The area of the shaded region is 75.48 rounded to the nearest hundredth, considering the areas of the circle and rectangle
How to calculate for the area of the shaded regionWe have to first calculate for the area of the rectangle, and then calculate for the area of half the circle and then subtract it from the area of the rectangle to get the area of the shaded region.
Area of rectangle = Length × breadth
Area of rectangle = 12 × 11(diameter of the circle is also the length of the rectangle)
Area of rectangle = 132.
Area of circle = πr²
Area of the circle = 3.14 × 6² (6 is the radius given that the diameter = 12)
Area of the circle = 3.14 × 36
Area of the circle = 113.04
Half the area of the circle = 113.04/2
Half the area of the circle = 56.52
Area of the shaded region = 132 - 56.52
Area of the shaded region = 75.48
Therefore, by calculating for areas of the circle and rectangle, we are able to derive the area of the shaded region to be 75.48
Learn more about area here:https://brainly.com/question/25292087
#SPJ1
Will give Brainliest if you can answer thesw questions
Based on this information we can conclude that in one hour, Oliver and his sister would get all of the windows washed. This means that it would take 5/6 hours which is equal to 50 minutes) for them to get all of the windows washed.
What is information?Information is defined as the content of a message which is passed from a source to its receiver.
The number of hours it takes for Oliver to wash the house windows = 2 hours, so in an hour = 1/2
The number of hours it takes his sister to wash the same house windows = 3 hours, so in an hour = 1/3.
To calculate for one hour for both would be addition of the derived fractions;
= 1/2 + 1/3
= 3+2/6
= 5/6
When converter to minutes, multiple by 60;
= 5/6 × 60
= 300/6
= 50 minutes.
Learn more about minutes to hours here:
https://brainly.com/question/25169144
#SPJ1
The UK currently has a progressive income tax system. The rules are as follows: Any earnings under 11,500 GBP are taxed at 0%. Any earnings between 11,500 GBP and 33,500 GBP are taxed at 20%. Any earnings between 33,500 GBP and 150,000 GBP are taxed at 40%. Any earnings above 150,000 GBP are taxed at 50%. A person earns 50,000 GBP gross. How much tax do they pay? Round your answer to the nearest GBP.
The amount of tax that the executive would pay on his income is; 20000 GBP
How to calculate tax deductions?Tax is defined as a compulsory payment that is levied on the income or on the sales of specific goods and services. Tax is usually imposed by the government to get a variety of macroeconomic objectives.
Now, income tax is the tax that is levied on the income of an individual. There are different types of taxes, such as progressive tax which levies a higher tax percentage on those that earn higher incomes This means invariably that the tax rate increases as income increases.
We are given;
Gross Amount executive earns = 50,000 GBP.
We are told that any earnings between 33,500 GBP and 150,000 GBP are taxed at 40%.
Thus;
Tax that would be paid = tax rate * gross income
Tax that would be paid = 50000 * 0.4 = 20000 GBP
Read more about Tax calculations at; https://brainly.com/question/10137785
#SPJ1
Answer: 11,000
Step-by-step explanation:
The person earns 50,000 GBP, so they will stop at the tier 3 level of tax.
The first 11,500 GBP is tax free. They will be taxed 20% on (33,500−11,500)=22,000 GBP, and they will be taxed 40% on (50,000−33,500)=16,500 GBP. Hence the total tax (in GBP) they need to pay is
Total Income Tax=11,500×0%+22,000×20%+16,500×40%=0+22,000×20100+16,500×40100=0+4,400+6,600=11,000
A friend has a 85% average before the final for a course. That score includes everything but the final, which counts for 20% of the course grade. a.) What is the best course grade your friend can earn? % b.) What is the minimum score your friend would need on the final to earn a 75% for the course? % Give answers accurate to at least one decimal place.
The best course grade your friend can earn is 88%.
The minimum score your friend needs to have on the final to earn a 75% for the course is 35%.
What is the minimum score your friends needs to have on the final exam?If the final counts for 20% of the course grade, it means that the average of 85% counts for 80% (100 - 20%) of the total score.
The linear expression that can be used to determine the best course grade your friend can earn is:
(average that has already been accumulated x 80%) + (score on the finals x 20%)
(85% x 80%) + (20% x 100%)
(85% x 0.80) + (0.2 x 100%)
68 + 20 = 88%
The linear equation that can be used to determine the minimum score that can be earned on the final to have75% in the course is
Final grade = (total average before the final x 80%) + (score on the final x 20%)
75% = (85% x 80%) + (f x 20%)
75% = (85% x 0.80) + (0.20 x f)
75% = 68% + 0.20f
75% - 68% = 0.20f
7 = 0.20f
f = 7% / 0.20
f = 35%
To learn more about percentages, please check: https://brainly.com/question/25764815
#SPJ1
Which of the following is an example of a conditional statement?
A square banquet hall has an area of 3600m², what is the length of the room?
If the square banquet has area = 3600m² then length of the room is 60 m .
The Area of the Square with side "s" can be calculated using the formula
Area = s × s
In the question ,
it is given that ,
the area of the Square banquet is = 3600m² ,
let the length of the side of the room be "s" .
So , By the Area of the Square formula ,
we get ,
s × s = 3600
s² = 3600
taking quare root both the sides ,
we get
√s² = √3600
s = 60
the side = 60m
Therefore , If the square banquet has area = 3600m² then length of the room is 60 m .
Learn more about Area here
https://brainly.com/question/13368194
#SPJ9
Tristan, Kimberly, and Dominic had a challenge to see who could run the
most in one day. Tristan ran 7 miles. Kimberly ran 4 times as many miles as
Tristan, and Dominic ran 2 times as many miles as Kimberly. How many
miles did Dominic run?
Answer: 56 miles
Step-by-step explanation:
Tristan ran 7 miles, multiply by 4 because Kimberly ran 4 times as many miles as Tristan. 7x4=28
Next, 28x2=56 because Dominic ran 2 times as many miles as Kimberly, which is 28 times 2.
So Dominic ran 56 miles in total.
Identify each number between 2.6×10^-1 and 29.5%. Select all that apply. Responses 2.7×10^1
0.2875
2/7
2.8%
Numbers between 2.6×10^-1 and 29.5% are
0.28752/7How to write the numbers to decimal2.6 × 10^-1 in exponential form written in decimal as 0.26
29.5% in percentage written in decimal as 0.295
2/7 in fraction written in decimal as 0.2857
2.8% in percentage written in decimal as 0.028
0.2875 already in decimal form
the problem asks of numbers from 0.26 to 0.295
comparing the numbers shows that the numbers in this range are
0.2875 and 2/7
Learn more about decimal here:
https://brainly.com/question/29420599
#SPJ1
Use the discriminant to describe the roots of each equation. Then select the best description. 6x2 + 13x + 6 = 0
The quadratic equation 6 · x² + 13 · x + 6 = 0 has a positive discriminant and its roots are two distinct real numbers.
What is the nature of the roots of a quadratic equation?
In this problem we must infer the features of the two roots of a quadratic equation of the form a · x² + b · x + c = 0, this can be done by means of the discriminant from the quadratic formula:
D = b² - 4 · a · c
Where a, b, c are real coefficients of the quadratic equation.
There are three possibilities for the results of the discriminant:
D < 0, conjugated complex numbers.D = 0, equal real numbers.D > 0, different real numbers.First, write the quadratic equation:
6 · x² + 13 · x + 6 = 0
Second, collect the real coefficients of the polynomial:
(a, b, c) = (6, 13, 6)
Third, calculate the discriminant:
D = 13² - 4 · 6²
D = 169 - 144
D = 25
The quadratic equation has two roots that are real and different.
To learn more on discriminants of quadratic equations: https://brainly.com/question/28096706
#SPJ1
Solve for x: 6 over x equals 4 over 8 a 10 b 12 c 24 d 48
Answer:
B. 12
Step-by-step explanation:
please help me I don't understand pleaseeeee I'm begging youuuuu
The equation of the line passing through the points (9,9) and (1, 8) is 8y - x - 63 = 0 and the slope of the line is 1/8
Slope of the line that passes through the points (9,9) and (1, 8)
The equation of the line is
y -y₁ = ((y₂ - y₁)/ (x₂ - x₁)) (x - x₁)
y - 9 = ((8 - 9)/(1 - 9)) (x - 9)
y - 9 = (1/8) (x - 9)
8y - 72 = x - 9
8y - x - 63 = 0
8y = 1/8 (x + 63)
Therefpre, the equation of the line passing through the points (9,9) and (1, 8) is 8y - x - 63 = 0
To learn more about equation of the line refer here
https://brainly.com/question/18831322
#SPJ9
Assume that x=2 and y =9 find values of the 2 Expressions 7x +4y and 4y + 7y
Answer: 50, 99
Step-by-step explanation:
we just have to substitute the values of x and y in the given expressions.
7(2)+4(9)=50
4(9)+7(9)=99
Answer:
Step-by-step explanation:
7x + 4y= 50 and 4y + 7y= 99
Since, x=2 and y=9
7x + 4y= 7*2 + 7*9= 14 + 36= 50
and similarly
4y + 7y= 4*9 + 7*9= 36 + 63= 99
Check more about quadratic functions here:
https://brainly.com/question/27958964?referrer=searchResults
rename each of the following using the distributive property of multiplication so there are no parentheses in the final answer
(a+b)(c+d)
Answer:
ac + ad + bc + ad
Step-by-step explanation:
We are going to be using the FOIL (First, Outer, Inner, Last) method.
If we use this, we end up with:
ac + ad + bc + ad
There are 4 times as many alligators as crocodiles. If the total number of alligators and crocodiles is 35 , how many alligators are there
Answer:
140
Step-by-step explanation:
It's 140 because 35 x 4 (4 TIMES) meaning you multiply. 35 x 4 is 140, meaning there are 140 alligators.
Four children (Sam, Inez, Mahmoud and
Katrina) are running a race. They are each
wearing a distinctive article of clothing (a
red shirt, a hat, sunglasses and a scarf).
Consider the following statements:
The child wearing a red shirt finished
before Sam but after the child wearing a
hat.
Katrina is wearing sunglasses.
The child wearing a scarf finished the race
last.
Inez finished the race before the person
wearing sunglasses.
Mahmoud is not wearing a hat.
Who won the race?
Inez had won the race.
What is sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. Similar to a set, it has members (also called elements, or terms). The length of the series is the number of elements (potentially infinite).
Sam finished the race after the youngster wearing the shirt, who finished after the child wearing the hat, according to the information provided.Sam, red shirt, hat is the order from last to first.Inez also finished before to Katrina. Sam must be the last person to put on a scarf because Mahmoud doesn't wear a cap.Sam, Mahmoud, Katrina, and Inez are listed in order from last to first.Thus, Inez had won the race.
Learn more about Sequence here:
https://brainly.in/question/46012600
#SPJ2
At the end of year 5, the account was valued at $3203.19. At the end of year 6, the account was valued at $3315.30. What was the interest rate, as a percent?
well, from the end of year 5 to the end of year 6 is only 1 year later, so
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$3315.30\\ P=\textit{original amount deposited}\dotfill & \$3203.19\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 3315.30=3203.19[1+(\frac{r}{100})(1)] \implies \cfrac{3315.30}{3203.19}=1+\cfrac{r}{100} \\\\\\ \cfrac{3315.30}{3203.19}-1=\cfrac{r}{100}\implies 100\left( \cfrac{3315.30}{3203.19}-1 \right)=r\implies \stackrel{\%}{3.5}\approx r[/tex]
MP Use Tools A bobsled team is practicing runs on
a track. Their first run takes 4.85 minutes. On each
of the next two runs, the team's time changes by
-0.27 minute compared to the previous time.
A. What was the team's time on their final run?
The team's time on their final run is 4.31 minutes.
According to the question,
We have the following information:
Their first run takes 4.85 minutes. On each of the next two runs, the team's time changes by -0.27 minute compared to the previous time.
Now, the second run will be 0.27 minutes less than 4.85 minutes.
Time for the second run = 4.58 minutes
Now, the third run will be the final run and 0.27 minutes less than the previous run.
Now, the time for the final run will be as given below:
4.58-0.27
4.31 minutes
Hence, the team's time on their final run is 4.31 minutes.
To know more about team's time here
https://brainly.com/question/29394890
#SPJ1
Simplify the power (-3x^2y)^4
⇒In this case I will use the law of exponents that states:
[tex](x^{m} )^{n} \\=x^{m*n}[/tex]
⇒[tex]=(-3x)^{2y*4} \\=(-3x)^{8y}[/tex]
Answer: 81x^8y^4
Step-by-step explanation:
1. DISTRIBUTE EXPONENT by using the power rule: (ab)^n = (a^n)(b^n)
> Apply PRODUCT RULE: -3x^2y = (-3x^2)^4y^4
>Apply PRODUCT RULE: -3x^2 = (-3)^4 (x^2)^4y^4
2. RAISE -3 to the power of 4 = 81(x^2)^4y^4
3. MULTIPLY THE EXPONENTS in (x^2)^4
> Apply POWER RULE and MULTIPLY EXPONENTS, (a^m)^n = a^mn
(81x^2*4)(y^4)
> MULTIPLY 2 by 4 = 81x^8y^4
And that is your answer, 81x^8y^4
Question 8 of 25
f(x) = 2x³ + 6x² - 5x - 3
g(x) = 3x - 4
Find (f - g)(x).
A. (f- g)(x) = 2x³ + 6x²
OB. (f-g)(x) = 2x³ + 6x²
Oc. (f- g)(x) = 2x³ + 6x²
D. (fg)(x) = 2x³ + 6x²
www
*****
www
2x+1
8x7
2x - 7
8x +1
For the given function f(x) = 2x³ + 6x² - 5x - 3 , g(x) = 3x - 4 , the value of
(f -g)(x) = 2x³ + 6x² -8x + 1 .
As given in the question,
Function is given by :
f(x) = 2x³ + 6x² - 5x - 3 , g(x) = 3x - 4
Substitute the value in the given function and simplified it ,
( f - g )(x)
= { 2x³ + 6x² - 5x - 3 } - { 3x - 4 }
= 2x³ + 6x² - 5x - 3 -3x + 4
= 2x³ + 6x² -5x -3x -3 + 4
= 2x³ + 6x² - 8x + 1
Therefore, for the given function f(x) = 2x³ + 6x² - 5x - 3 , g(x) = 3x - 4 , the value of (f -g)(x) = 2x³ + 6x² -8x + 1 .
The complete question is:
If for the given function ,
f(x) = 2x³ + 6x² - 5x - 3 , g(x) = 3x - 4
Find the value of (f - g)(x).
a. 2x³ + 6x² -8x + 1
b. 2x³ + 6x² + 2x+1
c. 2x³ + 6x² + 2x -7
d. 2x³ + 6x² + 8x⁷
Learn more about function here
brainly.com/question/5975436
#SPJ1
Find the inverse of f(x) = 4x-1/-2x +2
The inverse of the function f(x) = (4x - 1)/(-2x +2) is equal to f⁻¹(x) = (2x + 1)/(4 + 2x).
What is an inverse function?In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In order to determine the inverse of this function f(x) = (4x - 1)/(-2x +2), we would interchange both the input value (x) and output value (y) as follows:
y = (4x - 1)/(-2x +2)
x = (4y - 1)/(-2y +2)
Cross-multiplying, we have:
x(-2y +2) = 4y - 1
2x - 2xy = 4y - 1
Next, we would rearrange the function by collecting like terms as follows:
4y + 2xy = 2x + 1
y(4 + 2x) = 2x + 1
Dividing both sides of the function by (4 + 2x), we have:
y = (2x + 1)/(4 + 2x)
y = f⁻¹(x) = (2x + 1)/(4 + 2x)
Read more on inverse function here: brainly.com/question/4242416
#SPJ1
1) Graph the function by plotting the ordered pairs (0, 0) (10, 125) (20, 250) (30, 375) (40, 500) and
drawing a straight line through the points. Label the axes with appropriate
variable
quantities
and units. Label the points with the correct ordered pairs. Include a title for the graph.
The graph of the given function is attached below.
We are given a function. A function connects an input and an output. It is analogous to a machine with an input and an output. And the output is somehow related to the input.
The coordinates of several points are given. We need to graph the function by plotting the ordered pairs (0, 0), (10, 125), (20, 250), (30, 375), and (40, 500).
The function is a straight line. A straight line is a one-dimensional figure with an infinite length. It is made up of an infinite number of points connected on both sides of a point. We also need to draw the line through the points. The graph is attached below.
To learn more about functions, visit :
https://brainly.com/question/5975436
#SPJ1
Bro... Please.. Help im desperate. I swear I will give brainliest.
Answer:
A: Ira begins walking
B: Ira stops at a diner
C: Ira leaves the diner
D: Ira visits his grandmother
E: Ira walks from grandma’s house to home
Step-by-step explanation:
Hopes this helps please mark brainliest
which expressions describe the end behaviors of the function, f(x)=(3.25)^x+6, modeled by the graph.
Select each answer,
As x decreases without bound, f(x) increases without bound
As x increases wthout bound f(x) increases without bound
As x decreases without bound, f(x) approaches the line y=6
As x increases without bound, f(x) approaches the line y=6
For the given function, f(x)=(3.25)^x+6 As x decreases without bound, f(x) increases without bound
To describe the end behaviors of the function modeled by the graph,
f(x)=(3.25)^x+6
What are functions?
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.
Here,
The function given is,
f(x)=(3.25)^x+6
Given function contains equality so the function has no boundaries and the function is described from negative infinity to positive infinity, But the function has inverse behavior as when x is negative the function is positive.
Thus, for the given function, f(x)=(3.25)^x+6 asAs x decreases without bound, f(x) increases without bound
To learn more about function refer here:
brainly.com/question/21145944
#SPJ1
-6.4 = x + 4.3 how do I figure this question out (I’m trying to figure out what number x is)
Answer: x = -10.7
Step-by-step explanation:
-10.7 + 4.3 = -6.4
617/50 into simplest form
Since fractions are the same as division, divide 617 by 50. The remainder will remain in fraction form.
617/50
600/50 = 12
617/50 = 12 17/50
12. Brandi solves the problem
could she check her answer?
1,621 /4 = 404 R1
Using simple mathematical operations, we know that Brandi's answer which is 404 is incorrect.
What are mathematical operations?A mathematical function known as an "operation" in mathematics is one that converts zero or more input values into a precisely specified output value.
The quantity of operands has an impact on the operation's complexity.
Exponents, PEMDAS, parenthesis, multiplication, and division.
So, to check whether Brandi's answer is correct:
1621/4 = 404
So, to check it is ts correct, multiply 404 by 4.
If the answer is correct, then the product will be 1621.
If the answer is wrong, the product will not be 1621.
Calculate as follows:
404 × 4 = 1,616
Therefore, using simple mathematical operations, we know that Brandi's answer which is 404 is incorrect.
Know more about mathematical operations here:
brainly.com/question/28937023
#SPJ1
6. Given AACP ALNX, find each missing measure. N 29° 13 cm P CX V L 21 cm a) XL = b) AC= c) PC = d) m/L= e) m/C= f) m/X=
The missing measure is ∠P =∠X = 122°
Given △ACP ≅ △LNX
XL = 13 cm, m∠L = 29°
AC = 21 cm, m∠C = 29°
PC = 13 cm, m∠Y = ?? (there is no angle Y)
On the right shows the triangles are isosceles, with XL = XN. That means also PA = PC. Those side lengths are all the same: 13 cm.
PA = PC = XL = XN = 13 cm
In the same way, ...
LN = AC = 21 cm
Of course, the angles have a similar relationship:
∠A = ∠C = ∠L = ∠N = 29°
The two base angles in the triangle add to 58°, so the third angle is ...
180° -58° = 122°
∠P =∠X = 122°
As is often the case in over-specified problems, the numbers shown are not consistent. The length LN is actually incorrect for the angle and side specified for triangle ACP, or the angles are incorrect for the side lengths specified. What this means is that the answers you get will depend on how you work the problem. Above, we have taken the given numbers and relationships at face value, even though we know they are incorrect.
Hence the answer is The missing measure is ∠P =∠X = 122°
To learn more about angels click here https://brainly.com/question/25716982
#SPJ9
A coach has to form 4 doubles teams from 8 badminton players. In how many ways can he form the teams? (A doubles team is a pair of players, and a player cannot be a member of more than one doubles team.)
The number of ways he can form the teams would be = 336 ways.
What is badminton?Badminton is a type of racket game that makes use of single or double players where by they make use of a racket to hit a shuttlecock over the net to their opponents side.
The number of players available for the badminton game = 8
The number of teams to the formed = 4
To find the number of ways to form 4 double teams from these 8 players would be to find the factorials of 8 divided by factorial 4.
That is ;
8!/4! = 8×7×6×4×3×2×1/4×3×2×1
= 8064/ 24
= 336 ways.
Learn more about factorials here:
https://brainly.com/question/25997932
#SPJ1
Purchase price $ 70,000
Delivery cost $ 3,000
Installation charge $ 1,000
Estimated life 5 years
Estimated units 140,000
Salvage estimate $ 4,000
Purchase price $ 70,000
Delivery cost $ 3,000
Installation charge $ 1,000
Estimated life 5 years
Estimated units 140,000
Salvage estimate $ 4,000
Straight-line YR1 and YR2
Double-declining YR1 and YR2
Unit-of-production YR1 and YR2
($$ amounts)
Using the straight line method, the depreciation expense in year 1 and 2 is $14,000.
Using the double declining method, the depreciation expense in year 1 is $29,600 and $17,760 in year 2.
Using the unit of production method, the depreciation expense in year 1 is $18,000 and $19,000 in year 2.
What are the depreciation expenses?The straight line depreciation method is a depreciation method in which the the depreciation amount each year of the asset's useful life is the same.
Straight line depreciation = (cost of the asset - salvage value) / useful life
Cost of the asset = $70,000 + $3000 + $1000 = $74,000
Straight line depreciation = ($74,000 - $4,000) / 5 = $14,000
The double declining method entails depreciating an asset at twice the rate of the straight line method.
Depreciation expense = cost of the asset x depreciation factor
Depreciation factor = 2 x (1/useful life)
Depreciation expense in year 1 = (2 /5) x $74,000 = $29,600
Book value in year 2 = $74,000 = $29,600 = $44,400
Depreciation expense in year 2 = (2 /5) x $44,400 = $17,760
The depreciation in the unit of production method depends on the output of the machine each year.
Depreciation = (output in a year / total output) x (cost of the asset - salvage value)
Depreciation in year 1 = ($74,000 - $4,000) x (36,000 / 140,000) = $18,000
Depreciation in year 2 = ($74,000 - $4,000) x (38,000 / 140,000) = $19,000
To learn more about the unit of output depreciation method, please check: https://brainly.com/question/28019636
#SPJ1
Here is the rest of the question:
Units produced in Year 1 = 36,000 units
Units produced in Year 2 = 38,000 units.
Just please help im desperate( 3 different questions)
Answer:
7. what are the fold down options for this question exactly?
1. C and E
3. B and D
Step-by-step explanation:
7.
1. function 1 has a slope of 2/3 and function 2 has a slope of 3 so they are both positive rates of change, and the y intercept (the value that y has when it passes through x = 0) for function 1 is -6 while the y intercept for function 2 is -3.
3. K has a y intercept of 8 compared to the 3 that J has, and J has a slope of 5 compared to the 3 that K has.
Savannah is flying a kite, holding her hands a distance of 2.5 feet above the ground
and letting all the kite's string play out. She measures the angle of elevation from her
hand to the kite to be 32. If the string from the kite to her hand is 75 feet long, how
many feet is the kite above the ground? Round your answer to the nearest tenth of a
foot if necessary.
Answer:
feet Submit Prowes
Z
Answer:
42.2 ft
Step-by-step explanation:
The given scenario can be modelled as a right triangle (see attached diagram), where the angle of elevation is 32°, and the length of the kite string (75 ft) is the hypotenuse.
We want to find the distance the kite is above the ground, so we want to find the side of the right triangle that is opposite the given angle. To do this, we can use the sine trigonometric ratio.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
Substituting θ = 32° and H = 75 into the ratio, we get:
[tex]\sin 32^{\circ}=\dfrac{\sf O}{75}[/tex]
[tex]\textsf{O}=75\sin 32^{\circ}[/tex]
[tex]\textsf{O}=39.7439448...\; \sf ft[/tex]
The angle of elevation is the angle between the horizontal plane and the line of sight from an observer to an object located at a higher position.
In this scenario, the angle of elevation is measured from Savannah's hand, which is a distance of 2.5 ft above the ground. Therefore, we need to add 2.5 ft to the value of O found using the sine ratio.
[tex]\implies 39.7439448...+2.5=42.2\; \sf ft\;(nearest\;tenth)[/tex]
Therefore, the kite is 42.2 ft above the ground (rounded to the nearest tenth).