Answer:
[tex](a)\ g(x) = \frac{2}{3}(x+1)[/tex]
[tex](b)\ h(y) = \frac{1}{3}[1 + 4y][/tex]
[tex](c)[/tex] [tex]P(x>0.5) =\frac{5}{12}[/tex]
Step-by-step explanation:
Given
[tex]f(x,y) = \left \{ {{\frac{2}{3}(x+2y)\ \ 0\le x \le 1,\ 0\le y\le 1} \right.[/tex]
Solving (a): The marginal density of X
This is calculated as:
[tex]g(x) = \int\limits^{\infty}_{-\infty} {f(x,y)} \, dy[/tex]
[tex]g(x) = \int\limits^{1}_{0} {\frac{2}{3}(x + 2y)} \, dy[/tex]
[tex]g(x) = \frac{2}{3}\int\limits^{1}_{0} {(x + 2y)} \, dy[/tex]
Integrate
[tex]g(x) = \frac{2}{3}(xy+y^2)|\limits^{1}_{0}[/tex]
Substitute 1 and 0 for y
[tex]g(x) = \frac{2}{3}[(x*1+1^2) - (x*0 + 0^2)}[/tex]
[tex]g(x) = \frac{2}{3}[(x+1)}[/tex]
Solving (b): The marginal density of Y
This is calculated as:
[tex]h(y) = \int\limits^{\infty}_{-\infty} {f(x,y)} \, dx[/tex]
[tex]h(y) = \int\limits^{1}_{0} {\frac{2}{3}(x + 2y)} \, dx[/tex]
[tex]h(y) = \frac{2}{3}\int\limits^{1}_{0} {(x + 2y)} \, dx[/tex]
Integrate
[tex]h(y) = \frac{2}{3}(\frac{x^2}{2} + 2xy)|\limits^{1}_{0}[/tex]
Substitute 1 and 0 for x
[tex]h(y) = \frac{2}{3}[(\frac{1^2}{2} + 2y*1) - (\frac{0^2}{2} + 2y*0) ][/tex]
[tex]h(y) = \frac{2}{3}[(\frac{1}{2} + 2y)][/tex]
[tex]h(y) = \frac{1}{3}[1 + 4y][/tex]
Solving (c): The probability that the drive-through facility is busy less than one-half of the time.
This is represented as:
[tex]P(x>0.5)[/tex]
The solution is as follows:
[tex]P(x>0.5) = P(0\le x\le 0.5,0\le y\le 1)[/tex]
Represent as an integral
[tex]P(x>0.5) =\int\limits^1_0 \int\limits^{0.5}_0 {\frac{2}{3}(x + 2y)} \, dx dy[/tex]
[tex]P(x>0.5) =\frac{2}{3}\int\limits^1_0 \int\limits^{0.5}_0 {(x + 2y)} \, dx dy[/tex]
Integrate w.r.t. x
[tex]P(x>0.5) =\frac{2}{3}\int\limits^1_0 (\frac{x^2}{2} + 2xy) |^{0.5}_0\, dy[/tex]
[tex]P(x>0.5) =\frac{2}{3}\int\limits^1_0 [(\frac{0.5^2}{2} + 2*0.5y) -(\frac{0^2}{2} + 2*0y)], dy[/tex]
[tex]P(x>0.5) =\frac{2}{3}\int\limits^1_0 (0.125 + y), dy[/tex]
[tex]P(x>0.5) =\frac{2}{3}(0.125y + \frac{y^2}{2})|^{1}_{0}[/tex]
[tex]P(x>0.5) =\frac{2}{3}[(0.125*1 + \frac{1^2}{2}) - (0.125*0 + \frac{0^2}{2})][/tex]
[tex]P(x>0.5) =\frac{2}{3}[(0.125 + \frac{1}{2})][/tex]
[tex]P(x>0.5) =\frac{2}{3}[(0.125 + 0.5][/tex]
[tex]P(x>0.5) =\frac{2}{3} * 0.625[/tex]
[tex]P(x>0.5) =\frac{2 * 0.625}{3}[/tex]
[tex]P(x>0.5) =\frac{1.25}{3}[/tex]
Express as a fraction, properly
[tex]P(x>0.5) =\frac{1.25*4}{3*4}[/tex]
[tex]P(x>0.5) =\frac{5}{12}[/tex]
Solve for the value of r.
Answer:
14
Step-by-step explanation:
The two given angles are opposite angles and opposite angles always have the same measure. Knowing this, we can construct the following equation:
7r+6=8r-8
Subtract both sides by 6
7r+6-6=8r-8-6
7r=8r-14
Subtract both sides by 8r
7r-8r=8r-14-8r
-r=-14
Divide both sides by -1
r=14
I hope this helps!
Can anyone help me!!
