50 POINTS A point in the figure is selected at random. Find the probability that the point will be in the shaded region.
about 70%
about 80%
about 95%
about 67%
Answers
The first step that we need to take before attempting to solve the problem is to understand what the problem is asking us to do and what they are giving us to help solve the problem. Looking at the problem statement they are asking for us to determine the probability that a point will randomly be plotted in the shaded region. We are not given much of anything else which means that we will need to use our own numbers.
The picture that was provided has a square with four equal circles inside right next to each other. Therefore, we can say that each side of the square is going to be 2 units which causes the diameter of the circle to be half that or 1 unit. We can go even further and determine that the radius is going to be 0.5 units for each circle. Let's determine the area of all the shapes.
Area of the square
[tex]A_{square} = s^2[/tex][tex]A_{square} = (2\ units)^2[/tex][tex]A_{square} = (2)^2 * (units)^2[/tex][tex]A_{square} = 4\ units^2[/tex]Area of a circle
[tex]A_{circle} = \pi * r^2[/tex][tex]A_{circle} = \pi * (0.5\ units)^2[/tex][tex]A_{circle} = \pi * (0.5)^2 * (units)^2[/tex][tex]A_{circle} = \pi * (0.25\ units)^2[/tex][tex]A_{circle} = 0.7854\ units^2[/tex]The area that we got from the circle only gives us the area for one of the circles so we need to multiply the number by four to give us the total area of the circles.
Total area of the circles
[tex]A_{circles} = 0.7854\ units^2 * 4[/tex][tex]A_{circles} = 3.1416\ units^2[/tex]Now that we determined the area of both the square and the circles we can move onto the part of finding the probability of a point randomly landing on a circle.
Determine the probability
[tex]\textsf{probability = circles / square}[/tex][tex]\textsf{probability = } \frac{3.1416\ units^2}{4\ units^2}[/tex][tex]\textsf{probability = } \frac{3.1416}{4}[/tex][tex]\textsf{probability = } 0.785[/tex]However, now that we have determined what the probability, looking at the answer options we can see that all of the are in percentages. So let's convert our probability into a percentage.
Convert to percentage
[tex]\textsf{probability = } 0.785 * 100[/tex][tex]\textsf{probability = } 78.5\%[/tex]Therefore, looking at the options given, the option that would best fit this choice would be option B, about 80%.
Related Questions
What's the least common
denominator of ¾,
⅘, and ⅔?
O A. 15
O B. 12
O c.20
O D. 60
Answers
Answer:
D. 60
Step-by-step explanation:
60 is the only number that 3 and 4 and 5 all go into.
4 does not go into 15, so not answer A.
5 does not go into 12, so not answer B
3 does not go into 20, so not answer C
D is correct. 4 and 5 and 3 all go into 60.
if you want to calculate your take home pay you will need to determine the amount of taxes that will be taken out of your paycheck to do this you will:
a. subtract your gross income by your net pay.
b. multiply your gross income by the percent of taxes then subtract the amount to find your net pay.
c. multiply your net income by the number of taxes then subtract the amount to find your net pay?
Answers
In order to determine your take home pay, multiply your gross income by the percent of taxes then subtract the amount to find your net pay.
How to determine the net pay?
Gross pay is the total income earned before any deductions. Net pay is the gross income less any deductions.
Assume your net pay is $10000 and tax is 10%, net pay is:
$10,000 - (0.1 x 10,000) = $9,000
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make mathematical expression and simplify. The sum of 4 and 5 is subtracted form one-third of the difference of 40 and 4.
Answers
Answer:
X= -3
Step-by-step explanation:
(4+5)-1/3(40-4)=X
X=9- 1/3(36)
X=9-12
Help! Select the correct answer from each drop-down menu.
Consider right triangle ABC.
(file is attached below!)
Answers
The value of Sin A = 9 / 41 and the value of Cos A = ( 40 / 41).
What is trigonometry?
The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The values of the angels will be calculated by using the trigonometry property.
Sin A = Perpendicular / Hypotenuse
Sin A = 9 /41
Cos A = Base / Hypotenuse
Cos A = 40 / 41
Therefore the value of Sin A = 9 / 41 and the value of Cos A = ( 40 / 41).
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If a fission reaction yields 4.50×10^9 kJ of energy, then how much mass was lost?
1.50×10^−6 kg
5.00×10^−2 kg
5.00×10^−5 kg
1.50×10^−3 kg
Answers
Answer:
(c) 5.00×10^-5 kg
Step-by-step explanation:
The mass and energy are related by Einstein's formula E = mc².
__
Solving for mass in kg, we find it to be ...
m = E/c² . . . . . . . . where E is in joules, and c is in meters/second
m = (4.50×10^12 J)/(3×10^8 m/s)² = 5.00×10^-5 kg
The lost mass was about 5.00×10^-5 kg.
Answer:
5.00×10^−5 kg
Step-by-step explanation:
I took the test and it was correct! PLEASE LIKE and have a wonderful day!
how to Find the number of ways to distribute 5 bananas and 7 different books to 3 person
empty allowed
Answers
Answer:
In order for each child to receive a book, first distribute one book to each.
This can be done in [math] 5\times 4\times 3 = 60 [/math] ways.
The remaining two books can be distributed in [math] 3^2 [/math] ways.
Total number of ways[math] = 60 \ times 9 = 540 [/ math]
Find the solution to the system of equations by
using
substitution.
y = -2x + 13
4x + 8y = 20
Answers
Answer:
the solution is (7,-1)
Step-by-step explanation:
if you dont trust your boy look below
4x + 8(-2x+13)=20
4x -16x + 104 = 20
-12x + 104 *-104* = 20 -104
-12x/-12 = -84/-12
x = 7
y = -2(7) + 13
y = -14 + 13
y = -1
Situation:
A 8 gram sample of a substance that's a
by-product of fireworks has a k-value of
0.1001.
N = Noe-kt
No = initial mass (at time t = 0)
N = mass at time t
k = a positive constant that depends on
the substance itself and on the units
used to measure time
t = time, in days
Answers
The half life of the substance is 6.92 days.
What is the Half life ?Half life can be defined as the time required to reduce the concentration to half of its initial value.
Here the equation given is
[tex]\rm N = N_o e^{-kt}[/tex]
The concentration will reduce to half therefore
[tex]\rm N= \dfrac{N_o}{2}[/tex]
so,
[tex]\rm 39/2 = 39 e^{- 0.1001 * t_{1/2}}[/tex]
ln 0.5 = - 0.1001 * t(1/2)
-0.693 = -.1001 * t(1/2)
t(1/2) = 6.92 days.
Therefore the half life of the substance is 6.92 days.
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find X if X is equal to 9x=6
Answers
It continues are you sure this is the equation also if you need it rounded up
X= .667
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
[tex]\textsc{heya!}[/tex]
[tex]\square\!\!\!\!\checkmark[/tex]what we need to do:
find x if 9x=6[tex]\square\!\!\!\!\!\checkmark[/tex] what we are provided with:
9x=6[tex]\textsc{solution:}[/tex]
[tex]\bold{x=\frac{2}{3}}[/tex][tex]\textsc{explanation:}[/tex]
divide both sides by 9; after performing this operation, we obtain:
[tex]\bold{x=\frac{6}{9}}[/tex]
divide top & bottom by 3; we obtain the solution
[tex]\bold{x=\frac{2}{3}}[/tex]
[tex]\textsc{hopefully\;helpful!}[/tex]
by: [tex]^da_n^cIn_g}[/tex]
have a great rest of your day ahead ~ = )
~
Mr.khatiwada. is a unmarried secondary level mathematics teacher in a community school.His monthly salary is Rs 39990with Rs 2000 allowance and gets one months basic salary as festival expense.if 10%and next 13%of his basic salary is deposited in his provident fund and civil investment trust respectively,how much income tax should he pay in this year.
Answers
The income tax that will be paid for the year will be RS 4199.
How to calculate the tax?The total income that the ma gets will be:
= 39990 + 2000
= 41990
The tax rate is given as 10%. Therefore, the income tax that will be paid this year will be:
= 10% × 41990
= 4199
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If the value of a home is assessed at $110,000, and the homeowner pays property tax at a rate of 25 mills, how much would the homeowner have to pay in property tax each year?
$2,500
$3,125
$1,100
$2,750
Answers
Using proportions, it is found that the homeowner would have to pay $2,750 in property tax each year.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The tax at a rate of 25 mills means that for each $1,000 in value of the home, he pays $25 in taxes. Hence, for a home of value of $110,000, the amount he pays in taxes is given by:
A = 110 x 25 = $2,750.
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What is the pre-image of vertex A' if the image shown
on the graph was created by a reflection across the line
y=x?
O (10,-2)
O (-10, 2)
O (-2,-10)
O (2, 10)
Answers
Answer:
it is b
Step-by-step explanation:
The solution is Option A.
The coordinates of the vertex A before the reflection across the line y = x is given by A = A ( 10 , -2 )
What is Reflection?Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.
The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Given data ,
Let the coordinates of the point A be A ( x , y )
Now , the vertex A is reflected over the line y = x
When you reflect a point across the y = x , the y-coordinate gets interchanged with x-coordinate. The reflection of point (x, y) across the line y = xis ( y , x )
So , the coordinates of the point A' ( -2 , 10 )
Now , the coordinates of the point A will be
A ( x , y ) = A ( 10 , -2 )
Therefore , the value of A is A ( 10 , -2 )
Hence , the coordinates of the point before reflection is A ( 10 , -2 )
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Math need help please
Answers
Answer:
none
Step-by-step explanation:
4x - 6 = 2(2x + 3)
4x - 6 = 4x + 6
Everything cancels out meaning there are no real solutions
What is the measure of AC?
Answers
Answer:
The measure of a minor arc is less than 180° , and equal to the measure of the arc's central angle . A major arc is the longer arc connecting two endpoints on a circle. The measure of a major arc is greater than 180° , and equal to 360° minus the measure of the minor arc with the same endpoints.
the graph of the function 10/x
Answers
The function will have a vertical asymptotes of x = 0 and horizontal asymptotes of y = 0.
What are rational functions?Rational function are functions that are written as a ratio. For instance a/b can be expressed as rational function.
According to the question, we are to plot the graph of the function 10/x
The function will have a vertical asymptotes of x = 0 and horizontal asymptotes of y = 0.
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Right triangle ABC is reflected over AC, then dilated by a scale factor of Two-thirds to form triangle DEC. Which statements about the two triangles must be true? Select three options.
△ABC ~ △DEC
∠B ≅ ∠E
3BC = 2EC
3DE = 2AB
3m∠A = 2m∠D
2m∠A = 3m∠D
Answers
The triangle △ABC and △DEC are similar to each other. Then the correct option is A, B, and D.
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
Right triangle ABC is reflected over AC.
Then dilated by a scale factor of Two-thirds to form triangle DEC.
The triangle △ABC and △DEC are similar to each other.
△ABC ≅ △DEC
The dilation is 2/3. Then we have
DE / AB = 2 / 3
3AB = 2DE
∠B ≅ ∠E = 90
There is no effect of dilation on angle.
Then the correct option is A, B, and D.
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Answer:
A. △ABC ~ △DEC
B. ∠B ≅ ∠E
D. 3DE = 2AB
Step-by-step explanation:
got it right on edge 23
Pls help me I need answers in summer school teachers won’t help!!
Answers
Answer:
21. x = 18.1
22. x =28.7
Step-by-step explanation:
SOH = sin(theta) = opp/hyp
CAH = cos(theta) = adj/hyp
TOA = sin(theta) = opp/adj
21. You would be using tangent.
tan(theta) = Opp/Adj
tan(32°) = x/29
x = 29 * tan(32°)
x = 18.1
22. You would be using cosine
cos(theta) = Adj/Hyp
cos(43°) = 21/x
x * cos(43°) = 21
x = 21 / cos(43°)
x = 28.7
Use a Calculator to help you solve for those side lengths or degrees.
If you were to search of SOHCAHTOA online and find an image you would be able to see their example problem done using
SOHCAHTOAI am not sure if I am allowed to use an online example image since I got warned for some reason without explanation to the warning.
An arithmetic sequence starts
-10, -13, -16,
Find the sum of its first 35 terms.
Answers
Answer:
-10,-13,-16 and importance of being in a good night friends ni pta nhi hai to you
A student is reading a newspaper article about a new playground being built in the community. The article says that the playground will benefit the community for a number of reasons. The student wants to figure out whether the author’s claims are strong. In 1–2 sentences, explain how the student could analyze and evaluate the author’s claims.
Answers
The student should check if the author's claims are more opinions or facts. The student should see how the author's claims are helpful.
How to verify a claim?
We are told that the author of the article is making a claim that a playground will benefit a particular community.
Now, when trying to verify a claim by someone it is very important to try to get facts and figures about that fact to start with before asking for opinions.
Thus, what the student do is that he should look for opinions, the student should check if the author's claims are more opinions or facts. The student should see how the author's claims are helpful.
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Try: Re-reading the question.
Answer: The student should check if the author's article provides more facts or evidence than opinions.
What is the difference between facts and opinions? Facts provide real statements that have been proved with solid evidence by experts. Meanwhile, on the other hand, opinions are what people think. It is more like thinking than something with evidence. It hasn't or can't be proved. If it includes more facts then the author's claims are strong with solid evidence. If it includes more opinions then the author's claims are not strong, they are weak. Since it's only the author's point of view.
5. Se hizo una encuesta a estudiantes, de una carrera de un total de 6000 estudiantes encuestados el 75% le gusta leer. ¿Cuántos estudiantes les gusta leer?
Answers
La encuesta indica que de entre todos los estudiantes de una carrera, 4500 les gusta leer.
PercentageThe percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the example: [tex]\frac{30}{100} =\frac{3}{10}=0.3*100=30 \%[/tex].
The question gives:
6000 students75% of students like to readThen, you will have:
[tex]6000\cdot \frac{75}{100}\\ \\ 6000\cdot \frac{3}{4}\\ \\ \frac{18000}{4} =4500[/tex]
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A triangular prism has an equilateral base with side length x inches. The height of the prism is four times as long as the side length.
What is the lateral area of the prism?
12x square inches
12x2 square inches
36x square inches
36x2 square inches
Answers
The area of the prism is 12x² inches². Thus, the correct option is B.
What is a triangular prism?Suppose you've got a triangle. Now, stretch it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.
Usually, when we talk about a triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.
For a prism, the lateral sides of a prism are made up of rectangles which consist of the height and the length of the base. Therefore, a triangular prism has an equilateral base with a side length x inches. The height of the prism is four times as long as the side length. The lateral area will be,
Lateral Area = 3(x×4x) = 12x² inches²
Hence, the area of the prism is 12x² inches². Thus, the correct option is B.
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Two trains, Train A and Train B, weigh a total of 526 tons. Train A is heavier than Train B. The difference of their weights is 466 tons. What is the weight of each train?
Answers
Answer:
Train A = 466
Train B = 60
Step-by-step explanation:
E Homework: 3.1 Homework
Evaluate the function f(z) = 3z-8 at the indicated values.
a) Find f(-4).
1
b) Find f
2
c) Find f(z-7).
a) f(-4)=
(Simplify your answer. Type an integer or a simplified fraction.)
THINGS
Answers
The given function is f(z)=3z-8 for the values f(-4), f(2) and f(z-7) respectively -20, -2 and 3z-29 respectively.
The given function is f(z)=3z-8.
We need to find the value of f(-4), f(2), f(z-7).
What is a function?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
Now to find f(-4), replace z from -4.
f(-4)=3(-4)-8=-12-8=-20
Now to find f(2), replace z from 2.
f(2)=3(2)-8=6-8=-2
Now to find f(z-7), replace z from z-7.
f(z-7)=3(z-7)-8=3z-21-8=3z-29.
Therefore, the given function is f(z)=3z-8 for the values f(-4), f(2) and f(z-7) respectively -20, -2 and 3z-29 respectively.
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-2
Mark all of the statements that are true.
-2
A. The domain for this function is all
real numbers.
B. The domain for this function is
the set {3}.
+2
C. All real numbers are in the range of this function.
D. This graph is not a function because the value of y is the same for
every value of x.
E. The range for this function is the set (3).
Answers
Hope that helps!!
Mr. Garcia had some blueberries. He sold 2 3/4 kilograms of the blueberries and packed the rest equally into 9 bags. Each bag contained 1/4 kilogram of blueberries. Find the mass of blueberries that mr. Garcia had at first
Answers
Answer:
Mr. Garcia had 5 kilograms of blueberries at first
Step-by-step explanation:
to make this easiest, we can imagine that we're undoing mr. garcia's actions.
So, we can start by 'unpacking' mr garcia's bags
we know that each of the nine bags had 1/4 kilograms, so we can multiply 1/4 by 9 to find the collective mass packed into bags
(remember, multiplication is repeated addition. we could also add 1/4 + 1/4 + 1/4... nine times, but this would take a while)
so,
1/4 x 9 = 9/4
(9 = 9/1 [if that is how you're used to multiplying a fraction])
Then, he also sold 2 3/4 kilograms
so, we can add 2 3/4 + 9/4 to find the total mass of the blueberries at first
2 3/4 + 9/4 = 2 + 12/4
(12/4 = 3)
2 + 3 = 5
So, Mr. Garcia had 5 kilograms of blueberries at first
a. single $80,602
Determine the tax for each filing status and taxable income amount listed.
a. single $80,602
0/ 50000
b. head of household $83,572
0/ 50000
c. married filing jointly $77,777
0/ 50000
d. married filing separately $83,050
Answers
Based on the filing status and the taxable income, the tax for the following people are:
a single earning $80,602 is $15,950.head of household earning $83,572 is $15,216.married filing jointly earning $77,777 - $11,031.married filing separately $83,050 - $16,773.What are the taxes these people should pay?Based on the tax table, a single in the $80,600 - $80,650 bracket should pay $15,950.
A head of household in the $83,550 to $83,600 bracket would pay $15,216 and a married flling jointly in the $77,750 to $77,800 would pay $11,031.
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Find the slope please
Answers
find the size of an angle which is five times its supplement
Answers
Two supplementary angles when addd together equal 180.
let one angle = x
The second angle is 5 times that so would be 5x
x + 5x = 180
Simplify:
6x = 180
Divide both sides by 6:
X = 30
One angle is 30, the second angle would be 150
The answer is 150
please help me I'm almost done
Answers
Answer:
[tex]\mathsf {SA = 112 in.^{2} }[/tex]
Step-by-step explanation:
[tex]\textsf {Formula used :}\\\implies \textsf {SA = 2(length * width + width * height + length * height) }[/tex]
[tex]\textsf {Given :}\\\textsf {Length = 5 in.}\\\textsf {Width = 4 in.}\\\textsf {Height = 4 in.}[/tex]
[tex]\textsf {Solving :}[/tex]
[tex]\implies \mathsf {SA = 2 (5 * 4 + 4 * 4 + 5 * 4)}[/tex]
[tex]\implies \mathsf {SA = 2 (20 + 16 + 20)}[/tex]
[tex]\implies \mathsf {SA = 2 (56)}[/tex]
[tex]\implies \mathsf {SA = 112 in.^{2} }[/tex]
-9x²(x²+2x²y - 3y²)
Simplify
Answers
−9x^4−18x^4y+27x^2y^2
HAVE A NICE DAY!Answer:
=−18x^4y−9x^4+27x^2y^2
Step-by-step explanation:
(−9x^2)(x^2+2x^2y−3y^2)
=(−9x^2)(x^2+2x^2y+−3y^2)
=(−9x^2)(x^2)+(−9x^2)(2x^2y)+(−9x^2)(−3y^2)
=−9x^4−18x^4y+27x^2y^2
=−18x^4y−9x^4+27x^2y^2
---
Hope I helped! Have a great day :)