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
Samantha works part time at a store where she earns $462.30 each month. Write an expression that could be used to find the amount Samantha earns working any number of months, m.
Answers
Answer:
462.30m
Step-by-step explanation:
1 month = $462.30
You multiply by the number of months to find how much she made over that time so $462.30 * m = 462.30m
Answer:
Step-by-step explanation:
Find the area of the composite figure.
Answers
Answer:
Area = 139.27 m²
Step-by-step explanation:
Area of the composite figure = area of rectangle + area of semicircle
= (L*W) + ½(πr²)
L = 10 m
W = 10 m
r = ½ of 10 = 5 m
Plug in the values
Area = (10*10) + ½(π*5²)
Area = 100 + 39.27
Area = 139.27 m²
Just need help with this question, would like an explanation as to how you got the answer so I can know for further assignments!
Answers
Answer:
p=0, p=.25
Step-by-step explanation:
p*(4p-1)=0
p=0. when the product of factors equals zero at least one factor is zero
4p-1=0
p=1/4 or .25
P=1/4 and P=0
For workup see attached photo below.
Good luck
If something is $1.75 with 34% markup what is the sale price?
Answers
Answer:
$2.65
Step-by-step explanation:
Can you find the slope-intercept equation of each line and type the correct code? Please remember to type in ALL CAPS with no spaces.
Answers
Answer:
Step-by-step explanation:
line 1 is H
line 2 is C
line 3 is D
line 4 is G
:)
The graph of a quadratic equation in two variables whose axis of symmetry is parallel to the y axis is a parabola.
Select one:
True
False
Answers
Answer:
The correct option is;
False
Step-by-step explanation:
The equation of the graphs of conic sections (all of which can have axis of symmetry that can be oriented parallel to the y-axis) includes;
Circle; (x - h)² + (y - k)² = r²
Parabola; y = a·(x - h)² + k
[tex]Ellipse; \dfrac{(x - h)^2}{a^2} + \dfrac{(y - k)^2}{b^2} = 1[/tex]
[tex]Hyperbola; \dfrac{(x - h)^2}{a^2} + \dfrac{(y - k)^2}{b^2} = 1[/tex]
The graph of a quadratic equation in two variables whose axis of symmetry is parallel to the y-axis can be either a circle, a parabola, an ellipse, or an hyperbola
Therefore, the graph may not be the graph of a parabola and the statement is false
Answer:
The correct answer is True
Step-by-step explanation:
I took the quiz and got it right.
8/12+1/4
ayuda por favor es para hoy
Answers
Multiply and then simplify completely: ( 8 + √ 10 ) ( 8 − √ 10 )
Answers
Answer:
54.
Step-by-step explanation:
( 8 + √ 10 ) ( 8 − √10)
= 8*8 - 8√10 + 8√10 +√10 * -√10
= 64 - 8√10 + 8√10 - 10
The 2 middle turns cancel out so we have:
64 - 10
= 54.
Write an expression that is equivalent to 7 - 314 – 2x) – 10x. Show your work.
Answers
Carry out the following division:
Answers
Answer:
Step-by-step explanation:
[tex]\frac{11xy^{2}z^{3}}{55xyz}=\frac{1xy^{2}z^{3}}{5xyz}\\\\=\frac{1}{5}x^{1-1}*y^{2-1}*z^{3-1}\\\\=\frac{1}{5}x^{0}*y{1}*z^{2}\\\\=\frac{1}{5}yz^{2}[/tex]
Hint:
[tex]\frac{a^{m}}{a^{n}}=a^{m-n}\\\\a^{0}=1[/tex]
"the quotient of 8 and 4, times 7, plus the difference of 38 and 15”
Answers
8+4=12
12x7=84
38-15=23
84+23= 107
Hope this helps!
Which one is not a characteristic of all parallelograms?
Answers
Answer:
Consecutive angles are supplementary is not character of parallelograms
What’s the answer ?(-3a^5)^3
Answers
Answer:
−27a^(15)
Step-by-step explanation:
Renting a pony for a birthday party costs $200, plus $40 per hour. Write an equation to represent the total cost, c, of renting a pony for hours.
Answers
Answer:
200+ 40h= c
Step-by-step explanation:
Can someone help me with this?
Answers
Answer:
270 degrees
Step-by-step explanation:
hexagons have 5 sides and a five-sided shape has a sum of 540 degrees interior angle so 160+170+90 (because the square in the corner is a right angle which always equals 90 degrees) =420 so minus 420 from 540 to get 120+150 which equals 270 degrees. hope this helped.
HEPL A BROTHER OUT PLS 18 POINTS
Answers
Answer:
She didn't put the negitive in the 2. the 2 bottom boxes should be '-8x' & '-6' which in the end simplyfis to 4x² - 5x - 6
Step-by-step explanation:
What kind of triangle is shown
Answers
Answer:
scalene triangle
..... .
14=2y/5
What’s the answer
Answers
PLEASE ANSWER THANK U I NEED HELP
Answers
Answer:
√340=18.43
Step-by-step explanation:
using, pythogoras theorem.
we should find h , where p=14 and b=12
thank you
Answer:
the answer would be ≈18.4
Step-by-step explanation:
I used the pythagorean theorem to find the value for the hypotenuse and then rounded the answer by the nearest tenth to get approximately 18.4 , hope this helps!
the product of a number and 7 less than the number is 30. what is the number?
Answers
Answer: 23
Step-by-step explanation: because you subtract
Calculate the rate per litre at which a car uses petrol,if it uses 20l of petrol to travel 180 km
Answers
Answer:
Rate per litre=180km ÷ 20l
=8km/l
Find the value of the expression.
b2 − a
for a = 4 and b = 5
Answers
using PEMDAS we solve the 5• 2 first
10 - 4
6 is the answer!
hope this helps :)
okay i only have 40 points left and i cant figure out my goformative that my teacher put up if i can get one of yalls discord or anything to were you can help me please do
Answers
Answer:
add me keegan#0839
Step-by-step explanation:
Name at least 3 angles for each diagram
Answers
Answer:
Acute angle, Obtuse angle, and Zero angle
Answer:
angle RSU.
angle RST
angle UST
Analyze the results of the correlation using the given residual plot.
Answers
Answer:
Last one
Step-by-step explanation:
Answer:Analyze the results of the correlation using the given residual plot.
Residual
Step-by-step explanation:
PLS PLS PLS PLS HELPPPP
Answers
Answer: 62.4 computers or 62
Step-by-step explanation:
Use this equation
48(n)
n will be 0.30 since the sales must increase by 30%
48(0.30)
14.4
Now add 48 and 14
48+14.4
62.4 or round it down to 62
The exchange rate at the Post Office is £1 = 1.17 euros.
How manys euros will you get for £360?
Answers
Answer:
421.2 euros
Step-by-step explanation:
1£ --> 1.17 euros
360 £ --> ?
(360×1.17) ÷ 1 = 421.2 euros
Select the expression that represents the following statement: add 24 to the quotient of 16 and 8.
a. 16 x 8 + 24
b. (16 ÷ 8) + 24
c. 24 − 8 + 16
d.(16 − 8) + 24
Answers
Answer:
Change the minus sign to a plus. 2. ... 24. = 8. 11. 24. Find each quotient. 1. 1. 3. 1. 6. 2. 5. 8. 1. 16. 2. 1. 3 x. 6. 1 = 6 ... Write a variable expression to represent the word phrase.
The correct expression for the given condition is,
⇒ (16 ÷ 8) + 24
What is an expression?An expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division is called mathematical expression.
We have to given that;
The algebraic expression is,
''add 24 to the quotient of 16 and 8.''
Now, We can write the expression as;
Quotient of 16 and 8 is,
⇒ 16 ÷ 8
And, Add 24 to the quotient of 16 and 8.
⇒ (16 ÷ 8) + 24
Thus, The correct expression for the given condition is,
⇒ (16 ÷ 8) + 24
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ3
Please help me with this and explain how you got the answer thank you
Answers
Question above please answer asappp the picture picture please
