For a data set with an odd number of observations that have been sorted from smallest to largest values, the median is located at [tex]\frac{x+1}{2}[/tex]
Given,
The conditions
There are odd number of observationThe observation have been sorted from smallest to largest valuesWe know,
Median is the middle number of ordered data set.
Consider the number of observations as x
Then the median is located at [tex]\frac{x+1}{2}[/tex]
Hence, for a data set with an odd number of observations that have been sorted from smallest to largest values, the median is located at [tex]\frac{x+1}{2}[/tex]
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The snallest flowering plant is the flowering aquatic duckweed found in australia. it is 0.0236 inch long and 0.0129 inch wide. write these dimensions as fractions in simplest form.
The dimension of the smallest flowering plant is 59/2500 in. long and 129/10,000 in. wide.
To convert Decimal into Fraction form:
Do the following Steps:
Step 1: Make a fraction with the decimal number as the numerator and a 1 as the denominator.
Step 2: Remove the decimal places by multiplication.
Step 3: Reduce the fraction.
Step 4: Simplify the remaining fraction to a mixed number fraction if possible.
Given,
The smallest flowering plant is the flowering aquatic duckweed found in Australia.
And it is 0.0236 inch long and 0.0129 inch wide.
Here we need to write these dimensions as fractions in simplest form.
Rewrite the decimal number as a fraction with 1 in the denominator
So,
=> 0.0236/1 and 0.0129/1
Now, Multiply to remove 4 decimal places. Here, you multiply top and bottom by 10⁴ = 10000.
Then we get,
=> 236/10000 and 129/10000
Now, reduce the fraction by dividing both numerator and denominator by GCF = 4,
=> 59/2500
But the fraction 129/10000 is not reducible.
Therefore, the fraction form is,
=> 59/2500 in. long and 129/10,000 in. wide.
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(2-a)³+(2-b)³+(2-c)³-3(2-a)(2-b)(2-c)
Pls step by step
The evaluation of (2-a)³+(2-b)³+(2-c)³-3(2-a)(2-b)(2-c) is mathematically given as
a^3+3 a b c-b^3-c^3+6 a^2-6 a b-6 a c+6 b^2-6 b c+6 c^2
This is further explained below.
What is the evaluation of (2-a)³+(2-b)³+(2-c)³-3(2-a)(2-b)(2-c)?(2-a)^3+(2-b)^3+(2-c)^3-3(2-a)(2-b)(2-c)
Use the Binomial Theorem.
2^3+3 * 2^2(-a)+3*2(-a)^2+(-a)^3 +(2-b)^3+(2-c)^3 -3(2-a)(2-b)(2-c)
8-12 a+6 a^2-a^3+(2-b)^3+(2-c)^3 -3(2-a)(2-b)(2-c)
Use the Binomial Theorem.
8-12 a+6 a^2-a^3+2^3+3 * 2^2(-b)+3 * 2(-b)^2+(-b)^3+(2-c)^3-3(2-a)(2-b)(2-c)
8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3 +(2-c)^3-3(2-a)(2-b)(2-c)
Use the Binomial Theorem.
8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+2^3+3 \cdot 2^2(-c)+3 \cdot 2(-c)^2+(-c)^3-3(2-a)(2-b)(2-c)
8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3 +8-12 c+6 c^2-c^3-3(2-a)(2-b)(2-c)
Apply the distributive property.
8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+8-12 c+6 c^2-c^3+(-3 * 2-3(-a))(2-b)(2-c)
Multiply -3 by 2 .
&8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+8-12 c+6 c^2-c^3 +(-6-3(-a))(2-b)(2-c)
Multiply -1 by -3.
8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3 +8-12 c+6 c^2-c^3 +(-6+3 a)(2-b)(2-c)
Expand (-6+3 a)(2-b) using the FOIL Method.
Combine the opposite terms in
8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+8-12 c+6 c^2-c^3-24+12 c+12 b-6 b c+12 a-6 a c-6 a b+3 abc
8+6 a^2-a^3+8+6 b^2-b^3+8+6 c^2-c^3-24-6 b c-6 a c-6 a b+3 abc
Simplify by adding numbers.
6 a^2-a^3+6 b^2-b^3+24+6 c^2-c^3-24-6 b c-6 a c-6 a b+3 abc
Combine the opposite terms in
6 a^2-a^3+6 b^2-b^3+24+6 c^2-c^3-24-6 b c-6 a c-6 a b+3 a b c
6 a^2-a^3+6 b^2-b^3+6 c^2-c^3-6 b c -6 ac-6 ab+3 abc
Re odrder
a^3+3 a b c-b^3-c^3+6 a^2-6 a b-6 a c+6 b^2-6 b c+6 c^2
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Anna is filling a 2.5 gallon bathroom sink at a rate of 0.25 gallons per minute. what is the domain of the function that represents the volume of water in the sink after x minutes?
The volume of water in the sink after x minutes can be represented by a function V(x) = 0.25 x and its domain is 0 ≤ x ≤ 10
After x minutes, the volume of water in the sink will be:
V = filling rate ⨉ time interval
Information from the problem:
filling rate = 0.25 gallons per minute
time interval = x
Substitute these parameters into the formula:
V = 0.25 x
The domain of a function is the set of all possible inputs, of which the function is defined.
In this problem, the function is the volume, which is a function of x.
V(x) = 0.25 x
To determine its domain, check the minimum and maximum values of V(x).
When the sink is empty, V = 0.
Then,
V(x) = 0.25 x
0 = 0.25 x
x = 0
When the sink is full, V = 2.5.
Then,
V(x) = 0.25 x
2.5 = 0.25 x
x = 10
Since V(x) has value 0 ≤ V(x) ≤ 2.5, its corresponding input should be 0 ≤ x ≤ 10. This is the domain.
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Evaluate |c2 + b2|, given a = 5, b = -3, and c = -2.
10
6
2
13
Answer:
10
Step-by-step explanation:
|-2(2) + (-3)(2)|
2(2) + 3(2)
4 + 6
| | indicate absolute value, negative numbers are turned to positive numbers in absolute value, making B and C (negative values) into positive values.
Hi, could I get help with this?
The segment AB is perpendicular to the segment CD because the two angles it creates are each 90 degrees .
A line is said to be perpendicular to another line if the two lines intersect at a right angle . The segment AB can be called the perpendicular from A to the segment CD . The point B is called the foot of the perpendicular from A to segment CD or simply , the foot of A on CD .If a first line is perpendicular to a second line , then the second line is also perpendicular to the first .
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Find the lengths of ABC and BD explain pls
Answer: The length of AB =4 units
The length of BD = 2.4 units.
Step-by-step explanation:
Given data,
AD = 3.2 unit
BC = 3 unit
CD = 1.8 units
Find : AB =? units
BD=? units
We can use the formula of Pythagorean theorem,
Define Pythagorean theorem :
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.
Hypotenuse2 = Perpendicular2 + Base2
c2 = a2 + b2
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse.
Let be a ΔABC,
[tex](AB)^{2} = (BC)^{2} +(AC)^{2}[/tex]
From the above formula now determined the value of AB and BD,
Firstly , find the value of BD
In ΔBDC, by applying Pythagorean theorem,
[tex](BC)^{2} = (BD)^{2} + (DC)^{2}[/tex] (Eq - 1)
Substitute BC and CD values in equation 1,
BC = 3 units and CD = 1.8 units
So,
We can write,
[tex]3^{2} = (BD)^{2} +(1.8)^{2}[/tex]
9 = [tex](BD)^{2}[/tex] + 3.24
[tex](BD)^{2}[/tex] = 9 - 3.24
[tex](BD)^{2}[/tex] = 5.76
[tex]BD = \sqrt{5.76}[/tex]
BD = 2.4 units (Eq - 2)
Now find the value of AB,
In ΔABD, by applying Pythagorean theorem,
[tex](AB)^{2} = (AD)^{2} +(BD)^{2}[/tex] (Eq - 3)
Substitute AD and BD values in equation 3,
AD = 3.2 units and BD = 3 units
So,
We can write,
[tex](AB)^{2} = (3.2)^{2} + 3^{2}[/tex]
[tex](AB)^{2}[/tex] = 10.24 + 5.76
[tex](AB)^{2}[/tex] = 16
AB = [tex]\sqrt{16}[/tex]
AB = 4 units
Therefore,
The length of AB =4 units
The length of BD = 2.4 units.
