assume the average speed on the 405 freeway is 50 mph and is normally distributed with a standard deviation of 12 mph. what is the probability that someone is driving slower than 35 mph?
The given information indicates that the average speed on the 405 freeway follows a normal distribution with a mean of 50 mph and a standard deviation of 12 mph. To find the probability that someone is driving slower than 35 mph, we need to calculate the deviation from the mean using the z-score formula:
z = (x - μ) / σ
where x is the value we are interested in (35 mph), μ is the mean (50 mph), and σ is the standard deviation (12 mph).
z = (35 - 50) / 12
z = -1.25
Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than -1.25. The probability is approximately 0.1056 or 10.56%.
Therefore, the probability that someone is driving slower than 35 mph on the 405 freeway is about 10.56%.
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A sphere of radius 0.62 inches, a 1 inch cube, and a 1×0.5×2 inch box all have a volume of approximately 1 cubic inch. Given that the surface area of a sphere with radius r is 4πr2, rank these objects, from highest to lowest, based on their surface area to volume ratios.
Answer:
good morning is that has to go to the one that has to be done by the time to khow hasgot is a good idea to go
Step-by-step explanation:
Rhodes college football and I will be done by then to khow hasgot and I will send it out to me and decor is he still in the one I will send you the election results and
The ranking from highest to lowest surface area to volume ratio is: 1. Sphere 2. Box 3. Cube.
To rank the objects based on their surface area to volume ratios, we need to compare the ratios of surface area to volume for each object. Let's start with the sphere. The surface area of a sphere with radius r is given by the formula 4πr².
In this case, the radius is 0.62 inches. Therefore, the surface area of the sphere is approximately 4π(0.62)² square inches. The volume of the sphere is given by the formula (4/3)πr³.
Substituting the radius of 0.62 inches, we find that the volume of the sphere is approximately (4/3)π(0.62)³ cubic inches.
To calculate the surface area to volume ratio, we divide the surface area by the volume. In this case, we have (4π(0.62)^2) / [(4/3)π(0.62)^3] = 3 / 0.62. Next, let's consider the cube.
The surface area of a cube with side length s is given by the formula 6s²
In this case, the side length is 1 inch. Therefore, the surface area of the cube is 6(1)² square inches. The volume of the cube is given by the formula s³
Substituting the side length of 1 inch, we find that the volume of the cube is 1³ cubic inch. Dividing the surface area by the volume, we have (6(1)²) / 1 = 6.
Finally, let's look at the box. The surface area of a box with dimensions length, width, and height is given by the formula 2(length × width + width × height + height × length). In this case, the dimensions are 1 inch, 0.5 inch, and 2 inches respectively. Therefore, the surface area of the box is 2(1 × 0.5 + 0.5 × 2 + 2 × 1) square inches. The volume of the box is given by the formula length × width × height. Substituting the dimensions, we find that the volume of the box is 1 × 0.5 × 2 cubic inches. Dividing the surface area by the volume, we have [2(1 × 0.5 + 0.5 × 2 + 2 × 1)] / (1 × 0.5 × 2).
Comparing the surface area to volume ratios, we find that the sphere has the highest ratio, followed by the box, and then the cube. So, the ranking from highest to lowest surface area to volume ratio is: 1. Sphere 2. Box 3. Cube
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a(n) select is a basic statistical tool that graphically shows the frequency or number of observations of a particular value or within a specified group.
A histogram is a basic statistical tool that graphically shows the frequency or number of observations of a particular value or within a specified group.
A histogram is a chart that displays data by dividing it into intervals, or "bins," and then counting how many data points fall into each bin. The x-axis of a histogram represents the range of values being analyzed, while the y-axis represents the frequency or count of values that fall within each bin.
Histograms are commonly used to illustrate the distribution of data. They provide a visual representation of the central tendency, variability, and shape of the data. In particular, histograms can reveal patterns in the data such as skewness, outliers, or gaps.
Histograms are frequently used in data analysis across many fields, including finance, biology, psychology, and engineering. They can be created using software programs such as Microsoft Excel, R, Python, or MATLAB.
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The given question is incomplete, the complete question is:
A(n)______ is a basic statistical tool that graphically shows the frequency or number of observations of a particular value or within a specified group
The midpoint of XY is (3,-5). Find the coordinates of point X. Y=(2.5,-6.5)
Answer:
x=(2,-5.3)
Step-by-step explanation:
Hope this helps
Sage needs 2 boards to make a shelf. One board is 260 cm long and the other is 1 1/4 m long. What is the total length of the shelf?
Answer:
385
Step-by-step explanation:
1 1/4 meters = 125 cm
125+260 = 385
Answer:
sum = 260 + 270 = 535 cm or = 5,35 m
Step-by-step explanation: take 11/4m = 2,75m * 100 = 275 cm
What is the equation of the line that passes through the point (-6,2)(−6,2) and has a slope of -3/2?
Given:
A line passes through the point (-6,2) and has a slope of \(-\dfrac{3}{2}\).
To find:
The equation of line.
Solution:
If a line passes though a point \((x_1,y_1)\) and has a slope m, then the equation of line is
\(y-y_1=m(x-x_1)\)
The line passes through the point (-6,2) and has a slope of \(-\dfrac{3}{2}\). So, the equation of line is
\(y-2=-\dfrac{3}{2}(x-(-6))\)
\(y-2=-\dfrac{3}{2}(x+6)\)
\(y-2=-\dfrac{3}{2}(x)-\dfrac{3}{2}(6)\)
\(y-2=-\dfrac{3}{2}(x)-9\)
Add 2 on both sides.
\(y=-\dfrac{3}{2}(x)-9+2\)
\(y=-\dfrac{3}{2}x-7\)
Therefore, the equation of line is \(y=-\dfrac{3}{2}x-7\).
find the area of the region bounded. y the curve y=f(x)=x^3-4x 1 and the tangent line to the curve y=f(x) at (-1,4)
Therefore, the area of the region bounded by the curve \(y = f(x) = x^3 - 4x + 1\) and the tangent line y = -x + 3 at (-1,4) is -3/4 square units.
To find the area of the region bounded by the curve \(y = f(x) = x^3 - 4x + 1\) and the tangent line to the curve at (-1,4), we need to determine the points of intersection between the curve and the tangent line.
First, let's find the equation of the tangent line. The tangent line at (-1,4) has the same slope as the derivative of f(x) at x = -1. Let's find this derivative: \(f'(x) = 3x^2 - 4\).
Evaluating the derivative at x = -1:
\(f'(-1) = 3(-1)^2 - 4 = 3 - 4 = -1.\).
Therefore, the slope of the tangent line is -1.
Using the point-slope form of a line, the equation of the tangent line is: y - 4 = -1(x + 1).
Simplifying, we get: y = -x + 3.
Next, we find the points of intersection by setting the curve equation and the tangent line equation equal to each other: \(x^3 - 4x + 1 = -x + 3\).
Rearranging and simplifying, we get:\(x^3 - 3x + 2 = 0\).
Factoring the equation, we find that x = -1 is a root: \((x + 1)(x^2 - x + 2) = 0\)
The quadratic term \(x^2 - x + 2\) has no real roots, so the only intersection point is (-1, 4).
Now, we can find the area of the region bounded by the curve and the tangent line by calculating the definite integral of the positive difference between the curve and the line over the interval from x = -1 to x = 0:
Area = ∫[-1,0] [f(x) - (-x + 3)] dx.
Let's find this integral:
Area = ∫[-1,0] (\(x^3 - 4x + 1 + x - 3\)) dx = ∫[-1,0] (\(x^3 - 3x - 2\)) dx.
Integrating term by term:
\(Area = [\frac{1}{4} x^4 - \frac{3}{2} x^2 - 2x] |[-1,0]\)
\(= [\frac{1}{4} (0)^4 - \frac{3}{2} (0)^2 - 2(0)] - [\frac{1}{4} (-1)^4 - \frac{3}{2} (-1)^2 - 2(-1)]\)
\(= 0 - [\frac{-1}{4} - \frac{3}{2} + 2]\)
\(= -\frac{1}{4} + \frac{3}{2} - 2\)
\(= -\frac{1}{4} + \frac{6}{4} - \frac{8}{4}\)
\(= -\frac{3}{4}\)
Therefore, the area of the region bounded by the curve \(y = f(x) = x^3 - 4x + 1\) and the tangent line y = -x + 3 at (-1,4) is -3/4 square units.
