Let $DEF$ be an equilateral triangle with side length $3.$ At random, a point $G$ is chosen inside the triangle. Compute the probability that the length $DG$ is less than or equal to $1.$
Answers
[tex]|\Omega|=(\text{the area of the triangle})=\dfrac{a^2\sqrt3}{4}=\dfrac{3^2\sqrt3}{4}=\dfrac{9\sqrt3}{4}\\|A|=(\text{the area of the sector})=\dfrac{\alpha\pi r^2}{360}=\dfrac{60\pi \cdot 1^2}{360}=\dfrac{\pi}{6}\\\\\\P(A)=\dfrac{\dfrac{\pi}{6}}{\dfrac{9\sqrt3}{4}}\\\\P(A)=\dfrac{\pi}{6}\cdot\dfrac{4}{9\sqrt3}\\\\P(A)=\dfrac{2\pi}{27\sqrt3}\\\\P(A)=\dfrac{2\pi\sqrt3}{27\cdot3}\\\\P(A)=\dfrac{2\pi\sqrt3}{81}\approx13.4\%[/tex]
Answer:
13.44%
Step-by-step explanation:
For DG to have length of 1 or less, point G must be contained in a sector of a circle with center at point D, radius of 1, and a central angle of 60°.
The area of that sector is
[tex]A_s = \dfrac{n}{360^\circ}\pi r^2[/tex]
[tex]A_s = \dfrac{60^\circ}{360^\circ} \times 3.14159 \times 1^2[/tex]
[tex] A_s = 0.5254 [/tex]
The area of the triangle is
[tex] A_t = \dfrac{1}{2}ef \sin D [/tex]
[tex]A_t = \dfrac{1}{2}\times 3 \times 3 \sin 60^\circ[/tex]
[tex] A_t = 3.8971 [/tex]
The probability is the area of the sector divided by the area of the triangle.
[tex]p = \dfrac{A_s}{A_t} = \dfrac{0.5254}{3.8971} = 0.1344[/tex]
Related Questions
Find the missing probability. P(A)=720,P(B)=35,P(A∩B)=21100 ,P(A∪B)=?
Answers
P( A U B) = 37/50
Step-by-step explanation:
7/20+3/5+21/100
IF YOU NEED MORE HELP LMK
If you can please mark this as the brainliest
PLEASE HELP ME Answer the following two questions in your own words: 1. Why can I divide instead of distribute? Why is that allowed? Ex. why can I divide by 6 in 6(3x + 4) = 12 instead of distribute the 6? 2. When creating common denominators, why do I have to multiply the numerator AND the denominator? Ex. why do I have to multiply 1 by 5 AND 2 by 5 when adding 1/2 + 3/10?
Answers
Answer:
1. You can divide both sides of an equation by any number except zero. If dividing both sides simplifies the equation, then it's better to do than than to distribute.
2. A fraction can be thought of as a ratio. To keep the value of the fraction the same, you must multiply or divide the numerator and denominator by the same number. If you multiply only the denominator by a number, the value of the fraction changes.
Step-by-step explanation:
1.
6(3x + 4) = 12
Since the goal in solving this equation is to isolate x, meaning you want x alone on the left side, you need to do whatever legal operations that will accomplish that. Since 6 is a factor and (3x + 4) is a factor in a multiplication, you can divide both sides by 6 simplifying the left side. It is also correct to distribute on the left side, but it will make the solution longer.
Method 1: start by dividing both sides by 6
6(3x + 4) = 12
Step 1: Divide both sides by 6
3x + 4 = 2
Step 2: Subtract 4 from both sides
3x = -2
Step 3: Divide both sides by 3
x = -2/3
Method 2: start by distributing on the left side
6(3x + 4) = 12
Step 1: distribute the 6 on the left side
18x + 24 = 12
Step 2: subtract 24 from both sides
18x = -12
Step 3: divide both sides by 18
x = -12/18
Step 4: reduce the fraction
x = -2/3
As you can see, the solution is the same. The only difference is one extra step with the reduction of the fraction in the case of distributing the 6.
2.
This has to do with the meaning of fractions.
For example, take the fraction 1/2.
This fraction means that you divided the unit into 2 equal parts, shown by the denominator of 2. Then you are taking 1 of those parts, shown by the numerator of 1. 1/2 means 1 out of 2. You can also think of 1/2 as the ratio of 1 to 2.
To add and subtract two factions, we need a common denominator. That means we must rewrite one or both fractions being added or subtracted in a way that they both have the same denominator. We need the fractions to represent the same amounts they did originally. If you changed only the denominator, you'd be changing the actual value of the fraction.
You need to add 1/2 and 3/10.
The least common denominator of 2 and 10 is 10, so we need to have both fractions with a denominator of 10. 3/10 already has a denominator of 10, so we just need to change 1/2 to a fraction with 10 in the denominator. By multiplying 2 by 5 we get 10, so we need to multiply the denominator of 1/2 by 5 to end up with a denominator of 10.
1/2 + 3/10
If you only changed the denominator of 1/2 to 10 by multiplying 2 * 5 = 10, you'd end up with
1/10 + 3/10,
but now think of the fraction 1/10 and compare it to 1/2.
1/2 means divide the unit into 2 equal parts and take 1 part.
1/10 means divide the unit into 10 equal arts and take 1 part.
1/2 is not the same as 1/10, so rewriting the addition
1/2 + 3/10 as 1/10 + 3/10 is actually changing the problem.
Now see what happens when we multiply both the numerator and denominator by the same number, in this case 5.
We change 1/2 to (1 * 5)/(2 * 5) = 5/10. 1/2 equals 5/10. If you divide a unit into 10 equal parts and you take 5 parts, you have taken the same number of parts as if you had divided the unit into 2 parts and taken 1 part.
In other words, 1/2 is exactly the same amount as 5/10. The only difference between 1/2 and 5/10 is the way they are written.
Now we can correctly continue with the addition:
1/2 + 3/10 = 5/10 + 3/10 = 8/10
Finally we reduce 8/10 to 4/5 by dividing both the numerator and denominator by 4.
Can someone help me find the domain and range of this graph
Answers
Answer:
Domain = x - values
Range = y - values
Step-by-step explanation:
main points I'll use as examples for the rest on graph are: (-3,4) (1,2) and (1,6)
Domain: simple numbers here are {-3,1} dont repeat the same x value twice!
Range: {2,4,6}
Make sure values are in numerical order.
Find the rest by these three points! (Which are on graph)
Hope this helps, have a good day :)
Answer:
try 2
Step-by-step explanation:
because it an X-value and it on the graph
what is the value of x ?
Answers
Answer:
35
Step-by-step explanation:
it's the same value each side
Find the area. Round to the nearest tenth.
6 in.
5 in.
9 in.
in.
Answers
Answer:
131 1/4 in.²
Step-by-step explanation:
To find the area of the figure, you would have to divide the figure into two parts. The figure can be divided into two rectangles.
Rectangle 1
The length is 11 3/4 in. The width is 6 in.
A = lw
A = (11 3/4 in.)(6 in.)
A = 70 1/2 in.²
Rectangle 2
The length is 9 in. The width is 6 3/4 in.
A = lw
A = (9 in.)(6 3/4 in.)
A = 60 3/4 in.²
Add the two areas together.
70 1/2 in.² + 60 3/4 in.² = 131 1/4 in.²
surface area of sphare
Answers
Surface area of sphere is what referred to as Total surface area or lateral surface area because here the surface is curved everywhere.
[tex] \large{ \boxed{ \rm{ \orange{Surface \: area \: of \: sphere = 4\pi {r}^{2} }}}}[/tex]
Total surface area of other 3-D shapes:
Cuboid = 2(lb + bh + hl)Cube = 4s²Cylinder = 2πr(r + h)Cone = πr(l + r)Hemisphere = 3πr²Lateral surface area of these shapes:
Cuboid = 2h(l + b)Cube = 6s²Cylinder = 2πrhCone = πrlHemisphere = 2πr²━━━━━━━━━━━━━━━━━━━━
The roots of the quadratic equation x^2/a^2-b^2=a+b/a-b are
Answers
Explanation:
x^2/ a^2 - b^2 = a+b/a-b
x^2/(a-b)(a+b) = a+b/a-b
x^2 = a+b/a-b x (a-b)(a+b)
x ^2 = (a+b)^2
x^2 - (a+b)^2 = 0
(x - a + b)(x + a + b) = 0
Set x - a + b = 0
x = a - b
Set x + a + b = 0
x = - a - b
Hope this helps!
Find the value of x. Round to the nearest tenth.Find the value of x. Round to the nearest tenth.
Answers
Answer:
x = 55.6Step-by-step explanation:
In order to find the value of x we use sine
sin ∅ = opposite / hypotenuse
From the question
x is the hypotenuse
the opposite is 19
So we have
sin 20 = 19/x
x = 19/sin 20
x = 55.55
We have the final answer as
x = 55.6 to the nearest tenthHope this helps you
Answer:
x = 55.6
Step-by-step explanation:
(x-yi)(3+5i) is the conjugate of 6+24i
Answers
Answer:
x=-3
y=3
(-3-3i)(3+5i)
Step-by-step explanation:
[tex](x-yi)(3+5i)\\=3x+5xi-3yi+5y\\=(3x+5y)+(5x-3y)i\\[/tex]
and we have that must equal
6-24i
3x+5y=6
5x-3y=-24 and if we work it we found out that the solutions are
x=-3 and
y=3
which of the following statements must be true about this diagram ? check ALL that apply
Answers
Answer:
Check A, B and DStep-by-step explanation:
A. m∠4 = 180° - m∠3
m∠1 = 180° - (m∠3 + m∠2)
m∠3 < m∠3 + m∠2 ⇒ m∠4 >m∠1
B. m∠4 = 180° - m∠3
m∠2 = 180° - (m∠3 + m∠1)
m∠3 < m∠3 + m∠1 ⇒ m∠4 >m∠2
C. Not necessarily {could be but not always}
D. m∠4 = 180° - m∠3
m∠1 + m∠2 + m∠3 = 180° ⇒ m∠1 + m∠2 = 180° - m∠3 = m∠4
E. m∠3 = m∠1 + m∠2 only if m∠3 = 90°
F. Not necessarily. {Could be but also could not be. In the picture is, but we don't know if the diagram is accurate or just approximate.}
If triangle ABC, m B = 90°, cos(9 = 17, and AB = 16 units.
Based on this information, m
Note that the angle measures are rounded to the nearest degree.
units.
Answers
Answer:
m∠A = 62°
m∠C = 28°
AC = 17 units
Step-by-step explanation:
In the given triangle ABC,
m∠B = 90°, Cos(C) = [tex]\frac{15}{17}[/tex] and AB = 16 units
Since, Cos(C) = [tex]\frac{\text{Corresponding side}}{\text{Hypotenuse}}[/tex]
Cos(C) = [tex]\frac{\text{Corresponding side}}{\text{Hypotenuse}}=\frac{15}{17}[/tex]
[tex]\text{C}=\text{Cos}^{-1}(\frac{15}{17})[/tex]
m∠C = 28.07°
m∠C ≈ 28°
Therefore, side BC = 15 units and AC = 17 units
Now we apply Sine rule in the given triangle.
Sin(A) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{\text{BC}}{\text{AC}}[/tex]
= [tex]\frac{15}{17}[/tex]
A = [tex]\text{Sin}^{-1}(\frac{15}{17} )[/tex]
A = 61.93°
m∠A = 62°
when the point ( k, 3 ) lies on each of these lines, find the value of k y= 3x+1 , y= 4x-2 , y=1/2x - 1 and 2x+3y=4
Answers
Answer:
see explanation
Step-by-step explanation:
Since (k, 3) lies on each of the lines, the point satisfies the equations.
Substitute x = k, y = 3 into each and solve for k
y = 3x + 1
3 = 3k + 1 ( subtract 1 from both sides )
2 = 3k ( divide both sides by 3 )
k = [tex]\frac{2}{3}[/tex]
-------------------------------------------------------
y = 4x - 2
3 = 4k - 2 ( add 2 to both sides )
5 = 4k ( divide both sides by 4 )
k = [tex]\frac{5}{4}[/tex]
--------------------------------------------------------
y = [tex]\frac{1}{2}[/tex] x
3 = [tex]\frac{1}{2}[/tex] k ( multiply both sides by 2 to clear the fraction )
k = 6
---------------------------------------------------------
2x + 3y = 4
2k + 3(3) = 4
2k + 9 = 4 ( subtract 9 from both sides )
2k = - 5 ( divide both sides by 2 )
k = - [tex]\frac{5}{2}[/tex]
Evaluate -3.28 - (-4.4) + (-p) where p = 9.7
Answers
Answer:
-8.58
Step-by-step explanation:
p = 9.7
=> -3.28 - (-4.4) + (-p)
=> -3.28 - (-4.4) + (- (9.7))
=> -3.28 - (-4.4) + (-9.7)
=> -3.28 - (-4.4) -9.7
=> -3.28 +4.4 -9.7
=> -12.98 +4.4
=> -8.58
Answer:
The evaluated answer for this equation is -8.58
Step-by-step explanation:
We are given a value of p so we will use this value for the equation.
-3.28 - (-4.4) + (-p)
Replace p with 9.7
-3.28 - (-4.4) + (-9.7)
Since there is a double negative in front of 4.4, then that means that we are going to be adding -3.28 to 4.4
1.12 + (-9.7)
Subtract 1.42 from 9.7 because there is negative sign in front of 9.7
-8.58
solve for x 16x - 5 = 18x -2
Answers
Answer:
x = -1.5
Step-by-step explanation:
16x - 5 = 18x -2
Subtract 16x from each side
16x-16x - 5 = 18x-16x -2
-5 = 2x-2
Add 2 to each side
-5+2 = 2x-2+2
-3 = 2x
Divide by 2
-3/2 = 2x/2
-3/2 =x
Answer:
-3/2
Step-by-step explanation:
To solve this problem, start by moving all of your x's on to one side, and all of your constants on to the other as such:
16x-5=18x-2
+2 +2
16x-3=18x
-16x -16x
-3=2x
-3/2 = x
P.S. please give me brainliest. Thank you! :)
A book contains 27 pages with print, 8 pages with print and pictures, and 3 blank
pages. What is the theoretical probability of NOT opening the book to a printed
page only?
P(NOT printed page) =
Answers
Answer:
P(NOT printed page) = 3/38
Step-by-step explanation:
Total pages = 27+8+3=38
Types of pages that satisfy requirement(s)= 3
Therfore, P(NOT printed page) = 3/38
Please help.. Offering 25 points and 5 stars with a thanks
Answers
Answer:
2/5
Step-by-step explanation:
There are 2 white and 4 yellow = 6
P(yellow) = yellow /total = 4/6 = 2/3
We keep the ball
Now there are 2 white and 3 yellow = 5
P(yellow) = yellow /total = 3/5
P ( yellow, keep, yellow) = 2/3 * 3/5 = 2/5
We are given 4 yellow balls and 2 white balls. In total, this adds up to 6.
Divide the number of yellow balls to the total number of balls:
4/6 -> 2/3
We are also given 3 yellow and 2 white.
Divide the number of yellow balls to the total number of balls:
3/5
Divide both fractions together:
3/5 * 2/3 = 6/15 = 2/5
Best of Luck!
I need help comrades, I will give you 5 stars and A big thank you comrades
Answers
Answer:
dicontinuity at (-4.-2)zero at (-2.0)
Step-by-step explanation:
answer c
this shoud be correct
Determine if the following table represents a quadratic function.
x 1 2
3 4 5
y 13 22 37 58 85
(1 point)
Answers
Answer:
The options are not visible enough (See Explanation)
Step-by-step explanation:
Given
x:- 1 || 2 || 3 || 4 || 5
y:- 13 || 22 || 37 || 58 || 85
Required
Determine if the function is quadratic
Calculate the difference between the values of y
[tex]Difference = 22 - 13 = 9[/tex]
[tex]Difference = 37 - 22 = 15[/tex]
[tex]Difference = 58 - 37 = 21[/tex]
[tex]Difference = 85 - 58 = 27[/tex]
The resulting difference are: 9 || 15 || 21 || 27
Next; Calculate the difference between the difference of values of y
[tex]Difference = 15 - 9 = 6[/tex]
[tex]Difference = 21 - 15 = 6[/tex]
[tex]Difference = 27 - 21 = 6[/tex]
The resulting difference are: 6 || 6 || 6
For the function to be quadratic, the above difference must be the same and since they are the same (6), then the function represents a quadratic function.
Tara has softball practice Tuesday,Wednesday Thursday and Sunday Each practice Is 1 /1 3 hours. Tara says she will have practice for 3 hours this week.
Answers
Answer and Step-by-step explanation:
For the first part
Tara is incorrect as she practices the softball in 4 days in a week and she do each practice of minimum one hour
So we can conclude that she practices minimum hours in a week
For the second part
Also in 4 days, she does practice [tex]1 \frac{1}{3}[/tex] hours per day i.e [tex]5 \frac{1}{3}[/tex]
Now convert [tex]1 \frac{1}{3}[/tex] this into a fraction which comes [tex]\frac{4}{3}[/tex]
For four days, it is
= [tex]4 \times \frac{4}{3} \\\\ \frac{16}{3} \\\\ 5 \frac{1}{3}[/tex]
Step-by-step explanation:
Without multiplying, explain how you know Tara is incorrect.
How long will Tara have softball practice this week? Write your answer as a mixed number.
Each practice is [tex]1\frac{1}{3}[/tex] hours
Each practice is more than 1 hour. so 4 days of practice is more than 4 hours.
So Tara is incorrect
Practice for 4 days
[tex]1\frac{1}{3}+1\frac{1}{3}+1\frac{1}{3}+1\frac{1}{3}=4\frac{4}{3}=5\frac{1}{3}[/tex]
More than 5 hours .
Tara will have [tex]5\frac{1}{3}[/tex] softball practice this week
Answer:
Tara will have [tex]5\frac{1}{3}[/tex] hours softball practice this week
If a 15% discount is applied to a 15,000,000 car, what will its price be.
Answers
Answer:
$12,750,000
Step-by-step explanation:
15,000,000 x 0.15 = 2,250,000
15,000,000 - 2,250,000 = 12,750,000
Answer:
12750000Step-by-step explanation:
[tex]15\% \: discount \:on \: 15,000,000\\\\= \frac{15}{100} \times 15,000,000\\\\\\= \frac{225000000}{100}\\ \\= 2250000\\\\15 000 000 - 225 0000= 12750000[/tex]
What is the slope of line p?
HURRY PLEASE
Answers
Answer:
2/3
Step-by-step explanation:
(3,2) and (0,0)
The slope of the line is given by
m = (y2-y1)/(x2-x1)
= (2-0)/(3-0)
2/3
The graph below shows the solution to which system of inequalities ?
Answers
Answer:
A
Step-by-step explanation:
A dotted line means its either greater than or less than. A undotted line means its also equal to the number aswell.
To find the right answer all you need is the first part because y has to be greater than or equal to 2 as shown from the graph. So the answer has to be A. As it is the only one that shows this.
Victoria is scuba diving off the coast of Hawaii. When she is ready to come back to the surface, she rises 40 yards at a safe speed. She climbs 1 foot every 2 seconds. How many minutes will it take her to reach the surface?
Answers
Answer:
it will take her 79.76 minutes to rise to the surface
Step-by-step explanation:
Total distance to the surface = 40 yards
speed of rising = 1 foot per seconds
1 foot = 1 second
since the total distance is in yards, let's convert from foot to yards:
1 yard = 3 feet
1 foot = 1/3 yards = 0.333 yards
0.33 yards = 1 second
Next, let's convert from seconds to minutes
60 seconds = 1 minute
∴ 1 second = 1/60 minute
1 second = 0.0167 minute
Therefore the speed at which she rose:
speed
0.333 yards = 0.0167 minutes
Now for a distance of 40 yards:
[tex]1\ yard = \frac{0.0333}{0.0167} minutes\\\therefore\ 40\ yards = \frac{0.0333}{0.0167} \ \times\ \frac{40}{1} \\= \frac{1.332}{0.0167} \\= 79.76\ minutes[/tex]
Answer:
4 minutes
Step-by-step explanation:
the king needs a 10th graders help DX
Answers
Answer:
12) 1/8 inch = 0.125 inch
= 0.003175 m
= 3.175 x 10-3 m
= 0.3175 cm
13) 2 is rational and π is irrattional. π is approximately 3.14 and is the bigger of two
14) C= 40,005,306.33 m
= 4.0005 x 107 m
15) 12,615,800,000
= 1.26158 x 1010
=126158 x 105
16) Let's take speed of ant as 1Km/h=1000m/h. Then time 1666.875 days
Step-by-step explanation:
33. Simplify:
[tex]a ^{2} \times a ^{4} [/tex]
HELP! answer if you can!!!
Answers
Answer:
a^2 × a^4
= a^2+4
= a^6
Remember:
a^n × a^m= a^n+m
Hope it helps
if u have any question let me know in comments ^_^
Answer:
[tex]a^2 * a^4 = \\a^{(2 + 4)} = \\a^6[/tex]
Step-by-step explanation:
Hope it helps!
Which of the following is a solution of y > |x| - 6? A(-1, -5) B(-5, 1) C(5, -1)
Answers
Answer:
B(-5, 1)
Step-by-step explanation:
We can test each value in the equation and see if the equation works out.
[tex]y > |x| - 6[/tex]
Let’s try A - (-1, -5).
[tex]-5 > |-1|-6\\\\-5 > 1-6\\-5>-5[/tex]
-5 is NOT greater than -5, it is equal so A doesn’t work.
Let’s try B, (-5, 1).
[tex]1 > |-5| -6\\1 > 5-6\\1 > -1[/tex]
1 IS greater than -1, so B works.
Let’s try C for fun.
[tex]-1 > |5| -6\\-1 > 5-6\\-1 > -1[/tex]
-1 is NOT greater than -1, it is equal, so it doesn’t work.
Hope this helped!
Answer:
B(-5,1)
Let us simply just write this in all scenarios.
A(-1,-5)
-5>|-1|-6
-5>-5
(False)
B(-5,1)
1>|-5|-6
1>-1
(True)
C(5, -1)
-1>|5|-6
-1>-1
False
*PLEASE ANSWER TY* What is the volume of this prism?
Answers
Answer:
80 cube units
Step-by-step explanation:
(I) Factorice completely
x³- 6x² + 11x-6
Answers
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Factor [tex]x^3 - 6x^2 + 11x - 6[/tex]
[tex]x^3 - 6x^2 + 11x - 6[/tex]
= [tex]( x - 1) ( x - 2) ( x - 3)[/tex]
So you would be : [tex]( x - 1) ( x - 2) ( x - 3)[/tex]
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If this helped you, could you maybe give brainliest..?
Also Have a great day/night!
❀*May*❀
Describe how to solve an absolute value equation
*will give brainliest*
Answers
Answer:
Step 1: Isolate the absolute value expression.
Step2: Set the quantity inside the absolute value notation equal to + and - the quantity on the other side of the equation.
Step 3: Solve for the unknown in both equations.
Step 4: Check your answer analytically or graphically.
Step-by-step explanation:
Answer:
Rewrite the absolute value equation as two separate equations, one positive and the other negative
Solve each equation separately
After solving, substitute your answers back into original equation to verify that you solutions are valid
Write out the final solution or graph it as needed
Step-by-step explanation:
A television network is about to telecast a new television show. Before a show is launched, the network airs a pilot episode and receives a report assessing favorable or unfavorable viewer response. In the past, 60% of the network's shows have received a favorable response from viewers, and 40% have received an unfavorable response. If 50% of the network’s shows have received a favorable response and have been successful, and 30% of the network’s shows have received an unfavorable response and have been successful, what is the probability that this new show will be successful if it receives a favorable response? A. 0.41 B. 0.53 C. 0.67 D. 0.70 E. 0.83
Answers
Let's first denote:
F - a favorable response
F' - an unfavorable response
S - successful
We know that:
[tex]P(F) = 0.6\\\\P(F')=0.4\\\\P(F\cap S)=0.5\\\\P(F'\cap S)=0.3[/tex]
So, from the conditional probability, we can calculate:
[tex]P(S|F) = \dfrac{P(S\cap F)}{P(F)} = \dfrac{0.5}{0.6}=\dfrac{5}{6}\approx\boxed{0.83}[/tex]
Answer E.
Answer:
E IS CORRECT
Step-by-step explanation:
