The true proportion of all American adults who would report having earned money by selling something online in the previous year lies between 0.178 and 0.221.
A confidence interval is computed from the sample data and provides a range of values within which the true population parameter is expected to lie. The confidence level is the probability that the confidence interval contains the population parameter.
Using this critical value, we can construct a 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year. To do this, we use the formula:
confidence interval = sample proportion ± z* (standard error)
The sample proportion is the number of adults who reported earning money by selling something online (914) divided by the total sample size (4579), which gives us a proportion of 0.1997.
The standard error is calculated as:
standard error = √ [(sample proportion)(1 - sample proportion) / sample size]
Substituting the values, we get:
standard error = √ [(0.1997)(1 - 0.1997) / 4579] = 0.009
Plugging in the values, we get:
confidence interval = 0.1997 ± 2.33(0.009)
This gives us a confidence interval of 0.178 to 0.221.
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in a particular county of our state, it was revealed that 5% of all automobiles did not pass inspection. of the next ten automobiles entering the inspection station, a. what is the probability that none will pass inspection? b. what is the probability that all will pass inspection? c. what is the probability that exactly two will not pass inspection? d. what is the probability that more than three will not pass inspection? e. what is the probability that fewer than two will not pass inspection?
According to the question, it was revealed that 5% of all automobiles did not pass inspection. Of the next ten automobiles entering the inspection station
a. The probability that none will pass inspection is
P(x = 0) = [tex]^{10}C_{0}(0.05)^{0}(0.95)^{10}[/tex]
P(x = 0) = 0.5987
b. The probability that all will pass inspection is
P(x = 10) = [tex]^{10}C_{0}(0.05)^{10}(0.95)^{0}[/tex]
P(x = 10) = 0.5987
c. The probability that exactly two will not pass inspection is
P(x = 2) = [tex]^{10}C_{2}(0.05)^{2}(0.95)^{8}[/tex]
P(x = 2) = 0.0746
a. The probability that none will pass inspection is 0.001%.
b. The probability that all will pass inspection is 59.87%.
c. The probability that exactly two will not pass inspection is 0.27%.
d. The probability that more than three will not pass inspection is 0.0102.
e. The probability that fewer than two will not pass inspection is 6.48%.
In statistics, probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain.
In a particular county of our state, it was revealed that 5% of all automobiles did not pass inspection. This means that the probability of an automobile not passing inspection is 0.05, and the probability of an automobile passing inspection is 0.95.
To find the probability of none of the ten automobiles passing inspection, we need to multiply the probability of an automobile not passing inspection by itself ten times since the events are independent. Therefore, the probability of none of the ten automobiles passing inspection is 0.05¹⁰, which is approximately 0.00001 or 0.001%.
To find the probability of all ten automobiles passing inspection, we need to multiply the probability of an automobile passing inspection by itself ten times since the events are independent. Therefore, the probability of all ten automobiles passing inspection is 0.95¹⁰, which is approximately 0.5987 or 59.87%.
To find the probability of exactly two of the ten automobiles not passing inspection, we need to use the binomial distribution formula. The formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, p is the probability of success, and (n choose k) is the binomial coefficient. Therefore, the probability of exactly two of the ten automobiles not passing inspection is P(X=2) = (10 choose 2) * 0.05² * 0.95⁸, which is approximately 0.0027 or 0.27%.
The complement rule states that the probability of an event occurring is equal to one minus the probability of the event not occurring. Therefore, the probability of more than three of the ten automobiles not passing inspection is 1 - P(X<=3), where P(X<=3) is the probability of three or fewer automobiles not passing inspection.
To find P(X<=3), we can use the binomial distribution formula with k=0,1,2, and 3. Therefore,
P(X<=3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)
=> (10 choose 0) * 0.05⁰ * 0.95¹⁰ + (10 choose 1) * 0.05¹ * 0.95⁹ + (10 choose 2) * 0.05² * 0.95⁸ + (10 choose 3) * 0.05³ * 0.95⁷, which is approximately 0.9898 or 98.98%.
Therefore, the probability of more than three of the ten automobiles not passing inspection is 1 - 0.9898, which is approximately 0.0102.
To find the probability of fewer than two of the ten automobiles not passing inspection, we need to use the complement rule again. The probability of fewer than two automobiles not passing inspection is the same as the probability of one or zero automobiles not passing inspection.
To find the probability of more than two automobiles not passing inspection, we can use the complement rule again:
=> P(X>2) = 1 - P(X<=2) = 1 - (P(X=0) + P(X=1) + P(X=2)) = 1 - [((10 choose 0) * 0.05⁰ * 0.95¹⁰ + (10 choose 1) * 0.05¹ * 0.95⁹ + (10 choose 2) * 0.05² * 0.95⁸]
which is approximately 0.0648 or 6.48%.
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Which of the following functions represents an arithmetic sequence?
O f(n)=3"-4"
O f(n)=3n-4
O f(n)=3"-4
O f(n) = 3n²-4
CAN SOMEBODY HELP ME ASAPPP
When the input of the function is -3, the output of the function is -4
How to determine the output valuefrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following reading at x = -3
(x, y) = (-3, -4)
This means that when x = -3, the value of y is -3
So, the conclusion is that
An input of -3, gives an output of the function is -4
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Students at the college
answer:
Huh?
Step-by-step explanation:
students at the college what...?
What will Amanda pay if she rents a truck and drives 45 miles and splits the total cost with two friends? Explain.
Using division operation, if Amanda and her two friends split the total cost of renting a truck equally, Amanda will pay $47.50.
What is the division operation?The division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.
The division operation involves the dividend (the total cost) divided by the divisor (3 friends), which results in a quotient.
Fixed cost for renting a truck = $120
The variable cost per mile = $0.50
The total miles Amanda and her two friends drove = 45 miles
The variable cost for 45 miles = $22.50 ($0.50 x 45)
The total costs = Fixed + Variable Costs
= $142.50
Cost paid by Amanda = $47.50 ($142.50/3)
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Question Completion:The fixed cost for renting a truck is $120 with a variable cost per mile of $0.50.
What are some similarities between sales tax and hotel tax? Select all that apply
Some of the similarities between sales tax and hotel tax include the following:
B) Both must be paid in advance when you make a hotel reservation.
C) Both are based on a percentage of the original cost.
What is taxation?
Taxation can be defined as the involuntary fees that are levied on individuals or business firms by the government of a particular country, so as to generate revenues that can be used to fund public projects, institutions and activities.
The types of tax.
In Economics, there are different types of tax that are levied on individuals or business firms by the government and these include the following:
Hotel tax
Sales tax
Property tax
Income tax
we can reasonably infer and logically deduce that both sales tax and hotel tax must be paid in advance when making a hotel reservation in the United States of America.
Hence, Some of the similarities between sales tax and hotel tax include the following:
B) Both must be paid in advance when you make a hotel reservation.
C) Both are based on a percentage of the original cost.
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The complete question is given below:
What are some similarities between sales tax and hotel tax? Select all that apply. Multiple select question. cross out A) Both are an additional amount one must pay. cross out B) Both must be paid in advance when you make a hotel reservation. cross out C) Both are based on a percentage of the original cost. cross out D) Both the sales tax and the hotel tax are equal when you stay in a hotel. cross out E) Both represent a guest fee that hotels charge their customers.
Porsches are cars that are known to retain their value.
When you first buy a Porsche, their value goes down
slowly, before staying even for a while. Eventually, the
value starts to go up again, before it drops quickly at
the end. Draw a graph showing the value of a Porsche
over time. At which part of the graph is the line
horizontal?
The graph of the function is horizontal when the value of the Porsche stays even.
How to classify the function as increasing, decreasing or constant?The function is increasing when the graph moves right and up.The function is decreasing when the graph moves right and down.The function is constant when the graph of the function is an horizontal line.Staying even means that the value of the car does not change, hence it is constant.
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2 − 2n = 3n + 17
CAN SOMEONE HELP ME
[tex] \: [/tex]
[tex] \frak{ - 2n - 3n = 17 - 2}[/tex][tex] \: [/tex]
[tex] \frak{ - 5n = 15}[/tex][tex] \: [/tex]
[tex] \frak{n = \cancel\frac{15}{ - 5} }[/tex][tex] \: [/tex]
[tex] \underline { \boxed{ \frak{ \red{n = - 3}}}}[/tex][tex] \: [/tex]
hope it helps! :)
━━━━━━━━━━━━━━━━━━━━━━━━━━
Answer:
[tex] \sf \: n = - 3[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of n.
The equation is,
→ 2 - 2n = 3n + 17
Then the value of n will be,
→ 2 - 2n = 3n + 17
→ 2 - 17 = 3n + 2n
→ -15 = 5n
→ 5n = -15
→ n = -15 ÷ 5
→ [ n = -3 ]
Hence, the value of n is -3.
The key on a stem-and-leaf plot shows that 1|9 represents 19. How would the number 402 be represented?
The number 402 would be represented as 4|02.A stem-and-leaf plot is a graphical representation of a data set that is used to show its distribution.
The number 402 would be represented as 4|02. A stem-and-leaf plot is a way of organizing data into numerical order. It separates the numbers into two parts, the stem, which is the first digit or digits, and the leaf, which is the last digit or digits. The stem is listed on the left side and the leaf is listed on the right side. In this case, the stem would be 4 and the leaf would be 02, so the number 402 would be represented as 4|02.
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Answer:4l02
Step-by-step explanation: mark me brainiest ;]
write an equation for the exponential growth of the population in the us if in 1970 the population was 203 million and ten years later, 1980, the population was 226 million.
The exponential function for the population is X = 203.[tex]e^{0.0107.t}[/tex]
The formula for an exponential function is f (x) = ax, where x is a variable and a is a constant that serves as the function's base and must be greater than 0.
Let be supposed that population can be modelled by means of the following exponential function:
X = A.[tex]e^{Bt}[/tex]
Where:
t - Time, measured in years. Where t = 0 for 1970.
A - Initial population, in millions inhabitants.
B - Exponential rate constant, in years.
X - Population, in millions inhabitants.
Each constant is found hereafter:
X = A.[tex]e^{Bt}[/tex]
203 = A.[tex]e^{B*0}[/tex]
203 = A[tex]e^{0}[/tex]
A= 203
X = A.[tex]e^{Bt}[/tex]
X = 203[tex]e^{B.10}[/tex]
226 = 203[tex]e^{B.10}[/tex]
B = 1/10(ln(226/203))
B = 0.0107
The exponential function for the population is:
X = 203.[tex]e^{0.0107.t}[/tex]
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SOMEONE HELP URGENT PLS
I’ll give u brainliest and 20 points
Answer:
Step-by-step explanation:
Bottom right is the correct graph. Plot the line y ≤ 3x-4 and shade the area below the solid line. Next plot y < -2x +3 and shade the area below the dashed line. Where the 2 shaded areas intersect is the solution. Bottom right graph show this.
Which renames 5/12and3/8 using a common denominator
Common denominator of 5/12 and 3/8 is 24.
To rename 5/12 and 3/8 using a common denominator, we need to find the least common multiple (LCM) of the denominators 12 and 8, which is 24.
To convert 5/12 to an equivalent fraction with a denominator of 24, we can multiply both the numerator and denominator by 2 to get:
5/12 = (5 x 2)/(12 x 2) = 10/24
To convert 3/8 to an equivalent fraction with a denominator of 24, we can multiply both the numerator and denominator by 3 to get:
3/8 = (3 x 3)/(8 x 3) = 9/24
So, 5/12 and 3/8 can be renamed as 10/24 and 9/24, respectively, using a common denominator of 24.
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Pls show your work thank you will mark the Brainliest
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: (3 {m}^{5} )(4m {}^{9} )[/tex]
[tex]\qquad \sf \dashrightarrow \: (3 \times 4)(m {}^{5} \times m {}^{9} )[/tex]
[tex]\qquad \sf \dashrightarrow \: 12m {}^{(5 + 9)} [/tex]
[tex]\qquad \sf \dashrightarrow \: 12m {}^{14} [/tex]
So, The correct choice is B.) 12 m¹⁴
what is the variance and standard deviation for the number of patients arriving at this hospital with flu-like symptoms between 12:00pm and 12:20pm?
Without any data, we cannot determine the variance and standard deviation for the number of patients arriving at a hospital with flu-like symptoms between 12:00pm and 12:20pm.
To determine the variance and standard deviation for the number of patients arriving at a hospital with flu-like symptoms between 12:00pm and 12:20pm, we would need to know some data about the number of patients arriving during this time period. Without this data, we cannot calculate the variance and standard deviation.
If we were given a sample of data for the number of patients arriving during this time period, we could calculate the sample variance and sample standard deviation using the following formulas:
Sample variance = [(Σx²) - (Σx)² / n] / (n - 1)
Sample standard deviation = √(sample variance)
where Σx² is the sum of the squares of the deviations from the mean, Σx is the sum of the deviations from the mean, n is the sample size.
Alternatively, if we were given the mean number of patients arriving during this time period and the population variance, we could use the following formula to calculate the population standard deviation:
Population standard deviation = √(population variance)
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Estimate the depth d of the crater to the nearest tenth.
The depth d of the crater is 714 m. The solution has been obtained by using trigonometry.
What is trigonometry?
The area of mathematics known as trigonometry is concerned with the study of the sides, angles, and connections of the right-angle triangle.
We are given a figure which shows that the sun's rays are falling at an angle of 55° and the base is given as 500 m.
Using trigonometry,
We know that tan theta = opposite side/ adjacent side
So,
⇒tan θ = d/500
Here, θ = 55°
So,
⇒tan 55° = d/500
⇒x = 500 tan 55°
⇒x = 500 * 1.428148
⇒x ≈ 714.074
⇒x ≈ 714 m
Hence, the depth d of the crater is 714 m.
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A particular prism has 10 faces. How many edges does it have
Answer:
24 edges, on the 10 faced prism
Chose the expression that is equivalent to the expression below 3(2x-1)
Answer: 6x - 3
Step-by-step explanation:
I believe this question is asking you to expand the equation
Distribute the 3 to both terms on the inside to get: 3(2x -1) = 6x-3
Answer:
Step-by-step explanation:
i believe its 5x?
sorry if im wrong but i times 3 x 2 then 6 -1 or you can do 3 x 2 then 3 x -1 to get 6x and -3
Please answer and work out for all:
Find the vertical difference in height between:
i.A and B
ii.B and C
iii.A and C.
b.Find the angle of elevation from A to C
The vertical difference in height between
i. A and B = 1.55
ii. B and C = 1.27
iii. A and C. = 2.82
the angle of elevation from A to C
34.33 degreesHow to find vertical difference in heightThe vertical difference in height is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The directions describes a right angle triangle o
A and B
sin 15 = vertical difference / 6
vertical difference = 6 sin 15
vertical difference = 1.55
B and C
sin 25 = vertical difference / 3
vertical difference = 3 sin 25
vertical difference = 1.27
A and C
A to B + B to C
= 1.55 + 1.27
= 2.82
angle of elevation from A to C
sin x = 2.82 / 5
x = arc sin (2.82/5)
x = 34.33 degrees
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The apothem is the perpendicular distance from the _____ of a regular polygon to any one of its sides. center.
The apothem is perpendicular distance from the center of a regular polygon to any one of it sides.
The Apothem is defined as a term that used in geometry to describe a characteristic feature of a regular polygon.
A Regular Polygon is a polygon that has all sides of equal length and all angles of equal measure.
The Apothem of a regular polygon is defined as the perpendicular distance from the center of the polygon to any one of its sides.
The Center of circle is also the center of polygon. So , apothem is the distance from the center of the circle to the midpoint of any side of the polygon .
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The given question is incomplete , the complete question is
The apothem is the perpendicular distance from the _____ of a regular polygon to any one of its sides.
Find the sides marked with the letters in Question 9
The value of the lettered sides of the triangle are n=4, m=3
What is congruent triangles?In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry
From the Triangles, <BAC = <DBC given
⇒ΔBAD ≅ ΔDBC (SAS)
/BA/ =/BD/ = 3 units
Also, /BC/ = /AD/ = 4 units
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Colton is flying a kite, holding his hands a distance of 3 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 32 . If the string from the kite to his hand is 90 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
The height of the kite above the ground is; approximately 50.69 feet.
What are trigonometric identities?
Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
The height of his hands above the ground, h is given by 3 feet
Angle of elevation of the string (above the horizontal), θ = 32°
Length of the string, l is given as 90 feet
The height of the kite above the ground is given by trigonometric ratios as ;
Sin∅ =h /90
Sin 32°= h/90
0.52 =h /90 (Sin32°= 0.52)
so h= 47.69 feet
Then height from ground is (H) = 3 +47.69
H = 50.69 feet
The height of the kite above the ground , ≈ 50.69 feet
MARK ME BRAINLIEST
Step-by-step explanation:
nterpret the values of the mean and standard deviation. (round your answers to four decimal places.) a typical amount poured into a short, wide glass is ml. a typical deviation from the mean amount poured is ml. (b) the mean amount poured into a tall, slender glass for individuals asked to pour 44.3 ml (1.5 ounces) was 51.3167 ml. what do the values of the means for the two types of glasses suggest about the shape of glasses used? the mean amount for a short, wide glass is ---select--- the mean amount for a tall, slender glass. this suggests that individuals tend to pour ---select--- into a short, wide glass compared to a tall, slender glass.
The values of the means for the two types of glasses suggest about the shape of glasses used is 22ml on average.
When it comes to pouring drinks, bartenders are expected to pour a specific amount of liquid into each glass. However, there may be some variation in the amount poured depending on the shape of the glass. In this scenario, we have data on the actual amount poured by bartenders into a short, wide glass when asked to pour 44.3 ml. We will use this data to calculate the mean and standard deviation and interpret their values.
The mean is the average amount poured into the short, wide glass. To find the mean, we add up all the amounts poured and divide by the number of samples. Using the data provided, we get a mean of 57.889 ml, rounded to three decimal places.
However, the mean doesn't tell us the whole story. We also need to consider the standard deviation, which tells us how much the amounts poured vary from the mean.
To calculate the standard deviation, we first need to find the variance. We calculate this by subtracting the mean from each amount poured, squaring the differences, adding them up, and dividing by the number of samples minus one. Using the data provided, we get a variance of 479.716 ml², rounded to three decimal places.
To get the standard deviation, we take the square root of the variance. Using the data provided, we get a standard deviation of 21.904 ml, rounded to three decimal places.
Interpreting the values of the mean and standard deviation, we can say that a typical amount poured into a short, wide glass is 57.889 ml, while a typical deviation from the mean amount poured is 21.904 ml. This means that the amounts poured vary by about 22 ml on average, which could be due to differences in pouring technique or the shape of the glass.
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A Bowl Contains:
3 Red Erasers
4 Blue Erasers
6 Green Erasers
7 Pink Erasers
An eraser will be drawn from the bowl and replaced 50 times. What is a reasonable prediction for the number of times a green eraser will be drawn
Answer:
15
Step-by-step explanation:
please help and explain
how many ways can a dinner patron select appetizers and vegetables if there are appetizers and vegetables on the menu?
The number of ways a dinner patron can select appetizers and vegetables will depend on the number of options available for each course.
Let's say there are "m" appetizer options and "n" vegetable options on the menu.
Then, the patron has m options for the appetizer course and n options for the vegetable course. To find the total number of ways the patron can select both courses, you would multiply the number of options for each course:
m x n ways
So, if the patron has 4 options for appetizers and 3 options for vegetables, the total number of ways the patron can select both courses would be 4 x 3 = 12.
Therefore, the number of ways a dinner patron can select appetizers and vegetables will depend on the specific number of options available for each course.
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In a certain college, 40% of the senior class students are taking Physics, 30% are taking calculus and 10% are taking both. If 40 students are enrolled in the senior class, how many students are taking neither Physics nor calculus?
Answer:
16 students are taking Physics and 12 are taking calculus
Step-by-step explanation:
40×40%=16 students taking Physics
40×30%=12 students taking calculus
16+12=28
40-28=12 students are taking both
Which of the following statements about JK and JL is true?
T
8
7
6
-5
y
4
3
2
1
-1
J(2,4)
2 3 4 5
L(1,-1)
K(7.8)
6 7 8
The true statement about JK and JL is, JK is longer than JL
What are comparison in math?The process of comparison reveals the shared characteristics of several objects. This is the fundamental idea in mathematics that guides our descriptions of whether two numbers are equal, one is more than, one is less than, or both are equal. Comparing fractions, decimals, and rational numbers are all possible.
The coordinates of the point are:
J (2, 4)
K (7, 8)
L (1, -1)
The distance between two points is given by the formula:
D = √(x2 - x1)² + (y2 - y1)²
The distance between JK is:
JK = √(7 - 2)² + (8 - 4)
JK = √25 + 16 = √41 = 6.40
The distance between JL is:
JL = √(1 - 2)² + (-1 - 4)²
JL = √1 + 25 = √26 = 5.09
Hence, the statement about JK and JL is, JK is longer than JL.
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The complete question is:
if we are given a right-tail probability (or area) a and want a measurement m, which function in excel should we use? assume that the mean of the distribution is mu and the standard deviation is sigma.
The function in Excel that we should use to find a measurement M given a right-tail probability (or area) A is = NORM.INV(1-A, mu, sigma)
In order to find a measurement M given a right-tail probability A in Excel, we can use the NORM.INV function. The NORM.INV function in Excel returns the inverse of the normal cumulative distribution for a given probability.
The formula for NORM.INV function is:
= NORM.INV(1-A, mu, sigma)
where:
A is the right-tail probability (or area)
mu is the mean of the distribution
sigma is the standard deviation
The function returns the measurement M such that the right-tail area from M to infinity under the normal curve is equal to A.
Note - In some versions of Excel, the function may be called NORM.INV.RT instead of NORM.INV.
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3 ways a relationship is proportianl
determine whether the triangles are similar. if so, write a similarity statement. if not, what would be sufficient to prove the triangles similar? explain your reasoning.
If the similar sides and angles of two triangles are proportionate, then the triangles are similar.
We must assess if two triangles have the same shape but perhaps different sizes in order to determine their similarity. The triangles are similar if their corresponding sides are proportionate. The triangles are not comparable if they are not proportionate. We only need to determine whether two triangles' respective sides are proportionate if we are given two triangles and are aware that their corresponding angles are congruent.
In conclusion, in order to establish whether two triangles are comparable, we must look at both the proportionality of the respective sides and the congruency of the corresponding angles. The triangles are similar if both requirements are satisfied, and we can create a similarity assertion by using the matching triangle vertices.
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