To the nearest tenth, what is the area of the shaded segment when AG = 6 ft?
10.3 ft2
21.1 ft2
1.7 ft2
28.3 ft2
Answers
Answer:
Option A is correct.
Step-by-step explanation:
Given:
AG = 6 ft ⇒ Radius of the circle , r = 6 ft
⇒ GB = AG = 6 ft
To find: Area of shaded Segment.
Area of Shaded Segment = Area of Sector AGBA - Area of Δ AGB
Sector AGBA forming 90° angle at center. [tex]\implies\,\theta=90^{\circ}[/tex]
Area of Sector = [tex]\frac{\theta}{360}\times\pi r^2[/tex]
Area of Sector AGBA = [tex]\frac{90}{360}\times3.14\times6^2[/tex]
= [tex]\frac{1}{4}\times3.14\times36[/tex]
= [tex]28.26\:ft^2[/tex]
ΔAGB is a right angled triangle.
So, Area of ΔAGB = [tex]\frac{1}{2}\times AG\times GB[/tex]
= [tex]\frac{1}{2}\times6\times6[/tex]
= [tex]6\times3[/tex]
= [tex]18\:ft^2[/tex]
Area of Shaded Segment = 28.26 - 18 = 10.26 ≈ 10.3 ft²
Therefore, Option A is correct.
Related Questions
what are solutions to the equation sinx cosx = square root 3 over4
Answers
WZ and XR are diameters of circle C. The diagram is not drawn to scale.
What is the measure of convex arc upper ZWX?
Answers
WZ + 41 = ZWX
From here, we must clear We must replace the value of WZ.
The value of WZ is given by
WZ=180
We have then:
ZWX = 180 + 41
ZWX = 221 degrees
Answer:
the measure of convex arc upper ZWX is:
ZWX = 221 degrees
The measure of convex arc upper ZWX is 180 degrees.
Explanation:The measure of convex arc upper ZWX can be found by considering the angles formed by the diameters WZ and XR. Since WZ and XR are diameters of the circle, they intersect at the center of the circle. The angle formed by the diameters at the center is a right angle, which means that arc upper ZWX is a semicircle. A semicircle has a measure of 180 degrees. Therefore, the measure of convex arc upper ZWX is 180 degrees.
Norma stopped to get gas for her car before beginning a trip. her odometer read 2587 miles, and she filled up her tank with 26 gallons. at the end of her trip, her odometer read 3295 miles. what is her car's miles per gallon?(round to the closest gallon)
Answers
Assuming that at the end of the trip all the gas had been consumed, a total of 26 gallons was consumed.
Therefore,
Car consumption = 708/26 = 27.23 miles/gallon
Mr. and Mrs. Yeager want to buy a home valued at $320,000. If they have 15% of this amount saved for a down payment, how much have they saved? a. $480 b. $4,080 c. $4,800 d. $48,000
Answers
Answer:
The correct answer is D
Step-by-step explanation:
I got it right on Edge.2020. Have a great day!
If they have 15% of this amount saved for a down payment, then they saved 48000 dollar.
So option D) $48,000 is correct.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given that Mr. and Mrs. Yeager want to buy a home valued at $320,000.
If they have 15% of this amount saved for a down payment, then
15% =15/100=0.15
Therefore, we get;
0.15 (320000)=48000
If they have 15% of this amount saved for a down payment, then they saved 48000 dollar.
So option D) $48,000 is correct.
Learn more about multiplications;
https://brainly.com/question/14059007
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please help...
The radius of the planet is 4100 miles. Find the distance d to the horizon that a person can see on a clear day from a height of 1298 feet above the planet. (hint: use the conversion 1 mile = 5280 ft) Round your answer to the nearest 10th, and don't forget to convert feet to miles.
Answers
[tex]1298ft*\frac{1mi}{5280ft}= \frac{59}{240} mi[/tex]
Next, we are going to set up a right triangle using the radius of the Earth and the distance above the planet.
The hypotenuse of our triangle will be the radius of the Earth + the distance above the planet. One of the legs of our triangle will be the radius of the Earth, and the other leg, [tex]d[/tex], will be the distance that a person will see on a clear day.
Using the Pythagorean theorem:
[tex]d^2= (\frac{984059}{240} )^2-4100^2[/tex]
[tex]d= \sqrt{(\frac{984059}{240} )^2-4100^2} [/tex]
[tex]d=44.9[/tex] miles
We can conclude that the distance, [tex]d[/tex], to the horizon that a person can see on a clear day from a height of 1298 feet above the planet is 44.9 miles.
A box contains 16 transistors, 5 of which are defective. if 5 are selected at random, find the probability that
a. all are defective. and. none are defective.
Answers
Only one way of selecting the 5 defective transistors:
Number of ways of selections available = 6C5 = 16!/[5!*(15-5)!] = 4368
Probability they are all defective = Number of ways of selecting 5 defectives/Total number of ways possible = 1/4368 ≈ 0.000229
Part (b): None are defective
Total number of non defectives = 16 -5 = 11
Number of ways of selecting 5 non defective = 11C5 = 462 ways
Total number of ways possible = 16C5 = 4368
Probability of selecting 5 non defectives = 462/4368 = 11/104 ≈ 0.1058
A - all defective
B - none defective
[tex] \displaystyle
|\Omega|=\binom{16}{5}=\dfrac{16!}{5!11!}=\dfrac{12\cdot13\cdot14\cdot15\cdot16}{2\cdot3\cdot4\cdot5}=4368\\
|A|=1\\
|B|=\binom{11}{5}=\dfrac{11!}{5!6!}=\dfrac{7\cdot8\cdot9\cdot10\cdot11}{2\cdot3\cdot4\cdot5}=462\\\\
P(A)=\dfrac{1}{4368}\approx0.02\%\\
P(B)=\dfrac{462}{480480}=\dfrac{1}{1040}\approx0.1\% [/tex]
Write an equation of a line containing (2, 1) and (3, 4) in point-slope form.
Answers
Your equation is:
(y₂ - y₁)/(x₂ - x₁) = Slope
Let:
(2,1) = (x₁,y₁)
(3,4) = (x₂,y₂)
Plug into corresponding numbers
(4 - 1)/(3 - 2) = 3/1
3/1 is your slope
hope this helps
How would you find the width of a golden rectangle if your givin the length?
Answers
Given the length, you would divide by 1.618 to find the width.
Edit: The exact value is [tex] \frac{ 1+\sqrt{5} }{2} [/tex], but 1.618 should suffice.
Subtract. (4x^2+8x−2)−(2x^2−4x+3) Enter answer, in standard form
Answers
HELP ! I've been stuck on this for over 15 mins. :(
What are the explicit equation and domain for an arithmetic sequence with a first term of 8 and a second term of 5?
an = 8 − 5(n − 1); all integers where n ≥ 1
an = 8 − 5(n − 1); all integers where n ≥ 0
an = 8 − 3(n − 1); all integers where n ≥ 1
an = 8 − 3(n − 1); all integers where n ≥ 0
Answers
Plug in a1 = 8:
an = 8 + (n - 1)d
FInd d:
Given that a2 = 5
5 = 8 + (2-1)d
5 = 8 + d
d = -3
Plug in d = -3:
an = 8 -3(n - 1)
Answer: an = 8 -3(n - 1) ; n ≥ 1
A multiple choice test has 9 questions each of which has 5 possible answers
Answers
Which sequence is modeled by the graph below? coordinate plane showing the points (1, 1) (2, 2) (3, 4) and (4, 8)
a. an = 1(2)n − 1
b. an = 2(1)n − 1
c. an = 1 + (2)n − 1
d. an = (2)(n − 1)
Answers
Answer: The correct option is d.
Explanation:
From the given information it is noticed that the coordinate plane showing the points (1, 1) (2, 2) (3, 4) and (4, 8).
The coordinates are in the form of (x,y), it means the value of xth term of the sequence is y.
The point (1,1) represents that the first term is 1. Similarly from (2, 2) (3, 4) and (4, 8) points we can say that the second term is 2, third term is 4 and fourth term is 8.
The sequence is 1,2,4,8.
It can be written as,
[tex]2^0,2^1,2^2,2^3[/tex]
Since the base is common that is 2 and the power is one less than the position of term. So the sequence is in the form of,
[tex]a_n=2^{n-1}[/tex]
Therefore, the correct option is d.
What is the value of y in the equation 2(3y + 6 + 3) = 196 − 16?
Answers
2(3y + 9) = 196
6y + 18 = 196
6y + 18 - 18 = 196 - 18
6y = 178
Divide both sides by 6
y = 178 / 6
y ≈ 29.667
Center c of the circle above has coordinates of (4, 3). what is the circumference of the circle?
Answers
C = 2 * pi * r = (2)(3.14)(3) = 18.8 or so
What did the prince do whenever he found a girl who might be cinderella
Answers
Final answer:
When a prince in fairy tales finds a potential Cinderella, he typically engages in a quest to determine if she is the one, reflecting the theme of male heroism and romantic pursuit found in traditional literature and films.
Explanation:
The passage raises the theme of romantic endeavors and the traditional role of women in classical literature and film, typically anchored within the context of royalty and fairy tales. When the prince in such stories finds a girl that could potentially be Cinderella, typically he would engage in a quest to discover if she truly is the one - often symbolized by a glass slipper fitting or other identifying item. This quest underscores the narrative of countless romantic tales where the male lead seeks to find and often rescue his female counterpart, a concept reflected in various Disney princess movies.
In the greater realm of literature and films, the prince often represents the chivalrous savior. This tradition is evident in the series of princess-centric stories produced by Disney, where a common girl becomes royalty by marriage or starts as a princess whose ultimate happiness is achieved through romance. Although contemporary stories may showcase more agency in their female protagonists, the motif of the male hero remains prevalent.
You plan on financing a new road bike for $2,500. The bike shop offers a 13.5% APR for a 24 month loan. Use this information, and the table above, to determine the monthly payments. Round your answer to the nearest cent.
Answers
Given that the financing is for a new road bike of $2,500 and that the bike shop offers a 13.5% APR for a 24 month loan.
Thus, PV = $2,500; r = 13.5% = 0.135; t = 12 payments (since payment is made monthly); n = 2 years (i.e. 24 months)
Thus,
[tex]2500=P\left( \frac{1-\left(1+ \frac{0.135}{12} \right)^{-2\times12}}{ \frac{0.135}{12} } \right) \\ \\ =P\left( \frac{1-\left(1+ 0.01125 \right)^{-24}}{ 0.01125 } \right)=P\left( \frac{1-\left(1.01125 \right)^{-24}}{ 0.01125 } \right) \\ \\ =P\left( \frac{1-0.764531}{ 0.01125 } \right)=P\left( \frac{0.235469}{ 0.01125 } \right)=20.9306P \\ \\ \Rightarrow P= \frac{2500}{20.9306} =119.44[/tex]
Therefore, his monthly payment is $119.44
Slips of paper numbered 1 through 14 are placed in a hat. in how many ways can two numbers be drawn so that the sum of numbers is 12
Answers
1 and 11
2-10
3-9
4-8
5-6
6-6
so there are 6 ways
What is log base 5(4*7 )+log base 5 of 2 written as a single log?
A.log base 5 of 21
B.log base 5 of 26
C.log base 5 of 30
D.log base 5 of 56
Answers
D. log base 5 of 56
The explanation is show below:
1. You have the following logarithm expresssion:
log5(4*7 )+log5(2)
2. By the logarithms properties, you can rewrite the logarithm expression as following:
log5(28)(2)
log5(56)
3. Therefore, as you can see, the answer is the option mention before.
Answer:
D. log base 5 of 56
Step-by-step explanation:
Since, by the multiplication law of logarithm,
[tex]log_a(m)+log_a(n) = log_a(mn)[/tex]
Given expression is,
log base 5(4*7 )+log base 5 of 2
[tex]=log_5(4\times 7)+log_5(2)[/tex]
[tex]=log_5(28)+log_5(2)[/tex]
By the above property,
[tex]=log_5(28\times 2)[/tex]
[tex]=log_5(56)[/tex]
= log base 5 of 56
Hence, Option D is correct.
The spoke of a wheel reaches from the center of the wheel to its room if the circumference of the rim of the wheel is 42 inches how long is each spoke
Answers
so to find the (d) you divide 48÷3.14=15.29 inches. As the spoke goes from the center to its rim, it it is the radius, which is half of the diameter.15.29/2 is
B) 7.64 inches.
Please help i'm really confused.
0! = 0
True
False
Answers
0! is defined to be 1
How many questions can i miss on a 28 question test to get a 70%?
Answers
0.7(28) = 19.6
You need to get 19.6 points for a 70%. To calculate the points missed, subtract this from the total points on the test:
28 - 19.6 = 8.4
You can only miss 8.4 points on the test, or no more than 8 questions, to get a grade of 70%.
What is the height of the trapezoid?
Answers
40 *2 = (10+6)*h
80/16 = h
5 unit = h
The square root of the sum of a number and 7 is 8. find the number
Answers
Possibility 1: 8 = sqrt(x+7) in which the answer is 57.
Possibility 2: 8 = sqrt(x) + 7, in which the answer is 1.
Hope this helps! I'm sorry if I get it wrong.
Anyone know this geometry question?
Answers
∠JEK + ∠DFH = 90°
Find:
relationship, if any, of ∠JEK to angles CFL, HFG, LFE
Solution:
We note that ∠DFG = 90° = ∠DFH + ∠HFG, so ∠JEK ≅∠HFG.
We also note that ∠HFG and ∠CFL are vertical angles, so ∠JEK ≅∠CFL.
And ∠LFE and ∠DFH are vertical angles, so ∠JEK + ∠LFE = 90°.
Evaluating the choices, we find
A) false. The angles are not complementary, they are equal.
B) false. The angles are not equal, they are complementary.
C) false. The angles are not supplementary, they are equal.
D) TRUE. The angles are equal.
The appropriate choice is ...
D) ∠JEK ≅∠CFL
An integer greater than 1 that is not prime is called composite. if the two-digit integer n is greater than 20, is n composite?
Answers
eg 21 is composite and 23 is prime.
Look at the figure rectangle PQRS, find m angel P
Answers
Answer: [tex]144^{\circ}[/tex]
Step-by-step explanation:
In the given figure , we have given a parallelogram .
We know that the opposite sides and angles of a parallelogram are equal.
Thus from the given parallelogram PORS we have
[tex]\angle {Q}=\angle {S}\\\\\Rightarrow\ (4\alpha-12)^{\circ}=3\alpha^{\circ}\\\\\Rightarrow\ 4\alpha-12=3\alpha\\\\\Rightarrow 4\alpha-3\alpha=12\\\\\Rightarrow\ \alpha=12[/tex]
Also, the value of angle p is given by :-
[tex]\angle {P}=12\alpha^{\circ}\\\\\Riightarrow\ \angle {P}=12(12)^{\circ}\\\\\Riightarrow\ \angle {P}=144^{\circ}[/tex]
A 20-ounce candle is expected to burn for 60 hours. A 12-ounce candle is expected to burn for 36 hours. Assuming the variables are directly related, how many hours would a 9-ounce candle be expected to burn?
18
27
33
45
Answers
to find the rate it burns:
20 ounce / 60 hours = 1/3 ounce per hour
divide 9 ounces by 1/3 ounce per hour to find total time:
9 / 1/3 = 27 hours
Answer:
B. 27.
Step-by-step explanation:
We have been given that a 20-ounce candle is expected to burn for 60 hours. A 12-ounce candle is expected to burn for 36 hours.
We know that a direct proportional equation is in form [tex]y=kx[/tex], where k represents constant of proportionality.
Let is find value of k by substituting [tex]x=20[/tex] and [tex]y=60[/tex] in above equation as:
[tex]60=k*20[/tex]
[tex]\frac{60}{20}=\frac{k*20}{20}[/tex]
[tex]3=k[/tex]
The equation [tex]y=3x[/tex] represents our given direct proportional relation.
Now, we will substitute [tex]x=9[/tex] to solve for y as:
[tex]y=3*9[/tex]
[tex]y=27[/tex]
Therefore, a 9-ounce candle would be expected to burn for 27 hours and option B is the correct choice.
If a single die is rolled twice there are how many possible outcomes
Answers
Two trains leave towns 1250 km apart at the same time and travel toward each other. one train travels 10 km/hr slower than the other. if they meet in 5 hours, what is the rate of each train?
Answers
(n represents train A's speed)
A: n
B: n + 10
We know it is 5 hours, and total distance, so:
5(n) + 5(n + 10) = 1250
5n + 5n + 50 = 1250
10n = 1200
Divide:
n = 120
One train goes 120, the other goes 130
able below shows the relative frequencies of the color of cars bought last month by males and females. Which percentage represents the car bought most often? Male Female Total Blue Car 0.04 0.12 0.17 Black Car 0.08 0.06 0.13 White Car 0.11 0.20 0.31 Gray Car 0.02 0.09 0.11 Red Car 0.17 0.10 0.27 Total 0.43 0.57 1.00
Answers
Answer:
31%
Step-by-step explanation:
Answer:
31%
Step-by-step explanation: