Answers
Answer:
60.46%
Step-by-step explanation:
Question: On this dartboard, the circle with 1-m radius is inscribed in an equilateral triangle. Find the probability that a dart that hits the board lands in the circular region. Justify your answer.
Let's start by finding the length of one of the sides of the equilateral triangle. We can do this by creating a 30-60-90 triangle from the radius of the inscribed circle.
I attached an image of what this should look like.
Solving for the length of half of the base of the equilateral triangle gives us 1√3. To get the length of the entire base of the triangle, we will double this value:
s = 2√3The area of an equilateral triangle is [tex]\displaystyle A=\frac{s^2 \sqrt{3} }{4}[/tex].
We can substitute the known value of s (side length) into the formula and solve for A.
[tex]\displaystyle A_t=\frac{(2\sqrt{3})^2\cdot \sqrt{3} }{4}[/tex] [tex]\displaystyle A_t=\frac{4(3) \cdot \sqrt{3} }{4}[/tex] [tex]\displaystyle A_t=3\sqrt{3}[/tex]The area of the equilateral triangle is 3√3.
Now, let's solve for the area of the inscribed circle. The formula for the area of a circle is [tex]\displaystyle A= \pi r^2[/tex].
We know the radius of the circle is 1, so let's substitute 1 for r:
[tex]A_c= \pi (1)^2[/tex] [tex]A_c=\pi[/tex]The area of the inscribed circle is π.
To find the probability of the dart hitting a specific area on the dartboard, we will divide the desired area by the total area of the dartboard.
[tex]\displaystyle P=\frac{\text{Desired area}}{\text{Total area}}[/tex] [tex]\displaystyle P=\frac{\pi}{3\sqrt{3} }[/tex] [tex]\displaystyle P=\frac{\pi \sqrt{3} }{9}[/tex] [tex]P \approx 0.60459978[/tex]The probability that a dart that hits the board lands in the circular region is about 60.46%.
Related Questions
WILL GIVE BRAINYEST!!! PLS HELP!!!
Mr. Hudson walked 12 miles in 3 hours. At this rate,
how far will he walk in 5 hours? Write your answer in
a complete sentence AND show your work.
Answers
Mr. Hudson is going to walk 20 miles in 5 hours
help me on math pls plss I'm stuck agian:(((((
Answers
Answer:
the answer to a is 25, im unsure what B is.
Step-by-step explanation:
hope this helps!!!
a line has a slope of -3 and a y-intercept of 5. write the equation of the line in slope-intercept form and explain how you would use the slope and y-intercept to graph the equation?
Answers
Answer:
y = -3x + 5
Step-by-step explanation:
Since the y-intercept occurs at the point (0,5), you can use that and the point slope equation to find the equation.
This looks like y - 5 = -3 (x - 0);
Solving for y, you get y = -3x + 5;
To graph this equation you would put one point at (0,5), then use the slope to count down three and to the left one to find other points, or you could just plug in numbers for x to find their corresponding y values and plot it like that.
Hopefully this helps- let me know if you have any questions!
26.) In a midnight sale in a mall, Charice bought a
shirt with 40% discount. How much did she pay if the
original price is Php 200?
A. PhP 80.00
C. PhP 140.00
B. PhP 120.00
D. PhP 160.00
I will give Brainliest
Answers
Answer:
B. 120.00
Step-by-step explanation:
200-40%=120
Answer:
the answer is very easy i calculated this so if my calculations are correct it will be PHP 160.00
please help me i really need help please
Answers
Answer:
90+42+x = 180
132+x=180
x=180-132
x=48
Answer:
48 DEGREES
Step-by-step explanation:
First you need to find the other two angles : 42 + 90 = 132 ( the 90 comes from the little square like shape on the other angle).
So x = 180 - 132 = 48 ( we use 180 because it is the sum of interior angles of a triangle.
HOPE THIS HELPED
which expression equals the sum 1+2+3+4+5+6..
Answers
Answer:
7 * 3
7+7+7
3+3+3+3+3+3+3
2+2+2+2+2+2+2+2+2+2+1
(2*10)+1
(10*1)+11....
...and so on
Step-by-step explanation:
I don't know what type of expression you are looking for
What is 12 1/2 - 7 6/7?
Answers
Answer:
4 9/14
Step-by-step explanation:
Answer:
The answer is 4 9/14
PLS HELP
i said 45 but it was marked incorrect, im super confused
Answers
Answer:
60
Step-by-step explanation:
trangles always equal 180 degrees on the inside angles
180-75-45 = 60
How do you Solve 20/3=10/9x
Answers
Answer:
200
Step-by-step explanation:
100✓9283+374+_+38_+_+_("#9#9_+
Answer:
x = 6
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Please helppp, worth 35!!!
Answers
Answer:
9.42
Step-by-step explanation:
Hey There!
The first step of this problem is to find the formula for arc length
[tex]arc-length=2\pi r(\frac{0}{360} )[/tex]
r=raduis
0 = angle
now we just plug in the values
[tex]arc-length=2\pi 10\frac{54}{360} \\2\pi =6.283185307\\6.283185307x10=62.83185307\\62.83185307\frac{54}{360}=9.424777961[/tex]
so the arc length equals 9.424777961
the last step is to round to the nearest hundreth
so your final answer is 9.42
Sam wants to buy a watch that cost $188. This is $48 more than 4 times
he sved last month. How much dia he save last month? *
Answers
Answer:
$35
Step-by-step explanation:
188-48 gives you the 4x what he saved
140/4 gives you the total which is 35.
Which property justifies the statement below?
a(2b+c)=a(c+2b)
a. commutative property of addition
b. commutative property of multiplication
c. associative property of addition
d. distributive property
Answers
Answer:
d. distributive property
Step-by-step explanation:
6) A packet of 1350 chocolates were distributed among 3 sections A, B, C of class VI in the ratio 6: 5:4. Find each section's share
A)510, 460, 350
B)540, 450, 360
C)520, 440, 335
D)500, 400, 450
Answers
Answer:
its a or d
Step-by-step explanation:
a or d but ptibably a
Tina bought 3.2 pounds of grapes. The grapes cost $1.45 per pound. How much did she pay for the grapes?
Answers
Answer:
4.64
Step-by-step explanation:
If you do 20% of 1.45, you would get 0.29, add that by 1.45 plus 1.45 plus 1.45, and you get 4.64. Hope this helps!
Answer:
$4.64
Step-by-step explanation:
3 x 1.45 = 4.35
1.45 x .2 = .29
4.35 +.29 = 4.64
need help horribly geometry question
Answers
Answer:
23.31 ft
Step-by-step explanation:
Reference angle = 47°
Opp = 25 ft
Adj = x
Apply trigonometry ratio TOA:
Tan 47 = Opp/Adj
Tan 47 = 25/x
x*Tan 47 = 25
x = 25/Tan 47
x = 23.3128772 ≈ 23.31 ft (to 2 d.p)
20 = 2(n – 3) solve.
Answers
explanation:
20 = 2(n - 3)
•first distribute
2xn= 2n
2x-3= -10
20 = 2n - 10
•add 10 to both sides (since the sign is negative do the opposite.)
30 = 2n
•divide both sides by 2.
Answer: 15
True or false. Explain.
The volumes of a rectangular-based pyramid and a triangular-based pyramid with congruent heights and equal base areas are equal
Answers
Answer:
true
Step-by-step explanation:
In a lab experiment, 130 bacteria are placed in a petri dish. The conditions are such
that the number of bacteria is able to double every 8 hours. How many bacteria
would there be after 21 hours, to the nearest whole number?
Answers
Answer:
y = 802
Step-by-step explanation:
Will mark Brainliest! What is the value of P. Thank you!
Answers
Answer:
question of number 10 is 3
help please i’ll give extra points & brainlist:)!
Answers
hope this helped :)
Meng conducted a survey to determine the favorite flavor of ice cream in
his hometown. Fifteen of the fifty people he surveyed like strawberry best.
How many of the 3,500 residents in the town would you expect to like
strawberry ice cream? *
Answers
Answer:
1,050
Step-by-step explanation:
It’s in my notebook, so I can’t show
Kevin correctly answered 75% of 32 test questions. How many questions did Kevin answer correctly? How many more questions would Kevin have had to answer correctly to get more than 80% correct?
Answers
Answer:
At least 26 questions to get around an 82% not 25 because that equals 78%
Step-by-step explanation:
Answer:
Kevin answered 24 questions correctly.
Kevin would have to answer 25.6 questions correctly to get more than 80%.
The farm raises some rabbits and native chickens. The number of native chickens is six times the number of rabbits, with a total of 560 feet. farm
Raised ? rabbit.
Answers
The farm raises some rabbits and native chickens. The number of native chickens is six times the number of rabbits, with a total of 560 feet. farm
Raised ? rabbit.
Find the slope of the line that passes through (3, 7) and (1, 10).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
Question 60/62 (3.p.)
KAH
ht
w
2011
Solve and choose the correct answer.
A water tank is in the form of a cylinder whose radiusis 2 m and length is
3.5 m. The quantity of water in litres that can be stored in the tank is
..
Answers
Answer:
Capacity of tank = 44,000 l
Step-by-step explanation:
Given:
Height of tank = 3.5 m
Radius = 2 m
Find:
Capacity of tank
Computation:
Volume of cylinder = πr²h
Volume of cylinder = (22/7)(2)²(3.5)
Volume of cylinder = 44 m³
1m³ = 1000 l
So,
Capacity of tank = 44 x 1,000
Capacity of tank = 44,000 l
In isosceles triangle WXY, XY is 13 inches in length and WY is 10 inches. What is the length of XZ? answer asap please
Answers
=============================================================
Explanation:
Notice the double tickmarks on segments WZ and ZY. This tells us the two segments are the same length. Let's say they are m units long, where m is a placeholder for a positive number.
That would mean m+m = 2m represents the length of segment WY, but that's equal to 10 as the diagram shows. We have 2m = 10 lead to m = 5 after dividing both sides by 2.
We've shown that WZ and ZY are 5 units long each. In short, we just cut that length of 10 in half.
-----------------------------------
Let's focus on triangle XYZ. This is a right triangle with legs XZ = unknown and ZY = 5. The hypotenuse is XY = 13.
We'll use the pythagorean theorem to find XZ
a^2 + b^2 = c^2
(XZ)^2 + (ZY)^2 = (XY)^2
(XZ)^2 + (5)^2 = (13)^2
(XZ)^2 + 25 = 169
(XZ)^2 = 169-25
(XZ)^2 = 144
XZ = sqrt(144)
XZ = 12
Segment XZ is 12 inches long.
Show that n(n – 1)(n + 1) + 6n ≡ n3 + 5n
Answers
Explanation:
n(n - 1)(n + 1) + 6n = n^3 + 5n
n(n^2 - 1) + 6n = n^3 + 5n
n^3 - n + 6n = n^3 + 5n
n^3 + 5n = n^3 + 5n (proven)
WILL MARK BRANL:IEST NO FAKE ANSWERS I NEED ASAP
Answers
Answer:
(-5, 9)
Step-by-step explanation:
Please help me answer this
Answers
9514 1404 393
Answer:
a) zeros: -2/3, 6
b) x < -2/3, signs: -, -; sign of product: +
-2/3 < x < 6, signs: +, -; sign of product: -
x > 6, signs: + +; sign of product: +
c) solution: x < -2/3 ∪ x > 6
Step-by-step explanation:
a) The zeros of the product are the values of x that make either factor zero. (A product is only zero if one of the factors is zero.)
3x +2 = 0 ⇒ x = -2/3
x -6 = 0 ⇒ x = 6
The zeros of the quadratic are x = -2/3 and x = 6.
__
b) For values of x left of the left-most zero, both factors are negative. For values of x between the zeros, the left factor is positive and the right factor is negative. For values of x greater than the right-most zero, both factors are positive. That is, for large negative values of x, all factors are negative. Working left-to-right, each time a zero is crossed, one factor changes sign.
__
c) The solution is where the signs of the factors match:
x < -2/3 or -6 < x
Can somebody solve this question for me it would be so helpful I will give brainliest first it needs to be rounded to the nearest 10th
Answers
Answer:
F. 824.8 ft³
Step-by-step explanation:
To find the volume of a cube, you want to multiply the length by width by height.
l = 8.2
w = 9.4
h = 10.7
l • w • h
8.2 • 9.4 • 10.7
= 824.756
Round to the nearest tenth.
824.8 ft³
Hope this helps!