Suppose that the length of a side of a cube X is uniformly distributed in the interval 9

Answers

Answer 1

Answer:

[tex]f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.[/tex]

Step-by-step explanation:

Given

[tex]9 < x < 10[/tex] --- interval

Required

The probability density of the volume of the cube

The volume of a cube is:

[tex]v = x^3[/tex]

For a uniform distribution, we have:

[tex]x \to U(a,b)[/tex]

and

[tex]f(x) = \left \{ {{\frac{1}{b-a}\ a \le x \le b} \atop {0\ elsewhere}} \right.[/tex]

[tex]9 < x < 10[/tex] implies that:

[tex](a,b) = (9,10)[/tex]

So, we have:

[tex]f(x) = \left \{ {{\frac{1}{10-9}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.[/tex]

Solve

[tex]f(x) = \left \{ {{\frac{1}{1}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.[/tex]

[tex]f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.[/tex]

Recall that:

[tex]v = x^3[/tex]

Make x the subject

[tex]x = v^\frac{1}{3}[/tex]

So, the cumulative density is:

[tex]F(x) = P(x < v^\frac{1}{3})[/tex]

[tex]f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.[/tex] becomes

[tex]f(x) = \left \{ {{1\ 9 \le x \le v^\frac{1}{3} - 9} \atop {0\ elsewhere}} \right.[/tex]

The CDF is:

[tex]F(x) = \int\limits^{v^\frac{1}{3}}_9 1\ dx[/tex]

Integrate

[tex]F(x) = [v]\limits^{v^\frac{1}{3}}_9[/tex]

Expand

[tex]F(x) = v^\frac{1}{3} - 9[/tex]

The density function of the volume F(v) is:

[tex]F(v) = F'(x)[/tex]

Differentiate F(x) to give:

[tex]F(x) = v^\frac{1}{3} - 9[/tex]

[tex]F'(x) = \frac{1}{3}v^{\frac{1}{3}-1}[/tex]

[tex]F'(x) = \frac{1}{3}v^{-\frac{2}{3}}[/tex]

[tex]F(v) = \frac{1}{3}v^{-\frac{2}{3}}[/tex]

So:

[tex]f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.[/tex]


Related Questions

Can someone help me with this problem

Answers

Answer:

3/11

Step-by-step explanation:

the answer is 9/110 zzzz

At the city museum, child admission is S5.80 and adult admission is $9.20. On Monday, twice as many adult tickets as child tickets
were sold, for a total sales of $895.40. How many child tickets were sold that day?

Answers

[tex]You can call c the number of children and a for adults; you get:5.20c+8.50a=1097.60anda=4c meaning that the number of adults was four times the children.Substituting this value of a into the first equation we get:5.2c+8.5(4c)=1097.65.2c+34c=1097.6rearranging:c=1097.639.2=28and so:a=4c=4⋅28=112[/tex]

I got:  28  children and  112  adults.

how old is sherif now ? ahmed is eight years younger than sherif in seven years, the sum of their ages will be 7/10 th of 100​

Answers

Answer:

32year

Step-by-step explanation:

let Ahmed be x years then sheriff will be x+8

in 7years time

sheriff will be x+8+7=x+15

Then Ahmed will be x+7

sum of their ages will be 7\10×100=70years

x+15+x+7=70

collect like terms

2x+22=70

2x=70-22

2x/2=48/2

x=24years

Sheriff=24+8

32years

6
1
10 points
Find the probability that a randomly selected person's birthday is not in May. Ignore leap years.
31
334
31
365
334
365
11
2
3
12
Previous

Answers

Answer:

c. [tex]\frac{334}{365}[/tex]

Step-by-step explanation:

May has 31 days and a normal year is 365 days, so the probability is [tex]\frac{31}{365}[/tex]

The probability that isn't in May is: 1 - [tex]\frac{31}{365}[/tex] = [tex]\frac{334}{365}[/tex]

Please help me answer this question if you have time

Answers

Answer:

C: [tex]\frac{7x}{4} + 5y[/tex]

Step-by-step explanation:

1. Realize that 12 inches is 1 feet and 36 inches is 1 yard.

2. Multiply it so that both are inches.

[tex]\frac{5y}{12} * 12 = 5y[/tex]

[tex]\frac{7x}{144} * 36 = \frac{7x}{4}[/tex]

3. Add together [tex]\frac{7x}{4} + 5y[/tex]

Answer:

C.

Step-by-step explanation:

I also recommend to just search these things on the internet. it would be much faster.

1 ft = 12 in

1 yd = 3 ft = 3×12 = 36 in

so, we need to multiply a given number of ft by 12, and a given number of yards by 36 to get the inches.

5y/12 × 12 = 5y

7x/144 × 36 = 7x/4

that is all there is to it.

The volume of a boys' basketball is 434 cubic inches. Dan would like to get a ball
with half the volume for his son. What is be the diameter of the ball that Dan will buy
for his son?
A 9.4 inches
B 4.7 inches
C 3.7 inches
D 7.4 inches

Answers

Answer:

The correct answer is A. 9.4 inches.

Step-by-step explanation:

Given that the volume of a boys' basketball is 434 cubic inches, and Dan would like to get a ball with half the volume for his son, to determine what is the diameter of the ball that Dan will buy for his son, the following calculation has to be done, knowing that the volume of a sphere is four thirds multiplied by pi multiplied by the radius cubed:

4/3 x 3.14 x X ^ 3 = 434

4.186 x X ^ 3 = 434

X ^ 3 = 434 / 4.186

X = 3√ 103.662

X = 4.7

In turn, since the radius of a sphere is equal to half its diameter, the diameter of the basketball is 9.4 inches (4.7 x 2).

Question 7 of 13
Find the solution to the system of equations,
5x - 3y - Z= 6
-4x + 5y + z = 6
Х
+ 3z = 10

Answers

Answer:

D. x = 4,  y = 4, z = 2

Step-by-step explanation

Plugged in given answers as trying to substitute is impossible, already tried all combinations

URGENT HELP

The gradient of the tangent to the curve y = ax + bx^3 at the point (2, -4) is 6.
Determine the unknowns a and b.
a=?
b=?

Answers

Answer:

a = -6

b = 1

Step-by-step explanation:

The gradient of the tangent to the curve y = ax + bx^3, will be:

dy/dx = a + 3bx²

at (2, -4)

dy/dx = a+3b(2)²

dy/dx = a+12b

Since the gradient at the point is 6, then;

a+12b = 6 ....1

Substitute x = 2 and  y = -4 into the original expression

-4 = 2a + 8b

a + 4b = -2 ...2

a+12b = 6 ....1

Subtract

4b - 12b = -2-6

-8b = -8

b = -8/-8

b = 1

Substitute b = 1 into equation 1

Recall from 1 that a+12b = 6

a+12(1) = 6

a = 6 - 12

a = -6

Hence a = -6, b = 1

The sum of two binomials is 12x2 − 5x. If one of the binomials is x2 − 2x, the other binomial is:

1. 11x2 − 7x.
2. 12x2 − 3x.
3. 11x2 − 3x.
4. None of these choices are correct.

Answers

Answer:

C. 11x² - 3x

Step-by-step explanation:

(12x² - 5x) - (x² - 2x)

12x² - 5x - x² + 2x

12x - x² - 5x + 2x

11x² - 3x

https://www.drfrostmaths.com/util-generatekeyskillpic.php?name=AnglePoint4&width=400&params=%5B61%2C0%2C%22y%22%2C4%5D

Answers

Answer:

Complementary angle

<y+61° =90°

<y = 90°- 61°

<y =29°

I Hope this helps.

simplify
log(125) + log(625) / log(25) - log(5)​

Answers

Answer:

3.39794000867

Step-by-step explanation:

first add log 125 and 625 and divide the answer by log 25 and minus the answer by 5

Answer:

The answer is 7.

distance between 4, -4 and -7, -4

Answers

Step-by-step explanation:

here's the answer to your question

Answer: Distance = 11

Step-by-step explanation:

Concept:

Here, we need to know the idea of the distance formula.

The distance formula is the formula, which is used to find the distance between any two points.

If you are still confused, please refer to the attachment below for a clear version of the formula.

Solve:

Find the distance between A and B, where:

A (4, -4)B (-7, -4)

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

[tex]Distance=\sqrt{(4+7)^2+(-4+4)^2}[/tex]

[tex]Distance=\sqrt{(11)^2+(0)^2}[/tex]

[tex]Distance=\sqrt{121+0}[/tex]

[tex]Distance=\sqrt{121}[/tex]

[tex]Distance=11[/tex]

Hope this helps!! :)

Please let me know if you have any questions

simplify 2√3 x 3√8
i’ll give u brainiest pls

Answers

Answer:

[tex]12 \sqrt{6} [/tex]

Step-by-step explanation:

[tex]2 \sqrt{3} \times 3 \sqrt{8} \\ (2 \times 3) \sqrt{(3 \times 8)} \\ 6 \sqrt{24} \\( 6 \times 2) \sqrt{6 } \\ 12 \sqrt{6} [/tex]

Suppose 5 men and 7 women are on a crowded elevator. At the next floor, four people get off the elevator. Find the probability that three are women.

0.010

0.354

0.424

0.25

Answers

Answer:

B. 0.354

Step-by-step explanation:

Combination of 4 out of 5 + 7 = 12 is:

12C4 = 12!/8!4! = 495

Combination of 1 man and 3 women is:

5C1*7C3 = 5*7!/4!3! = 5*35 = 175

Required probability:

P(3W) = 175/495 ≈ 0.353

Correct choice is B

Hi- how do we calculate the distance from C to D? Thanks so much!

Answers

Answer:

CD=20

Step-by-step explanation:

Use the pythagorean theorem: a²+b²=c²

(20√2)²-20²=a²

400(2)-400

800-400=400

√400=20

The thicknesses of 81 randomly selected aluminum sheets were found to have a variance of 3.23. Construct the 98% confidence interval for the population variance of the thicknesses of all aluminum sheets in this factory. Round your answers to two decimal places

Answers

Answer:

The confidence interval for the population variance of the thicknesses of all aluminum sheets in this factory is Lower limit = 2.30, Upper limit = 4.83.

Step-by-step explanation:

The confidence interval for population variance is given as below:

[tex][(n - 1)\times S^{2} / X^{2} \alpha/2, n-1 ] < \alpha < [(n- 1)\times S^{2} / X^{2} 1- \alpha/2, n- 1 ][/tex]

We are given

Confidence level = 98%

Sample size = n = 81

Degrees of freedom = n – 1 = 80

Sample Variance = S^2 = 3.23

[tex]X^{2}_{[\alpha/2, n - 1]} = 112.3288\\\X^{2} _{1 -\alpha/2,n- 1} = 53.5401[/tex]

(By using chi-square table)

[(n – 1)*S^2 / X^2 α/2, n– 1 ] < σ^2 < [(n – 1)*S^2 / X^2 1 -α/2, n– 1 ]

[(81 – 1)* 3.23 / 112.3288] < σ^2 < [(81 – 1)* 3.23/ 53.5401]

2.3004 < σ^2 < 4.8263

Lower limit = 2.30

Upper limit = 4.83.

Find the x- and y-intercepts of the following line: 4x − 3y = 12

Answers

Answer:

x-intercept: (3,0)

y-intercept: (0,-4)

Step-by-step explanation:

To find the x and y-intercepts, we first need to understand what they are. X and y-intercepts are points on the line that passes through the x-axis and y-axis. When a point is an x-intercept, it passes through the x-axis. This means the x-coordinate is an integer, while the y-coordinate is always 0. This can be denoted by (x,0). When a point is a y-intercept, it passes through the y-axis. This means the y-coordinate is an integer, while the x-coordinate is always 0. This can be denoted by (0,y).

Now that we know what x and y-intercepts are, we can plug in x=0 and y=0 to find the intercepts.

x-intercept

4x-3y=12            [plug in y=0]

4x-3(0)=12          [multiply]

4x-0=12              [add both sides by 0]

4x=12                 [divide both sides by 4]

x=3

---------------------------------------------------------------------------------------------------------

y-intercept

4x-3y=12            [plug in x=0]

4(0)-3y=12         [multiply]

0-3y=12             [subtract both sides by 0]

-3y=12               [divide both sides by -3]

y=-4

Therefore, the x-intercept is (3,0) and y-intercept is (0,-4).

I need help ASAP!!!!

Answers

A is the right answer try that one

HELP ASAP!!!!!!
Thank you so much

Answers

x_1=-1x2=7y1=1y2=7m:n=3:5

We know

[tex]\boxed{\sf P(x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)}[/tex]

[tex]\\ \sf\longmapsto p(x,y)=\left(\dfrac{3(7)+5(-1)}{3+5},\dfrac{3(7)+5(1)}{3+5}\right)[/tex]

[tex]\\ \sf\longmapsto p(x,y)=\left(\dfrac{21-5}{8},\dfrac{21+5}{8}\right)[/tex]

[tex]\\ \sf\longmapsto p(x,y)=\left(\dfrac{16}{8},\dfrac{26}{8}\right)[/tex]

[tex]\\ \sf\longmapsto p(x,y)=\left(2,\dfrac{13}{4}\right)[/tex]

m:n=3:5

We know

[tex]\boxed{\sf M(x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)}[/tex]

[tex]\\ \sf\longmapsto M(x,y)=\left(\dfrac{3(7)+5(-1)}{3+5},\dfrac{3(7)+5(1)}{3+5}\right)[/tex]

[tex]\\ \sf\longmapsto M(x,y)=\left(\dfrac{21-5}{8},\dfrac{21+5}{8}\right)[/tex]

[tex]\\ \sf\longmapsto M(x,y)=\left(\dfrac{16}{8},\dfrac{26}{8}\right)[/tex]

[tex]\\ \sf\longmapsto M(x,y)=\left(2,\dfrac{13}{4}\right)[/tex]

Which equation models the same quadratic relationship as function f? f(x) = 2x^2 - 12x + 11
A) y = 2(x + 6)^2 + 2
B) y = 2(x - 3)^2 -7
C) y = 2(x - 6)^2 + 5
D) y = 2(x + 3)^2 - 7

Answers

Answer:

im not sure but i think the answer is C) y = 2(x - 6)^2 + 5

The equation models the same quadratic relationship as function f(x) = 2x^2 - 12x + 11 will be 2(x-3)²-7.Option B is correct.

What is the equation?

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the function is,

f(x) = 2x^2 - 12x + 11

We have to find the equation models the same quadratic relationship as the given function,

⇒2x²-12x+11

Take common 2 in the complete equation,

⇒2(x²-6x+11/2)

Add and subtract 9 from the complete equation,

⇒2(x²-6x+9-9+11/2)

Rearrange the equation as,

⇒2[(x-3)²-(7/2)]

⇒2(x-3)²-7

Thus, the equation models the same quadratic relationship as function f(x) = 2x^2 - 12x + 11 will be 2(x-3)²-7.Option B is correct.

Learn more about the equation here,

https://brainly.com/question/10413253

#SPJ2

Select the correct answer. Which graph represents this inequality? y ≥ 4x − 3

Answers

Step-by-step explanation:

You didn't put the graph, but you can compare between your graphs and the picture.

Brainliest please

The graph that represents this inequality y ≥ 4x − 3 is attached below.

What is a solution set to an inequality or an equation?

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

We are given that the inequality is;

y ≥ 4x − 3

The slope of the inequality is 4.

The equation of the red line is y = 4x − 3  

The shading is above the line and the line is solid, that means  y is greater than or equal 4x − 3

The graph of this inequality y ≥ 4x − 3 is attached below.

Learn more about inequalities here:

https://brainly.com/question/27425770

#SPJ2

Which diagram best shows how fraction bars can be used to evaluate One-half divided by one-fourth? A fraction bar labeled 1. Under the 1 are 2 boxes containing one-half. Under the 2 boxes are 4 boxes containing one-fourth. 2 one-fourths are circled. A fraction bar labeled one-fourth. Under the one-fourth are 2 boxes containing one-half. Under the 2 boxes are 4 boxes containing 1. 2 boxes containing 1 are circled. A fraction bar labeled 1. Under the 1 are 4 boxes containing one-fourth. Under the 4 boxes are 8 boxes containing one-half. One box containing one-half is circled. A fraction bar labeled 1. Under the 1 are 4 boxes containing one-fourth. Under the 4 boxes are 2 boxes containing one-half. One box containing one-half is circled.

Answers

Answer:

Step-by-step explanation:

The description is too ambiguous to reconstruct the diagram. You need to post the actual diagram.

That diagram is just one way to view division by a fraction. An easier way: DIVIDING by a fraction is the same as MULTIPLYING by the upside-down fraction. For example,

(1/2) ÷ (1/4) = (1/2) × (4/1) = 2

That doesn’t help you answer this particular question, though.

Answer:

C

Step-by-step explanation:

What is the best interpretation of the y-intercept of the line

Answers

Answer:

vertical line

Step-by-step explanation:

because horizontal means horizon which goes left to right across a board

Hi there!

The y-intercept of a line represents its initial value. On a graph, the y-intercept would represent the value of y when the line crosses the y-axis.

For example, if an equation were to model the amount of money someone had in their bank account overtime starting from the day they opened their account, the y-intercept would represent the original amount of money they had.

I hope this helps!

Which graph shows the solution to the given system of inequalities? [y<6x+1 y<-3.2x-4

Answers

Answer:

VERY NICE RACK U HAVE MAM

Step-by-step explanation:

Answer:

Its a

Step-by-step explanation:

found on another thing and im taking test

the coefficients corresponding to k=0,1,2,5 in the expression (x+y)^5 are

Answers

Answer:

Step-by-step explanation: you got trolded

please help me with this on the image

Answers

Answer:

6ab

Step-by-step explanation:

Answer 6ab
Explanation 3xax2xb
3x2 =6
axb= ab
= 6ab

(2/5-1/2)+3/5 . [7/2-3/5÷(1/4-1/5)]

Answers

Answer: -8

Step-by-step explanation: So we after simplification we get

[(2/5) - (1/2) + (3/5)+ (7/2)] - [(3/5)/(1/4) - (1/5)]

After this I suppose it's just addition & subtraction, and can be easily done to get -8.

Work out 45% of $200.00

Answers

Answer:

If you are using a calculator, simply enter 45÷100×200 which will give you 90 as the answer.

Mark me brainliest plz.

First you change 45% to decimal form (move the decimal two places to the left) which gives .45

Then, you multiply .45 x $200.00

Your answer is $90

a gym class has 10 boys and 12 girls. how many ways can a team of 6 be selected if the team must have the same number of boys and girls

Answers

Answer:

The number of ways of selecting the team is 26,400 ways.

Step-by-step explanation:

Given;

total number boys in the gym, b = 10 boys

total number of girls in the gym, g = 12 girls

number of team to be selected, n = 6

If there must equal number of boys and girls in the team, then the team must consist of 3 boys and 3 girls.

Number of ways of choosing 3 boys from the total of 10 = [tex]10_C_3[/tex]

Number of ways of choosing 3 girls from a total of 12 = [tex]12_C_3[/tex]

The number of ways of combining the two possibilities;

[tex]n = 10_C_3 \times 12_C_3\\\\n = \frac{10!}{7!3!} \ \times \ \frac{12!}{9!3!} \\\\n = \frac{10\times 9 \times 8}{3\times 2} \ \times \ \frac{12\times 11 \times 10}{3\times 2} \\\\n = 120 \times 220\\\\n = 26,400 \ ways[/tex]

Therefore, the number of ways of selecting the team is 26,400 ways.

3w2 – 21w = 0

Need some help.

Answers

Answer:

The solutions are w=0 ,7

Step-by-step explanation:

3w^2 – 21w = 0

Factor out 3w

3w(w-7) =0

Using the zero product property

3w=0  w-7=0

w =0    w=7

The solutions are w=0 ,7

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