Answer:
help on chemistry is help on math for you
what is maintenance culture
Answer:
ways of thinking,behaviour,perciption
if the measure of arc LK is 56 degrees and the measure of arc LM is 187 degrees, what is m JKM angle KL = 56 degrees
Answer:
JKM is 123 degrees and the measure of arc KL is 56
PRACTICE ANOTHER A random sample of 100 people was taken. Eighty-two of the people in the sample favored Candidate A. We are interested in determining whether the proportion of the population in favor of Candidate A is significantly more than 79%. We know that the p-value is 0.2307. At the 0.05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is
Answer:
0.2307 > 0.05, which means that we accept the null hypothesis, that is, that the population proportion in favor of candidate A is close to 0.79, that is, it is not significantly more than 0.79.
Step-by-step explanation:
We are interested in determining whether the proportion of the population in favor of Candidate A is significantly more than 79%.
This means that the null hypothesis is:
[tex]H_{0}: p = 0.79[/tex]
And the alternate hypothesis is:
[tex]H_{a}: p > 0.79[/tex]
We know that the p-value is 0.2307. At the 0.05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is?
0.2307 > 0.05, which means that we accept the null hypothesis, that is, that the population proportion in favor of candidate A is close to 0.79, that is, it is not significantly more than 0.79.
solve the following equations
simultaneously;
2x-3y=0
2x-y=8
Answer:
x=6 y=4
Step-by-step explanation:
So, what I did was change positions of 2x to -2x=0-3y -2x=-8-y. Because -2x equal to two equations, I did -3y=-8-y. Once simplified, that equals to y=4. I plugged in to 2x-y(or 4)=8. Once that was simplified, 2x=12 or x=6.
find the square of 2a plus 3b
Here is your answer!!
Answer:
[tex]= 4a^{2} + 12ab + 9b^{2}.[/tex]
Step-by-step explanation:
[tex](2a+3b)^{2}[/tex]
[tex]= (2a + 3b) (2a + 3b)[/tex]
[tex]= 4a^{2} + 6ab + 6ab + 9b^{2}[/tex]
[tex]= 4a^{2} + 12ab + 9b^{2}.[/tex]
A. Find the volume of a rectangular room measuring 22.75 ft. x 30 ft. x 14 ft.
B. Find the BTUs needed for that room if it faces South with poor insulation.
Help asap
Answer:
12 BTU
Step-by-step explanation:
question is in picture please help!
Answer:
I’m not 100% sure but I think 120°.
Step-by-step explanation:
This is because, angles on a straight line add up to 180°. Because there is 60 degrees on one side of line B, this means the other section is 120° (120°+60°=180°) The angle labelled (3x) is alternate to the angle of 120°. Alternate angles are always equal, meaning that 3x is equal to 120°.
I hope this is right.
Given the following information, find the length of the missing side. Leave your answer as a simplified radical.
Answer:
Your answer would be:
[tex]5 \sqrt{3} [/tex]
Step-by-step explanation:
because
NEED HELP ASAP WILL GIVE BRAINLIEST REAL ANSWERS ONLY PLZ
Answer:
0.3
Step-by-step explanation:
in theory the chance to get heads is 0.5 however only two of the coin flips resulted in heads so the experimental probability is 0.2. the difference between these is 0.3.
Answer:
the correct answer is D because you have got 10flips with 2head the probability for it 2/10 or 0.02 and you know we don't always get the same result as always, and you wanna add some for the reason and you got 0.03 ( ◜‿◝ )♡
complete the table for the equation. plz helppp
what is the 3rd quartile ?
Answer:
The upper or third quartile, denoted as Q3, is the central point that lies between the median and the highest number of the distribution.
Step-by-step explanation:
5) Is this dilation an enlargement or reduction
A) Englargement
B) Reduction
———————
6) What is the scale factor for this dilation? Hint: First identity if it’s an enlargement or reduction
A) 2
B) 1/2
C) 3
D) 1/3
Which rectangular prism has a surface area of 56 square units? [Note: Art is not drawn to scale.]
A rectangular prism with a length of 5, width of 3, and height of 1.
A rectangular prism with a length of 2, width of 2, and height of 6.
A rectangular prism with a length of 5, width of 3, and height of 2.
A rectangular prism with a length of 6, width of 2, and height of 4.
Answer:
B
Step-by-step explanation:
i took the quiz have a nice day :)
Answer:
The correct answer is B
Step-by-step explanation:
2*2=4 2*6=12 2*6=12 4+12+12 = 28 28*2=56
Please help, will give brainliest.
Answer:
There is nothing.
Step-by-step explanation:
Answer:
A line that starts at with a constant positive slope
Step-by-step explanation:
Hope it makes sense!!
You have one chance in ten of winning the race.
Answer:
1/10?
Step-by-step explanation:
okay...
(x +y )(x -y), if x = -3, y=-5
PLS NO FILES OR I AM REPORTING YOU
Answer:
-16
Step-by-step explanation:
(X + Y)
= (-3 + -5)
= -8
(X - Y)
= (-3 - -5)
= 2
Because they're still in brackets in this form:
(-8) (2)
You multiply them both and you'll get the answer:
-16
hope this helped!
