By integrating the joint PDF over the specified region.
How to calculate the given probability?To compute the probability P(X ≤ 1.25, Y ≥ 0.75) using the given joint PDF, we need to integrate the joint PDF over the specified region.
The region of interest is defined as 1 ≤ x ≤ 1.25 and 0.75 ≤ y ≤ 10.
The joint PDF, FXY(x, y), is given by FXY(x, y) = (x - cy) for 1 ≤ x ≤ 2 and 0 ≤ y ≤ 10, and 0 otherwise.
To compute the probability, we integrate the joint PDF over the specified region:
P(X ≤ 1.25, Y ≥ 0.75) = ∫∫[FXY(x, y)]dydx
Breaking down the integral into two parts:
∫[∫[FXY(x, y)]dy]dx
First, integrate the inner integral with respect to y:
∫[FXY(x, y)]dy = ∫[(x - cy)]dy = xy - (cy[tex]^2[/tex])/2
Next, integrate the outer integral with respect to x over the given range:
∫[xy - (cy[tex]^2[/tex])/2]dx = ∫[(xy - (cy)[tex]^2[/tex]/2)]dx
Evaluate the integral over the range 1 ≤ x ≤ 1.25:
= [∫[(xy - (cy[tex]^2[/tex])/2)]dx] evaluated from 1 to 1.25
Substitute the limits of integration into the expression:
= [(1.25y - (cy[tex]^2[/tex])/2) - (y - (cy[tex]^2[/tex])/2)]
Simplifying the expression:
= 1.25y - (cy[tex]^2[/tex])/2 - y + (cy[tex]^2[/tex])/2
= 0.25y
Finally, evaluate the integral with respect to y over the range 0.75 ≤ y ≤ 10:
∫[0.25y]dy = (0.25/2)y[tex]^2[/tex] evaluated from 0.75 to 10
Substitute the limits of integration into the expression:
= (0.25/2)(10^2 - (0.75)^2)
= (0.25/2)(100 - 0.5625)
= (0.25/2)(99.4375)
= 12.4296875
Therefore, P(X ≤ 1.25, Y ≥ 0.75) is approximately equal to 12.4296875.
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Find the output, y, when the input, x, is -5. y=
Answer:
the picture has the answer (4y , 2.5x)
Step-by-step explanation:
Answer:
y = 7
Step-by-step explanation:
Locate x = - 5 on the x- axis, go vertically up to meet the graph at (- 5, 7)
Thus when the input is x = - 5, the output is y = 7
i need help hurry!!!!!!!! solve for x
Answer:
Original Equation: 10x-8/3-4x=6x
Add 4x to both sides: 10x-8/3=10x
Subtract 10x from both sides: -8/3=0
However, we know that -8/3 does not equal to 0, so there is no solution.
Hope this helps!
I NEED HELP AGAIN 6.0
Answer:
(-3,2) (-2,4)
Step-by-step explanation:
Origin to (-3,2)
Other dot (-2,4)
Ivan wants to rent a boat and spend less than $31. The boat costs $8 per hour, and Ivan has a discount coupon for $9 off. What are the possible numbers of
hours Ivan could rent the boat?
Write your answer as an inequality solved for t.
Answer:
he could have the boat for 4 hours with the coupon
t or time is the unknown here to be solved.
The hours Ivan rent the boat multiplied with $8 with $9 discount needs to be less than $31. Hence,
8t - 9 < 31
8t < 31 + 9
8t < 40
t < 5
The hours Ivan can rent the boat has to be less than 5. This is because he wants to spend LESS than 31, 31 sharp is not okay.
Please Help!!!!!!!!!
Answer:
you either need to multiply or add im on that question
Step-by-step explanation:
Answer:
x = 115°Step-by-step explanation:
Refer to attached picture
The small triangle on the top left has one angle 50° and the other two are same:
180° - x, as they for a straight angle with xSum of the angles in the triangle:
50° + 2(180° - x) = 180°50 + 180° - 2x = 02x = 230°x = 115°what is the domain for y=7^x
Answer:
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined. The range is the set of all valid y values. Use the graph to find the range.
Step-by-step explanation:
Explanation: y=7 is a straight line with zero slope and y-intercept 7 as shown below. Hence its domain (all allowed x-values) is all real numbers, and its range (all allowed y-values) is only 7.
I hope this helped~ <3
-Dream
Answer:
There are no real numbers
Today Ebuka opened a new cereal box. He ate a bowl of the cereal, which was 8% of the cereal in
the entire box. Approximately how many more bowls of cereal can Ebuka expect to get from this box
if he continues to eat the same amount of cereal in each bowl?
Answer:
he can get 12 bowls
Step-by-step explanation:
You have to divide 8% by 100% to get the answer but I rounded down
I need only help on 11-14 please someone help me
Linear function definition: a function that will create a straight line when graphed.
11 is not a linear function (not a straight line), but 12 is.
For the tables, you can either plot out the graph or just look at the number patterns. A linear function's numbers will always increase/decrease accordingly at a constant rate. For example, in 14, you notice that as x increases by 1, y decreases by 2. This means it is a linear graph.
In 13, as x increases by 1, the output y increases but at a different rate each time. It increased by 3 at first, then 5, then 7. Hence, it is not a linear function. What is it then? It is an exponential function.
what is the length of side n?
Answer:
6
Step-by-step explanation:
Given the sequence {2,-1,-4,-7} find a25
Answer:
-70
Step-by-step explanation:
This is an arithmetic progression with a difference of -3
Formula for AP is
Sn = a + (n - 1) d
Where
a is the first term, 2
n is the term we're looking for, 25
d is the arithmetic difference, -3
a25 = 2 + (25 - 1) -3
a25 = 2 + (24) -3
a25 = 2 - 72
a25 = -70
4x-4=4x + ___
What is the answer
Answer:
-4
Step-by-step explanation:
4x - 4 = 4x + ?
-4
4x - 4 = 4x + (-4) ---> 4x - 4 = 4x - 4
done
Answer:
it should just be-4
What is the domain of this function?
Answer:
c
Step-by-step explanation:
its c because I just cacuulated it
4+9= equals whattttttttt
Answer:
16
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
Happy Tuesday
The camp director packs 952 snack bags into plastic coolers. She packs 28 coolers with the same number of snack bags in each cooler.
How many snack bags are in each cooler?
Answer:
34
Step-by-step explanation:
Answer:
34
Step-by-step explanation:
952 / 28 is 34 (/= divide)
A function is given: f (x) = 2x + 3
What is the value of f(-2)?
Answer:
f(-2) = -1
Step-by-step explanation:
-2 is x, so replace x as -2 into the equation
f (-2) = 2(-2) + 3
f (-2) = -4 + 3
f (-2) = -1
A collection of all points in the plane of the form (x, f(x)) is the graph of a function f. The graph of f is defined as the graph of the equation y = f(x).
Find function:[tex]\to f (x) = 2x + 3[/tex]
[tex]\to f(-2) =?[/tex]
Putting the value "-2 " into the above given method:
⇒ f(-2) = 2(-2) + 3
⇒ f(-2) = -4 + 3
⇒ f(-2) = -1
Please find the graph file.
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the population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2% per year. Assuming that the world population follows an exponential growth model. whats the projected world population in 1991
idont knowwwwwwwwww it
A whale can stay underwater 7 times as long as x minutes more than a platypus can. Write an equation that states the relationship of the minutes these two mammals can stay underwater
Answer:
Step-by-step explanation:
Using the information provided we can create the following two equations each of which calculates the total number of minutes that the whale (w) or the platypus (p) can stay underwater. In order to solve each, you would need the value of at least 1 of the mammals.
w = 7 * (p+x)
p = (w / 7) - x
The w in these equations represents the number of minutes the whale can stay underwater while the p represents the number of minutes that the platypus can stay underwater.
hey just need some help.
whoever explains how that equals 17 and how to do it gets brainliest answer
Answer:
c^2=289
Step-by-step explanation:
this is because c^2=17×17=289
A student received a coupon for 20% off the total purchase price at a clothing store. Let z be the
original price of the purchase. Use the expression below for the new price of the purchase. Write an
equivalent expression by combining like terms.
Z-0.2z
Z-0.2z =
Answer:
i don't know
Step-by-step explanation:
mag-aral ka mabuti para maging matalino
Alex is y years old. Bella is 4 years older than him .Carla is double Alex's age. The sum total of their age is 32
Form and solve an equation to work out the ages of the three children
Answer:
Alex is 7, Bella is 11, and Carla is 14
Step-by-step explanation:
Equation is 32=y+2y+(y+4)
To solve:
First combine like terms (the y's)
32=4y+4
Subtract 4 from both sides
28=4y
Divide both sides by 4 to get y alone
7 =y (Alex's age)
Bella is 4 years older than Alex so 7+4 = 11
Carla is 2 times older than Alex so 2 • 7 = 14
Their ages are supposed to add up to 32.
7+11+14
18+14
32
find the X and the Y intercept of
4x-y=12
Answer:
x-intercept: (3,0)
y-intercept: (0, -12)
I hope this helps!
The distance between boston and chicago on a map is 9 inches. If the scale of the map is 1 inch : 95 miles, what is the actual distance from boston to chicago
What is the formula for finding the circumference for a circle with just the radius?
Answer: The formula is C=2 π r
Step-by-step explanation: Hope this helps
A taxi driver chargers $2.80 for an initial fee and $1.20 for each mile. Write and solve an equation to find out how many miles a passenger can travel for $20.
Answer:
14 miles
Step-by-step explanation:
2.80+1.20x=20
-2.80 -2.80
1.20x=17.20
1.20x/1.20= 17.20/1.20
x=14 miles
Hope this helps!
5 - X = -6
what is the variable
hii! please help. i’ll give brainliest if you give a correct answer thanks!
Answer:±
5 ÷9/10,4/5 ÷3/7Ф
Step-by-step explanation:≠
I hope this help if it´m wrong I´m so sorry but i´m sure its right tho≤≥
#Hope have nice day<3Δ~Regards~⇔-44014137⊄⊅Find the value of b + 19 when b=9.
Answer:
28.
Step-by-step explanation:
b + 19 =
(9) + 19 =
9 + 19 = 28
Answer:
28
Step-by-step explanation:
Substitute b with 9 so it's 19 + 9 = 28
Have a great day <3
x
-3
-2
-1
0
1
2
3
3
4.95
8.1675 13.476375
f(x) 0.6678... 1.1019... 1.8181...
g(x) 0.125 0.25
0.5
1
2
4
8
0.25
0.5
0.75
1
1.25
1.5
1.75
h(x)
k(x)
64
16
4
0
0.25
0.0625
0.0156
O A. h(x)
B. f(x)
OC. k(x)
D. g(x)
k(×)×95=-0.75 sume k+95=***
g(x) is the function from the table which gives values that could come from the exponential function.
What is a function?A relation is a function if it has only One y-value for each x-value.
We have to find the function from the table which gives values that could come from the exponential function.
The exponential function is a mathematical function denoted by .
As we observe the g(x) function.
When x =1, g(x)=2
x=2, g(x)=4
x=3, g(x)=8
g(x)=2ˣ is the required function which is in exponential form
Hence, g(x) is the function from the table which gives values that could come from the exponential function.
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IMPORTANT!! in a unit circle, what is the relationship between arc length and central angle?
Answer:
The measure of an arc refers to the arc length divided by the radius of the circle. The arc measure equals the corresponding central angle measure, in radians. That's why radians are natural: a central angle of one radian will span an arc exactly one radius long.
A rectangle measures 2 1/3 inches by 1 2/3 inches. What is its area?
Answer:
35/9 inches
Step-by-step explanation:
you can put this in a mixed fraction, its still correct:
3 8/9
The area of the rectangle is 35/9 square inches.
What is a rectangle?A rectangle is a 2-D shape with length and width.
The length and width are different.
If the length and width are not different then it is a square.
The area of a rectangle is given as:
Area = Length x width
We have,
To find the area of a rectangle,
We multiply the length by the width.
Length = 2 1/3 = 7/3 inches
Width = 1 2/3 = 5/3 inches
Area = Length x Width
Area = (7/3) x (5/3)
Area = 35/9 square inches
Therefore,
The area of the rectangle is 35/9 square inches.
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