the length of a shadow of a tree is feet when the angle of elevation of the sun is . approximate the height of the tree.

Answers

Answer 1

The approximate height of the tree is feet.

The exact height of the tree cannot be determined without additional information. However, a rough estimate can be made using the following formula:

Height of Tree = Length of Shadow / Tan(Angle of Elevation of Sun)

In this case, the estimated height of the tree would be: Length of Shadow / Tan( ) = feet/tan( ).

The formula to calculate the height of a tree is:

Height of Tree = Length of Shadow * Tan(Angle of Elevation of the Sun)

In this case, Length of Shadow = feet and Angle of Elevation of the Sun

Therefore, the height of the tree can be calculated as follows:

Height of Tree = feet * Tan( )

Height of Tree = feet * 0.839

Height of Tree = feet

Therefore, By  the angle of elevation the approximate height of the tree is feet.

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Related Questions

what is the slope through the line of (-6, -3) and (-2, -8)

Answers

Answer:m=-5/4

Step-by-step explanation: The formula for finding slope is y1-y2 / x1-x2 so when plugging in these coordinates, you get -3-(-8)/-6-(-2). When simplified -3-(-8) is 5 and -6-(-2) is -4, so the answer is -5/4. You can also switch the numbers so its -8-(-3) / -2-(-6) and still get the same answer.

the answer is -5/4 .

Michelle made a bead necklace that was 13 inches long. The length of the necklace, in inches, is equal to 3 added to one-seventh the number of beads, b. How many beads did Michelle use for her necklace?

Answers

The number of beads used for Michelle necklace is 70.

How to find the number of necklace Michelle used for the necklace?

Michelle made a bead necklace that was 13 inches long.  The length of the necklace, in inches, is equal to 3 added to one-seventh the number of beads, b.

The number of beads Michelle used for her necklace can be calculated as follows:

number of beads she used for her necklace  = b

Therefore,

13 = 3 + 1 / 7 b

13 - 3 = 1 / 7 b

10 = 1 / 7 b

cross multiply

b = 10 × 7

b = 70

Therefore,

number of beads she used for her necklace  = 70

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High school students from grades 9–10 and 11–12 were asked to choose the kind of band to have play at a school dance: rap, rock, or country.

Their choices were as follows:
Grades 9–10: Rap 40; Rock: 25; Country: 60
Grades 11–12: Rap: 55; Rock: 30; Country: 40

Which of the following is a correct two-way relative frequency table for the data?



Rap Rock Country Total
Grades 9–10 16% 10% 24% 50%
Grades 11–12 22% 12% 16% 50%
Total 38% 22% 40% 100%


Rap Rock Country Total
Grades 9–10 22% 12% 16% 50%
Grades 11–12 16% 10% 24% 50%
Total 38% 22% 40% 100%


Rap Rock Country Total
Grades 9–10 40 25 60 125
Grades 11–12 55 30 40 125
Total 95 55 100 250


Rap Rock Country Total
Grades 9–10 55 30 40 125
Grades 11–12 40 25 60 125
Total 95 55 100 250
Points earned on this question: 0

Answers

The correct option is C for the frequency table.

What is a frequency table?

A table that depicts the frequency of occurrence of a given characteristic according to a specified set of class intervals.

The correct two-way frequency table for the date will look like this:

                                               RAP      ROCK     COUNTRY     TOTAL

Grades 9-10             40           30            55                  125

Grades 11-12            60           25            35                  120

TOTAL                    100          55            90                  245

The sum of the row total is equal to the sum of the column total

125 + 120 = 100 + 55 + 90

245 = 245

The correct option for the frequency table is C.

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The Institute of Medicine compared the United States to comparable high-income countries. Which of the following is accurate?
O The United States had lower rates of birth outcomes than other countries (including infant and maternal mortality),
O The United States had more years lost to alcohol and drug use than most other countries.
O The United States had longer life expectancy than most other countries.
O The United States had lower rates of adolescent pregnancy than most other countries.

Answers

The Institute of Medicine compared the United States to comparable high-income countries in terms of  various health outcomes.

The findings revealed that the United States had lower rates of birth outcomes than other countries (including infant and maternal mortality). The US also  life expectancy than most other countries, as well as more years lost to alcohol and drug use. Lastly, the US had lower rates of adolescent pregnancy than most other countries.

