a central angle that intersects your arc
6. Draw an inscribed angle that intersects an arc of 40 degrees
7.draw a tangent line
8. draw a secant line
9. write the equation of your circle
Answer:
search up the answers
Step-by-step explanation:
please help 9 10 ll and 12 need answers i have 1 hour to get answers please
1. The area of the circle with radius r = 4 is 200.96 square cm. 2. The area of the circle is approximately 113.04 square cm.
What is radius and diameter of the circle?A circle's radius is equal to twice its diameter. In other words, if d is the diameter and r is the radius, then d = 2r. On the other hand, a circle's radius is equal to half of its diameter. Finding the circumference or area of a circle are only two examples of computations involving circles for which this connection is crucial.
The area of the circle is given by the formula:
A = πr²
Substituting the value r = 8 we have:
Area = 3.14(8)² = 200.96 square cm
2. For circle with d = 12 cm we have the radius as:
r = 12/2 = 6
A = 3.14(6)² = 113.04 square cm
Hence, the area of the circle with radius r = 4 is 200.96 square cm. 2. The area of the circle is approximately 113.04 square cm.
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If the circumference of a circle is 70cm. Find the measure of it's radius and diameter. (22/7)
Select the correct answer. Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18, which equation represents this situation, and how old is Tina? A. The equation that represents this situation is t − 3 = 18. Tina is 21. B. The equation that represents this situation is t + 3 = 18. Tina is 15. C. The equation that represents this situation is 3 − t = 18. Tina is 21. D. The equation that represents this situation is -3 − t = 18. Tina is 15.
Step-by-step explanation:
A. t-3=18. Tina is 21. Here's your answer.
The correct option is A
The equation that represents this situation is [tex]t-3=18[/tex]. Tina is [tex]21[/tex].
The explanation for the correct option:
Option A:
It is given in the question, Tina's age is [tex]t[/tex].Cole's age is [tex]3[/tex] year less than Tina's age, that is [tex]t-3[/tex].It is given that Cole's age is given to be [tex]18[/tex].From the given question:
[tex]t-3=18[/tex]
Adding [tex]3[/tex] both sides in order to solve for [tex]t[/tex]:
[tex]t=18+3[/tex]
[tex]=21 \ years[/tex]
Therefore, the equation to find the age of Tina is [tex]t-3=18[/tex] and the age of Tina is [tex]21[/tex] years.
Hence, Option (A) is the correct option.
Find the quadratic function
Answer:Get a quadratic function from its roots. Enter the roots and an additional point on the Graph. Mathepower finds the function and sketches the parabola.
Step-by-step explanation:Solve a quadratic equation using the quadratic formula.
Write the quadratic equation in standard form, ax2 + bx + c = 0. Identify the values of a, b, and c.
Write the Quadratic Formula. Then substitute in the values of a, b, and c.
Simplify.
Check the solutions.
amy has 3 pound of raisins she didvides the raisins equaly into 12 bags how much puonds of rasins are in each bag :show your work
Answer:
May will have 0.25 pounds per bag.Step-by-step explanation:
We know that
Amy has 3 pounds of raisins.She wants to divide it into 12 bags.To now how many pounds will be in each bag, we have to divide
[tex]3 \ lb \div12 \ bags =0.25 \ lb/bag[/tex]
This means that May will have 0.25 pounds per bag, that is, a quarter pound of raisin in each bag.
If we divide this using the long method, we would have to add a zero to "3", because 3 is less than 12, so we have to transform it from "3" to "30". To be able to do that, we have to add a decimal point to the quotient, and then continue with the division.
zero vertical asymptote removable discontinuity
A zero vertical asymptote removable discontinuity means that there is a zero of the function at the input value where the vertical asymptote would occur,
How to explain the termA zero of a function occurs when the value of the function is zero. A vertical asymptote of a function occurs when the value of the function becomes unbounded (either positive or negative) as the input approaches a certain value.
A removable discontinuity of a function occurs when there is a hole in the graph of the function at a certain input value, but the function can be made continuous at that point by defining its value at that input.
In the case of a zero vertical asymptote removable discontinuity, this means that there is a zero of the function at the input value where the vertical asymptote would occur, and the function can be made continuous at that input value by defining its value to be the value of the function at that input.
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george flips an unfair coin $7$ times. the coin has a $\frac{1}{4}$ probability of coming up heads and a $\frac{3}{4}$ probability of coming up tails. what is the probability that he flips exactly $2$ tails?
The probability of getting exactly 2 tails in 7 flips of a coin with a probability of tails being 3/4 is 189/16384 or approximately 0.0115.
We can use the binomial distribution formula to solve this problem. Let X be the number of tails that come up in 7 flips of the coin. Then X follows a binomial distribution with n = 7 and p = 3/4 (since the probability of tails is 3/4).
The probability of getting exactly 2 tails is given by:
P(X = 2) = (7 choose 2) * (3/4)^2 * (1/4)^5
= (21 * 9/16 * 1/1024)
= 189/16384
So the probability that George flips exactly 2 tails is 189/16384, or approximately 0.0115.
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Find the sum of and .2푥+1
Answer:
2*22/7/27+1
Step-by-step explanation:
2*22/7*27+1
2*(594+1)/7
2*595/7
2*85
170 ans..
the coefficient of variation is best described as . multiple choice a relative measure of dispersion a relative measure of central location an absolute measure of central location an absolute measure of dispersion
Measure of the dispersion of a dataset relative to its mean.
The coefficient of variation is best described as a relative measure of dispersion. It is a measure of the dispersion of a dataset relative to its mean.
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A student has a rectangular bedroom. If listed as ordered pairs, the corners of the bedroom are (21, 18), (21, −7), (−12, 18), and (−12, −7). What is the perimeter in feet?
116 feet
58 feet
33 feet
25 feet
The perimeter of the rectangular bedroom is 116 feet.
How to get the perimeter?We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:
d = √( (x₂ - x₁)² + (y₂ - y₁)²)
Here the corners of the room are at: (21, 18), (21, −7), (−12, −7) and (−12, 18)
Let's find the distances between these points:
d₁ = √( (21- 21)² + (18 + 7)²) = 25
d₂ = √( (21 + 12)² + (-7 + 7)²) = 33
d₃ = √( (-12 + 12)² + (-7 - 18)²) = 25
d₄ = = √( (-12 - 21)² + (-7 + 7)²) = 33
The perimeter is the sum of these distances so we will get:
d₁ + d₂ + d₃ + d₄ = 25 + 33 + 25 + 33 = 116
The correct option is the first one.
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A parking lot was full of different colored cars. There were 12 red cars, 15 blue cars, and 3 green cars. At this rate, how many blue cars will there be if there were 120 total cars?
Find the area of the figure.
7 cm
11 cm
8 cm
The area is ? square centimeters.
pls help I'll mark brainlisest
Answer:
Area of the figure=126.5cm²
Step-by-step explanation:
As we can see based on the shape of the figure, we can divide it into a;
→ Triangle
→ Rectangle
Formulas that we need are;
⇒ Area of triangle =1/2×base×height
⇒ Area of rectangle =length × width
Let's solve the area of the triangle first;
Area of triangle =1/2 × base × heightArea of triangle=1/2 × 11cm × 7cmArea of triangle=38.5cm²Then the area of the rectangle;
Area of rectangle =length × widthArea of rectangle =11cm × 8cmArea of rectangle =88cm²Finally, we add the triangle and rectangle together-
Area of Triangle + Area of Rectangle = 38.5cm²+88cm²
Area of the figure=126.5cm²
RevyBreeze
The triangle below is isosceles. Find the length of side
�
x in simplest radical form with a rational denominator.
The length of side x in simplest radical form with a rational denominator is equal to 4.472 units.
An isosceles triangle is a triangle with two equal sides. Also, the angles opposite to the two equal sides are also congruent.
According to Pythagoras' theorem, the square on the hypotenuse of a right-angled triangle equals the sum of the squares on the remaining two sides.
So, the length of other side is also equal to [tex]\sqrt{10}[/tex].
Now, lets use Pythagoras theorem to find the length of x.
Length of Hypotenuse is equal to [tex]\sqrt{y^2 + y^2}[/tex]
x = [tex]\sqrt{y^2 + y^2}[/tex]
x = [tex]\sqrt{\sqrt{10}^2+\sqrt{10 ^2} }[/tex]
x = [tex]\sqrt[2]{10+10}[/tex]
x = 4.472 units
Therefore, the length of side x in simplest radical form with a rational denominator is equal to 4.472 units.
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44.0183 rounded to the nearest thousands
5% of a number is 23
1% of the same number is 4. 6
work out 16 % of the number
16 percentage of the unknown number is 73.6
To solve the problem, we can use the relationship between percentages and multiply/divide by factors of 100.
Let's start by finding the whole number that corresponds to 1% of the unknown number
1% of the number = 4.6
100 times 1% of the number = 100 x 4.6
Whole number corresponding to the unknown number = 460
We can now use this value to find 5% of the unknown number:
5% of the number = 5/100 x the number = (5/100) × 460 = 23
So we have confirmed that the number we found is correct.
Finally, to find 16% of the number, we can use the same approach
16% of the number = 16/100 x the number = (16/100) × 460 = 73.6
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Lily has a box of candies.
5
6
of the candies are pink.
1
2
of the pink candies are round.
What fraction of the candies are pink and round?
Answer:
1/12
Step-by-step explanation:
Out of the total number of candies, 1/2 of the pink candies are round.
To find the fraction of the candies that are pink and round, we need to multiply the fractions representing the proportion of pink candies and the proportion of round candies among the pink candies:
pink candies = 5/6
round candies among the pink ones = 1/5
Therefore, the fraction of candies that are pink and round is:
(5/6) x (1/2) x 1/5 = 1/12
So, 1/12 of the candies are pink and round.
Which equation matches the hanger diagram?
Equations are collections of two or more statements with equal signs.
I must locate the solution that the hanger diagram matches. [tex]3x=4[/tex] is the equation that fits the hanger diagram. Thus, option C is correct.
What is a hanger diagram?The hanger shows a total weight of 7 units on one side that is balanced with 3 equal, unknown weights and a 1-unit weight on the other.
Two or more expressions containing equal signs are called equations. I need to find the equation that corresponds to the hanger diagram. The hanger model is a visual representation of the equation.
Both sides must have the same weight to keep the hanger balanced. Like scales and barbells. There are 3 x on the left side of the hanger and 4 x on the right side.
So [tex]3x=4[/tex] is an equation that satisfies the given trailer diagram.
So option C is correct. [tex]3x=4[/tex] is the equation that fits the hanger diagram.
From the diagram we have,
Left=x+x+x
Right [tex]=1+1+1+1[/tex]
This gives
Left=[tex]3x[/tex]
Right [tex]=4[/tex]
Therefore, the equation [tex]3x =4[/tex]
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A party tent is used for an outdoor event. Ropes of equal length support each tent pole. The angle each rope makes with the ground is 52°.
What is the height of each tent pole?
Therefore, the height of each tent pole is approximately 8.07 meters.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It is used to solve problems involving triangles, such as finding the length of a side or the measure of an angle. Trigonometry is based on the use of trigonometric functions, which are ratios of the sides of a right triangle.
Here,
We can use trigonometry to solve this problem. Let's call the height of the tent pole "h" and the length of the rope "r". Then, we can use the tangent function to find the height:
tan(52°) = h/r
Rearranging this equation, we get:
h = r * tan(52°)
We know that the length of each rope is equal, so we can choose any arbitrary length for r. For simplicity, let's assume that each rope is 10 meters long. Then, we can plug in the values into the equation:
h = 10 * tan(52°)
Using a calculator, we get:
h ≈ 8.07 meters
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why mean absolute deviation is a better approach to handle outliers in a data than standard deviation
Mean absolute deviation (MAD) is sometimes considered a better approach to handle outliers in a data set than standard deviation because it is less sensitive to extreme values.
The reason for this is that MAD uses absolute differences between each data point and the median of the data set, rather than the squared differences used by standard deviation.
In a data set with extreme values, such as outliers, the squared differences used by standard deviation can significantly inflate the value, leading to a higher estimate of the overall variability in the data. MAD, on the other hand, uses absolute differences, which are not affected by the sign of the difference and thus are less affected by extreme values. Therefore, MAD can be a better measure of variability in a data set that includes outliers.
However, it is important to note that MAD also has some limitations. It is less widely used and less familiar to many analysts than standard deviation, and it has a more complex formula that can be harder to interpret. Additionally, MAD is not as efficient as standard deviation when the underlying distribution is normal, meaning it requires a larger sample size to achieve the same level of precision as standard deviation. Ultimately, the choice between MAD and standard deviation depends on the specific characteristics of the data set and the goals of the analysis.
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Becky bought a bag of dog food costing $8.42. If Becky received $1.53 in change, how much money did she give to the cashier?
Answer:9.95
Step-by-step explanation:
Answer: 9.95
Step-by-step explanation:
8.42 +1.53=9.95
A club sponsor collects and analyzes data to estimate the number of students, y
, in attendance at a club meeting x
weeks after the start of the school year. The linear model y=11x+41
can be used to represent the data when x≥0
.
Which two best describe the value 41
?
Responses
change in number of students in attendance per week
change in number of students in attendance per week
initial number of students in attendance when x=0
initial number of students in attendance when x = 0
slope
slope
x
-intercept
x -intercept
y
-intercept
y -intercept
Since the linear model y = 11x + 41 can be used to represent the data when x≥0, the two statement which best describe the value 41 include the following:
B. initial number of students in attendance when x = 0.
E. y-intercept.
What is the slope-intercept form?In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represent the vertical intercept, y-intercept or initial number.Based on the information, an equation that models the line is given by this mathematical expression;
y = mx + c
y = 11x + 41
By comparison, we have the following:
mx = 11x
Slope, m = 11.
Initial number or y-intercept, c = 41.
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of a group of 200 workers, 15 are chosen to participate in a survey about the number of miles they drive to work each week
In this situation, the sample consists of the [ ]workers selected to participate in the survey.
the population consists of [ ] workers.
The sample consists of the 15 workers selected to participate in the survey.
The population consists of 200 workers.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Out of a group of 200 workers, 15 are chosen to participate in a survey about the number of Miles they drive to work each week.. In this situation the samples consist of the 15 workers selected to participate in the survey.The population consist of 200 workers
SAMPLE: This is a representative part of a population on which a research is about the population is administered
POPULATION: This is the large collection of people or objects that is the focus of a scientific query or research. Often times, the logistics involved in reaching the entire population may be unavailable, so a sample is taken
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triangle ABO has been rotated 80° about point O. Choose all statements that are true
Be aware that the other claims are untrue as 80 degrees is the angle B'OA and Triangles ABO and A'B'O are similar triangles are true .
what is triangle ?A closed triangle is a two-dimensional plane shape with three angles and three straight sides. Three non-collinear points are connected with straight line segments to create one of the fundamental shapes in geometry. The lengths of the sides can vary depending on the type of triangle, but the sum of the interior angles of a triangle is always 180 degrees. Triangles with all three sides equal, such as equilateral triangles, isosceles triangles, and scalene triangles, are examples of frequent triangle types (where no sides are equal).
given
According to the diagram, the following claims are accurate:
80 degrees is the angle B'OA.
Triangles ABO and A'B'O are similar triangles.
Angle A'B'O and angle ABO are equivalent.
Line segment AB and line segment A'B' are congruent.
Be aware that the other claims are untrue as 80 degrees is the angle B'OA and Triangles ABO and A'B'O are similar triangles are true .
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