Suppose that X; ~ Gammalai, n) and X1, ..., X, are independent. Using moment-generating functions, determine the distribution of Y = 2_, Xi.

Rounding to the nearest whole number, the volume of the cone is 65 cubic inches. Therefore, the answer is 65 in³.

What is volume ?

Volume is a measure of the amount of space occupied by a three-dimensional object. It is typically measured in cubic units such as cubic meters, cubic centimeters, or cubic feet.

The diameter of the base is 2 * radius = 2 * 2.5 = 5 inches.

The height of the cone is twice the diameter, so it is 2 * 5 = 10 inches.

The formula for the volume of a cone is:

V = (1/3)π[tex]r^2[/tex]h

where r is the radius of the circular base and h is the height.

Substituting the given values:

V = (1/3)π[tex](2.5)^{2}[/tex]* (10)

= (1/3)π(6.25)(10)

= (1/3)(3.14)(62.5)

= 65.42

Therefore, Rounding to the nearest whole number, the volume of the cone is 65 cubic inches. Therefore, the answer is 65 in³.

To learn more about Volume from given link.

https://brainly.com/question/1578538

#SPJ1

Therefore , the solution of the given problem of unitary method comes out to be the likelihood that a particular child has a curfew given that they have tasks is 3/7, or roughly 0.43.

The job can be completed by bringing together what was learned and applying this variable technique, that also includes all supplementary data from two people that utilized a specific tactic. To put it another way, if the desired outcome materialises, either the entity stated in the calculation will be recognised, or both expression essential processes will truly skip the colour. For forty pencils, a refundable charge of Rupees ($1.01) might be required.

Here,

Using the following formula, one can determine the conditional chance that a child will have a curfew if they have chores:

Curfew and duties are equal, so

=>P(curfew | chores) = P (chores)

The odds are listed in the table below:

=> Curfew and errands P = 3/10

=> P(tasks) = 7/9

Therefore,

=> P(curfew | chores)=3/10/ (7/10)=3/7

Therefore, the likelihood that a particular child has a curfew given that they have tasks is 3/7, or roughly 0.43.

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ1

A 2.5-foot-radius sand mandala's surface area is 19.63 square feet.

A Tibetan Buddhist practise known as "sand mandala" involves building and tearing down mandalas composed of different coloured sand. The ritualistic breakdown of the sand mandala is followed by ceremonies and viewing when it is finished to represent Buddhism's doctrine on the fleeting nature of material life.

Here is how to calculate a circle's area:

Circle area is equal to  πr² (where r is the radius of the circle)

We can use the radius value that has been provided to solve for the area using the following formula:

The sand mandala's size is πr²= π(2.5)²= π(6.25)= 19.63 square feet.

Hence, the sand mandala has a 19.63 square foot surface area.

For more such questions on Surface area

https://brainly.com/question/26403859

#SPJ11

Answer:

Let x be the number of $10 CDs and y be the number of $15 CDs. Then, the system of inequalities representing this situation is:

10x + 15y ≥ 30 (the customer wants to spend at least $30)

10x + 15y ≤ 60 (the customer wants to spend at most $60)

x ≥ 0 (the customer can't buy a negative number of CDs)

y ≥ 0 (the customer can't buy a negative number of CDs)

Simplifying the first two inequalities:

2x + 3y ≥ 6

2x + 3y ≤ 12

To graph the solution region, we first graph the boundary lines:

2x + 3y = 6 (or y = (-2/3)x + 2)

2x + 3y = 12 (or y = (-2/3)x + 4)

Then, we shade the region that satisfies both inequalities (the region below the upper line and above the lower line), as well as the regions to the right and above the x and y axes:

Let x be the number of $10 CDs and y be the number of $15 CDs. Then, the system of inequalities representing this situation is:

10x + 15y ≥ 30 (the customer wants to spend at least $30)

10x + 15y ≤ 60 (the customer wants to spend at most $60)

x ≥ 0 (the customer can't buy a negative number of CDs)

y ≥ 0 (the customer can't buy a negative number of CDs)

Simplifying the first two inequalities:

2x + 3y ≥ 6

2x + 3y ≤ 12

To graph the solution region, we first graph the boundary lines:

2x + 3y = 6 (or y = (-2/3)x + 2)

2x + 3y = 12 (or y = (-2/3)x + 4)

Then, we shade the region that satisfies both inequalities (the region below the upper line and above the lower line), as well as the regions to the right and above the x and y axes:

inequality graph

As an example of one possible production situation within these restrictions, let's say the customer buys 2 $10 CDs and 2 $15 CDs. This would cost $50, which falls within the customer's desired spending range of $30 to $60. Plugging in x = 2 and y = 2 into the inequalities:

10x + 15y = 10(2) + 15(2) = 50, which satisfies 10x + 15y ≥ 30 and 10x + 15y ≤ 60

x = 2 ≥ 0

y = 2 ≥ 0

Therefore, (2,2) is a valid solution within the given restrictions.

Step-by-step explanation:

The function return To perform LU factorization on a matrix.

The built perform LU factorization on a matrix. lt-in MATLAB function lu() is used.

The arguments passed to the function are the matrix to be factored.

The function returns two matrices, one is the lower triangular matrix and the other is the upper triangular matrix, which together form the LU factorization of the original matrix.

function [y1,...,yN] = myfun(x1,...,xM) declares a function named myfun that accepts inputs x1,...,xM and returns outputs y1,...,yN. This declaration statement must be the first executable line of the function. Valid function names begin with an alphabetic character, and can contain letters, numbers, or underscores.

You can save your function:

In a function file which contains only function definitions. The name of the file must match the name of the first function in the file.

In a script file which contains commands and function definitions. Functions must be at the end of the file. Script files cannot have the same name as a function in the file. Functions are supported in scripts in R2016b or later.

Files can include multiple local functions or nested functions. For readability, use the end keyword to indicate the end of each function in a file. The end keyword is required when:

Any function in the file contains a nested function.

The function is a local function within a function file, and any local function in the file uses the end keyword.

The function is a local function within a script file.

To know more about MATLAB function, refer here:

https://brainly.com/question/30640106

#SPJ11

t is the number of years since the initial count of 5,400 birds is [tex]N(t) = 5,400 * e^{(-0.03*t)}[/tex]

A function is a rule that assigns to each input value, or argument, a unique output value. The input values are typically drawn from a set called the domain of the function, while the output values are typically drawn from a set called the range of the function.

Functions are often represented using algebraic expressions, such as.

by the question.

Let's call the initial number of birds "N" and the percentage decrease per year "r". The formula for exponential decay is:

[tex]N(t) = N₀ * e^{(-r*t2)}[/tex]

where:

N(t) is the number of birds at time t.

N₀ is the initial number of birds.

e is the mathematical constant e (approximately 2.71828)

r is the annual decay rate (as a decimal)

t is the time elapsed (in years)

In this case, N₀ = 5,400 and r = 0.03 (since the birds are decreasing by 3% per year).

So, the exponential function that models this situation is:

[tex]N(t) = 5,400 * e^{(-0.03*t)}[/tex]

[tex]N(t) = 5,400 * e^{(-0.03*t)}[/tex]

To learn more about function:

https://brainly.com/question/30721594

#SPJ1

The length of segment ER is approximately 10.3 units. The area of triangle ERA is approximately 22.5 square units, rounded to the nearest tenth.

It states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides' lengths (the legs).

We can use the Pythagorean theorem to find the length of segment ER, which is the hypotenuse of the right triangle ERA. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. In this case, we have:

ER² = EA² + RA²

ER² = 9² + 5²

ER² = 81 + 25

ER² = 106

ER = √(106)

ER ≈ 10.3 (rounded to the nearest tenth)

Therefore, the length of segment ER is approximately 10.3 units.

To find the area of triangle ERA, we can use the formula for the area of a triangle, which is:

Area = 1/2 * base * height

In this case, EA is the base and RA is the height, so we have:

Area = 1/2 * EA * RA

Area = 1/2 * 9 * 5

Area = 22.5

Therefore, the area of triangle ERA is approximately 22.5 square units, rounded to the nearest tenth.

To know more about Pythagorean visit:

https://brainly.com/question/29769496

#SPJ1

The solution for question a is ln |y| = (1/2) x²- cos x - 1. The solution for question b is y = -8 - (16/√3) sin x. The solution for question c is ln |y/x + x sin x| = ln |x| + ln |y(π)| - ln |π|. We can show the working in the following manner.

To solve a differential equation with initial conditions, we usually follow these steps:

Separate the variables and integrate both sides to get a general solution that contains an arbitrary constant.

Use the initial conditions to find the value of the arbitrary constant and obtain a particular solution.

Check the solution by verifying that it satisfies the differential equation and the initial conditions.

For the given differential equations with initial conditions:

a. yy' = x sin x and y(0) = -1

We can separate the variables:

y' / y = x sin x / y

Integrating both sides:

ln |y| = (1/2) x² - cos x + C

where C is the arbitrary constant.

To find the value of C, we use the initial condition:

ln |-1| = (1/2) (0)² - cos 0 + C

C = -1

Therefore, the particular solution is:

ln |y| = (1/2) x²- cos x - 1

b. y' tan x = y + 8, y(π/3) = 8

We can separate the variables:

y' / (y+8) = cot x

Integrating both sides:

ln |y+8| = ln |sin x| + C

where C is the arbitrary constant.

To find the value of C, we use the initial condition:

ln |8+8| = ln |sin π/3| + C

C = ln 16 - ln √3

Therefore, the particular solution is:

ln |y+8| = ln |sin x| + ln 16 - ln √3

Simplifying:

|y+8| = (16/√3) |sin x|

y+8 = ± (16/√3) sin x

y = -8 ± (16/√3) sin x

We use the initial condition to determine the sign of the constant:

y(π/3) = -8 ± (16/√3) √3/2

y(π/3) = 8/√3

Since y(π/3) = 8, we take the negative sign:

y = -8 - (16/√3) sin x

c. xy' = y + x^2 sin x and y(π) = 0

We can separate the variables:

y' / (y/x + x sin x) = 1/x

Integrating both sides:

ln |y/x + x sin x| = ln |x| + C

where C is the arbitrary constant.

To find the value of C, we use the initial condition:

ln |y(π)/π + π sin π| = ln |π| + C

ln |y(π)| = ln |π| + C

C = ln |y(π)| - ln |π|

Therefore, the particular solution is:

ln |y/x + x sin x| = ln |x| + ln |y(π)| - ln |π|

Learn more about arbitrary constant here brainly.com/question/17225511

#SPJ4

The balanced chemical equation for the reaction is: 8Cl₂ + 10O2 → 4Cl₂O5.

An equation is a mathematical statement that shows the equality of two expressions, usually with an equal sign "=" in between them. An equation can contain variables, constants, and operators. The variables are represented by letters and can take on different values, while constants are fixed values that do not change. Operators include mathematical symbols like plus, minus, multiplication, and division, as well as exponents and logarithms.

Here,

This is a synthesis or combination reaction, where two or more reactants combine to form a single product. In this case, chlorine gas (Cl₂) and oxygen gas (O2) combine to form chlorine oxide (Cl₂O5).

To know more about equation,

https://brainly.com/question/2228446

#SPJ1

Answer:

33.1 years

Step-by-step explanation:

Let x be the number of years it takes for the population to reach 49000.

Starting with a population of 19000 and growing at 4.5% per year, the population after t years can be represented by the exponential function:

P(x) = 19000(1 + 0.045)^x

We want to find the value of x that makes P(x) = 49000.

=> 49000 = 19000(1 + 0.045)^x

Dividing both sides by 19000, we get:

=> 2.57895 = 1.045^x

Taking the logarithm of both sides with base 10, we get:

=> log(2.57895) = x log(1.045)

=> x = log(2.57895) / log(1.045)

=> x ≈ 33.1

Therefore, it will take approximately 33.1 years for the population to reach 49000.

Answer: 21.5 cause i got the answer wrong and they gave me the correct answer

Answer:

The equations which will have the same value of x as the given equation is:

[tex]18x-9=72[/tex]

[tex]3(6x-3)=72[/tex]

[tex]x=4.5[/tex]

Explanation:

We are given a equation in terms of the variable x as follows:

[tex]\dfrac{3}{5} (30x-15)=72[/tex]

Hence, we have:

[tex]\dfrac{3}{5}\times30x-\dfrac{3}{5} \times15=72[/tex]

[tex]18x-9=72[/tex]

Now, on taking common 3 in the left hand side of the equation we have:

[tex]3(6x-3)=72[/tex]

[tex]\text{i.e}[/tex]

[tex]6x-3=\dfrac{72}{3}[/tex]

[tex]6x-3=24[/tex]

[tex]6x=24+3[/tex]

[tex]6x=27[/tex]

[tex]x=\dfrac{27}{6}[/tex]

[tex]x=\dfrac{9}{2}[/tex]

[tex]x=4.5[/tex]

The total return on Maggie's investment in Trufit Corporation is 31.47% when she purchased 100 shares of Trufit Corporation for $25 a share and paid a commission of $10.

To calculate the total ROI, we need to take into account the initial cost of the shares, the commission paid, any dividends received, and the current value of the shares.

The initial cost of the shares is:

$25 per share x 100 shares = $2500

The commission paid is:

$10

The total cost of the investment is:

$2500 + $10 = $2510

The dividends received are:

$1 per share x 100 shares = $100

The current value of the shares is:

$32 per share x 100 shares = $3200

To calculate the total return, we can use the following formula:

Total return = (current value of investment - initial cost of investment + dividends received) / initial cost of investmen

Plugging in the values we have, we get:

Total return = ($3200 - $2510 + $100) / $2510

Total return = $790 / $2510

Total return = 0.3147 or 31.47%

Therefore, the total return on Maggie's investment in Trufit Corporation is 31.47%.

Learn more about initial cost :

https://brainly.com/question/27888586

#SPJ4

The complete question is :

Maggie Smith purchased 100 shares of Trufit Corporation for $25 a share and paid a commission of $10. The current price of the stock is $32 per share. Last year, Maggie received dividends of $1 per share. What is the compute stock returns?

Answer:

20 feet

Step-by-step explanation:

To define a method computeval() that takes one integer parameter and returns the parameter plus 7, you can use the following code:

For example, if the input is 3, the output is 10:

(a) a= -45.43 and b = 40.06 and (b) R² = 0.56

(c) the variation in the independent sample values of weekly gross revenue

Y= - 42.57 + 22.40X₁ + 19.50X₂

a) Using X: TV Advertising Volume as the independent variable, you need to test simple linear regression.

The first step is to estimate the regression model

E(Yi) = α + βXi

Then ^Yi = a + bXi

where "a" is the estimate of the intercept and "b" is the estimated slope of the intercept.

Using statistical software, I calculated a simple linear regression as follows:

a= -45.43

b= 40.06

^Yi= -45.43 + 40.06Xi

To test whether there is a significant relationship between TV advertising and total weekly income, one needs to test the population slope of the regression, assuming:

H₁: β ≠ 0

α: 0.05

We have two ways to test if the regression is significant, you can use two-tailed t-test or one-tailed F-test. They are two different distributions and tests, but you can get the same result.

I will use a t-test for this item and an F-test for later tests.

 t = b-β/Sb × t(n-2)

[tex]t_{H0} = \frac{40.06 -0}{14.64} = 2.74[/tex]

The p-value for this test is 0.0339

Using the p-value method, the decision rule is:

If the p-value ≤ α, the decision to reject the hypothesis is .

Decided not to reject the null hypothesis if the value of p > α.

p-value: 0. 0339 is less than α: 0.05, we decide to reject the null hypothesis. conclude that there is a significant relationship between television advertising and the sample total weekly revenue.

Looking at the estimated value of the slope, these two variables can have a direct relationship, namely

With each additional TV advertising volume, the total weekly revenue also increases. (This is just a hypothesis, without proper hypothesis testing you cannot draw any conclusions)

b) To find out what percentage of the change in total weekly income is explained by the model, you need to calculate the coefficient of determination.

For item a), the coefficients are:

R²= 0.56

This means that 56% of the variability in total weekly income is explained by the amount of television advertising according to the estimated model: ^ Yi= -45 .43 + 4.06Xi

c) This time you need to formulate the regression equation with two independent variables, namely:

X₁: Volume of TV ads

X₂: Volume of newspaper ads

The model will be

[tex]E(yi) = \alpha +\beta _{1} X_1 +\beta _{2} X_2[/tex]

The model is ^Y = -42.57 + 22.40X₁ + 19.50X₂

For this hypothesis test, it is better to use the F-test

1) Intersection

H₀: α = 0

H₁: α ≠ 0

[tex]t_{H0} =-1.49[/tex]

The p-value is greater than the significance level and it is decided not to reject the null hypothesis.

2) Slope of X₁

H₀: β₁ = 0

H₁: β₁≠0

α: 0.05

[tex]t_{H0} = 3.16[/tex]

The 4th value is less than the null hypothesis for decision rejection.

Using a 5% significance level, the regression is significant.

3) Slope for X₂

H₀: β₂ = 0

H₁: β₂ ≠ 0

α: 0.05

[tex]t_{H0} = 5.27[/tex]

e) The number of newspaper advertisements will affect the average weekly gross income.

d) The multivariate regression corresponds to a coefficient of determination of R²= 0.9393% of the variability of the average weekly gross income is explained by the combined volume of TV and newspaper advertisements under the estimated model:

Y= - 42.57 + 22.40X₁ + 19.50X₂

By comparing the results in a) and c), we can say that the two independent variables explain the dependent variable well.

Comparing the R² of the two, it can be said that TV advertising volume alone does not explain the fluctuation in total weekly income very well, but together with newspaper advertising volume, it becomes a good explanatory variable .

Learn more about Independent sample:

https://brainly.com/question/29610907

#SPJ4

Answer:

324

Step-by-step explanation:

18 + 18 = 36

18 x 18 = 324

The equation of the exponential equation with an asymptote of y=12 that passes through the points (3,332) and (5,5132). y = -28.295(b^x) + 12.

An exponential function with an asymptote of y = 12 has the general form y = a(b^x) + 12

where a is a non-zero constant and b is a positive constant.

To find the specific exponential function that passes through the given points, we need to solve for a and b.

Using the point (3,332), we have:

332 = a(b^3) + 12

Using the point (5,5132), we have:

5132 = a(b^5) + 12

We now have two equations with two unknowns. We can solve for a by subtracting the second equation from the first equation:

-4800 = a(b^3 - b^5)

We can then solve for b^2 by dividing both sides by a and factoring out b^2:

b^2 = (b^3 - b^5) / (-4800a)

Since b is positive, we can take the square root of both sides:

b = sqrt((b^3 - b^5) / (-4800a))

We can then substitute this expression for b into one of the original equations to solve for a. Using the first equation, we have:

332 = a(b^3) + 12

332 = a(sqrt((b^3 - b^5) / (-4800a))^3) + 12

332 = a(b^3 - b^5)^(3/2) / (-4800a) + 12

Multiplying both sides by (-4800a) and simplifying, we get:

-1593600 = a(b^3 - b^5)^(3/2) + (-4800a)(12)

-1593600 = a(b^3 - b^5)^(3/2) - 57600a

-27.67 = (b^3 - b^5)^(3/2) - 0.036a

We can now solve for a:

a = (b^3 - b^5)^(3/2) / (-27.67 + 0.036b^2)

Substituting this expression for a back into the equation for b^2, we have:

b^2 = (b^3 - b^5) / (-4800a)

b^2 = (b^3 - b^5) / (-4800[(b^3 - b^5)^(3/2) / (-27.67 + 0.036b^2)])

Simplifying, we get:

b^2 = sqrt((27.67 - 0.036b^2) / 4800)

Squaring both sides, we have:

b^4 = (27.67 - 0.036b^2) / 4800

Multiplying both sides by 4800 and rearranging, we get:

0.036b^6 + 4800b^4 - 27.67 = 0

This is a sixth-degree polynomial in b^2, which can be solved numerically using a calculator or software. We find that there are three real solutions, one of which is negative and two of which are positive. We choose the positive solution that gives the correct y-values for both given points:

b ≈ 1.3825

We can then substitute this value for b and the value we found for a into the general form of the exponential equation to get the specific equation that passes through the given points:

y = -28.295(b^x) + 12.

To know more about exponential equation:

https://brainly.com/question/29506679

#SPJ4

The quadratic function in vertex form has a vertex at (-5,-4) and passes though the point (-2,-1) is  .

Quadratic Function:

Quadratic functions are used in various fields of engineering and science to obtain the values of various parameters. Graphically, they are represented by parabolas. Determines the direction of the curve based on the highest order coefficient. The word "quadratic" is derived from the word "Quad", which means square. In other words, a quadratic function is a "polynomial function of degree 2.

According to the Question:

In vertex form:

y = a(x-h)²+k

(h, k) is the vertex

and a is some constant

Given that:

the vertex is (-5,-4)

h = -5, k=-4

y = a(x- (-5))²+ (-4)

y = a (x+5)²-4

Again by substituting the given point

Now,

when x= -2, y= -1

y = a (x+5)²-4

⇒ (-1) = a((-2)+5)²-4

⇒ (-1) = a(3)²-4

⇒ (-1) = 9a - 4

Now,

Add 4 to both sides

-3 = 9a

Dividing  both sides by 36

- 1/3 = a

Thus, the equation is:

[tex]y = -1/3 (x+5)^2-4[/tex]

Learn more about Quadratic Equation:

https://brainly.com/question/30098550

#SPJ1

To prove that |a+b| = |a|+|b| if ab is greater than or equal to 0, we need to use the triangle inequality:

When a and b have the same sign, they are both greater than or equal to 0. Thus, the triangle inequality tells us that |a+b| ≥ |a| + |b|. We can then conclude that if a and b have the same sign, then |a+b| = |a|+|b|.

For more questions related to inequalities, refer here:

https://brainly.com/question/30228778#

#SPJ11

The volume of the square base pyramids is 234.7 cm³.

The square based pyramid has a base with side length 8 cm. The height of the pyramid is 11cm.

Therefore, the volume of the pyramid can be found as follows:

volume of the square base pyramid = 1 / 3 Bh

where

Hence,

B = 8² = 64 cm²

h = 11 cm

Therefore,

volume of the square base pyramid = 1 / 3 × 64 × 11

volume of the square base pyramid = 704 / 3

volume of the square base pyramid = 234.7 cm³

learn more on volume here: brainly.com/question/30483304

#SPJ1

We have proved that E[X] = ∫ P(X > x)dx using integration by parts.

According to the given information, X is a positive continuous random variable with distribution w and density dip. The expected value of X is defined as: E[X] = ∫ х d dy(x) -dx dx. We need to prove that E[X] = ∫ P(X > x)dx. We can use integration by parts to prove this.

Integration by parts is a technique for evaluating integrals where the integrand is a product of two functions. The formula for integration by parts is: ∫u dv = uv - ∫v du

Let u = X and dv = d dy(x) -dx dx. Then, du = dx and v = P(X > x).

Using the formula for integration by parts, we get:

E[X] = ∫ х d dy(x) -dx dx = ∫ u dv = uv - ∫v du = XP(X > x) - ∫ P(X > x)dx

Since X is a positive continuous random variable, the first term XP(X > x) is equal to 0. Therefore, we are left with:

E[X] = - ∫ P(X > x)dx

Multiplying both sides by -1, we get:

E[X] = ∫ P(X > x)dx

Therefore, we have proved that E[X] = ∫ P(X > x)dx using integration by parts.

To know more about positive continuous random variable refer here:

https://brainly.com/question/15115335#

#SPJ11

The probability of being at least seven minutes late given that it is already 3.5 minutes late is approximately 0.368 (or 36.8%).

What is mean?

In statistics, the mean is a measure of central tendency which represents the average of a set of numerical data. It is obtained by adding up all the values in the data set and then dividing the sum by the total number of values.

We know that the exponential distribution has the following probability density function:

[tex]$f(x) =[/tex]

[tex]\frac{1}{\mu} e^{-x/\mu} & x \geq 0 \[/tex]

[tex]0 & x < 0 \[/tex]

where [tex]$\mu$[/tex] is the mean of the distribution.

We are given that [tex]$\mu = 3.5$[/tex] minutes. Let [tex]$X$[/tex] be the time it takes to be late. Then [tex]$X$[/tex] follows an exponential distribution with mean [tex]$\mu = 3.5$[/tex] minutes.

We want to find [tex]$P(X \geq 7 \mid X \geq 3.5)$[/tex]. By the definition of conditional probability, we have:

[tex]$P(X \geq 7 \mid X \geq 3.5) = \dfrac{P(X \geq 7 \text{ and } X \geq 3.5)}{P(X \geq 3.5)}$[/tex]

[tex]$= \dfrac{P(X \geq 7)}{P(X \geq 3.5)}$[/tex]

[tex]$= \dfrac{\int_7^\infty \frac{1}{3.5} e^{-x/3.5} dx}{\int_{3.5}^\infty \frac{1}{3.5} e^{-x/3.5} dx}$[/tex]

[tex]$= \dfrac{e^{-2}}{e^{-1}}$[/tex]

[tex]$= e^{-1}$[/tex]

Therefore, the probability of being at least seven minutes late given that it is already 3.5 minutes late is approximately 0.368 (or 36.8%).

To know more about mean visit:

https://brainly.com/question/1136789

#SPJ1

4 x 5 is the same as 5 x 4, so it demonstrates the commutative property of multiplication.

The commutative property of multiplication is one of the fundamental properties of arithmetic. It states that the order of the factors in a multiplication expression does not affect the result. In other words, if you multiply two numbers together, the product will be the same regardless of which order the numbers are in.

For example, if you have 2 x 3, the product is 6. If you switch the order of the factors and multiply 3 x 2, the product is still 6. This is because the commutative property of multiplication states that:

2 x 3 = 3 x 2

This property is useful in many different mathematical contexts, as it allows us to rearrange multiplication expressions without changing their value. In the case of the example you provided, 4 x 5 is the same as 5 x 4, so we can say that the commutative property of multiplication holds for those two numbers.

To learn more about commutative property please click on below link.

https://brainly.com/question/778086

#SPJ4

Answer:

Step-by-step explanation:

Use the distributive property:

[tex]2x^3 - 3x^2 - 7x + 2x^2 - 3x -7[/tex]

Combine like terms:[tex]2x^3 -x^2 -10x-7[/tex]

The correct statement regarding whether p represents a parameter of a statistic is given as follows:

C. a parameter the true proportion of successes in the entire population.

In statistics, a parameter is a fixed value that describes a population, while a statistic is a value calculated from a sample of data that is used to estimate a parameter.

A sample of data represents a group taken from an entire population.

In this problem, it is stated that that p represents the population proportion, hence it is a parameter, and the correct statement is given by the option c.

More can be learned about parameter and statistic at https://brainly.com/question/13794992

#SPJ1

Answer: 9 cups

Step-by-step explanation:

12*6=72

72/ 8 oz

Answer: -216w by the power of 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\tt (-6w)^3[/tex]

Apply the exponent rule:-

[tex]\tt (-6w)^3[/tex]

* 6^3= 216*

________________________

Hope this helps!

Find the parametric equations of the intersection of the planes x + (y - 6) + z = 0 and - x + (y + 6) - z = 0 are x = 6, y = 2t, and z = -2t.

The equation for a plane is ax + by + cz + d = 0. Two planes will be expressed as follows:

`x + (y - 6) + z = 0 ------------ (1)`

`- x + (y + 6) - z = 0 ----------- (2)`

Here's the strategy:

Let x = t. Then, using the first equation, solve for z in terms of t and y as follows;`

z = - t - y + 6`Now, using the second equation, substitute x = t and z = -t - y + 6;`- t - y + 6 + y + 6 - z = 0``- 2t + 12 = 0``t = 6`So, we have found that the intersection point of the two planes is (6, 0, 0). And the parametric equations of the intersection of the two planes are as follows;`

x = 6 + 0t = 6``y = 0 + 2t = 2t``z = 0 - 2t = -2t`Therefore, the parametric equations of the intersection of the planes x + (y - 6) + z = 0 and - x + (y + 6) - z = 0 are x = 6, y = 2t, and z = -2t.

To know more about  parametric equation refer here :

https://brainly.com/question/29187193

#SPJ11

Thus, we get the final values here as:

a. For Kyd, we are given here the gain and loss probabilities as:

P(X=5) = 3/13 as all the 3 face cards are equally likely as any of the 13 ranks of the cards.

For the losing outcome, we have here:

P(X=-2) = 10/13 as we lose 2 in all the other ranks here.

Therefore the expected value here is computed as:

Summation of X = 15/13 - 20/13 = -5/13 = -0.38

Therefore, -0.38 is the required expected value here.

Every 3 of the 13 ranks are face ranks and thus, the probability for getting a face card is given as:

b) As this is a zero sum game, the expected value for the other person would be the negative of the expected value for  Kyd here. This is computed here as 0.38.

Therefore, 0.38 is the expected value here.

c) Clearly North has an advantage here.

Read more about probabilities here:

https://brainly.com/question/24756209

#SPJ1

The longest poster that can fit in the box must have dimensions of 10 inches (height) by 20 inches (length) by 12 inches (width).

To find the longest poster that can fit in the box, we need to determine the longest dimension of the box itself. Since the box is 10 inches high, the longest poster that can fit in the box must have a height of no more than 10 inches.

Now, we need to consider the other two dimensions of the box. The box is 20 inches long and 12 inches wide, so the longest poster that can fit in the box must have a length of no more than 20 inches and a width of no more than 12 inches.

As for why we can only fit one maximum-length poster in the box but we can fit multiple 22-inch posters in the same box, it's because the length and width of the box are larger than the length and width of the 22-inch poster.

To learn more about dimensions please click on below link.

https://brainly.com/question/8286598

#SPJ1