The Institute of Medicine also calculated the health gap between the US and other countries, which was defined as the difference between the health outcomes of the US and the health outcomes of the other countries. This gap was calculated by subtracting the US health outcome rate from the average of the other countries' health outcome rates. For example, to calculate the infant mortality gap, the infant mortality rate in the US (5.8 deaths per 1,000 live births in 2018) was subtracted from the average infant mortality rate of the other countries (3.5 deaths per 1,000 live births). This resulted in a health gap of 2.3 deaths per 1,000 live births.

Overall, the Institute of Medicine's comparison revealed that the US was lagging behind other countries in terms of various health outcomes.

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cab fare in new york city is $7.50 for for the first mile, +$3 for each additional mile. what is the longest distance you can travel for $30

Answers

Answer:7

Step-by-step explanation:

let y equal 30, and x equal the amount of miles.

30=3x+7.50
-7.50 -7.50

22.5=3x

divide by 3 to isolate x,

x=7.5

you can travel 7.5 miles with $30

A dinner was held to raise money for a children's museum. A ticket for one person cost $200 and a ticket for a couple (two people) cost $350. A total of 130 people attended the dinner, and the ticket sales total was $24,000. What is the total number of tickets that were sold?

Answers

There were 50 single tickets sold and 40 couples tickets were sold.

What is the equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that is equal.

Let's call the number of single tickets sold "x". Then the number of couple tickets sold would be "y".

We know the total number of attendees is 130, so we can write the equation:

x + 2y = 130

We also know that the total revenue from the ticket sales is $24,000, so we can write another equation using the cost of the tickets:

200x + 350y = 24,000

We now have a system of two equations that we can solve for x and y then we get the values are:

x = 50 and y = 40

So, 50 single tickets were sold and 40 couples tickets were sold.

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Match the statistical measure to its notation or name. population mean [Choose ] sample mean [Choose) population variance [Choose] sample variance [Choose ]population standard deviation [Choose] sample standard deviation [Choose ] number of population data values [ Choose] number of sample data values [Choose]

Answers

Population Mean is the statistical indicator to its designation or nomenclature.

What is meant by Population Mean?A population is a distinct group of individuals that can be distinguished for the purposes of data collection and analysis by at least one feature. Populations are used in statistics and other branches of mathematics. The population mean can be computed by dividing the sum of all values in the given data/population by the total number of values in the given data/population. We can refer to the total of a set of numbers as a sum. An entire set of people is referred to as a population, regardless of whether that set includes an entire country or just a number of people who share a certain trait. In statistics, the group of people from which a statistical sample is taken for a research is referred to as a population.

Therefore,

The formula for the population mean, which is the population's average score on a certain variable, is:  μ = ( Σ Xi ) / N. The population mean is represented by the symbol "."

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A company sells two different safes. The safes have different dimensions, but the same volume. What is the height of Safe B?

Answers

Answer:

h = 18 in.

Step-by-step explanation:

Both safes are in the shape of a rectangular prism

The volume of a rectangular prism = L X w X H

where L = length, W = width and H = height

Safe A has volume 18 x 15 x 24

Safe B has volume 20 x 18 x h

Both volumes are equal and we have to find h

Equating both expressions

20 x 18 x h = 18 x 15 x 24

Dividing by 18 on both sides will get rid of the 18 in the product

(20 x 18 x h)/18 = (18 x 15 x 24)/18

20h = 15 x 24

20h = 360

h = 360/20

h = 18 in.

for all graphs, be sure to correctly and completely label all axes and curves and use arrows to indicate the direction of any shifts. (10 points)

Answers

Due to weaker aggregate demand, the negative demand shock will cause the aggregate demand curve to move to the left.

Result: A lower output and price level.

Part B:

Explanation of part B

Result of negative supply shock , aggregate demand falls cause the lower demand for the money . This will lead towards the left shift in money demand.(MD 1 TO MD 2(R1 TO R2)

Part c:

Interest rate and bond price are related inversely . Due to negative demand shock the interest rate falls down. vice-versa bond price will rise.

Part D:

Due to fall in the interest rate central banks will follow contractionary fiscal policy which will increase interest rate and reduce the money supply.

Part E :

If the central banks need to increase the money supply by $80 billion. Central banks need to buy securities in exchange of cash .This will Raise the money supply.

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If the angle of elevation of P from Q is 38, then the angle of depression of Q from P is:​

Answers

Answer:

52°

Step-by-step explanation:

The angle of depression is 90 - angle of elevation

So angle of depression = 90 - 38 = 52°

For the following exercises, find the level curves of each function at the indicated value of c to visualize the given function. h(x,y) = 2x-y, c=0, -2,2

Answers

The level curves of the function h(x,y) = 2x-y at c = 0, -2, 2 are y = 2x, y = 2x + 2, y = 2x - 2 respectively.

A level curve (also called a contour line or an isocline) of a function is a curve that represents all the points where the function has a constant value. To find the level curve of a function at a given value of c, we need to set the function equal to c and solve for the variables.

For h(x,y) = 2x-y, we can find the level curves at c = 0, -2, 2 by setting the function equal to c and solving for x and y:

c = 0: 2x - y = 0y = 2xc = -2: 2x - y = -2y = 2x + 2c = 2: 2x - y = 2y = 2x - 2

The level curves of h(x,y) = 2x-y at c = 0, -2, 2 are the lines y = 2x, y = 2x + 2, y = 2x - 2 respectively. Each line represents a different value of c and separates the domain of x and y into different regions where the function takes on that constant value.

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U and V are similar figures. The scale factor of V to U is 5 : 1. What would be the area of figure U, if the area of figure V is 75 square yards?answer choices75 square yards9 square yards3 square yards15 square yards

Answers

The area of the figure/geometric shape U will be 15 yard^2.

What are geometric shapes in mathematics?

In Mathematics, Geometric shapes are the figures which demonstrate the shape of the objects we see in our everyday life. In geometry, shapes are the forms of objects which have boundary lines, angles and surfaces. There are different types of 2d shapes and 3d shapes.

Shapes are also classified with respect to their regularity or uniformity. A regular shape is usually symmetrical such as a square, circle, etc. Irregular shapes are asymmetrical. They are also called freeform shapes or organic shapes. For example, the shape of a tree is irregular or organic.

In plane geometry, the two-dimensional shapes are flat shapes and closed figures such as circles, squares, rectangles, rhombus, etc.  In solid geometry, the three-dimensional shapes are cube, cuboid, cone, sphere and cylinder. We can observe all these shapes in our daily existence also. For example books (cuboid shape), glasses (cylindrical shape), traffic cones (conical shape) and so on.

Now

As the scale factor for similar shapes V and U is 5:1.

Then their area should also be in same ratio.

Given Area of V=75 square yard

Therefore,

                Area of U=75/5

                 Area of U =15 square yard

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pls help me

Josh is the owner of CranBog, a Cranberry Bog in Massachusetts. Cranberry production at CranBod can be represented by the inequality y ≤ 150x - 3100
under normal climate conditions, where y
is the annual production of cranberries at CranBog, in thousands of pounds, and x
is the number of acres of land that produce cranberries.

Answers

The TRUE statements about the inequality y ≤ 150x - 3100 are:

A) For a solution to be viable, both x and y must be integers.E) The ordered pair (40, 2900) is a solution to the inequality and means that with 40 acres of land, CranBog can produce 2,900 (in thousands of) pounds of cranberries.

What is inequality?

Inequality refers to a mathematical statement claiming the inequality of two or more mathematical expressions.

The following types and inequality symbols represent inequalities:

Less than (<)Greater than (>)Not equal to (≠)Less than or equal to (≤)Greater than or equal to (≥).

Check:

Ordered pairs (40, 2900)

y ≤ 150x - 3100

y ≤ 150(40) - 3100

y ≤ 6,000 - 3100

y ≤ 2900

Thus, the true statements about this inequality are Options A and E.

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What is the answer for -7g+3-8-3g+7h

Answers

Answer:

= -10g - 5 + 7h

Step-by-step explanation:

= -7g +3 - 8 - 3g + 7h

Grouping of like terms

= -7g -3g + 3 - 8 +7h

= -10g - 5 + 7h.

Karin wants to use the distributive property to mentally find the value of
19⋅42+19⋅58
.

Which expression can she use?

Answers

Answer:

19(42 + 58)

Step-by-step explanation:

19(100)

1900

in an equilateral triangle the altitude is sqrt7 find the length of the sides​

Answers

Answer:

Length of each side = 3.055

Step-by-step explanation:

The relationship between altitude h and side a of an equilateral triangle is

[tex]h = \dfrac{\sqrt{3} }{2} a\\\\\\\rightarrow a = \dfrac{ 2h}{{\sqrt{3} }}\\\\[/tex]

Given h = √7.

we get

[tex]a = \dfrac{2\sqrt{7} }{\sqrt{3} }\\\\a = 2 \sqrt{\dfrac{7}{3}}\\\\a = 2\times 1.5275\\\\a = 3.055\\\\[/tex]

find the missing term in the series given below 3,12,25,42?88

Answers

Answer:

63

Step-by-step explanation:

the value of the difference between the terms increases by 4 as the series continues.

basically, this shows that the difference between 3 and 12 is 9, the difference between 12 and 25 is 13 (which is 4 more than 9), the difference between 25 and 42 is 17 (which is 4 more than 12), and so on.

using this pattern, all we have to do is find the next difference- the one between 42 and the missing term.

to do this, we take the previous difference, 17, and add 4. this gives us 21.

we then add 21 to 42 to get the next term: 63.

hope this helped, good luck!

Express the area of the shaded region in the room shown algebraically

Answers

to find the shaded area you have to subtract the unshaded small rectangles area from the larger rectangles total area

the larger rectangles area (L) is found by multiplying base by height:
(x+3) • 2x = 2x^2 + 6x

the smaller rectangles area (S) is also found by multiplying base by height:
x • 5 = 5x

then to find the unshaded area take the largest rectangle area and subtract the smaller rectangle (L-S):
2x^2 + 6x - 5x = 2x^2 + x

answer: 2x^2 + x

The solution of a system of equations is (3,2). One of the solutions in the system is 2x + 3y = 12. Write an equation in slope-intercept form that could be the second equation in the system.

Answers

y = -2/3x + 4 is an equation in slope-intercept form that could be the second equation in the system.

What are Systems of equations?

simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given, The solution of a system of equations is (3,2). One of the solutions in the system is 2x + 3y = 12.

From the general formula of Slope intercept form:

y = mx + c

where,

m = slope

c = y-intercept of the equation

Thus in our case,

2x + 3y = 12

=> 3y = -2x + 12

=> y = -2/3x + 4

thus, the Slope of the line = -2/3

and another coordinate (0, 4)

Therefore,  an equation in slope-intercept form that could be the second equation in the system is y = -2/3x + 4.

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Let f and g be the functions given by f (x) = e^x and g (x) = x^4. On what intervals is the rate of change of f (x) greater than the rate of change of g (x)? (A) (0.831, 7.384) only(B) (0.831) and (&.384)(C) (0.816) and (1.430, 8.613)(D) (0.816, 1.430) and (8.613)

Answers

The rate of change of a function at a point is given by its derivative. To compare the rate of change of f(x) and g(x) at different points, we need to find the derivative of both functions and compare them.as explained below :

The derivative of f(x) = e^x is f'(x) = e^x

The derivative of g(x) = x^4 is g'(x) = 4x^3

Now we need to compare the two derivatives to find on which intervals the rate of change of f(x) is greater than the rate of change of g(x). To do this, we will find the point of intersection between the two functions and compare them.

e^x = 4x^3

Taking the natural logarithm of both sides we get:

x = ln(4x^3) / ln(e)

Approximating we get x ≈ 0.816 and x ≈ 1.430 and x ≈ 8.613

For x < 0.816, e^x < 4x^3, so the rate of change of f(x) is smaller than the rate of change of g(x)

For x > 8.613, e^x > 4x^3, so the rate of change of f(x) is greater than the rate of change of g(x)

Between 0.816 < x < 1.430 and 1.430 < x < 8.613, e^x = 4x^3, so the rate of change of f(x) is equal to the rate of change of g(x).

So the answer is (D) (0.816, 1.430) and (8.613)

Note that the answer (B) (0.831) and (&.384) is not possible as the point of intersection is a number and not an interval and the answer (A) (0.831, 7.384) is not correct as the point of intersection is 1.430 and 8.613 not 0.831 and 7.384

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5 1/8 equals 4 + 1 + 1/8 = 4 + blank 8 + 1/8 =

Answers

The blanks in the equation are filled as below

5 1/8 = 4 + 1 + 1/8 = 4 + 1/8 8 + 1/8 = 5 1/8

How to fill the blanks in the equation

To fill the blanks the equation is written completely in figures

5 1/8 = 4 + 1 + 1/8 = 4 +   8 + 1/8 =  

From the knowledge of equality to maintains a true equation the last blank should be equal to 5 1/8.

With this information, we use addition operation to solve for the first blank as follows.

let the first blank be x

4 +   8 + 1/8 = 5 1/8

4 + x * 8 + 1/8 = 5 1/8

4 + 8x + 1/8 = 5 1/8

collection like terms

8x = 5 1/8 - 4 - 1/8

8x = 1

divide both sides by 8

x = 1/8

the blanks are 1/8 and 5 1/8

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Which of the following statements correctly reflect the rule governing rounding in a calculation? Select all that apply. Check all that apply. O The number of significant figures in the answer are determined by an average of the number of significant figures in all the quantities involved. O The least certain measurement determines the certainty of the answer. O Rounding is necessary when there are too many digits after a calculation. O All answers are rounded to two decimal places after a calculation. Read about this Do you know the answer?

Answers

The least certain measurement determines the certainty of the answer.

What guidelines apply when rounding sig figs?

(1) The final digit that is preserved is raised by one if the digit to be eliminated is greater than 5. As an illustration, 12.6 is rounded to 13.

                                      (2) The last digit that remains is left alone if the digit to be dropped is less than 5. As an illustration, 12.4 is rounded to 12.

Which of the following statements best describes the significant figures rule?

Use the following 3 principles to calculate how many significant figures are present in a number: The significance of non-zero digits is constant.

                                   A significant zero is one that comes in between two significant digits. ONLY the decimal part has any significance when there is a final zero or trailing zeros.

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Find the measure of each angle that adds up to 180

Answers

Answer:

? = 50°

Step-by-step explanation:

we have a right triangle, therefore with an angle of 90° (red sign) and an angle of 40°, knowing that the sum of the interior angles of all triangles is 180° we remove the known angles from 180° and find the value of angle "?"

180 - 90 - 40 =

50°

BA
6. Kathleen spent $231 on concert tickets
for herself and 11 friends. Each ticket
cost the same.
Part A
Estimate the cost of each ticket. Write an
equation to show your work.
Part B
Find the exact cost of each ticket.
Compare your answer to your estimate
to check for reasonableness.

Answers

The equation of cost of each ticket is 11k = 231 and the exact cost of each ticket is $21.

What is algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants .

Given,

Kathleen spent $231 on concert tickets for herself and 11 friends. Each ticket cost the same.

So we have to find the cost of each ticket. Write an equation to show your work and the exact cost of each ticket. Compare your answer to your estimate to check for reasonableness.

From the given information ,

The equation to show the work could be ,

231 = k * 11

SO, this is the equation 11k = 231 .

we can say that,

= $231 / 11

= $21

Hence, the equation of  cost of each ticket is 11k = 231 and the exact cost of each ticket is $21

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which of the following time-series plots is the most appropriate? hint: pay close attention to the title, axes labels, and scale.

Answers

The most appropriate time-series plot will depend on the data being visualized. The title, axes labels, and scale should all be chosen to accurately describe the data and provide the clearest understanding of the data.

The most appropriate time-series plot for a particular dataset will depend on the data being visualized. The title, axes labels, and scale should all be chosen carefully to accurately describe the data and provide the clearest understanding of the data. For example, for a time series of stock prices, the title could be "Stock Price Over Time", the axes could be labeled "Time" and "Price", and the scale could range from the lowest to the highest stock price. Additionally, the time intervals should be appropriately labeled, such as monthly, quarterly, or annually. It is important to choose the right type of plot to ensure that the data is accurately and clearly represented.

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The complete question is

which of the following time-series plots is the most appropriate? hint: pay close attention to the title, axes labels, and scale should all be chosen to accurately.

Jada measured the height of a plant in a science experiment and finds that, to the nearest 1/4 of an inch, it is 4.75 inches.

Answers

The actual length of the tree based on the information is 19 inches.

How to calculate the word problem?

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

Since Jada measured the height of a plant in a science experiment and finds that, to the nearest 1/4 of an inch, it is 4.75 inches.

The actual length will be:

= 4.75 × 4

= 19 inches

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Complete question

Jada measured the height of a plant in a science experiment and finds that, to the nearest 1/4 of an inch, it is 4.75 inches. What is the actual length of the tree?

Polynomial 1: 4x2
+ 5x − 4
Polynomial 2: 4x2
+ 4x − 2
Question 1



What is the difference when polynomial 2 is subtracted from polynomial 1?
Responses


A x − 2x − 2


B x − 6x − 6


C x + 6x + 6


D x + 2

Answers

Answer:

x + 2  (Choice D)

Step-by-step explanation:

The two polynomials are
P1 = 4x² + 5x - 4  

and

P2 = 4x² + 4x - 2

P1 - P2

==>  (4x² + 5x - 4 ) -  (4x² + 4x - 2)

Expanding brackets we get

==> 4x² + 5x - 4 - 4x² - 4x + 2        (signs inside the second parentheses are    

                                                 reversed because of the - sign preceding it)

Group similar terms and add the coefficients

==> (4x² - 4x²) +(5x - 4x) +(-4 + 2)

==> 0 + x + 2

==> x + 2  (Choice D)

During the week Jimmy spent $45 eating out, gained $55 mowing lawns and spent $15on gas. What was Jimmy's change in dollars at the end of the week?

Answers

The change in dollars at the end of the week is - $5

How to determine the amount received as change

From the question, we have the following parameters that can be used in our computation:

Amount spent = $45

Amount gained = $55

Amount spent on gas = $15

The change is then calculated as

Change = Amount gained - Amount spent - Amount spent on gas

Substitute the known values in the above equation, so, we have the following representation

Change = 55 - 45 - 15

Evaluate

Change = -5

Hence, the change is a deficit of $5

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Another way to express cis 75∘+cis 83∘+cis 91∘+⋯+cis 147∘

Answers

the value of theta in the given complex expression is equal to 16°.

Given, a number. [tex]rcis\theta, is[/tex] expressed by.

cis75° + cis83° + cis91°+.... + cis147°.

we have to find the value of angle in degrees.

The function cisA is a shorthand way of writing the equivalent expression cisA=cosA+i sinA

By definition: CisA=CosA+iSinA

This form simplifies complex arithmetic and allows for the study of complex analysis, as well as reduces the workload in writing the expressions.

now, we have to find the sum of the given expressions.

[tex]cis75+cis83+cis91+...+cis147 as, cis\theta=e^{i\theta}[/tex]

[tex]e^{75i}+e^{83i}+e^{91}+....+e^{147i}\\\\e^{\frac{75\pi}{180} }+e^{\frac{83\pi}{180} }+.....+e^{\frac{147\pi}{180} }[/tex]

on using geometric sum of the series we get,

[tex]Sum=\frac{e^{\frac{75i\pi}{180}}(1-e^{\frac{72i\pi}{180} ) }}{(1-e^{\frac{8i\pi}{180} })}\\ \\\theta=16[/tex]

the value of theta of the angle be 16 degree.

the complete question is.

The number cis 75 + cis 83 + cis91 +...+ cis 147 is expressed in the form r cis(theta), where 0 <= theta < 360.

Find theta in degrees.

learn more about complex analysis.

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Question 2 (1 point) The results of a survey of 70 Programming students on learning preferences were as follows: 50 liked to learn visually, 45 liked learning through listening and 35 liked learning through videos. 5 liked using all three channels, 32 liked to learn visually and through listening, 22 liked to learn both visually and videos, 14 liked to learn through listening and videos. How many preferred learning only through videos? options-(9, 17 ,13, 4)​

Answers

9 students preferred learning only through videos.

What is inclusion-exclusion from the data provided?

Inclusion-exclusion is a principle used in counting to find the total number of elements in a union of sets by subtracting the elements that are counted multiple times and adding back in the elements that are not counted at all.

The number of students who preferred learning only through videos is 17.

This can be found by using the principle of inclusion-exclusion:

35 students liked to learn through videos

14 students liked to learn through listening and videos

5 students liked all three channels

So, 35 - 14 + 5 = 26 students liked to learn through videos and listening

Therefore, 35 - 26 = 9 students preferred learning only through videos.

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