At this year's State Fair, there was a dice rolling gamne. If you rolled two dice and got a sum of 2 or 12, you won $12. If you rolled a 7, you won $5. Any other roll was a loss. It cost $1 to play one game with one roll of the dice. What is the expectation of the game? Round your answer to the nearest cent.
The expectation of this game is approximately dollars.
Answers
the expectation of the game is $0.22 per game. This means that on average, for every game played, the player can expect to win $0.22. However, this does not guarantee that the player will actually win $0.22 every time they play the game. It simply means that over many plays of the game, the player's winnings will average out to $0.22 per game.
How to solve the probability?
To find the expectation of the game, we need to calculate the probability of winning and losing and multiply them by their corresponding payoffs.
First, let's calculate the probability of rolling a sum of 2 or 12. There is only one way to roll a sum of 2 or 12, which is by rolling a pair of ones or a pair of sixes, respectively. So, the probability of rolling a sum of 2 or 12 is:
P(2 or 12) = P(1,1) + P(6,6) = (1/6) * (1/6) + (1/6) * (1/6) = 1/18
Next, let's calculate the probability of rolling a 7. There are six ways to roll a sum of 7, which are: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). So, the probability of rolling a 7 is:
P(7) = P(1,6) + P(2,5) + P(3,4) + P(4,3) + P(5,2) + P(6,1) = 6 * (1/6) * (1/6) = 1/6
Finally, the probability of losing is:
P(loss) = 1 - P(2 or 12) - P(7) = 1 - 1/18 - 1/6 = 11/18
Now, we can calculate the expectation of the game as follows:
E(X) = (12 * P(2 or 12)) + (5 * P(7)) - (1 * P(loss))
= (12 * 1/18) + (5 * 1/6) - (1 * 11/18)
= 2/9 + 5/6 - 11/18
= 0.22
So, the expectation of the game is $0.22 per game. This means that on average, for every game played, the player can expect to win $0.22. However, this does not guarantee that the player will actually win $0.22 every time they play the game. It simply means that over many plays of the game, the player's winnings will average out to $0.22 per game.
To know more about probability visit :-
https://brainly.com/question/13604758
#SPJ1
Related Questions
The height in inches of a candle that has been burning for x hours is represented by the equation h=12−x . What is the meaning of the y-intercept in the context of the burning candle?
Answers
the y-intercept of the equation h=12−x represents the initial height of the candle when it is first lit, which is 12 inches in this case.
How to solve the question ?
In the given equation, h represents the height of the candle in inches and x represents the number of hours for which the candle has been burning.
The y-intercept of the equation is the point where the graph of the equation intersects the y-axis, which occurs when x is equal to 0. Substituting x=0 in the equation, we get:
h=12-0
h=12
Therefore, the y-intercept of the equation is 12, which means that when the candle is first lit (x=0), its height is 12 inches.
In the context of the burning candle, the y-intercept represents the initial height of the candle before it starts to burn. This is the height of the candle when it is first lit and before any wax has melted. As the candle burns and wax melts, the height of the candle decreases, and this is represented by the negative slope of the equation.
In summary, the y-intercept of the equation h=12−x represents the initial height of the candle when it is first lit, which is 12 inches in this case.
To know more about height visit:-
https://brainly.com/question/28122539
#SPJ1
need help writing a equation for this in the picture
(100 points)
Answers
The equation of circle with endpoints at (-3, 0) and (3, 0) is x² + y² = 9
What is the equation of circle?The end points (-3, 0) and (3, 0) represent the endpoints of a diameter of the circle. The center of the circle is the midpoint of this diameter. We can find the midpoint of the diameter by averaging the x-coordinates and the y-coordinates of the endpoints:
Midpoint = ((-3 + 3)/2, (0 + 0)/2) = (0, 0)
So the center of the circle is at the point (0, 0). The radius of the circle is half the length of the diameter, which is:
Radius = 1/2 * distance between (-3, 0) and (3, 0)
= 1/2 * 6
= 3
Therefore, the equation of the circle with endpoints at (-3, 0) and (3, 0) is:
(x - 0)² + (y - 0)² = 3²
Simplifying:
x² + y² = 9
So the equation of the circle is x² + y² = 9.
Learn more on equation of circle here;
https://brainly.com/question/3778683
#SPJ1
1 + tan ( θ ) ÷ 1 − sin ( θ ) = ( tan ( θ ) + csc ( θ ) 2
Answers
Answer:
4655
Step-by-step explanation:
this is not correct question because I know that is omath question
use the number lineto find the difference 3 1/2 - 5
a. -8 1/2
b. -1 1/2
c. 2 1/2
d. -2 1/2
Answers
Answer:
Step-by-step explanation:
Find the area of this shape
Answers
200.55ft³
12×12= 144 (area of the square)
pi×radius² = area of a circle but since it is only half a circle, divide the answer by two and add the area of the semi circle and square for the total area
which expression represents the situation "add seven to the product of a number and ten?
A-10(z+7)
B-7+z+10
C-10z+7
D-7z+10z
Which one?
Answers
The situation "add seven to the product of a number and ten" can be represented by the expression 10z + 7, where z is the number. The expression 10z represents the product of a number and ten, and adding 7 to it gives the final result. Therefore, the correct answer is C-10z+7.
There are 200 members in a club. 60% of them are males. How many percent more males than females are there?
Answers
im struggling with this question could someone help me please
Answers
Answer:
9
Step-by-step explanation:
= 6 ÷ 2(1 + 2)
= 6 ÷ 2 x 3
= 9
hope that helps!
Riku Book has 49 pages. The front cover is 9. Inches long and 6. Inches wide what. Is the area of the front cover?
Answers
Hi
Covert is a rectangle. Area if rectangle is side x side
so one side is 6 and the other 9.
I let you conclude.
Answer: The area of the front cover is 54 inches squared
Step-by-step explanation:
To find the area of any rectangle all you have to do is multiply the base by the height. In this case, you would multiply 6 ( The base ) by 9 ( The height ) getting you 54 inches squared.
enter an equation for which the solution is the daily room charge, in dollars per day, when a person stays at the hotel for 3 day and is charged a total of $234.
Answers
Using equations, the daily room charge, in dollars per day, is $78 per day.
What are Equations?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let x be the daily room charge, in dollars per day.
Then the total charge for staying for 3 days is 3x dollars.
According to the problem statement, the total charge for staying for 3 days is $234. So we can set up the equation:
3x = 234
To solve for x, we can divide both sides by 3:
[tex]3x/3 = 234/3[/tex]
x = 78
Therefore, the daily room charge, in dollars per day, is $78 per day.
To learn more about Equations, click on the link:
https://brainly.com/question/27893282
#SPJ1
The graph of a piecewise function is shown.
What is the end behavior of the function?
Answers
The end behavior of the function is As x → -∞, f(x)→ -∞ and as x→ ∞, f(x)→ -∞, so correct option is C.
Describe function ?In mathematics, a function is a rule that assigns a unique output or value to each input or element in a given set. It is a mathematical object that describes how one quantity (the output) depends on another quantity (the input).
A function can be represented by a graph, a table, or an algebraic equation. The input values are usually denoted by the variable x, while the output values are denoted by the variable y, f(x), or some other symbol. The notation f(x) is read as "f of x" and is used to represent the output value of the function when the input value is x.
A function can be defined in various ways:
Geometrically, by specifying a curve or surface in the plane or in space.
Algebraically, by specifying a formula or equation that gives the output in terms of the input.
Numerically, by specifying a table of input-output pairs.
Verbally, by giving a description of how the output depends on the input.
The end behavior of the function is As x → -∞, f(x)→ -∞ and as x→ ∞, f(x)→ -∞, so correct option is C.
To know more about equation visit:
https://brainly.com/question/22964920
#SPJ1
recently, alicia went on a trip. on the first part of the trip, she drove 260 miles to visit her grandparents. this distance is 4/5 of the total she traveled. what equation can you use to find d, the total length of her trip in miles
Answers
The equation that can be used to find d, based on the options for the parts of the equation is; (4/5) × d = 260
What is an equation?An equation is a statement of equivalence between expressions.
The specified equation is; _ _ d = _
The distance of the first part of Alicia's trip = 260 miles
The part of the total distance traveled of the trip represented by the first part of Alicia's trip = 4/5
The total length of Alicia's trip = d
An equation that can be used to find the total length of Alicia's trip therefore is; (4/5) × d = 260
The total distance traveled, d, can be obtained from the above equation when d is made the subject of the equation as follows;
(4/5) × d = 260
d = 260/(4/5) = 260 × 5/4 = 325
The total distance Alicia traveled, d = 325 miles
The correct equation is therefore; (4/5) × d = 260
Learn more on writing equations here: https://brainly.com/question/18713037
#SPJ1
Question
Use a net of the square pyramid, if necessary, to find the surface area of the pyramid.
3and3
Answers
The steps to find surface area of pyramid using a net of square pyramid is given below.
find the surface area of a square pyramid using a net:
Start with a net of the square pyramid. A net is a 2-dimensional representation of a 3-dimensional object that can be folded into the shape of the object. Identify the different faces of the pyramid. A square pyramid has one square base and four triangular faces.Calculate the area of the base. The base of a square pyramid is a square, so its area is equal to the length of one side squared.Calculate the area of each triangular face. To find the area of a triangle, you can use the formula A = (1/2)bh, where b is the base of the triangle and h is its height. In a square pyramid, each triangular face has a base that is equal to one side of the square base and a height that is equal to the slant height of the pyramid.Add up the areas of all the faces to find the total surface area of the pyramid.The slant height of a square pyramid can be found using the Pythagorean theorem, where a and b are the length of one side of the base and h is the height of the pyramid:
slant height = √(a² + (1/2×h)²)
To learn more about square pyramid click here
brainly.com/question/27350043
#SPJ4
pleaseeee and thanks
Answers
1. The function has x-intercepts at x = -2 and x = 3, so the answer is
A.(- 2, 0) * and(3, 0).
2. The y-values are increasing on the interval from x = -3 to x = -1, and from x = 1 to x = 3. So the answer is B, -3 < x < -1.
What is x-intercept?
1. To find the x-intercepts of the quadratic function, we need to find the values of x for which y is equal to 0.
The x-intercept of a function is the point at which the graph of the function intersects the x-axis. At the x-intercept, the value of y (the output of the function) is equal to zero, which means that the corresponding input value of x causes the function to have an output of zero.
From the table, we can see that the function has x-intercepts at x = -2 and x = 3, so the answer is A.
What is an interval?
2. To determine where the function is increasing, we need to look for intervals where the y-values are increasing as x increases.
From the table, we can see that the y-values are increasing on the interval from x = -3 to x = -1, and from x = 1 to x = 3. So the answer is B, -3 < x < -1.
To know more about x-intercept, visit:
https://brainly.com/question/14180189
#SPJ1
I really need some help
Answers
a) Annual interest = 0.18
b) Compoundings = 3
c) Number of years = 7 years
d) Total Compoundings = 21
Compound interest:Compound interest is the concept of adding interest to the principal amount of a loan or investment and then calculating the interest for the next period based on the new total.
This means that the interest earned or charged on an investment or loan is not only depends on the principal amount and the interest rate but also on the time period and the frequency of compounding.
Here we have
18% compounded every 4 months for 7 years
a) The annual interest rate as decimal = 18% = 18/100 = 0.18
b) Number of compoundings = 12/4 = 3
[∵ Compounded for every 4 months ]
c) Number of years = 7 years
d) Total number of compoundings is 7 × 3 = 21
Therefore,
a) Annual interest = 0.18
b) Compoundings = 3
c) Number of years = 7 years
d) Total Compoundings = 21
Learn more about Compound interest at
https://brainly.com/question/14295570
#SPJ1
Goods in transit worth K95 480 were insured against damage at k 682 in every K27 200 worth of goods. Find the premium for insuring the goods.
Answers
Answer: To find the premium for insuring the goods, we need to determine the total amount of insurance that is needed and then calculate the cost of the insurance based on the given rate.
The total amount of insurance needed is equal to the value of the goods in transit, which is K95 480.
To determine the cost of the insurance, we can use the given rate of K682 for every K27 200 worth of goods. We can set up a proportion:
(K682 / K27 200) = (premium / K95 480)
To solve for the premium, we can cross-multiply and simplify:
K682 * K95 480 = K27 200 * premium
premium = (K682 * K95 480) / K27 200
premium = K1 897.12
Therefore, the premium for insuring the goods is K1 897.12.
Step-by-step explanation:
what dimensions does an rectangle havee
Answers
This is a picture of a cube and the net for the cube.
What is the surface area of the cube?
Answers
The surface area of the cube from the net has a value of 1176 square centimeters.
What is the surface area of the cube?The surface area of a cube is given by the formula:
Surface area = 6 × (length of a side)^2
If the length of the side of the cube is 14 centimeters, then the surface area is:
Surface area = 6 × (14 cm)^2
Surface area = 6 × 196 cm^2
Surface area = 1176 cm^2
Therefore, the surface area of the cube is 1176 square centimeters.
Read more about surface area at
https://brainly.com/question/16519513
#SPJ1
Rizio Company purchases a machine for $10,300, terms 1/10, n/60, FOB shipping point. Rizio
paid within the discount period and took the $103 discount. Transportation costs of $233
were paid by Rizio. The machine required mounting and power connections costing $712.
Another $336 is paid to assemble the machine, and $40 of materials are used to get it into
operation. During installation, the machine was damaged and $250 worth of repairs were
made.
Complete the below table to calculate the cost recorded for this machine.
Amount Included in Cost of Equipment:
Invoice price of machine
Net purchase price
recorded
0
0
Answers
Amount Included in Cost of Equipment:
Invoice price of machine = $10,300
Less: Discount received = $103
Net purchase price = $10,300 - $103 = $10,197
Additional costs incurred:
Transportation costs = $233
Mounting and power connections = $712
Assembling cost = $336
Materials cost = $40
Repair cost = $250
Total additional costs = $233 + $712 + $336 + $40 + $250 = $1,571
Cost recorded for this machine:
Net purchase price + Total additional costs = $10,197 + $1,571 = $11,768
Therefore, the cost recorded for this machine is $11,768.
question in picture thank you
Answers
Solve each absolute value inequality and show its solution set.
|5t-1|>21
Answers
The solution set of the given inequality is (-4, 4.4)
Here are the steps to follow when solving absolute value inequalities:
Isolate the absolute value expression on the left side of the inequality.
If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions.
Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.
|5t-1| > 21
case 1)
for positive
5t-1 > 21
5t > 22
t > 4.4
for negative
-(5t-1) > 21
-5t+1 > 21
-5t > 20
t< -4
hence the solution set of the given inequality is (-4, 4.4)
learn more about absolute value inequalities:
https://brainly.com/question/30201926
#SPJ1
what is the constant of 20x+6
Answers
Answer:
6
Step-by-step explanation:
PLS HELP ASP!!!!
A race car drove around a circular track that was 0.5 mile. If 1 mile = 5,280 feet, what is the radius of the track, in feet? Use π = 3.14 and round to the nearest hundredth.
124.20 feet
248.41 feet
420.38 feet
840.76 feet
Answers
the radius of the track is approximately 420.38 feet.
Why is it?
The circumference of the circular track is 0.5 miles or 0.5 × 5280 = 2640 feet.
The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
Therefore, 2640 = 2 × 3.14 × r
Simplifying the equation: 2640 = 6.28r
Dividing both sides by 6.28: r ≈ 420.38 feet
Therefore, the radius of the track is approximately 420.38 feet.
Circumference is the distance around the edge of a circle or any other curved, circular object. It is also the perimeter of the circle. It is calculated by multiplying the diameter of the circle by pi (π), which is a mathematical constant that is approximately equal to 3.14.
To know more about Circumference related question visit:
https://brainly.com/question/28757341
#SPJ1
PLEASE HELP
At this year's State Falr, there was a dice rolling game. If you rolled two dice and got a sum of 2 or 12, you won $12. If you rolled a 7, you won SS. Any other
roll was a loss. It cost $1 to play one game with one roll of the dice. What is the expectation of the game? Round your answer to the nearest cent.
The expectation of this game is approximately dollars.
Answers
Expectation of the gain for the given outcomes on rolling fair dice is:
E = $0.5
Explain about the total outcome:The total number of outcomes for such probability experiment is known as the total number of outcomes in probability.
For rolling sum 2 and 12 - {(1,1), (6,6)}
Total number of possible outcomes = 2 (that is 2 and 12)
As, either 2 or 12 will appear. So, there will be 1 gain and one loss.
Gain for rolling 2 or 12 is $12 and for loss $1
Gain = 12 - 1 = $11
For rolling sum 7 - {(1,6),(6,1),(2,5),(5,2),(4,3),(3,4)}
Gain for rolling 7 - $5 and for loss $1
Total number of possible outcomes = 6
Gain = 5 - 1 = $4
For others:
Total number of possible outcomes = 36 - (2+6) = 28
Loss = -$1
Expectation of total gain;
E = (2×11 + 6×4 - 28×1)/36 = 18/36
E = 1/2
E = $0.5
Thus, Expectation of the gain for the given outcomes on rolling fair dice is: E = $0.5
Know more about the total outcome
https://brainly.com/question/16357763
#SPJ1
Complete question:
At this year's State Falr, there was a dice rolling game. If you rolled two dice and got a sum of 2 or 12, you won $12. If you rolled a 7, you won $5. Any other roll was a loss. It cost $1 to play one game with one roll of the dice. What is the expectation of the game? Round your answer to the nearest cent.
The expectation of this game is approximately dollars.
use compensation to add or subtract the following (a) 468+59. (b)458-49. (c) 499+599+699. d 10000- 599
Answers
Answer: A = 527
Step-by-step explanation:
468+59 = 468+(1+58)=(468+1)+58=527
The given addition and subtraction can be done using compensation as follows.
What is Compensation?Compensation is the method of adding or subtracting numbers by making the numbers easier.
(a) 468 + 59
We add 1 to 59 and make it 60, which make it easier to add.
468 + 60 = 528
Subtract the added 1.
528 - 1 = 527
(b) 458 - 49
Subtract 1 and make 49 to 50
458 - 50 = 408
Add 1 and we get, 408 + 1 = 409
(c) 499 + 599 + 699
Add 3 adding one to each, we get,
500 + 600 + 700 = 1800
Subtracting 3, 1800 - 3 = 1797
(d) 10000 - 599
Adding 1, 10000 + 600 = 9400
Subtracting the before added 1, 9400 - 1 = 9399
Hence the operations are done.
Learn more about Compensation here :
https://brainly.com/question/11212342
#SPJ2
what is the period of the sinusoidal function
Answers
The period of the sinusoidal function is 4 seconds
What is period of a wave?The period of a wave is the time it takes for one complete cycle of the wave to occur. In other words, it is the time required for a wave to repeat itself exactly.
The period of a wave is typically denoted by the symbol "T" and is measured in units of time, such as seconds.
In the function plotted the time to complete one oscillation is solved to be 4 seconds
The solution is obtained by taking two successive crests or troughs
using two successive troughs we have
= 5 - 1
= 4
Learn more about sinusoidal function at:
https://brainly.com/question/29529184
#SPJ1
you can make one of the following investments:
Option 1: $50 initial investment with an average annual growth rate of 9% starting at age 30
Option 2: $50 initial investment with an average annual growth rate of 8% starting at age 20
Option 3: $100 initial investment with an average annual growth rate of 7% starting at age 25
Answers
Answer:
To determine which investment option would yield the highest return, we can calculate the future value of each investment at a certain age. Let's assume we're looking at the value of each investment at age 65. Option 1: $50 initial investment with an average annual growth rate of 9% starting at age 30 Using a compound interest calculator, we can find that the future value of this investment at age 65 would be approximately $1,338. Option 2: $50 initial investment with an average annual growth rate of 8% starting at age 20 Again, using a compound interest calculator, we can find that the future value of this investment at age 65 would be approximately $1,088. Option 3: $100 initial investment with an average annual growth rate of 7% starting at age 25 Using the same calculator, we can find
0
Solve for x. x+8|=-2
Answers
Answer:
To solve for x in the equation x+8|=-2, we first need to isolate the absolute value expression on the left side of the equation. We can start by subtracting 8 from both sides: x + 8 | = -2 x + 8 - 8 | = -2 - 8 x | = -10 Now we can solve for x by considering the two cases for the absolute value: 1. x + 8 = -10 2. -(x + 8) = -10 Solving for x in each case, we get: 1. x = -18 2. x = 2 Therefore, the solutions for x are -18 and 2.
Solving Systems of Linear Equations
Performance Assessment
You are the student council member responsible for planning a school dinner dance. You will
need to choose a caterer, hire a band, analyze costs, and choose flowers for decoration. You
need to keep the ticket price as low as possible and still cover the costs.
Part 1 Choosing a Band
Band A charges a flat fee of $500 to play for the evening.
Band B charges $350 plus $1.50 per student.
Part A: Write a system of equations to represent the cost of the two bands.
Part B: Graph the system of equations and find the number of students for which the cost of
the bands would be equal.
Part 2: Choosing a Caterer
A caterer charges a fixed amount for preparing a dinner plus a rate per student served. The
total cost is modeled by the equation:
Total cost = fixed amount + rate * number of students
You know that the total cost for 50 students will be $450 and the total cost for 150 students
will be $1050. Find the caterer's fixed cost and the rate per student served. Explain your
answer.
Part 3: Analyzing cost
Use the information from Items 1 and 2. Assume that 100 students come to the dinner dance.
Decide which band you should choose and what the total cost per ticket should be to cover
the expenses of the band and caterer. Then repeat your calculations for 200 students.
Explain your reasoning.
Part 4: Choosing Flowers
You can spend no more than $500 on flowers for the event. A bouquet of daisies cost $25
each and a bouquet of roses cost $35 each.
Part A: Write and graph an inequality that represents the number of each type of flower that you can buy.
Part B: Suppose you buy 15 bouquets of daisies. What is the maximum number of bouquets
of roses you can afford? Explain.
Answers
1.Band A: Cost = $500
Band B: Cost $350 + $1.50x
2. The caterer's fixed cost is $150 and the rate per student served is $6.
3.Cost per ticket $12.50
4.we can buy at most 3 bouquets of roses.
What are linear equations?
The first-degree equations are linear equations. The straight line's equation can be found here. ax+by+c=0 is the most common form of a linear equation, where a and b are zeros.
Part 1:
Let x be the number of students.
Band A: Cost = $500
Band B: Cost $350 +$1.50x
The system of equations representing the cost of the two bands is:
CostA = 500
CostB = 350+ 1.5x
Part 2:
Let F be the fixed cost and R be the rate per student served.
From the given information, we can write two equations:
50R + F = 450
150R + F = 1050
Subtracting the first equation from the second, we
get:
100R = 600
Therefore, R = 6.
Substituting R in the first equation, we get:
50(6)+F450
Therefore, F = 150.
So, the caterer's fixed cost is $150 and the rate per student served is $6.
Part 3:
For 100 students:
CostA 500
CostB = 350+ 1.5(100) 500
Both bands have the same cost, but Band A has a lower variable cost.
So, we should choose Band A.
Total cost for 100 students = 500 + 150+ 6(100) =
$1250
Cost per ticket = Total cost / Number of students = 1250/100 = $12.50
For 200 students:
CostA = 500
CostB = 350+ 1.5(200) = 650
Band A still has a lower cost, so we should choose Band A.
Total cost for 200 students 500+ 150 + 6(200) = $1850
Cost per ticket = Total cost / Number of students =
1850/200 $9.25
Part 4:
Let D be the number of bouquets of daisies and R be the number of bouquets of roses.
The cost of daisies is $25 per bouquet and the cost of roses is $35 per bouquet. We want to spend no more than $500, so we can write:
25D +35R < 500
If we buy 15 bouquets of daisies, then we can spend at most $425 on roses:
25(15) + 35Rs 500
375 +35R ≤ 500
35R ≤ 125
If we buy 15 bouquets of daisies, then we can.
Mathematics College spend at most $425 on roses:
25(15)+35R ≤ 500
375 +35R≤ 500
35R ≤ 125
R≤ 3.57
So, we can buy at most 3 bouquets of roses.
know more about inequality visit
https://brainly.com/question/30238989
#SPJ1
A tree casts a shadow 21 m long. The angle of elevation of the sun is 51°. What is the height of the tree? Record your answer in the table below.
Answers
Answer:
17.2 meters
Step-by-step explanation:
We can use the tangent function to solve this problem. Let's denote the height of the tree as h. Then we have the following:
tan(51°) = h / distance from the tree to the end of the shadow
We can find the distance from the tree to the end of the shadow by using the length of the shadow and the angle of elevation of the sun. Since the shadow is 21 meters long, and the angle of elevation of the sun is 51°, we can use the following trigonometric relationship:
tan(51°) = h / distance from the tree to the end of the shadow
tan(51°) = h / x (where x is the distance from the tree to the end of the shadow)
To find x, we can use the following trigonometric relationship:
tan(39°) = h / x (where 39° is the complementary angle to 51°)
We can solve for x by rearranging this equation as follows:
x = h / tan(39°)
Substituting this expression for x into the first equation, we have:
tan(51°) = h / (h / tan(39°))
Simplifying this equation, we get:
h = (21 m) * tan(51°) / tan(39°)
Using a calculator, we find h to be the following:
h = 17.2 meters
Therefore, the height of the tree is approximately 17.2 meters.