Q3 A dart is randomly thrown and lands within the boundaries of a 6 foot by 6 foot square. The unshaded regions are each a quarter of an inscribed circle. What is the probability that the dart lands in one of the shaded regions? Express your answer as a common fraction in terms of pi. PLEASE GIVE THE FULL EXPLANATION AND NOT JUST THE ANSWER!!!
Answers
Answer:
[tex]Pr = \frac{8 - \pi}{8}[/tex]
Step-by-step explanation:
Given
See attachment for square
Required
Probability the [tex]dart\ lands[/tex] on the shaded region
First, calculate the area of the square.
[tex]Area = Length^2[/tex]
From the attachment, Length = 6;
So:
[tex]A_1 = 6^2[/tex]
[tex]A_1 = 36[/tex]
Next, calculate the area of the unshaded region.
From the attachment, 2 regions are unshaded. Each of this region is quadrant with equal radius.
When the two quadrants are merged together, they form a semi-circle.
So, the area of the unshaded region is the area of the semicircle.
This is calculated as:
[tex]Area = \frac{1}{2} \pi d[/tex]
Where
[tex]d = diameter[/tex]
d = Length of the square
[tex]d =6[/tex]
So, we have:
[tex]Area = \frac{1}{2} \pi (\frac{d}{2})^2[/tex]
[tex]Area = \frac{1}{2} \pi (\frac{6}{2})^2[/tex]
[tex]Area = \frac{1}{2} \pi (3)^2[/tex]
[tex]Area = \frac{1}{2} \pi *9[/tex]
[tex]Area = \pi * 4.5[/tex]
[tex]Area = 4.5\pi[/tex]
The area (A3) of the shaded region is:
[tex]A_3 = A_1 - A_2[/tex] ---- Complement rule.
[tex]A_3 = 36 - 4.5\pi[/tex]
So, the probability that a dart lands on the shaded region is:
[tex]Pr = \frac{A_3}{A_1}[/tex] i.e. Area of shaded region divided by the area of the square
[tex]Pr = \frac{36 - 4.5\pi}{36}[/tex]
Factorize:
[tex]Pr = \frac{4.5(8 - \pi)}{36}[/tex]
Simplify
[tex]Pr = \frac{8 - \pi}{8}[/tex]
Related Questions
A seventh-grade teacher asks her students a survey question. Which questions are appropriate for the teacher to ask her population? Select three options.
Answers
Answer:
The questions that are appropriate for the teacher to ask her population are:
How many hours of sleep do you get per night?
On average, how long does it take you to complete your homework?
What time do you leave for school in the morning?
Step-by-step explanation:
The survey is conducted among the seventh grade students so the valid question their teacher would have asked them is:
How many hours of sleep do you get per night?
On average, how long does it take you to complete your homework?
What time do you leave for school in the morning?
while the other two questions are invalid as it the students are young and they are not legal to vote.
also it is not necessary that they would arrive to school by car. Please mark the brainliest!
Claire can make an origami swan in 2 1/2 minutes what fraction shows the number of swans she can make per minute
Answers
Answer:
2/5
Step-by-step explanation:
Number of swans Claire can make in one minute = 1 ÷ 21/2
convert 2 1/2 to an improper fraction
to convert to improper fraction, take the following steps :
1. Multiply the whole number by the denominator
2. Add the numerator to the answer gotten in the previous step
3. divide the number gotten in the previous step by the denominator
2 1/2 = 5/2
1 ÷ 5/2
1 x 2/5 = 2/5
What is the code? Please help!
Answers
find the slope of line AB From the Given figures
please help me and solve him
Answers
Answer:
slope of AB = 0
Step-by-step explanation:
The slope of the x- axis OX = 0
Since AB is parallel to the x- axis and parallel lines have equal slopes, then
slope of AB = 0
Since, the line AB is parallel to X - axes, so every point on the the line AB will have equal Y - coordinates.
lets take it as Y ( y - coordinate is same )
slope :
=》
[tex] \dfrac{y2 - y1}{x2 - x1} [/tex]
but since y2 and y1 are equal, so
[tex] \dfrac{ Y - Y }{x2 - x1} [/tex]
=》
[tex] \dfrac{0}{x2 - x1} [/tex]
=》
[tex]0[/tex]
4 divided by 5 long division
I need help on this please
Answers
1 with a remainder of 1
Can someone help me???
Answers
Answer:
p to the power of 12
Step-by-step explanation:
hope this helps!
The answer is
(p3)4=p?
p3×4=p12
solve: 3x^2+16x+5=0
I did it but apparently its wrong so, please help it would literally probably help me finish high school.
Answers
Answer:
(3x+1)(x+5)
Step-by-step explanation:
Sorry for my handwriting lol hope this makes sense
use the geometric mean (leg) theorem. what is the value of a?
Answers
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the concept of Geometric Mean (leg) theorem.
So according to the rule, we know that, here altitude = h and left side is 6 and right side is 14 , so we get as,
==> altitude/left = right/altitude
==> h/6 = 14/h
==> h^2 = 14*6
==> h^2 = 84
2.) so now we apply the Pythagoras theorem in triangle ∆DCB
so we get as,
==> (14)^2 + h^2 = a^2
==> 196 + 84 = a^2
==> 280 = a^2
==> a = √280
==> after simplified => a = √70*4
==> a = 2√70 units
hence the correct answer is a => 2√70 units.
Calculate the surface area of an open cylinder measuring 35cm in diameter and 60cm high.
Answers
Answer:
6598.2 in^2
Step-by-step explanation:
Given data
Diameter= 35in
Radius= d/2= 35/2= 17.5in
Height = 60cm
The expression for the curve surface area of a cylinder is
CSA=2πrh
substitute
CSA= 2*3.142*17.5*60
CSA= 6598.2 in^2
Hence the CSA is 6598.2 in^2
answer number 3 plz (i give brainliest)
Answers
Answer:
Pretty sure it's B.)
Step-by-step explanation:
I wrote 6 x 10^5 in standard form (6 x 100000 = 600000).
Divided the product by 15 (600000 divided by 15 = 40000).
The only choice that matches is /B/ (4 x 10^4 ---> 4 x 10000 = 40000).
(6+1) to the power of 2. For some reason I forgot how to do this.
Answers
Just add what’s in the bracket then square it.
(6+1)^2
7^2
= 49
Answer:
49
Step-by-step explanation:
see the image below:)
find the hypotenuse of traingle, which has base = 8 and perpendicular = 6,
please help me otherwise I will fail :(
Answers
Answer:
10 is the hypotenuse
Step-by-step explanation:
a² + b² = c²
Given:
a = 8
b = 6
Work:
a² + b² = c²
8² + 6² = c²
64 + 36 = c²
100 = c²
[tex]\sqrt{c^2} =\sqrt{100}[/tex]
c = 10
Step-by-step explanation:
hope it is helpful to you
For the equations given below, which statement is true? A. The equations do not have the same solution because the second equation can never be obtained when multiplying the first equation by any value. B. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first equation by −3. C. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first equation by 3. D. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first equation by −4.
Answers
Which of the following sine values is the lowest
Sin(82)
Sin(3)
Sin(78)
Sin(15)
Answers
In which of the following do you expect the correlation coefficient to be closest to 1?
Answers
Answer:
the answer is -1.0 to positive 1.0
Step-by-step explanation:
and i used my head
what's 3/12 - 1/6 - 1/4 - 1/4
Answers
Answer:According to the calculator it says -0.41666666666
Step-by-step explanation:don know if its correct but dc byeee
Answer: -5/12
Step-by-step explanation:
Data: 3/12-1/6-1/4-1/4=x
Step one, Find the common demoninator of the fractions
3/12-1/6-1/4-1/4 = 3/12-2/12-3/12-3/12
Reason: You can't subtract fractions that don't have the same denominatory so by finding the common demoninator you allow the problem to be solved.
Step two, Subtract
3/12-2/12= 1/12-3/12=-2/12-3/12=-5/12
Reason: You subtract fractions(With the same denominator) like normal numbers but you keep the denominator the same. When subtracted, the end result is -5/12 since subtracting a bigger number from a smaller number creates a negative.
Answer: -5/12
I hope this helps!
solve for x
20
30
40
56
Answers
Answer:
30
Step-by-step explanation:
brainliest?
Answer:
40
Step-by-step explanation:
please give me answer please
Answers
......................................................................................
someone please explain this
Answers
Answer:
Step-by-step explanation:
110=4t+90(being vertically opposite angles)
110-90=4t
20/4=t
5=t
Answer:
Hello! answer: t = 5 degrees
Step-by-step explanation:
these are vertical angles meaning they will have the same measure! 4 × 5 = 20 and 20 + 90 = 110 therefore t = 5 HOPE THAT HELPS!
X divided by 3-6=6 please hurry:)
Answers
x/3=12
x=36
done !
I need answers now please!
Answers
Answer:
option C
Step-by-step explanation:
if each box represents 1 miles, what is the shortest distance from the school to the skate park.
Answers
The shortest distance between two points is a straight line.
Use the distance formula for points.
In the diagram, we are given two points:
(4,2) and (-3,0).
Let d = distance between the two points.
d = sqrt{(-3 -4)^2 + (0-2)^2}
d = sqrt{(-7)^2 + (-2)^2}
d = sqrt{49 + 4}
d = sqrt{53}
d = 2.2360679775
d = 2.2 miles
Can anyone help?????
Answers
The long sides are 5 more than the short base (4x-2) hence each long side is (4x-2)+5 which is simplified to 4x+3.
Keep the perimeter as a hint because it is the total of all the sides, this gives x.
Make the equation
4x+3+4x+3+4x-2 = 64
Simplify
12x+4=64
x=60/12
x=5
The length of one long side is (4*5+4)=24
I hope it’s correct because I’m not sure if they saying that both the sides are 5 inches longer or each of the longer sides are 5 inches longer. It would make a difference.
Hopefully this helped
Someone help pls :,)
Answers
Answer:
B=70.41 m^2V=675.41 m^3
Step-by-step explanation:
I'm in a hurry
please please help me i’m failing math!!!
Answers
Answer:
go to school, do your work, you are only cheating yourself, not the school, or end up homeless
Step-by-step explanation:
(two times pi times your radius)
Your midpoint is at (5,0) and seeing as it crosses straight through the middle, your radius is 5 units. Input it into the formula and you’ll get your answer.
2π • 5
Answer: C ≈ 31.42 units
help help 100 points
Answers
Answer:
all of them except the first and the 4th
Step-by-step explanation:
Answer:
Step-by-step explanation:
All but 4
I need help please !!!!!!
Answers
Explanation:
Isosceles triangle is where two side lengths are equal.
Equilateral triangle is where all side lengths are equal.
Scalene Triangle is where all side lengths have different measures.
Since this triangle has two side lengths with the same measure it is an isosceles triangle.
Candice babysat 2 hours each night for 12 nights. She earned a total of $312 babysitting. Candice wants to calculate her hourly rate. How much did Candice earn per hour of babysitting? plz i need the answer
Answers
Answer:
$13
Step-by-step explanation:
Solve the equation 3 (x+ 4.5) = 36 one step at a time. Use the diagram to help you
(EXPLAIN. step BY step)
Answers
Then you get x+4.5=12
Move the constant to the right-hand side and change its sign x=12-4.5
Then you want to subtract the numbers Subtract the numbers
Then your answer is X=7.5 have a great day
Hey guys! Can i get some help on this one? Thank u!
Answers
Answer:
x=-1
Step-by-step explanation:
-2x-3=x
add 2x to both sides
-3=3x
divide both sides by 3
-1=x