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Alguien me puede ayudar pls
Answer:
hola
Step-by-step explanation:
Yo can anyone help me, you’ll get BRAINLY if you answer correctly
We get the translation rule as (x-4, y+5) for triangle ABC.
We are given a triangle:
ABC where
A = (3, -1)
B = (7, -5)
C = (-2, -2)
And, we are also given the translation of the triangle as A'B'C'
where
A' = (-1, 4)
B' = (3, 0)
C' = (-6, 3)
We need to tell the translation rule for it,
For the x coordinate, we can see that:
- 1 - 3 = - 4
3 - 7 = - 4
- 6 - (-2) = -4
So, the rule for x coordinate will be:
x - 4
Now for y coordinate:
4 - (-1) = 5
0 - (-5) = 5
3 - (-2) = 5
So, the rule for y coordinate will be:
y + 5
Translation rule then becomes:
(x-4, y+5)
Therefore, we get the translation rule as (x-4, y+5) for triangle ABC.
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Select the car that travels the fastest. choose 1 answer: choose 1 answer: (choice a, checked) a 50 50 km/h km/hcar a (choice b) b car b travels a distance of d dd kilometers in h hh hours, based on the equation 55 h = d 55h=d55, h, equals, d. (choice c) c car c travels 135 135135 kilometers in 3 33 hours. see more
The car with the speed of 50 Km/h travels the fastest.
We have given with three choices for selecting the fastest speed from them. The three choices are
First choice is 50 Km/h.
Second Choice is car b travels a distance of d kilometers in h hours, based on the equation 55 h = d , h, equals, d.. So from this be can conclude that this car is moving with the speed of (1/55)km/h.
Third choice is car c travels 135 kilometers in 3 hours. So from this be can conclude that this car is moving with the speed of (135/3) Km/h i.e., 45 Km/h.
So, from the given choices we can conclude that the car with the speed of 50 Km/h travels the fastest.
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Determine whether the line integral of each vector field (in blue) along the semicircular, oriented path (in red) is positive, negative, or zero.
Considering the images (a),(b),(c),(d),(e),(f) the oriented path is
(a) Negative
(b) Positive
(c) Positive
(d) Zero
(e) Zero
(f) Zero
calculating each quadrant's line integral and symmetry.
In calculus, a line integral is an integral where the function being evaluated is along a curve. A line integral is also known as a route integral, curve integral, or curvilinear integral.
What does a Line integral mean?
A line integral makes it possible to figure out a surface's area in three dimensions. Numerous situations call for the use of line integrals. They can be used, for instance, in electromagnetics to determine the work done on a charged particle moving along a curve in a force field that is represented by a vector field.Path, curvilinear, and curve integrals are other terms for line integrals. There are several uses for line integrals, including electromagnetics, where it is used to calculate the force exerted on a charged particle moving along a curve in a force field created by a vector field.To learn more about Line integral, visit:
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g(x)= 3x find g(-5)
Answer: -15
Step-by-step explanation:
x=-5
g(-5)=3(-5)
g(-5)=-15
question 4 suppose the fraction of high school students who can drive is 15% and the fraction of college students who can drive is 23%. if one-fifth of the students are college students and the rest are high school students, what is the probability that a student who can drive is a college student? select the correct probability.
The probability that a student who can drive is a college student is 0.2771 or 27.7%
It will be sooved using Baye's theorem -
P(college) = P(C) / 1/5 = 0.2
P(high school students) = P(H) = 4/5 = 0.8
P(college drives) = 0.23
P(high school drives) = 0.15
We have to find, probability that a student who drives is a college student.
That is, we have to find P(C/D).
P(C/D) = P(C ∩ S)/P(S)
Since P(C ∩ S) is an independent event.
P(C ∩ S) = P(C) × P(S)
P(C ∩ S) = 0.2 × 0.23
= 0.046
Using bayes's theorem, we will get
P(C/D) = 0.2771 or 27.7%
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How do I solve this? step by step please 30 POINTS!
The solution to the system of equations is (-7, 5)
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2x + y = -9
3x + 5y = 4
Make y the subject in 2x + y = -9
So, we have
y = -2x - 9
Substitute y = -2x - 9 in 3x + 5y = 4
So, we have
3x + 5(-2x - 9) = 4
Open the bracket
So, we have
3x - 10x - 45 = 4
Evaluate the like terms
-7x = 49
Divide both sides by -7
x = -7
Substitute x = -7 in y = -2x - 9
y = -2(-7) - 9
Evaluate
y = 5
Hence, the solution to the system of equations is (-7, 5)
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Solve for the value of q
Answer:
q = 20
Step-by-step explanation:
Angles on a straight line add up to 180 degrees.
180 - 78 = 102
so
5q+2 = 102
subtract 2 from both sides
5q = 100
100 / 5 = 20
5q / 5 = q
q = 20
Hope this makes sense.
If 8 tacos cost $5.60. Find the unit price. Round to the hundredths if necessary.
Answer:
0.7¢
Step-by-step explanation:
Find unit price[tex]8 \cdot 7 = 56\\= 56 - 56\\= 0.7\:\mathrm{R0}[/tex]
How is ahow is a linear relationship between two variables measured in statistics? explain. select all the true statements.
The following are the linear relationships between two variables measured in statistics:
Correlation coefficients are a group of numerical measures of correlation.The correlation coefficient is between -1 and +1. Values near +1 or -1 indicate a strong linear relationship.The correlation coefficient remains constant when the values of x and y are swapped.What is a linear relationship?A linear relation, or simply relation, among elements of a vector space or a module, is a linear equation with these elements as a solution in linear algebra. A linear relationship (or linear association) is a numerical term that describes a two-variable relationship that follows a straight line. Linear relationships can be represented graphically or mathematically as the equation y = mx + b.So,
The following are the linear relationships between two variables measured in statistics:
Correlation coefficients are a group of numerical measures of correlation.The correlation coefficient is between -1 and +1. Values near +1 or -1 indicate a strong linear relationship.The correlation coefficient remains constant when the values of x and y are swapped.Therefore, the following are the linear relationships between two variables measured in statistics:
Correlation coefficients are a group of numerical measures of correlation.The correlation coefficient is between -1 and +1. Values near +1 or -1 indicate a strong linear relationship.The correlation coefficient remains constant when the values of x and y are swapped.Know more about the linear relationships here:
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Cecilia bought 187.6 pounds of crushed limestone in a total of eight bags. if all the bags were identical, what was the weight of each?
The weight of each bag is 23.25 pounds.
For given question,
Cecilia bought 187.6 pounds of crushed limestone in a total of eight bags.
If all the bags were identical, we need to find the weight of each bag.
Let 'm' be the weight of each bag.
As Cecilia bought 187.6 pounds of crushed limestone in a total of eight bags and all the bags were identical, we get an expression.
8 × m = 187.6
now we solve above expression to find the value of m i.e., to find the weight of each bag.
⇒ 8 × m = 187.6
⇒ m = 187.6 / 8
⇒ m = 23.25 pounds
Therefore, the weight of each bag is 23.25 pounds.
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PLEASEEE HELPPPPP ILL GIVE BRAINLIEST
60-100 bpm and that is the range of a 16 year old heart beat
Answer:
Step-by-step explanation:
Lower limit of range:
H = [tex]\frac{7}{10}[/tex](220-a)
a = 16 [given]
∴ H = [tex]\frac{7}{10}[/tex](220-16)
H = [tex]\frac{7}{10}[/tex](204)
H = [tex]\frac{7}{10}[/tex]×[tex]\frac{204}{1}[/tex]
H = [tex]\frac{1428}{10}[/tex]
H = 142.8
H = 143 beats per minute [as an integer]
Rosa paid $107.40 for 12 audio books that were all the same price. Which is the best estimate of the cost of each audio book?
Answer:
$8.95
Step-by-step explanation:
Divide 107.4 by 12 and you end up with the price of each audio book.
The same can be said for each problem you want find the individual amount of
Answer:
Each audio book costs $8.95
Step-by-step explanation:
Since 12 audio books that are at all the same prize equal $107.4, therefore in order to find the total of each book we divide $107.4 by 12
➟ 107.4 ÷ 12
➟ 8.95
∴ $8.95 is the cost of each book
Does one frequency distribution provide a better summary of the data than the other? explain.
Changing the class width from 4,000 to 3,000 increases the details of the frequency distribution, thereby providing a better summary of the data.
How can changing the class width affect the frequency distribution obtained?Based on a similar question, the possible part of the question appear left out includes.
To construct a second frequency distribution with a class width of 4,000, where the class width of the first frequency distribution is 3,000Construct a frequency histogram using the values in the frequency distribution constructed above.The correct response is; Yes, the value or magnitude categories of the data are increased using the smaller class width of 3,000 such that more details about the influence of the different classes on the results are seen, which provides a better summary of the information in the data than the frequency distribution that a 4,000 class width.
The overall shape of the frequency histogram remains almost the same for both class widths
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The standard deviation for a data set is 0. Determine whether each conclusion about the data is true or false.
a. The standard deviation measures the variation of the data. If the standard deviation is 0, then there is some variation, so all the data are different.
b. All the data must be equal to the mean because the sum of the squares of the differences of the data from the mean is 0. So, all the data take the same value.
Statement a : "The standard deviation measures the variation of the data. If the standard deviation is 0, then there is some variation, so all the data are different" is false.
Statement b : "All the data must be equal to the mean because the sum of the squares of the differences of the data from the mean is 0. So, all the data take the same value" is true
What is standard deviation?
This is a term in statistics that represent the amount of variation in a data set or simply put the spread of the data set. Standard deviation is solved from the mean of the data, that is we get mean first before solving for standard deviation.
From the definition, if all the data is the same then the data should be equal to the mean. If the data is equal to the mean there will be no spread or variation leading to a zero standard deviation.
Hence we can conclude that statement b is true and statement a is false
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Just the answer please
The x-intercept of the line is -3
y-intercept: None
x-intercept and y-interceptFrom the question, we are to find the y-intercept and x-intercept of the given line
The x-intercept of a line is the point where the line crosses the x-axis on a cartesian plane
The y-intercept of a line is the point where the line crosses the y-axis on a cartesian plane
From the graph, we can observe that the line only crosses the x-axis at the point (-3, 0). That is, at the point where x = -3
Thus,
The x-intercept of the line is -3
The graph does not cut through the y-axis
Thus,
There is no y-intercept
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Find the sum of the first 13 terms of the sequence 2, 5, 8, 11,....
The sum of the first 13 terms is 260
How to calculate the sum of the first 13 terms ?The first term(a) is 2
The common difference(d) is 3
n= 13
The formular is
n/2(2a + (n-1)d)
= 13/2 [ 2(2) + (13-1)3]
= 6.5 [4 + 12(3)]
= 6.5 [4 + 36]
= 6.5(40)
= 260
Hence the sum of the first 13 terms is 260
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A point at the origin is repeatedly translated c units horizontally and d units vertically. Write the coordinates
of the translated point if the translation sequence is repeated n times.
The coordinates of the translated points if the translation sequence is repeated n times according to the task content is; (nc, nd).
What are the coordinates of the translated point after n translation sequences?It follows from the task content that the point in discuss is at the origin. Hence, the point is; (0, 0).
Also, since the point is repeatedly translated c units horizontally and d units vertically, it follows from transformations that the resulting point is;
((0+c), (0+d))
Ultimately, when the translation sequence is repeated n times; the resulting pair of coordinates is; ((0+nc), (0+nd)).
And upon simplification, we have; (nc, nd).
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Albert bought 6 bags of candy. There were 7 pieces of candy in each bag. How many pieces
of candy did Albert buy?
pieces of candy
42 pieces of candy because math
A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let r be the radius of the top of the can and let h be the height. The surface area of the cylinder, A , is A=2πr2+2πrh (two circles, one for the top and one for the bottom plus a rolled up rectangle for the sides).
A round cylinder with a circle top and base with radius r and a height of h
Part a: Assume that the height of your cylinder is 8 inches. Consider A as a function of r , so we can write that as A(r)=2πr2+16πr. What is the domain of A(r) ? In other words, for which values of r is A(r) defined?
Part b: Continue to assume that the height of your cylinder is 8 inches. Write the radius r as a function of A. This is the inverse function to A(r) , i. E. , to turn A as a function of r into r as a function of A.
r(A)=
Preview Change entry mode
Hints:
To calculate an inverse function, you need to solve for r. Here, you would start with A=2πr2+16πr. This equation is the same as 2πr2+16πr−A=0 which is a quadratic equation in the variable r , and you can solve that using the quadratic formula. You will want to keep A as a variable when you plug the values into the quadratic formula.
If you want to type in 3π+1x+1 in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is more information in the Introduction to Mobius unit.
Part c: If the surface area is 100 square inches, then what is the radius r ? In other words, evaluate r(100). Round your answer to 2 decimal places.
Hint: To compute a numeric square root such as 17. 3−−−−√ , you could
Use a spreadsheet such as Microsoft Excel or OpenOffice Calc and type in =sqrt(17. 3)
Use a browser to connect to the Internet and type in sqrt(17. 3) into a search field
Use a calculator
The radius is
inches if the surface area is 100 square inch
a) r>0 is the domain of A. b) r = (4/2π + 16)^1/2 - 4
A(r) is a function representing the surface area of a cylinder of height = 8inches and radius = r.
A(r) = 2п[tex]r^{2}[/tex] + 16пr
r must be a positive number, as we can't have a radius of negative length, so the domain of A(r) is r>0.
Solving for r in terms of A is an odd question, and a little challenging but possible using completing the square:
A/2п = [tex]r^{2}[/tex] + 8r
A/ 2п + 16 = [tex]r^{2}[/tex] + 8r + 16
A/2п + 16 = [tex](r + 4)^{2}[/tex]
r =( A/2п + 16) ^1/2 - 4
Therefore we get to know the range of r i.e., r>0 and radius = (A/2п + 16 )^1/2 - 4
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A rectangular pool is 20 feet by 30 feet. The depth of the pool is 60 inches, but the depth of the water is 3/4 of the depth of the pool. Find each measure to the nearest tenth. (Lesson 1-7)
b. the volume of water in the pool
The water in the rectangular pool which has a depth of 3/4 of the pool's depth has a volume of 2250 cubic feet.
If the depth of the water is 3/4 of the depth of the pool and the depth of the pool is 60 inches, then
depth of the water = 3/4 of the depth of the pool
depth of the water = 3/4(60 inches)
depth of the water = 45 inches = 3.75 feet
Volume is defined as the amount of space any object occupies. The volume for a rectangular prism is given by the formula:
V = lwh
where v is the volume
l is the length
w is the width
h is the height
Since the water occupies the inside of the rectangular pool, to solve the volume of the water, use the formula for the volume of a rectangular prism.
V = lwh
V = 20 feet(30 feet)(3.75 feet)
V = 2250 cubic feet
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3 cups of peanut mix 2 cups of raisins 4.5 cups of peanut mixed 3 cups of raisins are the ratios equivalent for two mixed
The ratios are equivalent
How to find equivalent ratios?Ratio shows the relationship that exists between values. It shows the proportion of one value in another value.
In other words, ratios says how much of one thing there is compared to another thing.
Therefore,
Ratio of peanuts to raisins in the first version = 3 : 2
divide both numbers by 2
1.5 : 1
Ratio of peanuts to raisins in the second version = 4.5 : 3
divide both numbers by 3
1.5 : 1
The ratios of the first and second trail mix are equivalent because they are both 1.5 : 1
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please help I will give brainly if its right
If m< EBC = 3y+10 and m< ABE = 2y-20, find m< EBF.
By using the fact that EBC and ABE are supplementary angles, we will see that the measure of angle EBF is 106 degrees.
How to find the measure of the angle EBF?First, we can notice that angles EBC and ABE are supplementary angles, which means that their measures add up to 180°.
Then we can write:
m∠EBC + m∠ABE = 180°
Replacing what we know we get:
3y + 10 + 2y - 20 = 180°
Now we can solve this linear equation for y, we will get:
5y - 10 = 180
5y = 180 + 10
y = 190/5 = 38
Then we have that:
EBC = 3*38 + 10 = 124°
ABE = 2*38 - 20 = 56°
Now, in the image it says that:
ABE = 2b = 56°
then b = 56°/2 = 28°
And ABF = 7b - 24 = 162°
Then:
EBF = ABF - ABE = 162° - 56° = 106°
We conclude that the measure of angle EBF is 106 degrees.
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