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]
A cupcake recipe calls for 3/6 cups of milk, and you have cups of milk in the 5/8 refrigerator. How many cups of milk will you have remaining after baking the cupcakes ?
Answer:
1/6 = 4/24 5/8 = 15/24
15 - 4 = 11 11/24 cups of milk left
Step-by-step explanation:
PLZ ANSWER NO FAKE LINKS
Answer:
Draw a Rectangle with 3/10 at the bottom and 1/2 at the top
Step-by-step explanation:
Have a Nice Day!
Which expression can be used to find the surface area of the following square pyramid?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
10+10+8+8+8+810+10+8+8+8+810, plus, 10, plus, 8, plus, 8, plus, 8, plus, 8
(Choice B)
B
100+40+40+40+40100+40+40+40+40100, plus, 40, plus, 40, plus, 40, plus, 40
(Choice C)
C
100+80+80+80+80100+80+80+80+80100, plus, 80, plus, 80, plus, 80, plus, 80
(Choice D)
D
100+80100+80
Answer:
A
Step-by-step explanation:
1/6 and 2/6 have the same numerator
Is this a question? and no they dont, the numerater is the number on top.
Answer: No, 1/6 and 2/6 do not have the same numerator.
Step-by-step explanation:
this is because the 1 in 1/6 is a numerater and the 6 is the denominator, this works the same for 2/6
in this figure, ST is a line what is the value of x?
ST is a Straight line, x=108 degrees.
Step-by-step explanation:
Since ST is a straight line, it measures 180 degrees.
This means that:
x+(2/3)x=180
The simplified version is 5x/3=180.
Now, we multiply both sides by 3.
The equation becomes 5x=540;
which is ultimately x=108.
Therefore, ST is a straight line , x=108.
To know more about Straight line.
https://brainly.com/question/30241852
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given that 16 ounces is 1 pound, how many ounces are in 12.4 pounds.
A. 192
b.198.4
c. 201.6
d. 208
what are the variables 8 x + 7 - y
plzz I'll give BRAINLIEST
Answer:
x and y
Step-by-step explanation:
Those are variables that could be any number. The integers are considered to be coefficients.
What is the surface area of the triangular prism? (please help)
Answer:
72 sq ft.
Step-by-step explanation:
Surface area of Triangular prism=[2*(1/2)*3*4]+(5*5)+(3*5)+(4*5)=12+25+15+20=72 sq ft.
Maximizing yield. Hood Apple Farm harvests an average of 30 bushels of apples per tree when 20 trees are planted on an acre of ground. If 1 more tree is planted per acre, the yield decreases by 1 bushel (bu) per tree as a result of crowding. How many trees should be planted on an acre in order to get the highest yield
Answer:
In order to get the highest yield, 25 tress should be planted
Step-by-step explanation:
Given the data in the question;
Let n be number bushel, b is bushels per tree, t is number of trees
from the question, if t = 20, b = 30
and if t = 21 then b = 29
so t + b is constant
t + b = 50 ----- let this be equation
now, n = t × b
so b = n / t
hence from equation, we input b = n/t
t + n/t = 50
n/t = 50 - t
n = t(50 - t)
n = 50t - t²
now we get the derivatives
Note, The maximum amount of trees is simply where the derivative is equal zero, so;
0 = 50 - 2t
2t = 50
t = 50/2
t = 25
Therefore, In order to get the highest yield, 25 tress should be planted
What is the diameter of a circle with a circumference of 132 ft? Use 227 for π . Round your answer to the nearest whole number.
Answer:
The answer is 132 feet
Step-by-step explanation:
That's the diameter.
C = pi * d
C = 3.14 * 42
C = 131.88
Thar rounds to 132 feet.
Q:An athlete throws her javelin 9.5 yards. She throws it this distance 2 times. How far does she throw the javelin in total?
18.5 yd
19 yd
19.5 yd
20 yd
Answer: 19 yd
Step-by-step explanation:
hope this helped. :)
4.09434456 rounded to the nearest thousand
Answer:
4.094
Step-by-step explanation:
in our thousandths spot is the 4 4.094, in our ten-thousandths spot is the 3 4.0943, so we do not add one, so our final answer is 4.094
Zoe is calculating the volume of this rectangular prism.

Zoe calculates the volume as 16 cubic units because 8 units long + 5 units high + 3 units wide = 16 cubic units. Which of the following describes the mistake Zoe made in her calculation?
Zoe is wrong because she calculated the volume 8 + 5 + 3 = 16 instead of 8 × 5 + 3 = 43.
Zoe is wrong because she added all the dimensions instead of only adding the length and width.
Zoe is wrong because she calculated the volume 8 + 5 + 3 = 16 instead of 8 + 5 – 3 = 10.
Zoe is wrong because she added all the dimensions instead of multiplying all the dimensions.
It’s the last one :)
What is the total surface of the square
pyramid
Answer:
960.
Step-by-step explanation:
what is the area of this partial circle with a radius of 14 inch
Step-by-step explanation:
Since this circle is partial we will divide the area of the whole circle by 2
the area of a circle is expressed by [tex]\pi r^2[/tex] so insert 14 for the radius.
[tex]14^2\pi[/tex]
[tex]196\pi[/tex]
divide the area by 2
[tex]98\pi=307.876[/tex]
Hope that helps :)
Which fraction is greater?
2/3 or 3/8
Answer:
you have to find common denominators first.
Step-by-step explanation:
24 is their common
8x2=16/24
3x3=9/24
your first fraction is larger!
please consider marking me as brainliest! Have an amazing day lovely!
answer:
2/3
explanation:
convert to a decimal then compare the two and the one with the biggest number is greater
the 5 sources of data
Answer:
The Top 5 Sources of Data on your Website
Reports: Conversion funnel and pathing. Study these reports.
