in a circle with a radius of 8 ft, an arc is intercepted by a central angle of 34 radians. what is the length of the arc? responses 2 ft 2 pi, ft 3 ft , 3 pi, ft 6 ft , 6 pi, ft 9 ft

in a circle with a radius of 8 ft, an arc is intercepted by a central angle of 3π4 radians. what is the length of the arc? responses 2π ft 2 pi, ft 3π ft , 3 pi, ft 6π ft , 6 pi, ft 9π ft

Answers

Answer 1

The length of an arc in a circle can be calculated using the formula: arc length = radius * central angle.

In this case, the circle has a radius of 8 ft and the central angle is 3π/4 radians. We need to multiply the radius by the central angle to find the length of the arc. Using the given values, the length of the arc can be calculated as follows: Arc length = 8 ft * (3π/4) = 6π ft. Therefore, the length of the arc intercepted by a central angle of 3π/4 radians in a circle with a radius of 8 ft is 6π ft.

To know more about central angles here: brainly.com/question/29150424

#SPJ11

Related Questions

The important difference to note for the scales of measurement and how they are analyzed is whether they involve Oratios, intervals categories, ration O numbers, categories O numbers, intervals as responses on the scale.

Answers

The important difference to note for the scales of measurement and how they are analyzed is whether they involve ratios, intervals, categories or numbers. The scales of measurement can be divided into four types: nominal, ordinal, interval, and ratio.

Nominal scales use categories or numbers to group data, but these categories or numbers have no inherent order or value. Examples of nominal scales include gender, race, or eye color. Ordinal scales use categories or numbers to group data, but these categories or numbers have a specific order or rank. Examples of ordinal scales include educational attainment, income, or level of agreement on a survey question.

Interval scales use numbers as responses on the scale, but the distance between the numbers is not meaningful. Examples of interval scales include temperature measured in Celsius or Fahrenheit, or IQ scores. Ratio scales use numbers as responses on the scale, but the distance between the numbers is meaningful and there is a true zero point. Examples of ratio scales include height, weight, or income.

In summary, the important difference to note for the scales of measurement and how they are analyzed is whether they involve categories or numbers, and whether the numbers have a specific order or rank, a meaningful distance between them, or a true zero point.

Know more about scales of measurement here:

https://brainly.com/question/13086959

#SPJ11

F(x_1,x_2,x_3) = (y_1,y_2,y_3) Set

(1) x_1/ (x_1 + x_2 + x_3) = y_1

(2) x_2/ (x_1 + x_2 + x_3) = y_2

(3) x_3/ (x_1 + x_2 + x_3) = y_3

1. Prove that F is injective.
2. Without appealing to the Inverse Function Theorem, find the investment directly.
3. Find the domain of F
4. Find the range of F, which is the domain of F^-1.
5. Explain why J_f(x) 6=0 when x € Dom (F)

Answers

1. Proof that F is injective. Suppose that two different elements in the domain of F have the same image; that is, if x and y are elements of the domain of F and F(x)= F(y). We need to show that x=y. Let F(x) = F(y). This means that y1= x1/ (x1 + x2 + x3) = y1, y2= x2/ (x1 + x2 + x3) = y2 and y3= x3/ (x1 + x2 + x3) = y3.Now adding (1), (2), and (3), we have:y1+y2+y3= x1/ (x1 + x2 + x3) + x2/ (x1 + x2 + x3) + x3/ (x1 + x2 + x3)But this is equal to 1, therefore,x1 + x2 + x3= y1 + y2 + y3 = 1, or, equivalently, y1= 1- y2 - y3x1= (1- y2 - y3)(x1 + x2 + x3) = (1-y2 - y3), x2= y2(x1 + x2 + x3) = y2, and x3= y3(x1 + x2 + x3) = y3Thus, we have constructed an element of the domain of F, with different elements of the domain, that have the same image. Therefore, F is injective.

2. Find the investment directly without appealing to the Inverse Function Theorem. F(x1,x2,x3) = (y1,y2,y3)So, x1= (1- y2 - y3), x2= y2, and x3= y3Thus, the inverse of F is F-1(y1,y2,y3)= ((1-y2-y3),y2,y3)3. The domain of F. The domain of F is the set of all three-tuples, F(x1,x2,x3) where 0 ≤ xi ≤ ∞, and where at least one xi is positive. That is, Dom (F)={(x1,x2,x3)|x1≥0, x2≥0, x3≥0 and (x1,x2,x3)≠(0,0,0)}4. The range of F, which is the domain of F-1. The range of F is the set of all three-tuples, F(y1,y2,y3) where 0 ≤ yi ≤ 1, and where at least one yi is positive.

That is, Rng(F)={(y1,y2,y3)|y1≥0, y2≥0, y3≥0 and y1+y2+y3=1}5. We have J_f(x) = ∣∣ ∂(y1,y2,y3) /∂(x1,x2,x3) ∣∣= ∣∣ ∂y1/∂x1 ∂y1/∂x2 ∂y1/∂x3 ∂y2/∂x1 ∂y2/∂x2 ∂y2/∂x3 ∂y3/∂x1 ∂y3/∂x2 ∂y3/∂x3 ∣∣= ∣∣ (1 / (x1 + x2 + x3) ) - (x1/ (x1 + x2 + x3)2) - (x1/ (x1 + x2 + x3)2) 0 1 / (x1 + x2 + x3) - (x2/ (x1 + x2 + x3)2) 0 0 1 / (x1 + x2 + x3) - (x3/ (x1 + x2 + x3)2) ∣∣= (1 / (x1 + x2 + x3) )((1 - y2 - y3) (1 - y2 - y3 - y3) - y2 (1 - y2 - y3) - y3(1 - y2 - y3)) = (1 / (x1 + x2 + x3) )((1 - y2 - y3 - y2 + 2y2y3 + y2 - y3 - 2y2y3 + y3 - y2y3 - y3 + y2y3)) = 1 / (x1 + x2 + x3) which is non-zero in the domain of F. Therefore, J_f(x) ≠ 0 when x ∈ Dom (F).

Know more about Inverse Function Theorem:

https://brainly.com/question/31423480

#SPJ11

Please Help — Neil is going to a bookstore 45 miles away. The bridge was closed on the way back, so
he had to take an alternate route and had to drive 15 mph slower, which make the trip
back take 7 minutes longer. How fast was he going on the way to the bookstore??

Answers

I agree to the first person

8^15÷8^−3 it needs to like this 43^5 I can't find out the answer

Answers

Answer:

Hello!

The answer is 8^18.

Step-by-step explanation:

Answer:

8^12

Step-by-step explanation:

Exponents are confusing at first. You subtract them when dividing, and add them when multiplying, if the base number is the same.

Picture 8 to the 15th as a numerator of:

8x8x8x8x8x8x8x8x8x8x8x8x8x8x8 over a denominator of

8x8x8

To solve that, you'd cancel out 3 of the top 8s and the three bottom 8s, marked in bold to be easier to see. This leaves you with

8^12

Does that help?

Happy to answer questions.

What is the line of symmetry for the parabola whose equation is y = x2 + 10x + 25?

A-x = -5
B-x = 5
C-x = -10

Answers

Answer:

x = -5

Step-by-step explanation:

Please write this as y = x^2 + 10x + 25. Here the coefficients are {1, 10, 25}.

The equation of the axis of symmetry is x = -b/[2a], which here is

x = -10 / [2*1] = -5

Select all the properties of a right triangle.

A. Has a Right Angle
B. Has 1 Obtuse Angle
C. Has Parallel Lines
D. Has Perpendicular Lines
E. Has 3 Acute Angles

If u are an Expert PLzzz Answer Thisss!

Answers

Answer:

Sorry sis don't know the meaning

A bicycle has a listed price of $615.98 before tax. If the sales tax rate is 9.75%, find the total cost of the bicycle with sales tax included. Round your answer to the nearest cent, as necessary.

Answers

Step 1
Write your problem.
537.95 x 9.5% = ?

Step 2
Convert the % to a decimal:
9.5% to 0.095

Step 3
Rewrite the problem with decimal replacing the percentage.

Now the problem looks like this:
537.95 x 0.095 = 51.11
This problem gives the amount of the tax.

Step 4
Add the original price with the tax amount:
537.95 + 51.11 = $589.06 (total cost)

Organisms are present in ballast water discharged from a ship according to a Poisson process with a concentration of 10 organisms/m3 (the article "Counting at Low Concentrations: The Statistical Challenges of Verifying Ballast Water Discharge Standards"† considers using the Poisson process for this purpose).
For what amount of discharge would the probability of containing at least 1 organism be 0.993? (Round your answer to two decimal places.)

Answers

The amount of discharge for which the probability of containing at least 1 organism is 0.993 is approximately 0.14 m³.

To find the amount of discharge for which the probability of containing at least 1 organism is 0.993, we can use the Poisson distribution formula. The Poisson distribution describes the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence.

In this case, the concentration of organisms in the ballast water is given as 10 organisms/m³. Let's denote λ as the average rate of occurrence, which is equal to the concentration in this case, λ = 10 organisms/m³.

The Poisson distribution formula is:

P(X ≥ k) = 1 - P(X < k) = 1 - e^(-λ) * (λ^0/0! + λ^1/1! + λ^2/2! + ... + λ^(k-1)/(k-1)!)

We want to find the amount of discharge (let's call it x) for which P(X ≥ 1) = 0.993. Plugging in the values into the formula, we have:

0.993 = 1 - e^(-10) * (10^0/0! + 10^1/1!)

Simplifying the equation, we have:

0.993 = 1 - e^(-10) * (1 + 10)

Now we can solve for e^(-10) using logarithms:

e^(-10) = 1 - 0.993 / (1 + 10)

e^(-10) ≈ 0.0045

Substituting this back into the equation, we have:

0.993 = 1 - 0.0045 * (1 + 10)

Simplifying further, we get:

0.993 = 1 - 0.0045 * 11

Now, let's solve for the discharge amount x:

0.993 = 1 - 0.0495x

0.0495x = 1 - 0.993

0.0495x ≈ 0.007

x ≈ 0.007 / 0.0495

x ≈ 0.14 m³

Therefore, the amount of discharge for which the probability of containing at least 1 organism is 0.993 is approximately 0.14 m³.

Learn more about probability here

https://brainly.com/question/25839839

#SPJ11

find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 3e−x, y = 3, x = 2; about y = 6 v =

Answers

The volume (v) of the solid obtained by rotating the region about y = 6 is approximately 339.02 cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curves y = 3e^(-x), y = 3, and x = 2 about the line y = 6, we can use the method of cylindrical shells.

First, let's plot the curves and the line of rotation to visualize the region:

| y = 3e^(-x)

| _______

|__________| y = 3

| |

| |___ x = 2

y=6|_____________________

We can see that the line y = 6 is above the region bounded by the curves. To find the volume, we will integrate the circumference of each cylindrical shell multiplied by its height.

The height of each cylindrical shell is given by the difference between the line y = 6 and the curve y = 3e^(-x), which is 6 - 3e^(-x).

The radius of each cylindrical shell is given by the distance from the line y = 6 to the x-axis, which is 6 - 0 = 6.

The differential volume element is given by dV = 2πrh dx, where r is the radius and h is the height.

Therefore, the volume of the solid can be obtained by integrating this expression over the range of x from 0 to 2:

V = ∫[0,2] 2π(6 - 3e^(-x))(6) dx

Simplifying the expression:

V = 12π ∫[0,2] (6 - 3e^(-x)) dx

V = 12π [6x + 3e^(-x)] evaluated from 0 to 2

V = 12π [(12 + 3e^(-2)) - (0 + 3e^(-0))]

V = 12π (12 + 3e^(-2) - 3)

V = 12π (9 + 3e^(-2))

V ≈ 339.02 cubic units

Therefore, the volume (v) of the solid obtained by rotating the region about y = 6 is approximately 339.02 cubic units.

Learn more about volume here

https://brainly.com/question/27710307

#SPJ11

PLEASE HELP ME OUT! QUICK POINTS FOR YOU!

All information needed can be found in the image below
Thank you in advance.

Answers

Answer:

5π

Step-by-step explanation:

just need to find half of the circumference

question in screenshot

Answers

Answer:

Step-by-step explanation:

use pythagorean theorm

√(8^2+6^2) = 10

Student Council is selling T-shirts to raise money for new volleyball equipment. There is a fixed cost of
$200 for producing the T-shirts, plus a variable cost of $5 per T-shirt made. Council has decided to sell
the T-shirts for $8 each.

A. Write an equation to represent the total cost, C, as a function of the number, n, of T-shirts
produced.

B. Write an equation to represent the revenue, R, as a function of the number, n, of T-shirts
produced

C. Profit, P, is the difference between revenue (R(n)) and expenses (C(n)). Develop an algebraic
function to model the profit.

D. How many T-shirts does the Student Council have to sell to "break even," make a $0 profit?

Answers

Answer:

It is A

Write an equation to represent the total cost, C, as a function of the number, n, of T-shirts

produced.

Step-by-step explanation:

PLEASE HELP!
Write down the Equation of the following lines:

1)parallel to y=2x-1 and passing through (1, 8)

Answers

Answer:

y=2x+6

Step-by-step explanation:

We use this following formula to find the equation:

[tex]y-y_{1} =m(x-x_{1} )[/tex]

Now, we substitute the values in [tex]y_{1}[/tex] and [tex]x_{1}[/tex] :

[tex]y-8=2(x-1)[/tex]

Distribute the 2 inside the parentheses:

[tex]y-8=2x-2[/tex]

Now add 8 to both sides:

[tex]y=2x+6[/tex] is your answer.

Step-by-step explanation:

y=mx+b

m=slope

b=y-intercept

y=2x-1

2=slope

-1=y intercept

NOTE: parallel lines have the same slope

and we put the point (1,8) into y=mx+b with (x,y)

8=1m+b

now we put in 2 for the slope

8=1(2)+b

6=b

2=m

now insert that back into y=mx+b

y=2x+6

and that is the line that is parallel to y=2x-1 and passes through (1,8)

Hope that helps :)

12/5 divided by 21/10

Answers

exact form is 8/7 , as a decimal its 1.142 and mixed number form its 1 1/7

OK a quarter steam covers a 100' square feet how many courts should you buy to stay in the wheelchair ramp

Answers

Answer:

He should buy about 2 quart of stain

Step-by-step explanation:

Find the diagram attached

First we need to find the area of the given ramp

The ramp consists of two identical triangles, a larger and small rectangles

Since area of triangle = 1/2 * base * height

Area of the identical triangles = 1/2 * 25ft * 25/12 ft (Note that 1ft = 12in)

Area of the 2 identical triangles = 2* 625/24ft² = 625/12 ft²

Area of the large rectangle = Length * Width

Area of the large rectangle = 25 1/12 * 5

Area of the large rectangle = 301/12 * 5

Area of the large rectangle = 1505/12 ft²

Area of the small rectangle = 25/12 * 5

Area of the small rectangle = 125/12 ft²

Area of the figure = 625/12 + 1505/12 + 125/12

Area of the figure = (625+1505+125)/12

Area of the figure = 2255/12

Area of the figure = 187.917

Area of the figure = 187.917ft²

Since a quarter steam covers a 100' square fee, then;

1 quarter = 100ft²

x = 187.917ft²

Cross multiply

100 * x = 187.917

100x =187.917

x = 187.917/100

x = 1.87917

x ≈ 2

Hence he should buy about 2 quart of stain

Can someone please help me please I really need help please answer it correctly

Answers

Answer:

Princeton Florist

Let the total charge is y, the number of small arrangements is x.

Total charge will be:

y = 13x + 47Chad's Flowers

Total charge will be:

y = 17x + 35

Since the total charge is same in both shops, we have:

13x + 47 = 17x + 35

Solve for x:

17x - 13x = 47 - 354x = 12x = 3

Total cost is:

13*3 + 47 = 39 + 47 = 86

Small arrangements = 3, cost = $86

What is 0.0003246 expressed in scientific notation?
A.
32.46
×
10
−
5
B.
3.246
×
10
−
4
C.
3.246
×
10
4
D.
32.46
×
10
5

Answers

Answer:

Step-by-step explanation:

the notation answer would also be 3.246 × 10-4 i believe :)

Find the mean of the following probability distribution? Round your answer to one decimal. P(2) 0 0.0017 1 0.3421 2 0.065 3 0.4106 4 0.1806 mean = ___

Answers

The mean of the given probability distribution is 3.4.

To find the mean of a probability distribution, we multiply each value of x by its corresponding probability and then sum them up. Using the provided data:

P(2) 0

P(1) 0.0017

P(2) 0.3421

P(3) 0.065

P(4) 0.4106

P(5) 0.1806

mean = 2(0) + 1(0.0017) + 2(0.3421) + 3(0.065) + 4(0.4106) + 5(0.1806)

= 0 + 0.0017 + 0.6842 + 0.195 + 1.6424 + 0.903

= 3.4263

Therefore, the mean of the given probability distribution is approximately 3.4 (rounded to one decimal place).

To learn more about probability distribution: https://brainly.com/question/23286309

#SPJ11

I ask for your help fellow strugglers

Answers

Answer: C is false

Step-by-step explanation: If B is correct and C is saying otherwise that must mean it's the only false choice :) brainliest would be appreciated :)

An auto maker estimates that the mean gas mileage of its sports utility vehicle is at least 20 miles per gallon. A random sample of 36 such vehicles had a mean of 18 miles per gallon and a standard deviation of 5 miles per gallon. At α = .01 can you reject the auto maker's claim?

Answers

Answer:

Yes, we reject the auto maker's claim.

Step-by-step explanation:

H0 : μ ≥ 20

H1 : μ < 20

Sample mean, xbar = 18 ;

Sample size, n = 36

Standard deviation, s = 5

At α = 0.01

The test statistic :

(xbar - μ) ÷ s /sqrt(n)

(18 - 20) ÷ 5/sqrt(36)

-2 /0.8333333

= - 2.4

Pvalue from test statistic : Pvalue = 0.00819

Pvalue < α

0.00819 < 0.01

Hence, we reject the Null

He points (2, -3) and (2,5) represent the locaons of two towns on a coordinate grid, where 1 unit is equal to 1 mile. What is the distance, in miles, between the two towns?

Answers

Answer:

Distance between the points is 8 miles.

Step-by-step explanation:

Distance between tow points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is defined by,

Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Distance between the given points (2, -3) and (2, 5) will be,

Distance = [tex]\sqrt{(2-2)^2+(-3-5)^2}[/tex]

= 8 units

Since, 1 unit = 1 mile

Therefore, distance between these points will be 8 miles.

PLEASE HELP ASAP
Find the surface area and volume of the cylinder below:

Answers

Answer:

Surface Area: 848.23

Volume: 1727.88

Step-by-step explanation:

I know dis im in 8th grade iz ez!

I need help with this please help me.

Answers

Answer:

a) $93, $117.80, $86.80, $68.20

b) $365.80

Step-by-step explanation:

Add 12 hours to each p.m. time to make the subtraction of hours easier.

Also, use decimal numbers to do the subtraction. Remember that 0:30 means 30 minutes which is 0.5 hour, so 7:30 is the same as 7.5 as a decimal.

Monday: 8:00 to 15:30

15:30 - 8:00 = 1.5 - 8 = 7.5 hours

7.5 hours * $12.40/h = $93

Wednesday: 7:30 to 17:00

17:00 - 7:30 = 17 - 7.5 = 9.5 hours

9.5 hours * $12.40/h = $117.80

Friday: 9:00 to 16:00

16:00 - 9:00 = 16 - 9 = 7 hours

7 hours * $12.40/h = $86.80

Saturday: 10:30 to 16:00

16:00 - 10:30 = 16 - 10.5 = 5.5 hours

5.5 hours * $12.40/h = $68.20

b) Add all the daily amounts above.

$93 + $117.80 + $86.80 + $68.20 = $365.80

A game has a 10-sided die. What is the probability of rolling a number less than 3 or an odd number? All answers should be in FRACTION form ONLY.

Answers

The probability of rolling a number less than 3 or an odd number is 3/5 in fraction form.

To compute the probability of rolling a number less than 3 or an odd number, we need to calculate the probability of each event separately and then subtract the probability of their intersection.

The probability of rolling a number less than 3 is 2/10, as there are two numbers (1 and 2) that satisfy this condition out of the ten possible outcomes.

The probability of rolling an odd number is 5/10, as there are five odd numbers (1, 3, 5, 7, and 9) out of the ten possible outcomes.

To compute the probability of their intersection (rolling a number less than 3 and an odd number), we observe that there is only one number (1) that satisfies both conditions.

Therefore, the probability of their intersection is 1/10.

To compute the probability of rolling a number less than 3 or an odd number, we sum the probabilities of each event and subtract the probability of their intersection:

Probability of rolling a number less than 3 or an odd number = (2/10) + (5/10) - (1/10) = 6/10 = 3/5.

Therefore, the probability of rolling a number less than 3 or an odd number is 3/5.

To know more about probability refer here:

https://brainly.com/question/32117953#

#SPJ11

OMG HELP PLS IM PANICKING OMG OMG I GOT A F IN MATH AND I ONLY HAVE 1 DAY TO CHANGE MY GRADE BECAUSE TOMORROW IS THE FINAL REPORT CARD RESULTS AND I DONT WANNA FAIL PLS HELP-
AND CAN ANYONE PLS DRAW ME THE ANSWERS I CANT UNDERSTAND ANYTHING PLS I BEG U ILL GIVE U BRAINLEST

Answers

a. You need to compare 2/5, 1/2 and 3/4
2/5= .4
1/2= .5
3/4=.75
Therefore the bucket that is 2/5 full is less than 1/2 full

Answer:

The 2/5th’s bucket is the answer to question one.

for the second one, draw a square or rectangle and divide one of them by 5 (draw 4 lines in it) and fill in two of those lines.

the second fraction, draw another rectangle and draw 3 lines on the inside of it, filling in 3. (you’re creating a visual representation of the fractions. you can also look up ‘3/4 picture’ and ‘2/5 picture’ and copy off the internet.

Step-by-step explanation:

What is the mean? 2, 4, 7, 5, 8, 10
Remember- add all the
numbers, and then divide by the total
amount of numbers
6
9
5
36

Answers

Answer:

Step-by-step explanation:

2+4+7+5+8+10

=36÷6

$297.89 with a 9.5% tax

Answers

The exact answer is 326.18955. So about $316.19

A stem and leaf plot titled High Temperatures in degrees Fahrenheit. The stems are 4, 5, 6, 7. The first column of leaves are 9, 2, 0, 2. The second column of leaves are blank, 4, 1, 3. The third column of leaves are blank, 4, blank, blank. The fourth column of leaves are blank, 6, blank, blank. The fifth column of leaves are blank, 8, blank, blank. The stem and leaf plot shows high temperatures recorded each day at the beginning of the month. Which temperature occurs the most frequently

Answers

Answer:

The temperature with the highest frequency is 54

Step-by-step explanation:

Given

The above data

Required

The temperature with the highest frequency

The first step, is to plot the stem and leaf plot.

[tex]\begin{array}{cc}{4} & {9\ \ } & {5} & {2\ 4\ 4\ 6\ 8} & {6} & {0\ 1\ } & {7} & {2\ 3\ } \ \end{array}[/tex]

Next, is to identify the leaf with the highest frequency.

The leaf is 4 (with frequency 2)

Next, is to identify the accompanying stem of the leaf

The stem is 5

Hence, the temperature with the highest frequency is 54

Answer:

Step-by-step explanation:

edg 2021

If Tony wants to add a 22% tip to his $35 charge from the barbershop, how much should he add?

Answers

Answer:

Tony should add $7.70

Step-by-step explanation:

22% = 0.22

0.22 x $35 = $7.70

62.8571% im not quite sure its been a while

X and Y are two continuous random variables whose joint pdf f(x, y) = kr² over the region 0≤x≤1 and 0 ≤ y ≤ 1, and zero elsewhere. Calculate the covariance Cov(X,Y).

Answers

The covariance Cov(X, Y) can be calculated for the given joint probability density function (pdf) f(x, y) = kr² over the region 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1.

To calculate the covariance Cov(X, Y), we need to determine the joint probability density function (pdf) of X and Y and apply the formula for covariance.

First, we need to find the constant k by integrating the joint pdf over its entire range to ensure it integrates to 1 (since it represents a probability density function).

The integral of f(x, y) over the region 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 is given by:

∫∫ f(x, y) dy dx = ∫∫ kr² dy dx.

Integrating with respect to y first, we get:

∫[0,1] ∫[0,1] kr² dy dx = k∫[0,1] r² [y=0 to y=1] dx

= k∫[0,1] r² dx

= k[r²x] [x=0 to x=1]

= k(r² - 0)

= kr².

Since the integral of the joint pdf over its entire range equals 1, we have kr² = 1, which implies k = 1/r².

Now, we can calculate the covariance Cov(X, Y) using the formula:

Cov(X, Y) = E[XY] - E[X]E[Y],

where E denotes the expected value.

Since X and Y are continuous random variables with a uniform distribution over the range [0,1], we have E[X] = E[Y] = 1/2.

To calculate E[XY], we integrate the product XY over the range [0,1] for both x and y:

E[XY] = ∫∫ xy f(x, y) dy dx

= ∫∫ xy kr² dy dx

= k∫∫ xyr² dy dx

= k∫[0,1] ∫[0,1] xyr² dy dx.

Integrating with respect to y first, we get:

E[XY] = k∫[0,1] ∫[0,1] xyr² dy dx

= k∫[0,1] [(1/2)xr² [y=0 to y=1]] dx

= k∫[0,1] (1/2)xr² dx

= (k/2)∫[0,1] xr² dx

= (k/2)[(1/3)x³r² [x=0 to x=1]]

= (k/2)(1/3)r²

= (1/2)(1/3)r²

= 1/6r².

Finally, we can calculate the covariance:

Cov(X,Y) = E[XY] - E[X]E[Y]

= 1/6r² - (1/2)(1/2)

= 1/6r² - 1/4.

Therefore, the covariance Cov(X, Y) for the given joint pdf f(x, y) = kr² over the region 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 is 1/6r² - 1/4.

Learn more about covariance here:

https://brainly.com/question/32517036

#SPJ11

Other Questions