The p-value is less than a chosen significance level (alpha), such as 0.05, we reject the null hypothesis and conclude that there is evidence that the proportion of adults who would respond "yes" to the question changed from December 2007 to December 2008. Otherwise, we fail to reject the null hypothesis.
It is important to note that the sample size and the significance level used to calculate the p-value can affect the result of the test. Additionally, it's important to consider other factors that may have affected the results, such as economic conditions or media coverage.
Hypothesis Test Proportion ChangeTo determine if the proportion of adults in the United States who would respond "yes" to the question changed from December 2007 to December 2008, we need to perform a hypothesis test. The null hypothesis is that the proportion of adults who would respond "yes" to the question did not change from December 2007 to December 2008, and the alternative hypothesis is that the proportion of adults who would respond "yes" to the question did change.
One way to perform the hypothesis test is by using a two-sample proportion test. The test statistic is calculated as:
(p1 - p2) = (676/1009 - 622/1020) = 0.0548
where p1 is the proportion of adults who responded "yes" in December 2008 and p2 is the proportion of adults who responded "yes" in December 2007.
Then, we need to find the p-value for the test statistic, which represents the probability of observing a test statistic as extreme or more extreme than the one calculated if the null hypothesis is true.
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Solve the radical equation.
Check all solutions to eliminate extraneous solutions
and do not include them in your answer.
If your answer is not an integer then type it as a
decimal rounded to the nearest hundredth.
√2x+3-√x+2=0
x=
Check
There doesn't exist any extraneous solution for the given problem.
To assess whether or not your solutions are unnecessary, you must re-enter each one into the original equation.
When you square the two sides of a square root problem, there are two solutions, which leads to the appearance of extraneous solutions (the positive and negative number).
A solution that is added but does not fulfill the starting equation will therefore be represented by one of those figures.
Given, the equation is -
√2x+3-√x+2=0
⇒ √2x+3 = √x+2
Squaring on both sides
⇒ 2x + 3 = x + 2
⇒ 2x - x = 2 - 3
⇒ x = -1
Now, putting x = -1 back in the question,
⇒ √1 = √1
Hence, LHS = RHS, therefore, there doesn't exist any extraneous solution.
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bill invested some money at 5% annual interest, and Janette invested some at 7%. If thier combined interest was $310 on a total investment of 5,000, how much did bill invest?
Bill invested $2000 at 5% annual interest
How to determine how much Bill invested?
To solve for the word problem, you need to set up two equations.
Let B and J represent how much Bill and Janette invested respectively
The interest of 5% = 5/100 = 0.05 and 7% = 7/100 = 0.07
Based on the given info, we can write that:
J + B = 5000 --- (1)
0.05B + 0.07J= 310 --- (2)
From (1):
J = 5000 - B --- (3)
Put (3) in (2):
0.05B + 0.07(5000 - B) = 310
0.05B + 350 - 0.07B = 310
-0.02B = 310-350
-0.02B = -40
0.02B = 40
B = 40/0.02
B = $2000
Thus, Bill invested $2000
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Which equation has no solution 4 x 3 2x 6 x 2 5 2 3 2x x 3 x 1?
The equation given in B which is "5 + 2 ( 3 + 2x ) = x + 3 ( x + 1 )" has no solution.
In order to determine which equation has no solution we need to solve the equation to check to see if after solving they give the left-hand side (LHS) and right-hand side (RHS) equal.
If both LHS and RHS are equal, it means the equation has a solution; but if LHS and RHS are not equal, it means that the equation has no solution.
So first solve the equation given in A:
4 ( x + 3 ) + 2x = 6 ( x + 2 )
4 x + 12 + 2 x = 6x + 12
6 x + 12 = 6 x + 12
LHS is equal to RHS so this equation has the solution.
So now solve the equation given in B:
5 + 2 ( 3 + 2x ) = x + 3 ( x + 1 )
5 + 6 + 4 x = x + 3 x + 3
11 + 4 x = 4 x + 3
or
(4 x + 11) = (4 x + 3)
LHS is not 'equal' to RHS so this equation has no solution.
"
Complete question is
Which equation has no solution
A: 4 ( x + 3 ) + 2x = 6 ( x + 2 )
B: 5 + 2 ( 3 + 2x ) = x + 3 ( x + 1 )
"
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Edward drives his car 12,000 miles per year.how many kilometers does he drive per month
Edward drives 160.9 kilometres per month
How to calculate the distance that Edward travelled per month?Edward drives 12,000 miles per year
There are 12 months in a year, this means that Edward travels 12,000 miles in 12 month
The number of kilometres travelled per month can be calculated as follows
12,000= 12
x= 1
cross multiply both sides
x= 12,000/12
x= 100
The next step is to convert 100 miles to kilometres
100 × 1.609
= 160.9 kilometres
Hence Edward travelled 160.9 kilometres per month
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9.) Jenny refinished a wooden table. She used 1/3 can of varnish for a first coat, 1/4 can for a second coat, and 1/6 can for a third coat. What fraction of the can did she use in all?
Answer:
9/12 or simplified as 3/4
Step-by-step explanation:
We are given 3 fractions that we have to add because the question says "What fraction of the can did she use in all?"
First: Write down [tex]\frac{1}{3} + \frac{1}{4} +\frac{1}{6}[/tex]
Then: We can't just add up all these fractions, we need a LCM. The LCM (Least Common Multiple) We need all the denominators (3, 4, and 6) to be the same. To do that we need to find a number that they can multiply to get. Let's find out all the multiples of each number: (just write the first 5 down because most of the time we can find it easily from this list)
3: 3, 6, 9, 12, 15
4: 4, 8, 12, 16, 20
6: 6, 12, 18, 24, 30
After: just change all the fractions one at a time by whatever you multiply the bottom number to get 12, do it to the top:
[tex]\frac{1}{3} -- > \frac{4}{12}[/tex]
[tex]\frac{1}{4} -- > \frac{3}{12}[/tex]
[tex]\frac{1}{6} -- > \frac{2}{12}[/tex]
Finally we get to add everything up to get:
[tex]\frac{4}{12} +\frac{3}{12} +\frac{2}{12} =\frac{9}{12}[/tex]
(simplified as 3/4)
Click on the graph until the graph that best represents the given statement appears.
Height Above Ground
Time
The graph consists of the relationship between the height of the object and time.
What is the graph?The graph is a demonstration of curves that gives the relationship between the coordinate axes x and y-axis.
here,
In the figure,
The graph shows the relationship between the height of the object dependent on time. Where the vertical axis represents the height of the object, and the horizontal axis represents the time.
Thus, the graph shows the relationship between the height of the object and time.
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How do you write fractions in Python?
The fraction module in Python can be used to create fractions such as 3/4. This module can be imported and then the Fraction class can be used to create the fraction object. The fraction object can then be printed to display the fraction.
1. Import the fraction module: from fractions import Fraction
2. Create the fraction object: f = Fraction(3, 4)
3. Print the fraction: print(f)
4. The output will be: 3/4
The fraction module in Python is used to create and manipulate fractions. This module can be imported using the following command: from fractions import Fraction. Once imported, the Fraction class can be used to create the fraction object. The Fraction class takes two parameters which represent the numerator and denominator of the fraction. The fraction object can then be printed to display the fraction. For example, to create a fraction of 3/4, the following code can be used: f = Fraction(3, 4). This will create a fraction object which can then be printed with the print() function to display 3/4. The fraction module in Python is a great way to work with fractions in a programmatic way.
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What is the range of the relation plotted on
the graph?
A. {-1, 0, 1, 3}
B. (-2, 0, 1, 3}
C. {-2, -1, 0, 1, 2, 3}
D. {0, 1, 2, 3}
The range of the relation plotted in the graph is {-2, 0, 1, 3}.
What is the range?Range is a statistical measure of dispersion in mathematics, or how widely spaced a given data collection is from smallest to largest.
Given, A relation plotted on the graph in that there are four points whose coordinates are (0, -2), (3, 0), (-1, 1), and (1, 3)
Since The y-axis on a graph represents the possible output values, or range. Remember that the domain and range of the graph may be larger than the values seen if the graph extends beyond the area that is visible.
Therefore, The graphed relation's range is between -2, 0, 1, and 3.
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let f(x) = 1 2x . compute lim h→0 f(5 + h) − f(5) h .
The value of f(5 + h) - f(5)h when h =0 is 60.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = 12x
Now,
f(5 + h) = 12 (5 + h) = 60 + 12h
f(5) = 12 x 5 = 60
Now,
f(5 + h) - f(5)h
= 60 + 12h - 60h
h = 0
= 60 + 0 - 0
= 60
Thus,
The value of the limit is 60.
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a section of lawn that is 25.5 feet by 75.0 feet needs fertilizer. the fertilizer is sold in 5.00 pound boxes and 1.00 pound of fertilizer is needed for 10.0 square yards of lawn. if each box costs $1.65, how much will it cost to fertilize the lawn?
it cost 5 pound then = 1912.5*5= 9562.5 when the fertilizer is sold in 5.00 pound boxes and 1.00 pound of fertilizer is needed for 10.0 square yards of lawn. if each box costs $1.65
a section of lawn that is 25.5 feet by 75.0 feet needs fertilizer.
the fertilizer is sold in 5.00 pound boxes and 1.00 pound of fertilizer is needed for 10.0 square yards of lawn.
if each box costs $1.65, how much will it cost to fertilize the lawn?
We would solve this question by cross multiplication.
If a sound of fertilizer covers 45 square feet of lawn and the lawn is 8666.7 square feet
To get fertilizer quantity we have
1 pound = 45 square
Unknown = 8666.7 square feet
8666.7/45
= 192.59 when approximated we get 193.
Therefore she has to buy 193 pounds of fertilizer
total become 25.5*75=1912.5
it cost 5 pound then = 1912.5*5= 9562.5
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point b and c are on the opposite edges of a pond . find the length of the pond , a student of a class X makes a right triangle using a rope connecting a point b with anotther point a at a distance of 24 cm from it and connecting point c to a point at the distance of 60 cm from c and then connecting d to the point a , which is at the distance of 80 cm from it such that angle ADC = 90
Answer:
Step-by-step explanation:
It sounds like you have a right triangle with one angle of 90 degrees and the lengths of the sides are 24 cm, 60 cm, and 80 cm. If this is the case, then you can use the Pythagorean theorem to find the length of the hypotenuse, which is the side opposite the right angle.
The Pythagorean theorem states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, we have:
c^2 = a^2 + b^2
c^2 = 24^2 + 60^2
c^2 = 576 + 3600
c^2 = 4176
c = 64.47214
So the length of the hypotenuse, or the length of the pond, is approximately 64.47214 cm.
Which point on the number line represents the approximate volume of a cone with a radius of 3 units and a height of 4 units? Use 3.14 for π.
The point on the number line which represents the approximate volume of the cone is 38.
What is Cone?A cone is a figure in three dimensional geometry for which it has a circular base and the plane formed by set of all the points on the base connected to a point called vertex which is not located on the base.
Volume of a cone = [tex]\frac{1}{3}[/tex] π r² h, where r is the radius, h is the height of the cone and π is the pi constant with value 3.14.
Here, r = 3 units and h = 4 units.
Volume = [tex]\frac{1}{3}[/tex] π r² h
= [tex]\frac{1}{3}[/tex] × 3.14 × 3² × 4
= 37.68 unit³
≈ 38 units³
Hence the point 38 on the number line represents the approximate volume of the cone.
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Answer:
38-- the dot close to 40
Step-by-step explanation:
FOr every 5 coins Carmen gets she gives frankle 2 if Carmen has 9 how many dose frankle have
Answer:2
Step-by-step explanation:
She has 2
9 - 5 = 4
no more to give so only 2
wha is the equation of the line that passes through the point (-4,1) and has a slipe of -3/2
The equation that passes through the point (-4,1) y=-3/2x-5
What is the slope-intercept form of a line?The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line
Given here, the line that passes through the point (-4,1) and has a slope of -3/2 then let the equation of the line be y=mx+c then we get
⇒1= -3/2×-4+c
⇒c= -5
Hence, The equation that passes through the point (-4,1) y=-3/2x-5
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Use the zero product to find the solutions to the equation x*2+x-30=12
A. x=-7 or x=6
B. x= -7 or x =-6
C. x= -6 or x = 7
D. x=6 or x =7
Using the zero product, the solutions to the equation x² + x - 30 = 12 are A. x=-7 or x=6
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
x^2 + x - 30 = 12
Express the exponent as a proper superscript
So, we have the following representation
x² + x - 30 = 12
Subtract 12 from both sides
This gives
x² + x - 42 = 0
Expand
x² + 7x -6x - 42 = 0
When the equation is factored, we have
(x +_7)(x - 6) = 0
Solve for x
x = -7 and x = 6
Hence, the solutions are x = -7 and x = 6
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Which of the following statement is INCORRECT? A large sample drawn from the population will guarantee accurate results. A sample is a subset drawn from a population of interest. A statistic is a number calculated based on a sample. A parameter is an unknown quantity about a population.
The incorrect statement is that a large sample drawn from the population will guarantee accurate results. So, correct answer is option (I).
Population: It Contains all elements of a dataset, and measurable properties of the population such as mean and standard deviation are called parameters. For example, "Everyone in India" refers to India's population.
Sample: It Contains one or more observations drawn from a population, the measurable property of the sample is a statistic. Sampling is the process of selecting samples from a population. For example, some people living in India are a sample of the population. A sample statistic (or just a statistic) is defined as any number calculated from sample data. Examples include sample mean, median, sample standard deviation, and percentile. From the above discussion it is clear that sample is subset of population set and statistic and poplution are related terms of sample and poplution respectively. So, all the statements are correct except statement (I).
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Complete question:
Which of the following statement is INCORRECT? I) A large sample drawn from the population will guarantee accurate results.
II) A sample is a subset drawn from a population of interest.
III) A statistic is a number calculated based on a sample.
IV) A parameter is an unknown quantity about a population.
If you place a 24-foot ladder against the top of a 22-foot building, how many feet will the bottom of the ladder be from the bottom of the building? Round to the nearest tenth of a foot.
Answer:
9.5ft
Step-by-step explanation:
a²+b²=c²
equation
24²=c²
22²=a²
put in the variables
24²-22²=b²
Rearrange the equation
576-484=92
square
√92
Square root answer
9.5ft
Answer
What is the perimeter of a rectangle with a length of 8 1/6 feet and a width of 6 2/3 feet
Answer:
29 2/3 ft
Step-by-step explanation:
The perimeter is found using the formula
P = 2 ( l+w)
where l is the length and w is the width
P = 2(8 1/6 + 6 2/3)
Getting a common denominator
P = 2 ( 8 1/6 + 6 4/6)
= 2 ( 14 5/6)
= 28 10/6
Changing the improper fraction to a mixed number
= 28 + 1 4/6
Simplifying
= 29 2/3 ft
How many solutions does the equation y = -2x2 - 7x + 5 have?
The number of solutions which the equation y = -2x² -7x + 5 has as required in the task content is; 2.
What is the number of solutions for the given equation?As evident in the task content; the number of solutions which the given equation has is to be determined.
Since the given equation; y = -2x² -7x + 5 is a quadratic equation.
It follows that the number of solutions which the equation has is two.
PS; Quadratic equations are polynomials with degree 2 and hence, have two solutions.
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Alexander was offered a job that paid a salary of $34,000 in its first year. The salary was set to increase by 4% per year every year. If Alexander worked at the job for 5 years, what was the total amount of money earned over the 5 years, to the nearest whole number?
The total amount that is earned by Alex in five years is $41528.
What is the total amount that he earns in five years?We have to note that we need to look at the equation that shows the raise in the salary of Alex and we can be able to write from the equation that;
A =Pe^rt
A = amount that is earned after t years
r = rate of the increase of the salary
t = time taken to increase the salary
We now know from the question that
A = ?
P = $34,000
r = 0.04
t = 5
Thus;
A = 34000e^(0.04 * 5)
A = $41528
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"When 7 is added to 3 times a certain number,the result 22"
Answer:
The statement "when 7 is added to 3 times a certain number, the result is 22" can be written as an equation:
3x + 7 = 22
To solve for the unknown number (which we'll call "x"), we need to get x by itself on one side of the equation. We can do this by subtracting 7 from both sides of the equation:
3x + 7 - 7 = 22 - 7
Simplifying the left side gives us:
3x = 15
Finally, we can solve for x by dividing both sides of the equation by 3:
x = 15 / 3
= 5
So, the number that we were looking for is 5.
Step-by-step explanation:
Answer:
x = 5
Step-by-step explanation:
"When 7 is added to 3 times a certain number, the result 22"
Write this sentence algebraically.
7 + 3x = 22
We need to try and get 3x by itself to find its value, so subtract 7 from both sides.
3x = 22-7 = 15
3x = 15
3x simply means 3 multiplied by x.
So:
x = 15/3 = 5
x=5
the "certain number" is 5.
To check:
7 + 3x5 should equal 22.
7 + 15 = 22.
Hope this helps.
If a =2+√5/2 find the value of a2 +1/a2
.
Answer:4.9
Step-by-step explanation:
if a=2√5/2 it means it is equal to 2.23
So (2.23×2)/2+1/(2.23×2)
it means a2+1/a2=(2.23×2)/2+1/(2.23×2)= 2.23+0.22=4.9
The graph shows Michaela’s earnings over time. Marcus’s hourly rate is represented in the table. Who has a greater rate of pay, and how much more than the other will that person earn in 40 hours of work?
A. Complete the table, write an equation, and graph Marcus’s earnings A over time t.
k = 19/2 = ? A = ?
B. Use the graph to determine who is earning a greater rate of pay. Explain how you know.
C. What information do you still need in order to solve the problem? Solve the problem and show your work.
I still need...
Michaela
?/10 = k, or k = ?
A = kt
A = ?t
A = ? (?) = $480
Marcus:
A = kt
A = ?t
A = ? (?) = ?
The completed table is given as follows:
Earnings of $19.00 in 2 hours.Earnings of $38 in 4 hours.Earnings of $47.50 in 5 hours.Earnings of $57 in 6 hours.Earnings of $76 in 8 hours.The greater rate is that of:
Michaela.
The difference for 40 hours of work is given as follows:
$100.
Marcus' graph is given by the image at the end of the answer.
What is a proportional relationship?A proportional relationship is a linear function with an intercept of zero modeled as follows:
y = kx.
In which k is the constant of proportionality.
From the table, Marcus' hourly rate is given as follows:
k = 19/2 = 9.50.
Hence the proportional relationship is:
y = 9.5x.
Which is graphed at the end of the answer.
The table is completed as follows:
When time = 4, y = 9.5(4) = $38.When time = 5, y = 9.5(5) = $47.50.When earnings = 57, time = 57/9.5 = 6.When earnings = 76, time = 57/9.5 = 8.From the graph, Michaela's hourly rate is given as follows:
120/10 = $12.
Which is greater than Marcus'.
The hourly difference is given as follows:
12 - 9.5 = 2.5.
Hence the difference for 40 hours is given as follows:
40 x 2.5 = $100.
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car rental agency has two locations in a city. The boxplots below summarize the miles driven for one day of single day car rentals at each location Location A DO Location B 0 100 300 400 200 Miles Driven Based on the boxplota, which statement provides the best comparison of the two locations?A. The number of single day rentals is greater for location A than for location B. The number of single day rentals in less for location A then for location . C Compared with location A, the miles driven for location display more variability and the median is greater D. Compared with location A, the miles driven for location display lese variability, and the median in greater E. Compared with location A, the miles driven for location display less variability, and the median is about the name
Among the given statements, the following statement "Compared with location A, the miles were driven for location B display more variability and the median is greater" provides the best comparison of the two locations.
Hence, option (C) is the correct choice.
For finding the interquartile range for location, first, find the median (middle value) of the bottom half and upper half of the data before calculating the interquartile range (IQR). Quartile 1 (Q1) and Quartile 3 are these values (Q3). The IQR represents the variation between Q3 and Q1.
The interquartile range for location B is Q3 - Q1 = almost 140 - 40 = 100, while it is Q3 - Q1 = nearly 60 - 40 = 20 for location A.
Therefore, the miles travelled for position B are more variable than they are for place A.
Greater than Location A's almost 50 medians is Location B's nearly 80 median.
Therefore, location B's median miles driven is higher than it is for location A.
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What is the example of SAS congruence postulate?
HELPPPPPPP im to lazy
Answer: help is on the way
Step-by-step explanation:
Two congruent ellipses are perpendicular to each other. Squares fill the gaps between the two ellipses as shown. Show that the side of the square equals half the minor axis of the ellipse.
The side of the square equals half the minor axis of the ellipse.
To show that the side of the square is half the minor axis of the ellipse, we must prove that the angles of the ellipses and the squares are congruent. To do this, we must first draw in the diagonals of the square, which will form two additional isosceles triangles.
Since the ellipses are perpendicular, the angles of the ellipses and the squares will be the same. Since the angles of the isosceles triangles are equal, the side of the square must be equal to half of the minor axis of the ellipse. Therefore, the side of the square is equal to half of the minor axis of the ellipse.
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Two roses cost $3.50. How many roses can you
buy for $21?
Answer:
6 roses
Step-by-step explanation:
divide 21 and 3.50 hope this helps:)
Answer:6
Step-by-step explanation:
21 Divided by 3.5 = 6
100 PTS HELP
Use the distributive property or simplify to match the equivalent expressions.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
(3 × 4) + (3 × 7)
7(60 + 6)
32 +16 = 48
4(100 − 3)
(5 × 9) − (5 × 6)
(3 × 4) + (3 × 7) = 12 + 21 = 33
7(60 + 6) = 7(66) = 462
4(100 − 3) = 4(97) = 388
(5 × 9) − (5 × 6) = 45 − 30 = 15
So, the correct input-output pairs are:
(3 × 4) + (3 × 7) = 33
7(60 + 6) = 462
4(100 − 3) = 388
(5 × 9) − (5 × 6) = 15
Answer: 33,462,48,388, and 15
Step-by-step explanation:
The figures below are similar to each other. Find the scale factor of the smaller figure to the larger figure.
(Given that the triangles are oriented in the same direction)
35
5:2
2:5
20:7
7:20
40
25
14
16
The scale factor of the smaller figure to the larger figure is 5:2
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Given that two triangles are similar.
The side lengths of the triangle must be proportional.
Let us consider first triangle as ABC, where AB is 35, BC is 40 and AC is 25.
and triangle DEF as DE is 14 and EF is 16.
Now AB/DE=BC/EF
35/14=40/16
5/2=5/2
Hence, the scale factor of the smaller figure to the larger figure is 5:2
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