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-a2 - 2bc -lcl if a = -3, h = -5,
and c = 2
Answer:
24
plss mark me brainliesttt
Step-by-step explanation:
6+20-2
26-2
24
Find the largest six digits number which is divisible by 120 exactly.
Answer:
999,960
Step-by-step explanation:
let x be a multiple of 120
120x ≤ 999,999
999,999 / 120 = 8333.325
8333 ≤ x ≤ 8334
8333(120) = 999,960
8334(1200) = 1,000,080 this is a 7-digit number
Therefore, the largest 6-digit number that is exactly divisible by 120 is 999,960
PLz help :( i will mark barinliest
which best describes the meaning of the word theorem
A. A conjecture based on inductive reasoning
B. A statement that is accepted as true without proof
C. a statement explaining the meaning of a geometric term
D. A conclusion proved by deductive reasoning
Answer:
Step-by-step explanation:
It's D.
A theorem is true by some sort of mathematical logic.
It is not a definition. Not C
It is not in the end true because of inductive reasoning (a theorem may lend itself to inductive reasoning, but it must be proved.) Not A
It certainly not assumed to be true without proof. Not B
The population of fruit flies tripled every day and the population today is 200 fruit flies.
a) Write an equation modeling the growth in the population of fruit flies.
b) What was the population of fruit flies 3 days ago?
Answer:
Equation = 600nNumber of fruit flies after 3 days = 1800 fruit fliesStep-by-step explanation:
Given:
Number of fruit flies = 200
Rate of growth = 3 times per day
Find:
A . Equation
B . Number of fruit flies after 3 days
Computation:
A . Equation = 3n(200)
Equation = 600n
B. Number of fruit flies after 3 days
Number of fruit flies after 3 days = 600(3).
Number of fruit flies after 3 days = 1800 fruit flies
Graph the system of equations. y = 2x y = –x + 6 Two lines on a coordinate plane that intersect at the point 2 comma 4. One line has y intercept 0 and the other has y intercept 6. Two lines on a coordinate plane that intersect at the point negative 2 comma negative 4. One line has y intercept 0 and the other has y intercept negative 6. Two lines on a coordinate plane that intersect at the point 1 comma 2. One line has y intercept 0 and the other has y intercept 3. Two lines on a coordinate plane that intersect at the point 3 comma 3. One line has y intercept 0 and the other has y intercept 6.
The solution to the systems of equations graphically is (2, 4)
Solving the systems of equations graphicallyFrom the question, we have the following parameters that can be used in our computation:
y = 2x
y = -x + 6
Next, we plot the graph of the system of the equations
See attachment for the graph
From the graph, we have solution to the system to be the point of intersection of the lines
This points are located at (2, 4)
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Will make brainiest if 2 people answer :3
Answer:
1.6
Step-by-step explanation:
12.8/8 = 1.6
15.2/9.5 = 1.6
Scale factor = 1.6
what is the answer to this
\(72 \div 9\)
Suppose the linear regression line y=-0.3x+11.2 predicts the time, in minutes, it takes you to finish an obstacles course after training for x days. About how much time would it take you to finish the course after training for 5 days.
SOLUTION
From the equation, to find the time in minutes which is y, we plugging 5 (from 5 days) for x into the equation, we have
\(\begin{gathered} y=-0.3x+11.2 \\ y=-0.3(5)+11.2 \\ y=-1.5+11.2 \\ y=9.7\text{ minutes } \end{gathered}\)Hence the answer is option B
i begg someone just please helppp
Answer:
#4.
- 3 < - 2 1/2
If you consider the number line, the numbers increase from left to right. The number on the left is smaller than a number on the right.
- 3 is smaller than -2 1/2, it means -3 is on the left from the -2 1/2 on the number line.
#5.
Jada's score is positive, it means the number reflecting the score is to the right from zero on the number line.
Isabel's score is negative, it means the number reflecting the score is to the left from zero on the number line.
Since Isabel's score is to the left from the Jada's score, she has lower score than Jada.
With the lowest score, Isabel is the winner.
y = -63 y = 8x + 6
Use Substitution to solve
9514 1404 393
Answer:
(x, y) = (-8.625, -63)
Step-by-step explanation:
Substitute for y.
-63 = 8x +6
-69 = 8x . . . . . subtract 6
-69/8 = x = -8.625
The solution is (x, y) = (-8.625, -63).
PLEASEE HELP.!! ILL GIVE BRAINLIEST.!! *EXTRA POINTS* DONT SKIP:((
Answer:
2/3
Step-by-step explanation:
simplify below these questions
rule: little x means times not the other way round
A: 3X^2Y^4 x 2X^6Y
B: XZ^3 x 4X^4Z^5
C: 4A^3^2 x 3A^6B^5
D: 6S^5T x S^4T^2
A: \(3x^2y^4\cdot2x^6y=6x^8y^5\)
B: \(xz^3\cdot4x^4z^5=4x^5z^8\)
C: \(4a^3^2\cdot 3a^6b^5=12a^{15}b^5\)
D: \(6s^{5t}\cdot s^{4t}^2=6s^{16t^2+5t}\)
There was some ambiguity you posed with such exponents but I assumed strictly.
Hope this helps.
Define a relation ~ on R' by stating that (a, b) ~ (c, d) if and only if a3+ b' transitive but not symmetric.
A relation ~ on R' is defined as a relation where (a,b) ~ (c,d) if and only if a3+b3=c3+d3. This relation is transitive but not symmetric.
Transitivity of the relation states that if (a, b) ~ (c,d) and (c, d) ~ (e, f) then (a, b) ~ (e, f). This means that if a3+b3=c3+d3 and c3+d3=e3+f3 then a3+b3=e3+f3, thus, the relation is transitive.
Symmetry of the relation means that if (a, b) ~ (c, d) then (c, d) ~ (a, b). This, however, does not hold in this relation since it is possible for a3+b3=c3+d3 and yet c3+d3≠a3+b3. For example, (1,2) ~ (8,4), this is true since 13+23=83+43, however, this does not mean that (8,4) ~ (1,2) since 83+43≠13+23. Therefore, this relation is not symmetric.
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Can someone please help me ASAP?? It’s due today!! I will give brainliest If It’s correct.
The correct option that indicates how Christa sliced the rectangular pyramid is the second option.
Christa sliced the pyramid perpendicular to its base through two edges.
What is a rectangular pyramid?A rectangular pyramid is a pyramid with a rectangular base and four triangular faces.
The height of the cross section indicates that the location where Christa sliced the shape is lower than the apex of the pyramid.
The trapezoid shape of the cross section of the pyramid indicates that the top and base of the cross section are parallel, indicating that Christa sliced the pyramid parallel to a side of the base of the pyramid, such that it intersects two of the edges of the pyramid
The correct option is therefore the second option;
Christa sliced the pyramid perpendicular to its base through two edges
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5. MaryAnne painted 600 square feet of wall space using 1 1/2gallons of paint. The number of
square feet she can paint, y, is proportional to the number of gallons used, x.
k=
Equation:
The equation that represents the relationship between the number of square feet painted (y) and the number of gallons of paint used (x) can be expressed as follows:
\(\displaystyle\sf y = kx\),
where \(\displaystyle\sf k\) represents the constant of proportionality.
In this specific scenario, MaryAnne painted 600 square feet of wall space using 1 1/2 gallons of paint. To find the value of \(\displaystyle\sf k\), we can substitute the given values into the equation:
\(\displaystyle\sf 600 = k \cdot \left( \frac{3}{2} \right)\).
To solve for \(\displaystyle\sf k\), we can multiply both sides of the equation by \(\displaystyle\sf \frac{2}{3}\):
\(\displaystyle\sf \frac{2}{3} \cdot 600 = k\),
\(\displaystyle\sf k = 400\).
Therefore, the equation representing the relationship between the number of square feet painted (y) and the number of gallons of paint used (x) is:
\(\displaystyle\sf y = 400x\).
Determine Whether 5c/15c^2 +7d is a polynomial. If it is a polynomial, state the degree of the polynomial
As the size of the sample increases, what happens to the shape of the sampling distribution of sample means
As the size of the sample increases, the sampling distribution of sample means becomes more normally distributed.
What happens to the shape of the sampling distribution of sample means if sample size increases?The Central Limit Theorem (CLT) states that as the sample size increases, the distribution of sample means will become more normally distributed regardless of the shape of the population distribution.
