⇒ Yes X+Y and X-Y are independent
What is covariance?
Covariance is a measure of the combined variability of two random variables used in probability theory and statistics. The covariance is positive if the greater values of one variable primarily match the greater values of the other variable, and the same is true for the lesser values.
Define U=X+Y, V=X−Y
Then, [tex]x=\frac{(U+V)}{2}[/tex], and
[tex]Y=\frac{(U-V)}{2}[/tex]
Find the Jacobian J for the transformation.
Then, fU,V(u,v)= fX(x=(u+v)/2) fY(y=(u−v)/2)|J|
You will find that fU,V(u,v) factors into a function of u alone and a function of v alone. Thus, by the Factorization thm, U and V are independent.
b) Yes X+Y and X-Y are independent
a) Since , X+Y and X-Y are independent,
COV(X+Y , X-Y) = 0 Answer
Cov(X+Y , X-Y) = 0
b)
Yes these are independent
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For the circle centered at the origin with radius 4 and equation x^2+y^2=16 find dx/dt.
dx/dt = 4+3√3 in the case of the circle with radius 4 and the equation x²+y²=16.
What is implicit differentiation?The method of finding an implicit function's dependent variable's derivative by differentiating each term individually, symbolizing the derivative, and then solving the resulting expression for the symbol.
Without having to solve the provided equation for y, you may use the implicit differentiation technique to determine the derivative of y with respect to x.
Because we assume that y may be written as a function of x, the chain rule must always be applied when differentiating the function y.
So, the dx/dt will be:
The circle's equation is: x² + y² = 16
Assuming that x = 2, then:
2² + y² = 16
y² = 12
y = ±√12
Hence, the first quadrant is positive:
y = √12
y = 2√3
When implicit differentiation is used, we get that:
2x dx/dt + 2y dy/dt = 16
If fracdydt = -3, as is the case, then
2(2) dx/dt - 12√3 = 16
4 dx/dt = 16 + 12√3
dx/dt = 16+12√3/4
dx/dt = 4+3√3
Therefore, dx/dt = 4+3√3 in the case of the circle with radius 4 and the equation x² + y² = 16.
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The equation g equals three fifths times m represents the proportional relationship of the number of gallons of water (g) used by a washing machine over a certain period of time, in minutes (m). Create a written description for the equation. For each minute the washing machine runs, it uses five thirds gallons of water. For each minute the washing machine runs, it uses three fifths of a gallon of water. For each gallon of water the washing machine uses, it runs for three fifths of a minute. For each gallon of water the washing machine uses, it runs for 8 minutes.
The description of the proportional relationship in the context of this problem is given as follows:
For each minute the washing machine runs, it uses five thirds gallons of water.
What is a proportional relationship?A proportional relationship is a special case of a linear function, with intercept of zero, meaning that the output variable y is obtained as the multiplication of the input variable x and the constant of proportionality k, as follows:
y = kx.
In this problem, the relationship is given by the equation presented as follows:
g = 3/5m
The variables are given as follows:
Input m: number of minutes.Output g: number of gallons of water.The constant is of:
3/5.
Meaning that three fifths gallons of water are used each minute.
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Find the center and radius of the circle.
Answer:
5
Step-by-step explanation:
using the significance levels reported by forecast xtm, at what level can we reject a one-sided null relating to a slope coefficient's statistical significance such that we are 95% confident?
If the value of test statistic does not lie between -1.96 and +1.96 then, the difference would be significant and the null hypothesis will be rejected.
Using the significance levels as reported by forecast Xtm, we would check the difference of means between the two items.
The critical value of Z at 95% confidence level is 1.96.
Then we would calculate the Test statistic, viz, difference of means/ standard deviation.
Decision Rule:
If we find that the value of test statistic is more than the value of Z, i.e., the test statistic does not lie between -1.96 to +1.96, then, the difference would be significant and the null hypothesis must be rejected.
But, the other way round, if the difference between the two means is not significant at the 95% confidence level, then the null hypothesis should not be rejected.
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WILL GIVE BRAINLIEST!!!!
Prove that a line that divides two sides of a triangle proportionally is parallel to the third side. Be sure to create and name the appropriate geometric figures. (10 points)
Answer:
Use the Triangle Proportionality Converse. If the ratios are equal, then the lines are parallel.
A shirt regularly is priced $42. It is on sale 15% off of the regular price. whats is the sale price of the shirt
Answer:35.70
Step-by-step explanation:
Answer:
35.7
Step-by-step explanation:
Regular priced is=. ₹42
off persent is =15%
15/100×42=6.3
42-6.3=35.7
if the growth rate r of a population is positive and remains constant, the number of people added to the population:
The number of persons added to the population rises annually if the population's growth rate, r, is positive and stable.
Given statement,
If the growth rate r of a population is positive and remains constant, the number of people added to the population,
In the given case the solution will be the number of people added to the population " increases each year ".
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A school administrator believes that the mean class GPAs for a given course are higher than the preferred mean of 2.75 at a significance level of 0.05, and checks a randomly chosen sample of 50 classes. Create a histogram, and calculate x¯, the t-statistic, and the p-value.Here is the data for the class GPAS:3.092.732.582.682.842.682.642.622.352.722.632.772.723.032.712.962.743.012.882.682.833.022.832.712.672.792.652.562.782.892.402.382.412.832.863.012.802.842.952.752.932.482.342.972.852.742.843.102.622.77The questions to answer:From the histogram, can normality be assumed? Yes/NoX =T=P=Since the P-value is (greater/less than) than the significance level of 0.05, than the null hypothesis (fails to be rejected/is rejected). (sufficient/insufficient) evidences exists that the new mean GPA is greater than 2.75
The mean GPA is greater than 2.75.
A= 4.0, A- = 3.7, B+ = 3.three, and many others. Total the first-class factors, and overall the credit hours. Divide the overall satisfactory points by means of the overall credit score hours.
Grade Point Average (GPA):Grade point average (GPA) is the measure used to summarize your instructional fulfillment at Griffith. After the e-book of final grades every trimester, your software and career.
GPA is calculated and could be utilized by the college to tell choices, which include the subsequent: educational progression.
Divide the total range of grade factors earned with the aid of the total number of letter-graded units undertaken.
Mean GPA = total / 50
= 2.75.
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y= 5x the table for it
Answer:
The left side represents x, and the right side is y
Step-by-step explanation:
This table is simply going up by 5
What are the coordinates of point BBB on \overline{AC} AC start overline, A, C, end overline such that the ratio of ABABA, B to ACACA, C is 5:65:65, colon, 6? An x- y- coordinate plane where the x and y tick marks scale by one. A line segment has endpoint A at one, negative six and endpoint C at negative four, two.
Answer: The coordinate of C is (2, 1.8)
Let the coordinates of A and C be (2, 1) and (2, 4). If the line AC is divided into the ratio of 2:3. This coordinate of C is given as:
Get the coordinate of X;
X = ax1+bx2/a+b
X = 2(2)+3(2)/2+3
X = (4+6)/5
X = 10/5
X = 2
Get the coordinate of Y:
Y = ay1+by2/a+b
Y = 2(1)+3(4)/2+3
Y = (2+12)/5
Y = 14/5
Y = 1.8
Hence the coordinate of C is (2, 1.8)
Of the 33 students in 10 science, 4 are boys What fraction of the class are girls?
Lets break this down.
We are given the amount of students, which is 33, and so far the amount of boys in the class, which is 4. This can easily be written as [tex]\frac{4}{33}[/tex]. Now, we have a remainder of 29 students (most likely them being girls). This means that the fraction of the class that are girls would be [tex]\frac{29}{33}[/tex].
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Ginny and Bob are both locksmiths.
Ginny uses the function f(x) = 60z+80 to determine the charge to her customers, where x represents the number of hours of
labor.
The table shows what Bobcharges a customer for x hours of labor.
x (hours)
cost ($)
0
60
140
Which locksmith charges less for an initial fee for a service call?
Drag a value or name to the boxes to correctly complete the statements
Ginny initial charge = $80, Bob initial charge =$60 For the initial fee, Bob charges less than Ginny.
What is unit rate?
A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
Given that Ginny charges by uses the function f(x)=60x+80 where x represents the number of hours of labour.
Ginny initial charge = $80
Bob initial charge =$60
Hence, For the initial fee, Bob charges less than Ginny.
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Use Green's theorem and find the work that the force F performs when acting along the complete trajectory counterclockwise. The dimensions of the region R are b = 3 and d3 in ft. The force F is: F = [ay-cx ] lb; use a=2 and c=2. C, RC 0 c, d x
The work that the force F performs is -36.
How to calculate work using Green's Theorem?F = [ay - cx]
a = 2
b = 3
c = 2
d = 3
Green's theorem is theorem about the relationship between a integral line on a simple closed curve C and a double integral of a plane D bounded by C. So, from Green's Theorem we get,
∫Pdx + Qdy = ∫∫([tex]\frac{\partial Q}{\partial x}[/tex]-[tex]\frac{\partial P}{\partial y}[/tex])dA
Put the a and c value into force F equation. So,
F = [2y - 2x]
From this, we get
P = 2y
Q = -2x
[tex]\frac{\partial P}{\partial y}[/tex] = 2
[tex]\frac{\partial Q}{\partial x}[/tex] = -2
So, the integral formula become
∫∫([tex]\frac{\partial Q}{\partial x}[/tex]-[tex]\frac{\partial P}{\partial y}[/tex])dA = ∫∫(-2-2)dA
= -4 dA
Next, we calculate the work
Work = -4 × b × d
= -4 × 3 × 3
= -36
Thus, the work is -36 for the force F performs.
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The length of segment EF is 8 units and the length of segment ED is 10 units. Find the length of segment FD.
Answer:
6
Step-by-step explanation:
DF = [tex]\sqrt{10^2 - 8^2}[/tex]
[tex]\sqrt{10^2-8^2} = \sqrt{100-64}[/tex]
[tex]\sqrt{100-64} = \sqrt{36}[/tex]
[tex]\sqrt{36} =6[/tex]
which graph represents the peicewise function ?
Graph option B is the correct answer.
What is graphical representation?Graphical representation refers to the use of charts and graphs to visually display, analyse, clarify, and interpret numerical data, functions, and other qualitative structures.
Given are function,
y = x+1 ≤0 and y = 3x
The best demonstration of these functions can be seen in graph 2.
Hence, Graph option B is the correct answer.
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to obtain a 99.7% (virtually all-encompassing) confidence interval for the true population proportion, you would add and subtract about how many standard deviations to/from the sample proportion?
We would add and subtract about three standard deviations from the sample proportion to get a 99.7% (nearly full) confidence interval for the real population proportion.
What is a confidence interval?A confidence interval is a range of estimates for an unknown quantity in frequentist statistics.
The most frequent confidence level is 95%, but other levels, such as 90% or 99%, are infrequently used for generating confidence intervals.
To obtain a 99.7% (almost complete) confidence range for the real population proportion, you would add and deduct around three standard deviations from the sample proportion.
A confidence interval is a range of values that are bound by the statistic's mean and that is likely to include an unidentified population parameter.
The proportion of probability, or certainty, that the confidence interval would include the real population parameter when a random sample is drawn numerous times is referred to as the confidence level.
Therefore we would add and subtract about three standard deviations from the sample proportion to get a 99.7% (nearly full) confidence interval for the real population proportion.
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Correct question:
To obtain a 99.7% (virtually all-encompassing) confidence interval for the true population proportion, you would add and subtract about __________ standard deviations to/from the sample proportion.
At a movie theater, the size of popcorn bags decreased 33\frac{1}{3} 3 1 %. If the old bags held 24 cups of popcorn, how much does the new bags hold? At a movie theater, the size of popcorn bags decreased 33\frac{1}{3} 3 1 %. If the old bags held 24 cups of popcorn, how much does the new bags hold?
Answer:56
Step-by-step explanation:
An aircraft is taking a group of skydivers up into the air. Evan is dressed in his parachuting outfit, which brings his mass to a total of 90. 0 kg. The aircraft takes the group to a height of 5000. 00 m before the jump. How much gpe does evan gain before jumping?.
The gravitational potential energy gained by the group of skydivers before jumping is 4,410 kJ.
Explain the term Gravitational Potential Energy?The energy that an item has or acquires when its location changes as a result of being in a gravitational field is known as gravitational potential energy. Gravitational potential energy can be defined as an energy that has a connection to gravitational force or gravity.Gravitational Potential Energy (GPE) is estimated as;
GPE = m×g×h
In which
m = mass of parachuting outfit (kg)
g = acceleration due to gravity (m/s²)
h = height (meters)
Put the values in the formula.
GPE = 90× 9.8× 5000
GPE = 4,410,000 joules
GPE = 4,410 kJ
Thus, the gravitational potential energy gained by the group of skydivers before jumping is 4,410 kJ.
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Kim had 4 chocolate chip cookies and 3 sugar cookies. Kim’s sister ate two of her chocolate chip cookies. Kim shared her remaining cookies with her brothers. How many cookies does one brother get?
Answer:
Your answer would be 1 chocolate chip cookie and 1.5 sugar cookie each.
Step-by-step explanation:
We know that Kim's sister ate two Chocolate Chip cookies, so: [tex]4-2 =2[/tex] and we also know that the rest of the cookies were shared by two people, so:
[tex]3[/tex] ÷ [tex]2 = 1.5[/tex] and [tex]2[/tex] ÷ [tex]2=1[/tex]
Colin loves to eat tuna salad for lunch. His mom is always looking for a bargain on 12-ounce cans of tuna. Today, his local grocery store is offering 4 cans of Sea Star tuna for $3.28 and 2 cans of Ocean's Best tuna for $1.88. Which brand is the better deal?
Answer:
Sea star tuna
Step-by-step explanation:
lapeer flour mills purchased new equipment and made the following expenditures: purchase price $ 64,000 sales tax 5,450 shipment of equipment 890 insurance on the equipment for the first year 590 installation of equipment 1,780
The journal entry for the following transaction will be:
Equipment A/c....Dr. 73120
Prepaid Insurance A/c....Dr. 590
Cash A/c....Cr. 3260
Accounts payable A/c....Cr. 70450
Any cost that has been incurred by the company to make an asset ready to use, is also included in its purchasing price. So, any transportation, legal, or maintenance fee is also included in the asset cost.
The total cost of the new machine = Purchase price + Sales tax + Shipment of machine + Installation of machine
Total cost of new machine = 65,000 + 5,450 + 890 + 1,780
The total cost of the new machine = $73,120
Journal entry for the same:
Equipment A/c....Dr. 73120
Prepaid Insurance A/c....Dr. 590
Cash A/c....Cr. 3260
Accounts payable A/c....Cr. 70450
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a farmer is making a circular pen for his sheep. he has 213.52 yards of fencing to use. what should the diameter of the circle pen be?
The diameter of the circle pen for the sheep of the farmer is 68 yards.
Explain the term circumference of the circle?The distance along a circle's perimeter is referred to as its circumference. In other words, the circumference of a circle is equal to the length of a straight line formed by opening up the circle.The space around a circle is known as its circumference. By calculating the distance required to walk around the globe, we may determine the size of the earth's circumference.The total length of the fencing used for the preparation of the fencing for sheep is 213.52 yards.
Thus,
circumference = 213.52 yards
The formula for the calculation of the circumference of circle is,
circumference = 2πr,
In which,
π = 3.14 and radius r.
Thus,
213.52 = 2πr
r = 213.52 / 2π
r = 34
Diameter = 2 x radius
Diameter = 2 x 34
Diameter = 68 yards.
Thus, the diameter of the circle pen for the sheep of the farmer is 68 yards.
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The circumference of a circle is 22pi cm. What is the area, in square centimeters?
Answer:
Area = 121pi sq cm
Step-by-step explanation:
Circumference is the distance around the circle. The formula for circumference is:
C = pi•d
The question has the info in it that the circumference is 22pi.
C = 22pi
remember,
C = pi•d this means that the circle has a diameter (the d in the formula is diameter) 22cm.
The radius is half the diameter. The diameter is 22cm, so the radius is 11cm.
The formula for the area is:
Area = pi•r^2
= pi•11^2
= pi•121
= 121pi
The area is 121pi sq cm.
Shakira went bowling with her friends. She paid $3 to rent shoes and hen $4.50 for each games of bowling. If she spent a total of $21, how many games did Shakira bowl?
Answer: She bowled 4 games
Step-by-step explanation:
21 - 3 = 18
18 ÷ 4.50 = 4
Answer:
Shakira bowled 4 games.
Step-by-step explanation:
If Shakira paid $3 for rent, we can subtract 3 from 21.
21-3=18.
Now, find out how much 4.50 can go into 18.
First, multiply 4.50 by 2.
4.50x2=9
Now, Since 2 games is $9, multiply 9 by 2.
9x2=18
Now that we found out that 9x2=18, we can see that Shakira bowled 4 games.
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randy wants to attach a 20 foot string of lights to the top of the 19 foot mast of his sailboat. how far from the base of the mast should he attach the end of the light string? round your answer to two decimal places.
The distance between the base of the string and the base of the mast of the sailboat is 6.24.
Here we have to find the distance from the base of the mast that should be attached to the end of the light string.
Data given:
length of the string = 20 foot
length of the mast of the sailboat = 19 foot
Distance between the base of the mast and the light string = [tex]\sqrt{20^{2} - 19^{2} }[/tex]
= [tex]\sqrt{400 - 361}[/tex]
= √39
= 6.245
Therefore the distance between the string and the mast is 6.24.
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two gamblers are playing a coin toss game. gambler a has (n 1) fair coins; b has n fair coins. what is the probability that a will have more heads than b if both flip all their coins
The more coins that are tossed for both gamblers, the less advantageous Gambler A is. But when a few coins are tossed, Gambler A will continue to hold a significant edge.
The binomial distribution;
In probability theory and statistics, the binomial distribution with parameters n and p is used to describe the discrete probability distribution of the number of successes in a set of n independent experiments.
Let X be the number of wins in the first n flips by A, Y be the signal that the last flip by A also wins, and Z be the number of wins in the n flips by B.
As Y is unrelated to X and Z, the following follows:
P(X + Y > Z) = P(Y = 1) P(X ≥ Z) + P(Y = 0) P(X > Z)
= 1/2(P(X = Z) + 2P(X > Z))
P(X > Z) = P(Z > X)
Here,
The less favorable Gambler A is, the more coins are tossed for both players. However, Gambler A will continue to have a sizable advantage even after a few coins are tossed.
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An online furniture store sells chairs for $50 each and tables for $250 each. Every day, the store can ship no more than 36 pieces of furniture and must sell at least $3400 worth of chairs and tables. If 23 chairs were sold, determine all possible values for the number of tables that the store must sell in order to meet the requirements. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.
The values for the number of tables are 9, 10, 11, 12, and 13 the store must sell in order to meet the requirements.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
Let's assume that the number of tables would be x
According to the given information, we can write the inequality would be as:
x + 23 ≤ 36 ....(i)
23 × 50 + 250x ≥ 3400 ....(ii)
Simultaneus (i) and (ii)
9 ≤ x ≤ 13
Therefore, the value will be lies as 9, 10, 11, 12, and 13.
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Leon has already had 4 science quizzes this semester. Going forward, he expects to have 1 quiz per week. Write an equation that shows how the total number of science quizzes, y, depends on the number of weeks that have passed, x.
The equation that shows how the total number of science quizzes, y, depends on the number of weeks that have passed, x, is y = 4 + x.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, Leon has already taken 4 quizzes, and now, he will have 1 quiz per week.
The number of quizzes taken by Leon in x weeks is:
1x
=x
Since Leon already has 4 quizzes, the total number of quizzes after x weeks is:
y = 4 +x
Hence, the equation that shows how the total number of science quizzes, y, depends on the number of weeks that have passed, x, is y = 4 + x.
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13. Amelia has similar cake pans. The
first pan is 10 inches long and 8 inches
wide. The second pan is 14 inches
Tong. How wide is the second pan?
11.2 inches
B.
11 inches
C. 10.8 inches
D. 10.6 inches
A.11.2
B.11 inches
Width of second pan become 11.2 inches
What do you mean by similar figures?
Two figures are said to be similar if they share the same shape. Congruent objects are those that are precisely the same size and shape.
The term "similar figures" refers to two figures that share the same shape but differ in size.
When two figures are comparable, the sign ‘∼’ is used to indicate that they are.
It is given that Amelia has similar cake pans. The first pan is 10 inches long and 8 inches wide. The second pan is 14 inches long.
We know that the ratio of the sides of the similar figures is always equal,
So , [tex]\frac{10}{8}=\frac{14}{x}[/tex]
where x is the width of second pan.
Solve the above equation using cross multiplication we get,
x = [tex]\frac{14 \times 8}{10} = \frac{112}{10}=11.2[/tex]
Hence, width of second pan become 11.2 inches
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geometric sequence with a ratio of 2 and a first term of 1/3.
Answer:
1/3, 2/3, 4/3, 8/3, 16/3, 32/3
or
1/3, 2/3, 1 1/3, 2 2/3, 5 1/3, 10 2/3
Step-by-step explanation: