(1) To find the value of B that makes f_(XY)(x,y) a valid joint density function, we need to ensure that the total probability over the entire domain is equal to 1. In this case, the domain is |x|<1 and |y|<1.
The integral of f_(XY)(x,y) over the given domain should be equal to 1:
∫∫ f_(XY)(x,y) dx dy = 1
∫∫ B(1+xy) dx dy = 1
To solve this integral, we integrate with respect to x first and then with respect to y:
∫(∫ B(1+xy) dx) dy
∫[Bx + B(xy^2)/2] dy, integrating with respect to x
Bxy + B(xy^2)/2 + C, integrating with respect to y
Now, evaluate the integral over the given domain:
∫[-1,1] [Bxy + B(xy^2)/2 + C] dy
[Bxy^2/2 + B(xy^3)/6 + Cy] evaluated from -1 to 1
[B/2 + B/6 + C] - [-B/2 - B/6 - C]
(B/2 + B/6 + C) - (-B/2 - B/6 - C)
2B/3 = 1
Solving for B:
B = 3/2
Therefore, the value of B that makes f_(XY)(x,y) a valid joint density function is B = 3/2.
(2) To determine if X and Y are uncorrelated, we need to calculate the covariance between X and Y. If the covariance is zero, then X and Y are uncorrelated.
Cov(X, Y) = E[XY] - E[X]E[Y]
To calculate E[XY], we need to find the joint expectation:
E[XY] = ∫∫ xy f_(XY)(x,y) dx dy
E[XY] = ∫∫ xy (3/2)(1+xy) dx dy
Integrating over the domain |x|<1 and |y|<1, we can calculate E[XY].
Similarly, we need to calculate E[X] and E[Y] to determine Cov(X, Y).
If Cov(X, Y) is found to be zero, then X and Y are uncorrelated.
(3) To prove or disprove independence between X and Y, we need to check if the joint probability density function (pdf) can be factorized into the product of the marginal pdfs of X and Y.
If f_(XY)(x,y) = f_X(x)f_Y(y), then X and Y are independent.
To determine if this factorization holds, we need to compare the joint pdf f_(XY)(x,y) with the product of the marginal pdfs f_X(x) and f_Y(y). If they are equal, then X and Y are independent. Otherwise, they are dependent.
(4) To prove or disprove the independence between X^2 and Y^2, we follow a similar approach as in (3). We compare the joint pdf of X^2 and Y^2 with the product of their marginal pdfs. If they are equal, X^2 and Y^2 are independent. Otherwise, they are dependent.
By examining the factorization of the joint pdfs and comparing them with the product of the marginal pdfs, we can determine the independence relationships between the variables X, Y, X^2, and Y^2.
To know more about joint density function, visit
https://brainly.com/question/31266281
#SPJ11
Employees in 2016 paid 4.15% of their gross wages towards social security (FICA tax), while employers paid another 6.3%. How much will someone earning $47,000 a year pay towards social security out of their gross wages?
Someone earning $47,000 a year will pay a total of $4,911.50 towards social security out of their gross wages.
Understanding FICA TaxEmployee Contribution:
The employee paid 4.15% of their gross wages towards social security. So, to calculate the employee's contribution:
Employee Contribution = (4.15/100) * Gross Wages
For someone earning $47,000 a year:
Employee Contribution = (4.15/100) * $47,000
= (0.0415) * $47,000
= $1,950.50
The employee will pay $1,950.50 towards social security.
Employer Contribution:
The employer paid 6.3% of the employee's gross wages towards social security. So, to calculate the employer's contribution:
Employer Contribution = (6.3/100) * Gross Wages
For someone earning $47,000 a year:
Employer Contribution = (6.3/100) * $47,000
= (0.063) * $47,000
= $2,961.00
The employer will pay $2,961.00 towards social security.
Total Social Security Contribution:
To find the total social security contribution, we add the employee and employer contributions:
Total Contribution = Employee Contribution + Employer Contribution
Total Contribution = $1,950.50 + $2,961.00
= $4,911.50
Therefore, someone earning $47,000 a year will pay a total of $4,911.50 towards social security out of their gross wages.
Learn more about FICA tax here:
https://brainly.com/question/2288869
#SPJ4
Which graph represents all the real numbers, , where ≥−2? THIS IS LAST QUESTION PLEASE ANSWER! I WILL GIVE BRAINLYST.
Answer:
It's the one right under the first one
lora has 9 fish and dylan has 2 fish. lora wants to know how many more fish does she has then dylan lora has 9 fish and dylan has 2 fish. lora wants to know how many more fish does she has then dylan lora has 9 fish and dylan has 2 fish. lora wants to know how many more fish does she has then dylan lora has 9 fish and dylan has 2 fish. lora wants to know how many more fish does she has then dylan
Answer:
7
Step-by-step explanation:
Answer: 7
Because 9-2=7
Athletes were doing a timed 100-metre dash. Athletes times were organized into a Normal Curve distribution of frequencies. If the mean was 10 seconds (µ), with a standard deviation of 2(σ), create the 1-2-3 curve. Place the actual research data values in the 1-2-3 curve sketch.
If an athlete got a time of 9 seconds (x), calculate their Z-score and place it on the curve.
Use the Z-tables to determine what percentage of the team was below the athlete and above the athlete
The Z-score for an athlete with a time of 9 seconds is -0.5. Approximately 30.85% of the team was below the athlete, and approximately 69.15% of the team was above the athlete based on the Z-score.
To create the 1-2-3 curve, we can use the mean (µ) and standard deviation (σ) to mark the values on the curve. The 1-2-3 curve represents the standard deviations away from the mean.
1-2-3 Curve:
1st Standard Deviation: Mean ± σ
2nd Standard Deviation: Mean ± 2σ
3rd Standard Deviation: Mean ± 3σ
We have that the mean (µ) is 10 seconds and the standard deviation (σ) is 2 seconds, we can mark the 1-2-3 curve as follows:
1st Standard Deviation: 8 to 12 seconds
2nd Standard Deviation: 6 to 14 seconds
3rd Standard Deviation: 4 to 16 seconds
If an athlete has a time of 9 seconds (x), we can calculate their Z-score using the formula: Z = (x - µ) / σ.
Z-score: (9 - 10) / 2 = -0.5
Placing the Z-score of -0.5 on the curve, we find that it falls between the mean and the first standard deviation (8 to 12 seconds).
To determine the percentage of the team below the athlete and above the athlete, we can use the Z-table. Looking up the Z-score of -0.5 in the table, we find that the area below the Z-score is 0.3085. This means that approximately 30.85% of the team's times were below the athlete's time of 9 seconds.
To compute the area above the Z-score, we subtract the area below from 1: 1 - 0.3085 = 0.6915. This indicates that approximately 69.15% of the team's times were above the athlete's time of 9 seconds.
Therefore, approximately 30.85% of the team was below the athlete, and approximately 69.15% of the team was above the athlete based on the Z-score of -0.5.
To know more about Z-score refer here:
https://brainly.com/question/30557336#
#SPJ11
2
Select the correct answer from each drop-down menu.
Consider polynomial function f.
f(x) = (1 - 1)?(1 + 3)3 (+ 1)
Use the equation to complete each statement about this function.
The zero located at x = 1 has a multiplicity of , and the zero located at x = -3 has a multiplicity of
The graph of the function will touch, but not cross, the x-axis at an x-value of
Reset
Next
Answer:
2 of the 3 answers in picture
Step-by-step explanation:
Answer:
The answers are 2, 3, and 1 only
Step-by-step explanation:
This is the correct answer for plato users
Solve the following exponential equations
Answer:
x = 2, y = - 25
Step-by-step explanation:
(1)
note that 36 = 6² , then
[tex]6^{x}[/tex] = 6²
Since bases on both sides are equal then equate the exponents
x = 2
------------------------------------------
(2)
Using the rule of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
note that 25 = 5² , then
[tex]25^{11+3y}[/tex] = [tex](5^2)^{11+3y}[/tex] = [tex]5^{22+6y}[/tex]
Then
[tex]5^{5y-3}[/tex] = [tex]5^{22+6y}[/tex]
Since bases on both sides are equal then equate the exponents
22 + 6y = 5y - 3 ( subtract 5y from both sides )
22 + y = - 3 ( subtract 22 from both sides )
y = - 25
An angle measures 52° more than the measure of its complementary angle. What is the measure of each angle?
Similar to the univariate t-test, the bivariate t-test
a. requires ratio or interval data.
b. assumes that samples are drawn from populations with normal distributions.
c. is especially helpful when the sample size is large (n>80).
d. is useful when the population standard deviation is known.
e. All of the above
Similar to the univariate t-test, the bivariate t-test has all of the mentioned characteristics, so, E. All of the above.
What are the similarities?The univariate and bivariate t-tests are different in the fact that while one measures only one variable, the other measures two variables.
The similarities between these tests include the fact that they both require ratio or interval data, they are both drawn from populations with normal distributions and they are useful for analyzing large sample sizes. Also, the two tests ate useful when the population's standard deviation is known.
Learn more about t-tests here:
https://brainly.com/question/6589776
#SPJ4
Will mark brainiiest help please <3
Answer:
0.029g
Step-by-step explanation:
A computer selects a number X from 4 to 11 randomly and uniformly. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X-U b. Suppose that the computer randomly picks 35 such numbers. What is the distribution of for this selection of numbers. 2- N c. What is the probability that the average of 35 numbers will be more than 7.77 Hint: Some Helpful Videos: Progress saved Done 0/1 pt 0.1
The probability that the average of 35 randomly selected numbers will be more than 7.77 is approximately 0.2157.
How to calculate probability of average?a. The distribution of X is uniform, meaning each number from 4 to 11 has an equal probability of being selected. The probability of selecting any specific number is 1/8 since there are 8 numbers in the range.
b. If the computer randomly picks 35 numbers, the distribution of the selection can be approximated by a normal distribution. This is known as the Central Limit Theorem. The mean of the distribution will still be the same as in part a, which is (4 + 11) / 2 = 7.5. The standard deviation of the distribution can be calculated using the formula:
Standard deviation = (b - a) / √(12)
where a and b are the lower and upper bounds of the range, respectively. In this case, a = 4 and b = 11.
Standard deviation = (11 - 4) / √(12) ≈ 1.6794
Therefore, the distribution of the selection of 35 numbers can be approximated by a normal distribution with a mean of 7.5 and a standard deviation of 1.6794.
c. To find the probability that the average of 35 numbers will be more than 7.77, we need to calculate the z-score and then use the standard normal distribution table.
z-score = (7.77 - 7.5) / (1.6794 / √35) ≈ 0.7832
Using the standard normal distribution table or a calculator, we can find the probability associated with the z-score of 0.7832. Let's assume it is P(Z > 0.7832).
The probability that the average of 35 numbers will be more than 7.77 can be calculated as:
P(Z > 0.7832) = 1 - P(Z < 0.7832)
Referencing the standard normal distribution table or using a calculator, we find the probability to be approximately 0.2157.
Therefore, the probability that the average of 35 numbers will be more than 7.77 is approximately 0.2157 (rounded to 4 decimal places).
Learn more about distribution
brainly.com/question/29664127
#SPJ11
Help please with number 1. Writw the orderd pair that coresponds to Point H.
Answer: yeah you got it
Step-by-step explanation:
What are closing costs and how do you calculate closing costs?
Answer:
Closing costs are fees paid at the closing of a real estate transaction. Typically home owners will pay between 2 to 5 percent of the purchase price of their home in closing fees. So, if your home cost $150,000, you might pay between $3,000-$7,000 in closing costs.
19. Linda mixed 5.15 lb of cashews with 4.32 lb of pistachios. After filling up 6 bags that were the same size with the mixture, he had 0.05 lb of nuts left. What was the weight of each bag? Use a tape diagram and show your calculations. Focus
The weight of each bag of the mixture can be determined by using a tape diagram. Given that Linda mixed 5.15 lb of cashews with 4.32 lb of pistachios, and after filling up 6 bags that were the same size with the mixture, he had 0.05 lb of nuts left.
A tape diagram is a bar model that is used to represent fractions and ratios visually. It is useful when comparing different quantities that are related to each other.Tape DiagramTo solve the problem using a tape diagram, we begin by representing the total weight of the mixture and the weight of each bag using a single length unit. For example, we can choose 1 inch to represent the weight of 1 pound.
In this case, we would represent the total weight of the mixture as 5.15 + 4.32 = 9.47 inches. Next, we divide the total length by the number of bags to find the length of each bag. If the total length of the mixture is 9.47 inches and there are 6 bags, then the length of each bag is:9.47 ÷ 6 = 1.578 inches. Finally, we convert the length of each bag back to pounds by multiplying by the weight of 1 pound, which is 1 inch in our tape diagram. Thus, the weight of each bag is:1.578 × 1 = 1.578 lb. Therefore, the weight of each bag of the mixture is 1.578 lb.
Know more about tape diagram:
https://brainly.com/question/29208618
#SPJ11
PLZZZ HELP!! BRAINLIEST FOR WHOEVER GETS RIGHT ANSWER
The graphs below have the same shape. What is the equation of the red graph.
Answer:
2 - x^2
Step-by-step explanation:
Which is a better deal: 30 fluid ounces of shampoo for $3.55 or 50 fluid ounces of shampoo for $6?
30 fl oz for $3.55
if we make them each 10 fl oz then here are the costs:
$1.18 (originally 30 fl oz)
$1.20 (originally 50 fl oz)
A movie theater gave away coupons for smallmediumand large drinks. Customers could randomly pull a coupon from a box that held 75 small drink coupons , 125 drink coupons , and 150 large drink coupons . What is the probability that the first customer to pull a coupon from the box got a medium drink coupon ?
Answer: 35.7%
Step-by-step explanation:
First find out the total number of all coupons in the box.
= 75 + 125 + 150
= 350 drink coupons
There are 125 medium coupons so the probability that the first customer will pick a medium one is:
= Number of medium coupons / Number of total coupons
= 125 / 350
= 35.7%
For the linear function(straight line) y = 7x - 3,ar function(straight line) y = 7x - 3,
a) What is the slope of the given function?
b) Is the function increasing or decreasing?
c) What is the y-intercept(0, b) of the given function?
Answer:
a) slope is 7
b) slope is positive, so Increasing
c) y-intercept is -3
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Which is true about the solution to the system of inequalities shown?
y > 3x + 1
y < 3x – 3
On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.
Only values that satisfy y > 3x + 1 are solutions.
Only values that satisfy y < 3x – 3 are solutions.
Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.
There are no solutions. Edge 2022
MATH
NATION
The data from a survey of ages of people taking an exercise class was skewed to the left.
Part C: The box plot represents the data. Calculate the appropriate measure of spread.
Answer choices:
A. IQR= 45
B. IQR= 13
C. Standard deviation = 8
D. Standard deviation=55
Answer:
IQR=13 im pretty sure
Step-by-step explanation:
The measure interquartile range is 13 option (B) IQR= 13 is correct.
What is the box and whisker plot?A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.
We have a box plot, and the data from a survey of ages of people taking an exercise class was skewed to the left.
We know on the left side skewed has more data on the right and on the left side, there are fewer data.
From the dot plot, the end point is not given, so we are assuming the end point is 58.
IQR = 58 - 45 = 13
Thus, the measure interquartile range is 13 option (B) IQR= 13 is correct.
Learn more about the box and whisker plot here:
brainly.com/question/3209282
#SPJ2
Is (3,10) a solution to this system of equations?
y=2x+3
y=x+7
Answer: no
Step-by-step explanation:
plug in (3,10) to y=2x+3
10=2(3)+3
10=6+3
10[tex]\neq[/tex]9
WHAT IS THE SLOPE IF I HAVE (-3,5) AND (4,-5)
Answer:
-10/7
Step-by-step explanation:
Use slope formula
[tex]\frac{y2-y1} {x2-x1}[/tex]
x1= -3
y1 = 5
x2 = 4
y2 = -5
[tex]\frac{-5-5}{4--3}[/tex]
[tex]\frac{-5 + -5}{4 +3}[/tex][tex]\frac{-10}{7}[/tex]
use the information provided to write the equation of each circle
Answer:
1.
centre(h,k)=(-13,9)
radius (r)=6
we have
equation of the circle is
(x-h)²+(y-k)²=r²
(x+13)²+(y-9)²=6²
x²+26x+169+y²-18y+81=36
x²+y²+26x-18y+169+81-36=0
x²+y²+26x-18y +214=0
is a required equation of the circle.
2.
centre(h,k)=(1,-1)
radius (r)=11
we have
equation of the circle is
(x-h)²+(y-k)²=r²
(x-1)²+(y+1)²=11²
x²-2x+1+y²+2y+1=121
x²+y²-2x+2y=121-2
x²+y²-2x+2y=119
is a required equation of the circle.
In the June 1986 issue of Consumer Reports, some data on the calorie content of beef hot dogs are given. Here are the numbers of calories in 20 different hot dog brands: 186, 181, 176, 149, 184, 190, 158, 139, 175, 148, 152, 111, 141, 153, 190, 157, 131, 149, 135, 132. Assume that these numbers are the observed values from a random sample of independent normal random variables with standard deviation o= 4 calories. Find a 90% confidence interval for the mean number of calories u.
The 90% confidence interval for the mean number of calories is 155.3 to 158.4
Finding a 90% confidence interval for the mean number of calories u.From the question, we have the following parameters that can be used in our computation:
The dataset
The mean is calculated as
x = sum/count
So, we have
x = (186 + 181 + 176 + 149 + 184 + 190 + 158 + 139 + 175 + 148 + 152 + 111 + 141 + 153 + 190 + 157 + 131 + 149 + 135 + 132) / 20
x = 156.85
Calculate the margin of error using
E = t * σ/√n
Where t = 1.729 i.e. the critical value
So, we have
E = 1.729 * 4/√20
Evaluate
E = 1.55
The confidence interval is then calculated as
CI = x ± E
So, we have
CI = 156.85 ± 1.55
Evaluate
CI = 155.3 to 158.4
Hence, the 90% confidence interval for the mean number of calories is 155.3 to 158.4
Read more about confidence interval at
https://brainly.com/question/15712887
#SPJ4
please help me ......
Answer:
no solution
Step-by-step explanation:
PLS PLS HELP WILL MARK BRAINLIEST
Answer:
d: 83
e: 97
f: 83
Step-by-step explanation:
d: We first have to find out f, so f and d can be alternate interior angles, which means they can be congruent to each other.
e: e is a vertical angle to the given angle, which means they are congruent, making it also 97 degrees.
f: f is a supplementary angle to the given angle, which means we can subtract 97 from 180 to give us 83.
Going back to angle d, now that we know f is 83 degrees, then d is an alternate interior angle, so d=f, meaning d is also 83 degrees.
Hope this helps! :)
which point is on the line that passes through point h and is perpendicular to line fg?
The point on the line that passes through point H and is perpendicular to line FG is (–6, 10).
First, we need to find the slope of line FG. The slope of a line can be calculated by dividing the change in the y-coordinate by the change in the x-coordinate. In this case, the change in the y-coordinate is 10 and the change in the x-coordinate is 3, so the slope of line FG is 10/3.
Since the lines are perpendicular, their slopes are negative reciprocals of each other. The negative reciprocal of 10/3 is -3/10.
Now, we need to find the equation of the line that passes through point H and has a slope of -3/10. The general equation of a line is y = mx + b, where m is the slope and b is the y-intercept. In this case, we know that m = -3/10 and the y-coordinate of point H is 10. Plugging these values into the equation, we get y = -3/10*x + 10.
To find the x-coordinate of the point we are looking for, we can substitute in the y-coordinate of point H. 10 = -3/10*x + 10, so x = –6.
Therefore, the point on the line that passes through point H and is perpendicular to line FG is (–6, 10).
Learn more about negative reciprocal here:
brainly.com/question/29429946
#SPJ11
which values of p and q would make the value of the following expression equal to 58i? (3 – 7i)(p qi)i p = 3, q = 7 p = –3, q = 7 p = 3, q = –7 p = –3, q = –7
The values p = 3 and q = -7 would make the expression (3 – 7i)(p + qi)i equal to 58i.
Let's expand the expression:
(3 - 7i)(p + qi)i = (3 - 7i)(pi - q)
Using the distributive property, we have:
= 3pi - 7pi^2 - 3qi + 7qi^2
Since i^2 is equal to -1, we can substitute -1 for i^2:
= 3pi - 7p - 3qi - 7q
Now, equating the imaginary part to 58i:
-7p - 7q = 58
Dividing both sides by -7:
p + q = -8
From the given options, only p = 3 and q = -7 satisfy this equation:
3 + (-7) = -4
Therefore, the values p = 3 and q = -7 would make the expression (3 – 7i)(p + qi)i equal to 58i.
For more information on value of p and q visit: brainly.com/question/11014549
#SPJ11
6. give the figure at the right,what is the measure of dbc
A. 54°
b. 36°
C. 126°
D. 116°
Answer:
c.126
Step-by-step explanation:
180-54=126
which statement best explains why ben uses the width hi to create the arc at j from point k?
By using the property of CPCTC (corresponding parts of congruent triangles are congruent) he can prove ∠DEF ≅ ∠ABC.
Which statement best explains why Ben uses the width BI to create the arc JK from point E?
A. ∠DEF ≅ ∠ABC when BH = EK, BI = JK, and HI = EJ.
B. BI = JK when ∠DEF ≅ ∠ABC.
C. BI = EJ when ∠DEF ≅ ∠ABC.
D. ∠DEF ≅ ∠ABC when BH = EJ, BI = EK, and HI = JK.
The statement Ben explains why Ben uses the width BI to create the arc JK from point E is ∠DEF ≅ ∠ABC when BH = EJ, BI = EK, and HI = JK.
The correct option is (D).
Ben ensuring that for making an arc JK,
BH = EJ
BI = EK
HI = JK
These are the three congruent corresponding sides for making an arc.
then, he will use the congruence criteria to ΔDEF ≅ ΔABC.
By using the property of CPCTC (corresponding parts of congruent triangles are congruent) he can prove ∠DEF ≅ ∠ABC.
Learn more about Congruence here:
brainly.com/question/7888063
#SPJ4
Which statement best explains why Ben uses the width BI to create the arc JK from point E.
pls solve this
(-21) x [(-4) + (-6)] = [(-21) (-4)] +[(-21)×(-6)]
Answer:
ree kid it is 3409,3567
Step-by-step explanation:
Find the unit rate.
2 2/5 to 3 3/4
Answer:
2 2/5=5/5+5/5+2/5=12/5
3 3/4= [(3•4)+3]/4=15/4
(12/5) / (15/4)= 12/5 • 4/15=12•4/5•15=
48/75 kilometers in 1 minute
Step-by-step explanation:
How that this helps! :)
Have a great rest of your day/night!