As long as the sample size is sufficiently large (usually greater than 30).
This means that the mean and standard deviation of the sampling distribution of sample means will approach the mean and standard deviation of the population distribution.
In other words, when the sample size is small, the sampling distribution may not follow a normal distribution and may be skewed.
However, as the sample size increases, the effect of the individual observations' randomness on the mean becomes smaller.
Consequently, the distribution of sample means becomes more symmetrical and follows a normal distribution.
Thus, the larger the sample size, the more reliable the estimate of the population mean becomes, and the more likely the distribution of sample means will be normally distributed.
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Lakesha is taking three of her friends to see the latest movie. Each ticket is $5.50, and she is paying for all four tickets. How much money does Lakesha need to bring to pay for all of the tickets? A. $16.50 B. $22.00 C. $49.50 D. $55.00
Answer: $22
Step-by-step explanation:
$5.50 * 4 = 22
Answer:
B. $22.00
Step-by-step explanation:
The expression you need to set up is 5.5 times 4, since she needs to pay 4 tickets and each is $5.50. After you multiply, you should get 22, which is the answer.
let a and b be positive integers. 23^a x 23^b
Answer:
23 ^ ( a+b)
Step-by-step explanation:
23^a *23^b
Since the bases are the same, we can add the exponents
23 ^ ( a+b)
Answer:
23^(a+b)
Step-by-step explanation:
A^x*A^y = A^(x+y)
you can think of it like this
A^x = A*A*A*.......*A x times
A^y = A*A*A*....*A y times
therefore A^x * A^y = A*A*A*...*A (x+y) times
=A^(x+y),
so in our case A = 23, and x and y were a and b, so 23^a * 23^b = 23^(a+b)
Each week coaches in a certain football league face a decision during the game. On fourth-down, should the team punt the ball or go for a first-down? To aid in the decision-making process, statisticians at a particular university developed a regression model for predicting the number of points scored (y) by a team that has a first-down with a given number of yards (x) from the opposing goal line. One of the models fit to data collected on five league teams from a recent season was the simple linear regression model, E(Y) = Bo +Byx. The regression yielded the following results: ģ=5.19 – 0.49x, r2 = 0.11. Complete parts a and b below. a. Give a practical interpretation of the coefficient of determination, r2. Choose the correct answer below. A. There is a positive linear relationship between numbers of yards to the opposing goal line and numbers of points scored because 0.11 is positive. B. Sample variations in the numbers of yards to the opposing goal line explain 11% of the sample variation in the numbers of points scored using the least squares line. C. There is little or no relationship between numbers of yards to the opposing goal line and numbers of points scored because 0.11 is near to zero. D. Sample variations in the numbers of yards to the opposing goal line explain 89% of the sample variation in the numbers of points scored using the least squares line. b. Compute the value of the coefficient ofcorrelation, r, from the value of r squared. Is the value of r positive or negative? Why? Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) A. The coefficient of correlation, r = ------, is negative because the estimator of 161 is positive. B. The coefficient of correlation, r = -------, is positive because the estimator of 1B1 is positive. C. The coefficient of correlation, r = -----, is positive because the estimator of 1B1 is negative. D. The coefficient of correlation, r = is negative because the estimator of 181 is negative.
A. The correct option for the first question is option B. Sample variations in the numbers of yards to the opposing goal line explain 11% of the sample variation in the numbers of points scored using the least squares line.
b. The coefficient of correlation, r, can be calculated as the square root of r². Using the formula:r² = 0.11, hence r = √0.11= 0.331. The value of r is positive since it is the square root of r², which is positive. Therefore, the correct option is B. The coefficient of correlation, r = 0.331, is positive because the estimator of 1B1 is positive.
(a) The coefficient of determination, r^2, represents the proportion of the sample variation in the response variable (number of points scored) that can be explained by the variation in the predictor variable (number of yards to the opposing goal line) using the least squares line. In this case, r^2 is equal to 0.11.
The correct interpretation is:
B. Sample variations in the numbers of yards to the opposing goal line explain 11% of the sample variation in the numbers of points scored using the least squares line.
This means that approximately 11% of the variability in the points scored by a team can be attributed to the variability in the number of yards to the opposing goal line. The remaining 89% of the variability is due to other factors not accounted for by the linear regression model.
(b) The coefficient of correlation, r, can be obtained by taking the square root of the coefficient of determination, r^2. Since r^2 is given as 0.11, we can calculate r as follows:
r = sqrt(r^2) = sqrt(0.11) ≈ 0.332
The value of r is positive because the square root of a positive number is always positive. A positive value of r indicates a positive linear relationship between the number of yards to the opposing goal line and the number of points scored.
It suggests that as the number of yards to the opposing goal line decreases, the number of points scored tends to increase.
In summary, the coefficient of determination (r^2) tells us the proportion of the sample variation in points scored that can be explained by the variation in yards to the opposing goal line. In this case, it is approximately 11%.
The coefficient of correlation (r) is the square root of r^2 and measures the strength and direction of the linear relationship between the variables. In this case, r is approximately 0.332, indicating a positive relationship between yards and points.
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How is the number of Electoral College seats per state determined? A. by the number of party delegates assigned to the state B. by the total number of
Each state is given a specific amount of "votes" under the "Electoral College" system. The amount of "votes" each state receives is proportionate to its size.
What is the makeup of the Electoral College? There are 538 electors in all. The number of electors allotted to each state is equal to the sum of its two Senate seats plus the number of representatives in the House of Representatives.Three electoral votes are granted to the District of Columbia under the 23rd Amendment. According to the amount of each State's population as established by the Census, each State is given a certain number of electors equal to the sum of its U.S. Senators (which are always two) and U.S. Representatives.There are two steps involved in selecting each State's electors. The political parties in each State first select elector candidate slates before the general election. Second, during the general election, each State's voters choose its electors by voting ballots.To learn more about Electoral College refer to :
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HELPPPP ITS ON ORDERED PAIRSS AND THE ANSWER IS NOT B ACCORDING TO MY TEACHER
Explanation needed
Answer:
C
Step-by-step explanation:
B and D have repeat x values , which do not make functions.
Linear means goes in the same direction
A starts big gets smaller and then gets bigger
C starts big and keeps getting bigger. This is a linear function
Answer:
C.
Step-by-step explanation:
It isn't B because that is a vertical line x = 1 which is not a linear function. A linear function is of the form y = mx + b where m = slope and b = y-intercept.
To check for a linear function we find the slopes between adjacent points. If the slope is constant between each pair of points then it's linear.
A:
slope = (4 - 8) / (0 - -2) = -4/2 = -2.
(3 - 4) / (2 - 0) = -1/2
So its not A.
C. (12-7)/(0--2) = 5/2
(17-12)/(2-0) = 5/2
(22-17)/(4-2) = 5/2
This is a line of slope 5/2
This is a linear function.
C is the centroid of isosceles triangle ABD with vertex angle ∠ABD. Does the following proof correctly justify that triangles ABE and DBE are congruent?
It is given that triangle ABD is isosceles, so segment AB is congruent to DB by the definition of isosceles triangle.
Triangles ABE and DBE share side BE, so it is congruent to itself by the reflexive property.
It is given that C is the centroid of triangle ABD, so segment BE is a perpendicular bisector.
E is a midpoint, creating congruent segments AE and DE, by the definition of midpoint.
Triangles ABE and DBE are congruent by the SSS Postulate.
Triangle ABD with segments BC, DC, and AC drawn from each vertex and meeting at point C inside triangle ABD, segment BC is extended past C with dashed lines so that it intersects with side AD at point E.
There is an error in line 1; segments AB and BC are congruent.
There is an error in line 2; segment BE is not a shared side.
There is an error in line 3; segment BE should be a median.
The proof is correct
The proof does correctly justify that triangles ABE and DBE are congruent. The correct answer is the fourth option.
As we know that an isosceles triangle is one having two sides of the same length. The third side of an isosceles triangle that is not identical to the other two sides is referred to as the base. The two angles opposite the equal sides are the same.
AB and BD are congruent since triangle ABD is isosceles.
AB = BD
Here, C is the circumcenter.
Segment BE is a perpendicular bisector. However, the correct statement should be that segment BE is a median since C is the centroid.
So, BE bisect ∠ABD and AE = ED
So, BE ⊥ AD
Because BE = BE, and AB = BD
So, ΔABE ≅ ΔDBE
Thus, the proof is correct.
Hence, the correct answer is the fourth option.
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