Internal search queries. This seems like a no-brainer, but some brands forget to assess what people are searching for on their website.
Store locators.
Reviews & Customer Service inquiries.
Domain reports
Hope its what u r looking forward to..!
Imagine you deposit $4,500 into an account that pays 5,5 percent interest compounded
daily. How much interest will you earn in 30 days?
Answer:
500
Step-by-step explanation:
Juan deposited $450 in an account that earned 7.5% simple interest.
- He did not make additional deposits and he didn't withdraw any money from the account.
What was the balance in Juan's investment account after 3 years?
Answer:
$551.25
Step-by-step explanation:
$450 x 7.5% = 33.75
33.75 x 3 = 101.25
101.25 + 450 = 551.25
Which triangles must be congruent? Abc, fde, and gih.
Answer:
A. ΔABC, ΔFDE and ΔGIH
Step-by-step explanation:
From the given descriptions for the three triangles, it can be inferred that;
DE ≈ HI ≈ BC
AB ≈ FD ≈ GI
m<B = m<D = m<I
So that by Side-Angle-Side (SAS) relations among the triangles, the three triangles are congruent.
This implies that: ΔABC ≅ ΔFDE ≅ ΔGIH
The appropriate answer to the given question is A.
127.6÷105 What is this divided by?
1.215 This is the answer
It is divided by 105
Answer:
1.215
Step-by-step explanation: did this same question
A function is represented by the graph.
Complete the statement by selecting from the drop-down menu.
The y-intercept of the function y=2x−2 is
Choose...
the y-intercept of the function represented in the graph. bruru
Answer:
This graph is Greater than to because the graph has a y int at 1 and so does your formula given just make x=0 to find it by plugging that in and that one has a y int at 1. You can also see the line going up.
Step-by-step explanation:
Answer:
Greater Than
Step-by-step explanation:
The y-intercept of the function is 2
The y-intercept of the function represented in the graph is -2
2>-2
I know this is late, but just to help other people :)
ZABC and ZQRS are supplementary angles.
If the measure of ZABC = 140°, what is the
measure of ZQRS?
O
mZQRS = [?]
Enter
40° is your answer
Answer:
:
< ABC+<QRS=180
m<QRS=180-140=40°
Math 3rd grade can someone explain easy for 3rd grade child thanks
Answer:
A is 16, B just draw a line down from the inside square to make a rectangle, C. just multiply all the numbers around the square
Step-by-step explanation:
<<
Answer:
A) 72 in²
B) From the bottom right corner of the shaded square, draw a line either straight down or to the right.
C) 56 in²
Step-by-step explanation:
A) 8x9=72 in²
B) From the bottom right corner of the shaded square, draw a line either straight down or to the right.
C) The shaded area is 4x4=16, so you need to subtract that from the 72.
72-16=56 in²
Select the correct answer,
Factor the given expression,
X2 + 16x + 64
O A. (X + 8)(x-8)
OB. (x+ 16)(x + 4)
Oc. (x+4)?
OD. (x+8)?
Answer:
(x+8)^2
Step-by-step explanation:
x^2 +16x+64
What two numbers multiply to 64 and add to 16
8*8 = 64
8+8 = 16
(x+8)(x+8)
(x+8)^2
Find the area of the following figure:
Answer:
84
Step-by-step explanation:
6 * 14 = 84
Area: 69
So we can split the figure into two sections. One rectangle, and one triangle.
The rectangle's area would be 54.
Since the length of the figure is 14 in total. we can subtract 9 from 14
5 is the height of the triangle
to find the area of a triangle, it is height x width divided by 2
so 5 x 6 divided by 2 = 15
54 + 15 = 69
The average natural gas bill for a random sample of 21 homes in the 19808 zip code during the month of February was $311.90 with a sample standard deviation of $51.60. Based on the sample, construct a 90% confidence interval for the true mean natural gas bill for homes in the 19808 zip code area in February.
Answer:
The 90% confidence interval for the true mean natural gas bill for homes in the 19808 zip code area in February is between $292.48 and $331.32
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 21 - 1 = 20
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 20 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.7247
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.7247\frac{51.60}{\sqrt{21}} = 19.42[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 311.9 - 19.42 = $292.48
The upper end of the interval is the sample mean added to M. So it is 311.9 + 19.42 = $331.32
The 90% confidence interval for the true mean natural gas bill for homes in the 19808 zip code area in February is between $292.48 and $331.32
A car company is testing how well its cars handle skidding to a complete stop after hitting the brakes while going at different speeds on an asphalt road. The equation represents the car’s speed, in miles/hour, when the brakes are applied as a function of the distance, in feet, the car skids. The table of values represents the function S(D). Use the table of values to calculate the average rate of change between the given intervals. Then interpret what the average rate of change means in this context.
Answer:
D SD= sqrt(22.5D) Average Rate of Change
47 32.52
50 33.5 0.34
56 35.50 0.33
60 36.74 0.31
62 37.35 0.305
65 38.24 0.3
In the context of this problem, the average rate of change is the rate at which the car decelerates as it skids. As the distance that the car skids increases, the rate at which the car decelerates decreases at a gradual rate.
Step-by-step explanation:
ANSWER ASAP! SCAM LINKS REPORTED.
Answer:
b is correct
Step-by-step explanation:
i did this pls mark as branlyest
Answer:
I believe the answer is D
Step-by-step explanation:
How does the stimulus check impact society please help me please i really need help please
Answer: Stimulus checks are given to boost the economy by providing consumers with funds to spend. Consumer spending is an essential component of a healthy economy and, in times of economic uncertainty, it usually contracts.