the answer is 10ft hope I helped
A fast-food restaurant operates both a drive through facility and a walk-in facility. On a randomly selected day, let X and Y, respectively, be the proportions of the time that the drive-through and walk-in facilities are in use, and suppose that the joint density function of these random variables is,
f (x, y) ={2/3(x+2y) 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1
(a) Find the marginal density of X.
(b) Find the marginal density of Y .
(c) Find the probability that the drive-through facility is busy less than one-half of the time.
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]
can someone help me solve this
(show work)
Answer:
y=x+31.25
Because x stand for cauclator so 31.25 per x so it would end up being x+31.25
Step-by-step explanation:
PLEASE HELPPP
Given △ABC and altitude AH, decide whether each statement is necessarily true about △AHC. Select Yes or No for A − C.
ge80512
A. AH < HC
A Yes B No
B. AH < AC
A Yes B No
C. △AHC ≅ △AHB
Answer:
(a) AH < HC is No
(b) AH < AC is Yes
(c) △AHC ≅ △AHB is Yes
Step-by-step explanation:
Given
See attachment for triangle
Solving (a): AH < HC
Line AH divides the triangle into two equal right-angled triangles which are: ABH and ACH (both right-angled at H).
To get the lengths of AH and HC, we need to first determine the measure of angles HAC and ACH. The largest of those angles will determine the longest of AH and HC. Since the measure of the angles are unknown, then we can not say for sure that AH < HC because the possible relationship between both lines are: AH < HC, AH = HC and AH > HC
Hence: AH < HC is No
Solving (b): AH < AC
Length AC represents the hypotenuse of triangle ACH, hence it is the longest length of ACH.
This means that:
AH < AC is Yes
Solving (c): △AHC ≅ △AHB
This has been addresed in (a);
Hence:
△AHC ≅ △AHB is Yes
What is the value of this expression when a= -3 and b=5? a + b^2*
Answer:
22
Step-by-step explanation:
a+b^2
= -3+(5^2)
= -3+25
=22
Turn 6/10 into an equivalent fraction with a denominator of 80.
Answer:
48/80
Step-by-step explanation:
In order to get a denominator of 80, we need to turn the current denominator, 10, into 80. We do this by multiplying it by 8. We then have to multiply the top by 8 to keep it equal.
hope this helped :)
the number value of 2 in the number 4256
Answer:
200
Step-by-step explanation:
Answer: 200
Step-by-step explanation:
The two is in the hundredths place
Mrs. Nesbitt had 97 books in her classroom library she received a grant to expand her classroom library After spending the money she had 213 books what is the percent increase?
Answer:
219 percent
Step-by-step explanation:
97 goes into 213 two times which is a 200 percent increase which leaves 18 books. 18.5 percent of 97 is about 18 so rounded up it is a 219 percent increase
PLEASE HELP WILL MARK BRAINLIEST!!! No links and serious answers only!!
2. Write the equation of the line of best fit using the slope-intercept formula $y = mx + b$. Show all your work, including the points used to determine the slope and how the equation was determined.
3. What does the slope of the line represent within the context of your graph? What does the y-intercept represent?
4. Test the residuals of two other points to determine how well the line of best fit models the data.
5. Use the line of best fit to help you to describe the data correlation.
6. Using the line of best fit that you found in Part Three, Question 2, approximate how tall is a person whose arm span is 66 inches?
7. According to your line of best fit, what is the arm span of a 74-inch-tall person?
Patel bought a model rocket kit from a catalog. The
price of the kit was $125. A $10 charge for shipping will
be added. Patel received an allowance of $20 per
week. How many weeks will it take him to purchase
the kit?
Answer:
7 weeks
Step-by-step explanation:
add 10 to 125 then divide by 20
Answer: he will need to save to 7 weeks
Step-by-step explanation:
125+10=135
he needs 135 to get the kit
y=20x
135=20x
6.75=x
he will need to save to 7 weeks
VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
Answer:
I believe its c
Step-by-step explanation:
Answer:
(4, -11)
Explanation:
The coordinate's signs just change (negative becomes positive and vise versa)
Mr. Lloyd wants to buy a new television, but he does not have enough money in his bank account to pay for one. Which of these is NOT an option for Mr. Lloyd? OPTIONS:
F
He can use his credit card to buy the television now.
G
He can save money and pay cash for the television at a later date.
H
He can use his debit card to buy the television now.
J
He can save money and use his debit card to buy the television at a later date.
Answer:
The only option which is not available for Mr. Lloyd is to use his debit card to purchase the television now. The debit card can only be Used to make purchases when the account holder has funds or money in his or her account.
Step-by-step explanation:
7m=56. explanation please
Answer:
m=8
Step-by-step explanation:
Divide each term in
7
m
=
56
7
m
=
56
by
7
7
.
7
m
7
=
56
7
7
m
7
=
56
7
Cancel the common factor of
7
7
.
Tap for more steps...
m
=
56
7
m
=
56
7
Divide
56
56
by
7
7
.
m
=
8
m
=
8
Step-by-step explanation:
7m=56
you have to have m by itself so to do that divide 7 on both sides.
7m/7=56/7
the 7 gets cancels on the left side so now you have
m=56/7
you divide
you get m=8
Given: ΔSTQ
ST=TQ
SD⊥TQ
m∠1=32°
find: m∠S, m∠T, m∠Q
Answer:
∠ S = 58° , ∠ T = 64° , ∠ Q = 58°
Step-by-step explanation:
the sum of the 3 angles in Δ DQS = 180° , that is
∠ Q + ∠ 1 + 90° = 180°
∠ Q + 32° + 90° = 180°
∠ Q + 122° = 180° ( subtract 122° from both sides )
∠ Q = 58°
given ST = TQ , then Δ STQ is isosceles with base angles congruent, that is
∠ S = ∠ Q = 58°
the sum of the 3 angles in Δ STQ = 180° , that is
∠ T + ∠ S + ∠ Q = 180°
∠ T + 58° + 58° = 180°
∠ T + 116° = 180° ( subtract 116° from both sides )
∠ T = 64°
Hello pls help will give good old BRAINLYEST YAY
Answer:
D
Step-by-step explanation:
The mean, median, and mode all are 3
I BEG FOR MY LIFE EZ PLS
{{{{{{{PICTURE PROVIDED}}}}}}}}}
Answer:
B and D
Step-by-step explanation:
This is because for B you do 8x9x1 which is basically 8x9 which is 72. Then, for D you do 12x3x2. Do 3x2 first and you get 6. Then, do 6x12 which is also 72. So the correct answers that will give you the volume of 72 units cube is B and D. Hope this helps!
a city has a population of 34000. the value k is 0.0305. what is the population of the city after 9 years
Answer:
6
Step-by-step explanation: 6 9 0
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. Suppose that the mean income is found to be $23.7 for a random sample of 4825 people. Assume the population standard deviation is known to be $11.2. Construct the 90% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
A bag contains 2 yellow, 12 red, and 6 green marbles. What is the probability of selecting 1 yellow marble, not replacing it, then selecting a green marble
Without replacement is very important
Plssss helpppppp! 45 points!
Answer:
15 C
Step-by-step explanation:
C = 5/9( F - 32)
Let F = 59
C = 5/9( 59 -32)
Parentheses first
= 5/9( 27)
= 15
Pls help ignore my answers :v.
so u r already finished? don't post it next time
9 times 10 to the power of minus 9. As a normal number.
First, write the expression. Then solve.
9 x 10^-9
9 x 0.0000000010
0.000000009
---
sorry if i'm wrong, I haven't done this in a while
Pls help quick i beg please,Complete the explanation blank and blank 1 whole stirp could represent 1 blank and the 1/3 strip could represent blank. please help like please cause if you do it i make you The Brainliest
Answer:
Feet and yards; the 1 whole strip could represent 1 yd. and the [tex]\frac{1}{3}[/tex] strip could represent feet.
HELP AHHHHHHHHHHHHHHHH
Answer:
y = 3x+4
Step-by-step explanation:
slope formula is changes of y over the changes of x
[tex] \large \boxed{m = \frac{y_2-y_1}{x_2-x_1} }[/tex]
m is slope in y = mx+b.
Substitute the coordinate points in.
[tex] \large{m = \frac{7 + 2}{1 + 2} } \\ \large{m = \frac{9}{3}} \\ \large{m = 3}[/tex]
Since we know the slope, we rewrite by substituting m = 3 in the slope-intercept form.
[tex] \large{y = mx + b} \\ \large{y = 3x + b}[/tex]
Then we either substitute one of given coordinate points to find the value of b. I will substitute (1,7) in the equation.
[tex] \large{7 = 3(1)+ b} \\ \large{7 = 3 + b} \\ \large{7 - 3 = b} \\ \large{4 = b}[/tex]
Then rewrite the equation from y = 3x+b by substituting the value of b.
[tex] \large{y = 3x + b} \\ \large{y = 3x + 4}[/tex]
I have no clue how to do this! please help me!!!
Answer:
The equation has one solution.
A value of x that makes the equation true is 5, which when substituted into the equation and simplified makes the equation turn into 10=10
A value of x that makes the equation false is 6, which when substituted into the equation and simplified makes the equation turn into 12=10
Step-by-step explanation:
2x=10
Divide both sides by two:
2x/2=10/2
x=5. There is no other solution to the equation, because 5 is the only possible answer.
Brainliest for both correct answers
Answer:
Question 1: A
Question 2: D
Step-by-step explanation:
I hope it helps
Samiya had 45 grams of cookies to share with the class how many kilograms of cookies does she have
Answer:
0.045 kg of cookies
Answer: 0.045
Step-by-step explanation:
What’s the answer and work for this? Someone please tell me
Answer:
Step-by-step explanation:
# 12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
12 is a median of a data
VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
Answer:
(2, 5)
Step-by-step explanation:
(x,y) -> )- y,x)
VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
Answer:
D
Step-by-step explanation:
Answer:D
Step-by-step explanation:
pls pls pls :,) help me plssssssss no links no links NO LINKS pls and if you don’t know don’t answer because I really need help
Answer:
Step-by-step explanation:
use your calculator