let x and y be i.i.d. unif(0, 1). (a) compute the covariance of x y and x −y. (b)arex y andx−y independent?

dx/dt = 4+3√3 in the case of the circle with radius 4 and the equation x²+y²=16.

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.

Know more about implicit differentiation here:

https://brainly.com/question/25081524

#SPJ4

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.

To learn more about unit rate form the given link

brainly.com/question/11258929

#SPJ1

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

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

To learn more about the similar figures from the given link.

https://brainly.com/question/4381215

#SPJ1

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.

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.

Know more about the confidence interval here:

https://brainly.com/question/15712887

#SPJ4

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.

The diameter of the circle pen for the sheep of the farmer is 68 yards.

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.

To know more about the circumference of the circle, here

https://brainly.com/question/18571680

#SPJ4

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]

Answer:56

Step-by-step explanation:

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.

To know more about null hypothesis:

https://brainly.com/question/9546890

#SPJ4

Answer:

5

Step-by-step explanation:

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.

Learn more about binomial distribution here;

https://brainly.com/question/29650864

#SPJ4

Graph option B is the correct answer.

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.

For more references on graphical representation, click;

https://brainly.com/question/22070598

#SPJ1

The values for the number of tables are 9, 10, 11, 12, and 13 the store must sell in order to meet the requirements.

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.

Learn more about the inequalities here:

brainly.com/question/20383699

#SPJ1

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:

The gravitational potential energy gained by the group of skydivers before jumping is 4,410 kJ.

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.

To know more about the Gravitational Potential Energy, here

https://brainly.com/question/3120930

#SPJ4

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].

Hope this helps!

Answer:

The left side represents x, and the right side is y

Step-by-step explanation:

This table is simply going up by 5

Answer:

Use the Triangle Proportionality Converse. If the ratios are equal, then the lines are parallel.

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.

Hope this helps! :D

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.

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.

Learn more about equations here:

https://brainly.com/question/10413253

#SPJ1

The work that the force F performs is -36.

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.

Learn more about Green's Theorem here:

brainly.com/question/27549150

#SPJ4

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 ".

To learn more about growth rate click here:

brainly.com/question/29334875

#SPJ4

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]

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)

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.

To know more about the distance refer to the link given below:

https://brainly.com/question/17273444

#SPJ4

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) 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.

Learn more about Mean Grade Point Average:

https://brainly.com/question/16905011

#SPJ4

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.

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:

The constant is of:

3/5.

Meaning that three fifths gallons of water are used each minute.

More can be learned about proportional relationships at https://brainly.com/question/10424180

#SPJ1

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

Learn more about journal entries:

https://brainly.com/question/20421012

#SPJ4

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.

Answer:

Sea star tuna

Step-by-step explanation: