If P = (X, Y) is a point in the given square, then X and Y are i.i.d random variables each with distribution
[tex]\displaystyle P(X = x) = \begin{cases}\dfrac14 & \text{if } -2 \le x \le 2 \\ 0 & \text{otherwise}\end{cases}[/tex]
and so the joint density of X and Y is
[tex]\displaystyle P(X = x, Y = y) = \begin{cases}\dfrac1{16} & \text{if }-2 \le x \le 2 \text{ and } -2 \le y \le 2 \\ 0 &\text{otherwise}\end{cases}[/tex]
We want to find P(X² + Y² ≤ 1). Points that satisfy this inequality lie in the set
R = {(x, y) : -1 ≤ x ≤ 1 and -√(1 - x²) ≤ y ≤ √(1 - x²)}
but we can more easily describe the region in polar coordinates by setting
x = r cos(t) and y = r sin(t)
so that the set R is identical to
R' = {(r, t) : 0 ≤ r ≤ 1 and 0 ≤ t ≤ 2π}
Integrate the joint density over R' :
[tex]\displaystyle P(X^2 + Y^2 \le 1) = \iint_R \frac1{16} \, dx \, dy[/tex]
[tex]\displaystyle P(X^2 + Y^2 \le 1) = \iint_{R'} \frac r{16} \, dr \, dt[/tex]
[tex]\displaystyle P(X^2 + Y^2 \le 1) = \int_0^{2\pi} \int_0^1 \frac r{16} \, dr \, dt[/tex]
[tex]\displaystyle P(X^2 + Y^2 \le 1) = \int_0^{2\pi} \frac{1^2 - 0^2}{32} \, dt[/tex]
[tex]\displaystyle P(X^2 + Y^2 \le 1) = \frac1{32} \int_0^{2\pi} dt[/tex]
[tex]\displaystyle P(X^2 + Y^2 \le 1) = \frac{2\pi-0}{32}[/tex]
[tex]\displaystyle P(X^2 + Y^2 \le 1) = \boxed{\frac{\pi}{16}}[/tex]
Given f(x)=2x+1 and g(x)=7-x. Find g(f(x)).
Answer:
f(g(x)) = 2(7 - x) + 1
Step-by-step explanation:
f(x) = 2x + 1
g(x) = 7 - x
The question in the picture itself says to find f(g(x)) so i'll find that instead
f(g(x)) = 2(7 - x) + 1
f(g(x)) = 14 - 2x + 1
f(g(x)) = -2x + 15
If 4 gallons of milk cost $16.24, how much would 7 gallon of milk cost
Answer:
$28.42
Step-by-step explanation:
First let's calculate the cost per gallon.
We can do this by simply dividing the cost of 4 gallons by 4
1 gallon of milk cost 16.24/4 = 4.06
We want to find the cost of 7 gallons.
We can easily do this by multiplying the cost of one gallon by 7
7 gallons of milk cost 7 * 4.06 = $28.42
Is 666 = 37 positive or negative?
Answer: Positive (but not sure)
Step-by-step explanation: Are there answers to the questions is so i could help more but if correct hope i helped :)
PLEASE PLEASE HELP ME OUT
Answer:
It is 77 degrees
Step-by-step explanation:
Since line M and N are parralell, the angles are the same
Answer:
X=77
HOPE THIS HELPS
- Todo ❤️
Step-by-step explanation:
Alternative angle thingies are equal
Solve for x.
2x-30/X+60
90
50
Ο
70
20
Answer:
It's 50
Step-by-step explanation:
Hope it helped youuh
Answer:
x = 50
Step-by-step explanation:
2x-30+x+60 = 180
3x+30 = 180
3x = 150
x = 50
The hypotenuse of a certain number is 5 units and one leg is 3 units long. Find the area of the triangle
Answer:
Area: 6
Step-by-step explanation:
It's a five, four, three triangle. Multiply 3 by 4, then divide the answer by 2 to find the area.
Using the discriminate. Find the number of real solutions. 2^2+7x-15=0
Answer:
= 11/7
Step-by-step explanation:
write the equation of the line that passes through the points (3,1) and (-2,6) in slope intercept form
Answer:
y = - x + 4
Step-by-step explanation:
First find slope:
6-1/-2-3 = 5/-5 = -1
Then plug one point and slope into point slope form: y-y1 = k (x-x1)
Plug in (3, 1) and slope -1 --> y-1 = -1(x-3)
Simplify --> y - 1 = - x + 4
Then add 1 to both sides --> y = -x + 4
What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
[tex]y=-\frac{1}{4}x\\[/tex]
Step-by-step explanation:
The slope is calculated by "up ÷ across".
= -1 ÷ 4
= [tex]-\frac{1}{4}[/tex]
The y-intercept is just 0 (because the line meets at the y axis at 0).
So, using [tex]y=mx+b[/tex] (where m = slope and b = y-intercept),
[tex]y=-\frac{1}{4}x+0[/tex]
but the '+0' is unnecessary so we just say [tex]y=-\frac{1}{4}x[/tex]
PLS HELP, WILL GIVE BRAINLIEST!
Answer: The answer to this math question about translating this given expression to an English phrase is C). 3 more than the product of 7 and 4.
Step-by-step explanation: The keywords are times and the sum, which tells us that the 2 operations are multiplication and addition, let's translate this math expression into an English phrase by looking at the 2 operation signs "×" and "+" in order to find the words to translate the given math expression into an English phrase that looks in the equation form and an English phrase like this:
7×4+3 = 3 more than the product of 7 and 4.I hope that my full given answer with my full given step-by-step explanation is very helpful to your own math question about translating this given expression to an English phrase, please mark me as Brainliest after her answer was been reported by someone and got deleted by The Brainly Moderator, take care, always be safe, and have a great rest of the day! :D
Sincerely,
Jason Ta,
The Ambitious of The Brainly And The Role of The TDSB And WHCI Student of The High School.
Can anyone help me with this please I really need help with this rq .
Answer:
Step-by-step explanation:
g(x) = ax - b
-76 = 27a - b
-79 = 28a - b Subtract
3 = -a Multiply both sides by -1
a = -3
g(x) = -3x - b
-85 = -3*30 - b
-85 = - 90 - b Add 90 to both sides
90-85 = - b Combine
5 = - b Multiply both sides by - 1
-5 = b
g(x) = -3x - b
g(x) = -3x - (-5)
g(x) = - 3x + 5
Diedre’s sister works as a lifeguard. Last summer she earned $14 per hour. She earned a total of $5,180 working
as a lifeguard last summer. How many hours did Diedre’s sister work as a lifeguard last summer?
Answer:
370 hours.
Step-by-step explanation:
Divide $5,180/14 to get your answer of the hours she worked.
Answer:
370 hours is how many she worked
14×370= 5,180
hope this helps
can someone help me please, this is so stressful:/
Answer:
x=2
Step-by-step explanation:
To solve for x, you want to isolate it. To do this, move terms that are NOT x and use the opposite operation to get it to the other side.
10x - 3 = 17
(Add 3 to both sides)
10x = 20
Now isolate x (since 10x is really 10 * x, you divide)
10x=20
x=2
This is how you would solve to get the solution.
Hope this helps :D
11. Commercial jets fly between 30,000 ft and 36,000 ft. About how many hours of growing could
pass before the beanstalk might interfere with commercial aircrafts? Explain how you got your
answer
An exponential function is a function that increases rapidly as the time increases.
The number of hours that passes before the magical beanstalk interferes with commercial flight is approximately 9.384 hours.Reasons:
The function that gives the height of a beanstalk is presented as follows;
b(t) = [tex]3^t[/tex]
When the height is 30,000 ft., we have;
30,000 = [tex]3^t[/tex]
㏑(30,000) = t·㏑(3)
[tex]\displaystyle t = \mathbf{\frac{ln(30,000)}{ln(3)}} \approx 9.384[/tex]
The time it would take the beanstalk to grow 30,000 ft., t ≈ 9.384 hours
Similarly, the time it would take the beanstalk to grow to 36,000 ft. is found as follows;
[tex]\displaystyle t_{36,000} = \mathbf{\frac{ln(36,000)}{ln(3)}} \approx 9.55[/tex]
The time it would take the beanstalk to grow 36,000 ft., t ≈ 9.55 hours
The number of hours it will take the beanstalk to grow to 30,000 feet at
which it might interfere with commercial aircrafts is 9.384 hours.
Learn more here:
https://brainly.com/question/13917934
Triangle Slmliarity Assignment 2
1 of 15
12:28/01:00:00
POSSIBLE POINTS: 5
Determine whether the triangles are similar by AA-, SSS-, SAS-, or not similar
3.
B
MN
26
С
16
D
A
21
E
32
Ο ΑΑ
O SSS
OSAS
O Not Similar
HE
Type here to search
O
3
87%
77'
O A )
11
Answer: SAS
Step-by-step explanation:
There is an angle B or D and the sides being the 26, 21, and 32! (Sorry if I get it wrong)
25% of 80
Question: find the percent of the number
Other if you could also do: 30% of 70, 91% of 60, 40% of 85, 250% of 18
Answer:
20%
Step-by-step explanation:
1. 20%
2. 21%
3. 54.6%
4. 34%
5. 45%
13 cm
5 cm
7 cm
12 cm
Find the surface area.
Answer: 37cm
Step-by-step explanation: 5cm + 13cm + 7cm + 12cm = 37cm
Answer:
270 cm^2
Step-by-step explanation:
(13x7)+(12x7)+(5x7)+2(12x5/2)
= 91 + 84 + 35 + 60 =270 cm^2
Percent of 51,300-45,800
Answer: the percent is 112.01. please mark brainliest
Step-by-step explanation:
Determine which of the lines, if any, are parallel or perpendicular.
Line a: 4y - 12x = 20
Line b: 3y = -x + 2
Linec: y = 3x - 1
Step-by-step explanation:
ma=3,mb=_1/3, mc=3a and c are parallelb aree perpendicular to a and cis 10/110 an irrational or rational number
Hello there!
10/110 is a rational number because it can be expressed in the form p/q (where p is the numerator and q is the denominator)
Therefore, 10/110 is a rational number.Hope this helps you!
~Just a felicitous girlie
#HaveAGreatDay
[tex]SilentNature :)[/tex]
Please help 20 points
Answer: y = 42°
Step-by-step explanation: You can find the second angle in that triangle because it is next to another 90° angle. Then you add 90 and 48 and subtract that number from 180 and you get 42. Hope this helps!
Answer:
42
pls mark brainliest if correct
solve pls brainliest
Answer:
Mixed Number: 5 [tex]\frac{7}{10}[/tex]
Improper Fraction:[tex]\frac{57}{10}[/tex]
Step-by-step explanation:
A mixed number is when you express the decimal as a fraction, 0.7 is the same as [tex]\frac{7}{10}[/tex], so 5[tex]\frac{7}{10}[/tex] is your answer.
An improper fraction is a fraction where the numerator is bigger than the denominator, to do this you multipy the whole number 5, which can be written as [tex]\frac{5}{1}[/tex], by [tex]\frac{10}{10}[/tex].
[tex]\frac{5}{1}[/tex]·[tex]\frac{10}{10}[/tex]=[tex]\frac{50}{10}[/tex]
Then add 0.7, or [tex]\frac{7}{10}[/tex].
[tex]\frac{50}{10}[/tex]+[tex]\frac{7}{10}[/tex]=[tex]\frac{57}{10}[/tex]
Would you please mark my answer brainliest if it helped you? :D
Simple interest
A. cannot be paid by credit unions.
B. cannot be expressed as a percentage.
C. is another name for compound interest.
D. is paid only on the original principal.
Step-by-step explanation:
option D is correct according to my understanding
hope this answer helps you dear! take care
vanillaor chocolate?? xD lol >:>
Answer:
Chocolate for sure XD
Step-by-step explanation:
Hope this helps!! lol
Find the slope of a line parallel to each given line.
a
-7x = 3y + 12
Answer:
[tex] - \frac{7}{3} [/tex]
Step-by-step explanation:
Y = mX + c
, since ( -7X = 3y + 12)
, then -3y = 7x + 12
, then y=
[tex] - \frac{7}{3} x - 4[/tex]
Answer:
-7/3
Step-by-step explanation:-7x divided by 12 plus -3y would give you -7/3
Sketch the graph a x=2 and y= -1 then find the point a which the two graphs intersect
Answer: They intersect at (2,-1)
Step-by-step explanation:
Step-by-step explanation:
I hope my answer help you. Please, rate it as brainlest answer if it is right.
PLEASE HELP GIVING BRAINLIEST! :)
Answer:
10
Step-by-step explanation:
3a+b - 4
Let a =3 and b = 5
3(3) +5 -4
Multiply
9+5-4
Add and subtract
14-4
10
Answer:
10
Step-by-step explanation:
a = 3b = 5= 3a + b - 4
= 3(3) + 5 - 4
= (3 . 3) + 5 - 4
= 9 + 5 - 4
= 9 + 1
= 10
7.0g divided by 5.6g/cm cubed
Answer:
Should be 1.25cm
Step-by-step explanation:
What is the length of each side of this equilateral triangle?
A) 42
B) 30
C) 15
D) 12
Answer:
C I think hope you help this my answer
Answer:
15
Step-by-step explanation:
no explanation
Write a question that has the quotient of -3/8