Pls help me complet this
Answer: The number of times a blue cube will be drawn is 395 times.
Step-by-step explanation: So since the original amount a blue cube got drawn is 79 and they did it 240 times, we can set up a ratio.
79/240 = x/1200
We use 1200 since the question asks us how many times a blue cube will be drawn if they did the experiment 1200 times. To solve x, multiply 1200 and 79 and you get 94,800. Then divide that by 240, which is 395. Therefore it will get drawn 395 times.
Hope this helps.
April can buy a package of 8 folders for $2.40. What is the unit price for this package?
Answer:
0.3
Step-by-step explanation:
to get the unit rate you must divided
2.40 by 8
2.40/8=0.3
The cheerleaders are making a banner that is 8 feet wide the length of the banner is 1 1/3 times the width of the banner how long is the banner
Answer:10 2/3 feet
Step-by-step explanation: 8 times 4/3= 32/3=10 2/3 feet
Which equation represents a line passing through the point (8, 9) with a slope of 3?
A) y = 3x - 15
B) y = 3x - 8
C) y = 3x + 33
D) y = 3x + 9
Answer:
a
Step-by-step explanation:
basically the number with x is always the slope and I really just put the equations into a inspire and got the answer by which one matched
The equation of line passing through the point (8, 9) with a slope of 3
will be;
⇒ y = 3x - 15
Option A is true.
What is Equation of line?
The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope 'm' is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The slope of the line = 3
And, The point on the line = (8, 9)
Now,
Since, The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Hence, The equation of line passing through the points (8, 9) with slope '3' is defined as;
⇒ y - y₁ = m (x - x₁)
⇒ y - 9 = 3 (x - 8)
⇒ y - 9 = 3x - 24
⇒ y = 3x - 24 + 9
⇒ y = 3x - 15
Thus, The equation of line passing through the point (8, 9) with a slope of 3 will be;
⇒ y = 3x - 15
Learn more about the equation of line visit:
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Please help me if not that’s fine no links!
Answer:
30°
Step-by-step explanation:
53°+97°+x = 180°
The sum of three angles must equal 180°
Solve the equation.
150°+x = 180°
x = 180°-150°
x = 30°
Therefore, x = 30°
If the wholesale price of an item is $250 and the markup is 20%, find the retail price of the item. Please explain. Thank you.
Answer: 300
Step-by-step explanation:
20% of $250 is $50
So $300
find the least common factor of 4,5,6 no links or photo or I will report you
Answer:
60
Explanation:
The new superset list is
2, 2, 3, 5
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 3 x 5 = 60
In exponential form:
LCM = 22 x 31 x 51 = 60
LCM = 60
Therefore,
LCM(4, 5, 6) = 60
The mean midday temperature recorded in June in a city in South California is 36ºC, and the standard deviation is 3ºC. The number of days in the month of June is 30.
Assuming the data is normally distributed, the number of days in June when the midday temperature was between 39ºC and 42ºC is .
Answer:
About 4 days
Step-by-step explanation:
Convert 39 and 42 degrees C to a z score and then use the z-table
The number of days in June when the midday temperature was between 39°C and 42°C is equal to 4.0 days.
Given the following data:
Mean midday temperature = 36°C.
Standard deviation = 3°C.
How to determine the number of days in June?In order to determine the number of days in June when the midday temperature was between 39°C and 42°C, we would determine the z-score as follows:
Let the midday temperature be M.
P(39 < M < 42) = 1 - [P(M < 39) + P(M < 42)]
Evaluating, we have:
P(M < 39) = P(Z < [39 -36/3])
P(M < 39) = P(Z < [3/3])
P(M < 39) = P(Z < 1).
P(M < 39) = 0.84134.
P(M < 42) = P(Z < [42 -36/3])
P(M < 42) = P(Z < [6/3])
P(M < 42) = P(Z < 2)
P(M < 42) = 0.02275.
Substituting the parameters into the formula, we have;
P(39 < M < 42) = 1 - [P(M < 39) + P(M < 42)]
P(39 < M < 42) = 1 - [0.84134 + 0.02275]
P(39 < M < 42) = 1 - 0.86409
P(39 < M < 42) = 0.13591.
Now, we can determine the number of days in June when the midday temperature was between 39°C and 42°C:
No. of days = 0.13591 × 30
No. of days = 4.0 days.
Note: There are 30 days in the month of June.
Read more on z-scores here: https://brainly.com/question/4302527
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What is the answer please help me no links no links
Dawn is baking an Apple pie she has a European recipe that calls for 1500 decigrams of sugar. how many cups of sugar will she need?
Answer:
she needs exactly 3 cups
Step-by-step explanation:
The blue segment below is a radius of oo. What is the length of the diameter of the circle?
Answer:
Diameter = 25.4 unitsStep-by-step explanation:
radius = 12.7
Diameter = 2 × radius
= 2 × 12.7
= 25.4 units
I am not good at math, will give brainliest
Answer:
the answer is a
Step-by-step explanation: