Find the probability that a randomly selected point within the circle falls in the white area. Please, and thank you.
Answers
Answer:
About 68.2%.
Step-by-step explanation:
We want to find the probability that a randomly selected point lands in the white area.
To do so, we can find the probability that the point does not land in the white area (i.e. the red area) and then subtract it from 100%.
The circle has a radius of 4 cm. Note that the base of the triangle is the diamater, so the base measures 8 cm. The height of the triangle is the radius, so it measures 4 cm. Thus, the area of the triangle is:
[tex]\displaystyle \begin{aligned} A &= \frac{1}{2}bh \\ &= \frac{1}{2}(8)(4) \\ &= 16\text{ cm}^2\end{aligned}[/tex]
Likewise, the area of the entire circle will be:
[tex]\displaystyle \begin{aligned} A &= \pi r^2 \\ &= \pi(4)^2 \\ &=16\pi \text{ cm}^2\end{aligned}[/tex]
Then the probability that a randomly seleted point lands in the red area is:
[tex]\displaystyle P\left(\text{Red}\right) = \frac{\text{Red}}{\text{Total}} =\frac{16}{16\pi} = \frac{1}{\pi}[/tex]
The probability that the point lands in the red area or the non-red area (i.e. white area) must total 100%. In other words:
[tex]\displaystyle P\left(\text{Red}\right) + P\left(\text{White}\right) = 1[/tex]
Thus:
[tex]\displaystyle P\left(\text{White}\right) = 1 - P\left(\text{Red}\right)[/tex]
Substitute:
[tex]\displaystyle P\left(\text{White}\right) = 1 - \left(\frac{1}{\pi}\right)[/tex]
Use a calculator. Hence:
[tex]\displaystyle P\left(\text{White}\right) \approx 0.6817 = 68.2\%[/tex]
The probability that a randomly selected point lands in the white area is about 68.2%.
Related Questions
Can i please get some help im pretty desperate and will give brainiest to first answer with some steps, just try your best please
Answers
Answer:
To calculate the vertex you can use the vertex form ( i searched about the vertex and found it) but i don't know how to use it so i used another method.
The vertex is where the function inverts (y values) so it is going to be or a maximum or a minimum of the function. To calculate the min/max you derivate the function and then equal it to zero.
1) y = -3x^2 -12x -10
the derivative of y is y' = -6x -12 = -6(x+2)
y'=0 <=> -6(x+2) = 0 <=> x+2=0 <=> x=-2
y(-2) = -3(-2)^2 -12*(-2) -10 = 2
So the vertex is the point (-2,2) .
Because the slope of the equation is negative that means that the vertex is going to be the maximum , so the maximum is (-2,2) .
To find another 4 points you just have to pick values of x and replace them in the equation y = -3x^2 -12x -10 to find y.
2) y = -2x^2 -12x -16
Do the same thing we did in point 1
y'= -4x-12 = -4(x+3)
y'=0 <=> -4(x+3) = 0 <=> x+3=0 <=> x=-3
y(-3) = -2(-3)^2 -12*(-3) -16 = 2
So the vertex is the point (-3,2) .
HELP ASAP!
David invests $1000 in an account that earned 5.5% simple interest. How much money will be in his account in 24 months?
Answers
Answer:
Step-by-step explanation:
Interest is equal to principal times rate times time / 100
Interest =$110
Amount is equal to interest plus principal
Amount=$1110
Graph the function y= 3/2x^3. Plot five points on the graph of the function: one point with x = 0, two points with negative x-values, and two points with positive x-values.
Answers
Answer:
(a square +7a+12) ÷(a+3)
(y+2)(y^2-2y+4) ..........................
Answers
You can use the distributive property to multiply:
( y )( y² - 2y + 4 ) + ( 2 )( y² - 2y + 4) =
y³ - 2y² + 4y + 2y² - 4y + 8 =
y³ + 8
The -2y² and the 2y² cancel each other, and the 4y and -4y cancel each other out!
Identify the area of sector MOR in terms of π and rounded to the nearest hundredth.
Answers
Answer:
8.98π = 28.22 in^2.
Step-by-step explanation:
Area of the whole circle = πr^2 = 7^2 * π
= 49π
So the area of sector MOR
= (66/360) * 49π
= 8.98π = 28.22 in^2.
Gasoline is a non-polar liquid that will float on water. 400 grams of gasoline is spilled into a puddle of water. If the density of gasoline is 0.665 g/mL, what volume of gasoline is spilled?
Answers
Step-by-step explanation:
here's the answer to your question
problem that would represent
an elevator starts at street
level (main lobby) goes up 6
floors and then back down 8
floors to the parking garage.
1 + 7 - 8 = 0
0 + 8 + (-2) = 6
1 + 6 + (-8) = -1
0 + 6 + (-8) = -2
Answers
[tex]\\ \sf \longmapsto 1+6+(-8)[/tex]
Downward motion noted as negative and upward is positive.Lobby will be 1[tex]\\ \sf \longmapsto 1+6+(-8)[/tex]
[tex]\\ \sf \longmapsto 1+6-8[/tex]
[tex]\\ \sf \longmapsto 7-8[/tex]
[tex]\\ \sf \longmapsto -1[/tex]
option c is correct
Bobby think that 5^2 = 10. What is wrong with this answer
Answers
Answer:
see below
Step-by-step explanation:
5^2 means 5*5 not 5*2
5^2 = 5*5 = 25 not 10
Answer:
5*5 = 25
bobby mistake is doing 5*2 = 10
Step-by-step explanation:
Factor the expression
Thank you so muchh
Answers
Answer:
(x+8)(x-5)
Step-by-step explanation:
x^2 +3x-40
What two numbers multiply to -40 and add to 3
8 * -5 = -40
8+-5 = 3
(x+8)(x-5)
Answer:
(x + 8)(x - 5)
Brainliest, please!
Step-by-step explanation:
(x + )(x - )
Factors of 40: 1 and 40, 2 and 20, 4 and 10, 5 and 8
(x + 8)(x -5)
Please help me. if I don’t complete my course I’m getting sent back to my parents house, and I need to complete this course
This is similar polygons, and the lessons I get don’t help
Answers
For real though, I’m hoping you don’t get sent back there. I’m assuming you dislike it there, so good luck with your course. I’m here to help if you need it.
A can contains 1/2 pint of paint. If we use 2/3 of the paint, how much paint is left in the can?
A. 1/2
B. 1/3
C. 2/3
D. 1/6
E. 5/6
Answers
Answer:
d
Step-by-step explanation:
Quantity of paint used = (2/3) of (1/2)
[tex]=\frac{2}{3}*\frac{1}{2}\\\\=\frac{1}{3}[/tex]
Quantity left in the can = [tex]\frac{1}{2}-\frac{1}{3}[/tex]
[tex]= \frac{1*3}{2*3}-\frac{1*2}{3*2}\\\\=\frac{3}{6}-\frac{2}{6}\\\\=\frac{1}{6}[/tex]
Hello! Hello ! guys. or any genius of math. can you help me on this math problems. this question is out of my answer.
could you help me.
if your answer is correct there is a big changes to get brain list answer and 2 followers from my two accounts.
don't need to follow back.
Answers
Answer:
we have to convert that question centimeters to meters
Step-by-step explanation:
I think all are going to be less as you change all of them.
From 38 to 316 inclusive,how many integers can be found that are multiples of 12? 20 Points!
Answers
Answer:
The first multiple of 12 after 38 is 48.
The first multiple of 12 before 316 is 312.
So we have, 48, 60, 72... 312.
Divide by 12...
4, 5, 6, ... 26
Subtract 3 from each term to get... 1, 2, 3... 23
So there are 23 terms!
Hope this helps!
What are the solutions to this quadratic equation? -2x2+x+4=0
Answers
Answer:
=1±33√4
Step-by-step explanation:
Answer:
[tex]x =\frac{1+/-\sqrt{33} }{4}[/tex]
Step-by-step explanation:
It wouldn't let me put the symbol in the equation but +/- is just the same thing as ±
This answer is correct on edmentum/plato
b If a and a+10 are a pair paix of complementary angles. Find them.
Answers
Answer:
[tex]\sf{}[/tex]
Step-by-step explanation:
a+10 = 90
a = 90-10
a = 80
therefore a = b
b = 80
Answer:
Angles are : 40 , 50
Step-by-step explanation:
Sum of complementary angles are 90
a + a + 10 = 90
2a + 10 = 90
2a = 90 - 10
2a = 80
a = 80/2
a = 40
a + 10 = 40 + 10 = 50
Angles are : 40 , 50
find the surface area of the cylinder and round to the nearest tenth
Answers
Answer: A = 833.66 in^2
Step-by-step explanation:
Area of the base = (7^2)(pi) = 49 pi = 153.9 in^2
Height of the cylinder = 12 in
Circumference of the base = (2)(pi)(r) = 44in
Surface area = (2)(pi)(7)(12) + (2)(pi)(7) = 833.66 in^2
Find the slope of the line that passes through (2, 18) and (9, 9).
Answers
Answer:
m=-9/7
Step-by-step explanation:
Geometry, please answer question ASAP
Answers
Because,
Sum of interior angles of a pentagon = 540 degree
That is,
Angle A + angle B + angle C + angle D + angle E = 540 degree
87degree + 125 degree + 63 degree + 95 degree + angle D = 540 degree
So that gives angle D = 170 degree
Hope this helps.
ArmyCee:)
Answer:
m<D = 170°
Step-by-step explanation:
In a pentagon, the angles add up to 540°. This means the sum of <A, <B, <C, <D, and <E add up to that, and we can write an equation:
m<A + m<B + m<C + m<D + m<E = 540°
We are already given the measures of all the angles except D, so we can substitute them in:
87° + 125° + 63° + m<D + 95° = 540°
Now, we can simplify and solve for <D:
m<D + 370° = 540°
m<D = 170°
at the movie theatre admission is $6.30 an adult admission is $9.60. on thursday twice as many adult tickets as child tickets were sold for a total sale of $535.50 how many child tickets were solf that day
Answers
Answer:
number of child tickets sold on saturday is 21
number of adult tickets sold on saturday is 42
Step-by-step explanation:
Let's assume
number of child tickets sold on saturday is x
number of adult tickets sold on saturday is y
On saturday, twice as many adult tickets as child tickets were sold
so, we get
child admission is $6.30 and adult admission is $9.60
a total sales of $535.50
we get
now, we can plug y=2x
now, we can solve for x
now, we can find y
so,
number of child tickets sold on saturday is 21
number of adult tickets sold on saturday is 42.........Answer
The hypotenuse of a right triangle measures nem and one of its legs measures o em.
Mnd the measure of the other leg. If necessary, round to the nearest tenth.
Sun
attempt to
Answers
Using Pythagorean theorem
[tex]\\ \sf\longmapsto P^2=H^2-B^2[/tex]
[tex]\\ \sf\longmapsto P^2=11^2-9^2[/tex]
[tex]\\ \sf\longmapsto P^2=121-81[/tex]
[tex]\\ \sf\longmapsto P^2=40[/tex]
[tex]\\ \sf\longmapsto P=\sqrt{40}[/tex]
[tex]\\ \sf\longmapsto P=6.2cm[/tex]
Step-by-step explanation:
Given,
Hypotenuse = 11 cm
Base (One of the given leg) = 9 cm
Therefore,
According to Pythagoras Theorem,
[tex] {base}^{2} + {height}^{2} = {hypotenuse}^{2} [/tex]
[tex] = > {(9)}^{2} + {height}^{2} = {(11)}^{2} [/tex]
[tex] = > {height}^{2} = {(11)}^{2} - {(9)}^{2} [/tex]
[tex] = > {height}^{2} = 121 - 81[/tex]
[tex] = > {height}^{2} = 4 0[/tex]
[tex] = > height = \sqrt{40} [/tex]
=> height = 6.3245553203
When rounded to nearest tenth,
=> height = 6.3
Hence,
Required length of other leg is 6.3 (Ans)
Please help I will give you Brainlyest
Answers
Answer:
a. You can find the value of 4w by using inverse operations. Subtract 8 from both sides in the equation 4w+8=32. You will get 4w=24. Now, you divide 4 by both sides to get w by itself. You will soon get 6. Now multiply 6 and 4, coming to the conclusion that 4w=24.
b. To find the value of w using the value of 4w, which is 24, simply use inverse operations once more. Using the equation 4w=24, we can use division and divide 4 by both sides, leaving us with w by itself. We end up with w=6. The value of w is 6.
c. You can check if the value of w is correct by plugging in your number back into the equation. Our equation is 4w+8=32, so we replace w with 6, the value for w that we found. We end up with 4(6)+8=32. Multiply 4 by 6, ending up with 24, then add it to 8, coming up with 32. 4(6)+8=32, which shows us that 6 is the correct value for w.
helppppppppppppppppppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
x = -1
Step-by-step explanation:
14x + 2 = 9x -3
Transpose
14x -9x = -3 -2
5x = -5
x= -5/5
x = -1
Answer:
x = -1
Step-by-step explanation:
[tex]14x+2=9x-3\\\\5x+2=-3\\\\5x=-5\\\\x=-1[/tex]
In a math class of 28 students, 14 boys and 14 are girls. On a unit test, 5 boys and 9 girls made an A grade. A student is chosen at random from the class. What is the probability of choosing a girl or an A student?
A. 0.82
B. 0.68
C. 0.14
D. 0.50
Answers
Answer:
The probability of choosing a girl is 1/2.
The probability of choosing an A student who is a BOY is 5/28.
1/2 = 14/28, and 14/28 + 5/28 = 19/28. This can be simplified to 0.68
Thus, the answer is B. 0.68
Let me know if this helps!
The required probability of choosing a girl or an A student is 0.82. Option A is correct.
Given that,
In a math class of 28 students, 14 boys and 14 are girls. On a unit test, 5 boys and 9 girls made an A grade.
A student is chosen at random from the class. What is the probability of choosing a girl or an A student is to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Total sample space = 28
Number of girls = 14
Number of boys = 14
Number of girls A grade student = 9
probability of a girl = 14/28 = 0.5
probability of A grader girl = 9 / 28 = 0.32
Now the probability of choosing a girl or an A grader girl student,
= 0.32 + 0.5
= 0.82
Thus, the required probability of choosing a girl or an A student is 0.82. Option A is correct.
Learn more about probability here:
brainly.com/question/14290572
#SPJ5
The roof rafter of a house has been raised to a height of 13 yards at the ridge. Half of the length of the run measures 9 yards. Find
the length of the rafter. Round to the nearest 100th.
Answers
Answer:
15.81 = ?
Step-by-step explanation:
Since this is a right triangle we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
9^2 + 13^2 = ?^2
81 +169 = ?^2
250 = ?^2
Taking the square root of each side
sqrt(250) =?
15.8113883= ?
To the nearest 100th
15.81 = ?
Answer:
Using Pythagorean theorem:- [tex]a^{2} +b^{2} =c^{2}[/tex]
a= 13
b= 9
c= ? ( length)
[tex]13^{2} +9^{2} =?^{2}[/tex]
[tex]13^{2} =169[/tex]
[tex]9^{2} =81[/tex]
[tex]169+81=?^{2}[/tex]
[tex]250=?^{2}[/tex]
[tex]\sqrt{250}=15.811[/tex]
[tex]?=15.81[/tex]
OAmalOHopeO
Use the interactive to solve. What is the difference between –5 and 3?
Answers
difference is another way to say subtract so it could be shown as (-5) - 3
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{When you hear the word \underline{\underline{difference}} in math it means subtract/}\\\large\text{subtraction}[/tex][tex]\large\text{When you hear the word \underline{\underline{sum}} in math it means add/addition}[/tex][tex]\large\text{When you hear the word \underline{\underline{product}} in math it means multiply/}\\\large\text{multiplication}[/tex][tex]\large\text{When you hear the word \underline{\underline{quotient}} it means divide/division}[/tex][tex]\large\text{Question reads \underline{\underline{What is the \boxed{\large\text{DIFFERENCE}} between -5 \& 3}} ?}[/tex]
[tex]\large\text{Fun fact: you can use a number line to find your result as well.}\\\large\text{For example in this equation you START at -5 and move down 3}\\\large\text{spaces to your left}[/tex]
[tex]\large\text{REMEMBER: we said difference means \boxed{\large\text{subtract}}, so we have to}\\\large\text{\underline{subtract} both numbers from each other to find their differences.}[/tex]
[tex]\large\text{-5 - 3}\\\large\text{= \bf -8}[/tex]
[tex]\large\text{So, the DIFFERENCE between -5 \& 3 is \boxed{\bf -8}}[/tex]
[tex]\boxed{\boxed{\huge\text{The difference is: \boxed{\bf -8}}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
16. What is the measure of ZAOB?
Answers
Find the total of d1 and d2.
total of d1 and d2: 180 - 40 - 40 = 100 degrees
Find d1 and d2 separately.
100 divided by 2 = 50 degrees
Use d1 to find b1 to find total of a1 and a2.
b1 is parallel to d1 so b1 = 50 degrees
a1 and a2 = 180 - 50 - 50 = 80 degrees
a1 = 80 divided by 2 = 40
Since a1 and c1 are parallel due to alternate angles, c1 is 40 degrees
Find b2 now which requires you to do total - minus all angles in the triangle with angle b2.
180 - 40 - 50 - 40 = 50 degrees (angle b2)
AOB has b1 and a1.
40 + 50 = 90 degrees (a1 + b1 = AOB)
The answer is 90 degrees
Identify the compositions performed on XYZ to map onto X"Y"Z".
A) Translation: (x,y) - (x - 2, y + 1); 180° rotation about the origin
B) Translation: (x,y) - (x + 2, y - 1); 180° rotation about the origin
C) Reflection along the line y = x; 180° rotation about the origin
D) Reflection along the y-axis; 180° rotation about the origin
Answers
The correct answer is A) 180° rotation about the origin, followed by a translation (x, y) → (x - 2, y + 1).B) 180° rotation about the origin, followed by a translation (x, y) → (x + 2, y - 1).C) Reflection along the line y = x, followed by a 180° rotation about the origin.D) Reflection along the y-axis, followed by a 180° rotation about the origin.
To identify the compositions of transformations that map XYZ onto X"Y"Z", we need to analyze each option and determine the combination of transformations.
A) Translation: (x,y) - (x - 2, y + 1); 180° rotation about the origin
This option consists of a translation and a 180° rotation about the origin. To identify the composition, we perform the operations in reverse order. First, we apply the 180° rotation, and then the translation. Therefore, the composition of transformations for option A is a 180° rotation about the origin followed by a translation of (x, y) → (x - 2, y + 1).
B) Translation: (x,y) - (x + 2, y - 1); 180° rotation about the origin
Similar to option A, this option involves a translation and a 180° rotation. Again, we reverse the order of operations to determine the composition. So, the composition of transformations for option B is a 180° rotation about the origin followed by a translation of (x, y) → (x + 2, y - 1).
C) Reflection along the line y = x; 180° rotation about the origin
This option includes a reflection along the line y = x and a 180° rotation. The order of operations is important, so we perform the reflection first and then the rotation. Hence, the composition of transformations for option C is a reflection along the line y = x followed by a 180° rotation about the origin.
D) Reflection along the y-axis; 180° rotation about the origin
Option D involves a reflection along the y-axis and a 180° rotation. As with the previous options, we need to reverse the order. Thus, the composition of transformations for option D is a reflection along the y-axis followed by a 180° rotation about the origin.
In summary:
A) Composition: 180° rotation about the origin, then a translation (x, y) → (x - 2, y + 1).
B) Composition: 180° rotation about the origin, then a translation (x, y) → (x + 2, y - 1).
C) Composition: Reflection along the line y = x, then a 180° rotation about the origin.
D) Composition: Reflection along the y-axis, then a 180° rotation about the origin.
Learn more about rotation here:
https://brainly.com/question/2078551
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A board is 10.17 feet long. Sandy needs
to cut the board into 3 equal sections.
How long will each section be?
Answers
Answer:
3.39
Step-by-step explanation:
divide 10.17 by 3 to get the size of each section
I need help with 20-26 evens
Answers
this is simplify? I think it's simplify so I can give you an answer
Is 30 inches greater than 3 feet
Answers
Answer:
1 feet = 12 inch
so, 3 feet = 36 feet
therefore, 3 feet is greater than 30 inch
Answer:
Yes, 3o inches is greater than 3 feet
Step-by-step explanation:
