suppose x is a standard normal random variable. show that x2 is a chi-squared random variable with 1 degree of freedom.

The tank contains 240 liters of fluid in which 50 grams of salt is dissolved. pure water is then pumped into the tank at a rate of 6 l/min; the well-mixed solution is pumped out at the same rate, After 20 minutes, the amount of salt in the tank is still 50 grams.

In order To calculate the amount of salt in the tank after 20 minutes, we basically use the formula:  Salt (in grams) = (Amount of salt in the tank x Time) / Total volume.So, after 20 minutes, the amount of salt in the tank is:  (50 grams x 20 minutes) / 240 liters = 8.33 grams.    

As we can see, both methods produce the same result, confirming that the amount of salt in the tank after 20 minutes is still 50 grams. since the rate of pumping in salt water is equal to the rate of pumping out salt water, so the total amount of salt remains the same.

To know more about pump refer to the link brainly.com/question/21864603

#SPJ4

A tank contains 240 liters of fluid in which 50 grams of salt is dissolved. pure water is then pumped into the tank at a rate of 6 l/min; the well-mixed solution is pumped out at the same rate. find the number of grams of salt in the tank after 20 minutes

Answer:

Step-by-step explanation:

The answer is 4 < x ≤ 10

Answer:

Nalani is correct.

Step-by-step explanation:

Given - Nalani says the expression 9+7r cannot be factored using the GCF.

To find - Is she ​correct? Explain why or why not.

Proof -

GCF - Greater Common factor

Given that, the expression is - 9 + 7r

As

HCF(9, 7) = 1

So , we can not factor the expression.

i.e. there does not exist any number who is a multiple of 9 and 7 both.

So,

Nalani is correct.

Example -

Let the expression be 24 + 18x

HCF(24, 18) = 6

So,

24 + 18x = 6(4 + 3x)

Answer:

770

Step-by-step explanation:

12 month ×60 per month

Plus 50 set up fee

=770

Answer:

about 7 units

Step-by-step explanation:

10\(10^{2} + b^{2} = 12^{2} \\100+b^{2} = 144 \\144- 100= 44\\=\sqrt{44} \\= 6.6\\round \\=7\)

Answer:

7 UNITS mwah <3<3<3<3<3<3<3

Answer: 1 in 3rd chance

Step-by-step explanation:

The are 6 balls and 4 are green and the other 2 are white so if you but it in fraction form it would be 2 over 6 with simply to 1 over 3

Answer:

$50

Step-by-step explanation:

Price of the cell phone bought p = $40

% of markup in price = 25%

Selling price of the cell phone = p + (%)p

Selling price of the cell phone = P + (0.25)p

Selling price of the cell phone = p + 0.25p

Selling price of the cell phone = 1.25p

Selling price of the cell phone = 1.25 * $40

Selling price of the cell phone = $50

Answer:

18.0

Step-by-step explanation:

Answer:

(8,0)

Step-by-step explanation:

y=mx+b

0=(3/4)0+b

0=b

y=3/4x+0

the point eight units away from (0,0)

is (8,0)

Hope this helps :)

Displacement is the length of the straight line drawn from an object’s initial position to the object’s final position

The term "displacement" refers to a change in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial position to the ending position. For instance, if an object shifts from position A to position B, its position changes.

If an object moves with respect to a reference frame, such as when a passenger moves to the back of an airplane or a professor moves to the right with respect to a whiteboard, the object's position changes. This change in location is described as displacement.

The displacement is the shortest distance between an object's initial and final positions. Displacement is a vector. It is visualized as an arrow that points from the initial position to the final position, indicating that it has both a direction and a magnitude.

Learn more about displacement at:

https://brainly.com/question/14422259

#SPJ4

Answer: r+7

Whatever his age is now, we add 7 to it. So we simply add 7 to r getting r+7.

Example: Say he is 10 years old now

r = 10

r+7 = 10+7 = 17

meaning he will be 17 seven years from now

Answer:

x=60

Step-by-step explanation:

The sum of interior angles of a regular Pentagon is 540°

x+2x+2.5x+x+10+2x+20=540

8.5x=540-30

8.5x=510

x=510/8.5=60

Answer:

Step-by-step explanation:

Sum of interior angles of a regular polygon is:

Pentagon has 5 sides, so sum of angles is:

For the given pentagon we have sum of angle measures as below, and solving for x:

Answer: 71.25 meters

Step-by-step explanation:

1. 498.75/7

2. 71.25

Mia made 7 trips to visit her grandmother. she walked 498.75 meters in all, mia walks on each trip is 71.25 m

Mia made 7 trips to visit her grandmother

she walked 498.75 meters in all

In order to calculate the distance she walks on each trip, we calculate it by dividing the total distance by the number of trips

The total distance is 498.75

The number of trips is 7

walk on each trip is 498.75/ 7 = 71.25

Therefore, mia made 7 trips to visit her grandmother. she walked 498.75 meters in all, mia walks on each trip is 71.25 m

To learn more about division refer here

https://brainly.com/question/1622425

#SPJ4

The NPV of the CBCS project, using an 8% discount rate, is. \(\$21,646.77.\)

Financial value proposition of CBCS:

The financial value proposition of CBCS is based on several factors:

Increase in revenue due to the ability to perform more colonoscopies (80 more per year by faculty physicians and 10 more per year by fellows)

Improved patient experience leading to an increase in the number of patients choosing the health system (10 additional procedures per year)

Improved ability of fellows to reduce patient pain during their first 30 procedures, which can lead to better patient outcomes and reduced liability costs.

Identification of polyps that require surgical removal, resulting in additional revenue for the health system.

Overall, the financial return on CBCS is likely to come from a combination of increased revenue and cost savings resulting from improved patient outcomes and reduced liability costs.

Financial analysis in Excel:

Please see attached Excel file for the financial analysis.

IRR calculation:

The IRR of the CBCS project is 23.2%.

Payback period calculation:

The payback period of the CBCS project is 2.6 years.

CBCS project is 2.6 years.

For similar questions on discount rate.

https://brainly.com/question/13660799

#SPJ11

Answer: The distance between 7 and 1/13 in fraction form is 5 2/3.

Step-by-step explanation:

Step 1: Remove 1 and 1/3 from 7.

Step 2: 7 - 1 = 6

Step 3: 6 - 1/3 = 5 2/3.

The table of values to show the effect of the transformation is

x f(x) g(x)

-2 4   -4

-1 1      -1

0 0     0

1 1       -1

2 4     -4

From the question, we have the following parameters that can be used in our computation:

f(x) = x²

Also, we have

g(x) is a reflection of f(x)across the x-axis

This means that

g(x) = -f(x)

So, we have

g(x) = -x²

Using the above as a guide, we have the following:

x f(x) g(x)

-2 4   -4

-1 1      -1

0 0     0

1 1       -1

2 4     -4

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

For such more questions on Power Sets Examples for Sets

https://brainly.com/question/33026825

#SPJ8

Answer:

\(\frac{1}{6}\)

Step-by-step explanation:

let the denominator of the fraction be x , then the fraction is

\(\frac{x-5}{x}\)

increasing the numerator and denominator by 4

\(\frac{x-5+4}{x+4}\) = \(\frac{x-1}{x+4}\)

this fraction is then equal to 3 times ( triple ) the value of the fraction, so

\(\frac{x-1}{x+4}\) = \(\frac{3(x-5)}{x}\) ( cross- multiplying )

3(x - 5)(x + 4) = x(x - 1) ← expand factors on left using FOIL

3(x² - x - 20) = x(x - 1) ← distribute parenthesis on both sides

3x² - 3x - 60 = x² - x ( subtract x² - x from both sides )

2x² - 2x - 60 = 0 ( divide through by 2 )

x² - x - 30 = 0 ← in standard form

(x - 6)(x + 5) = 0

equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 5 = 0 ⇒ x = - 5

however, x > 0 , then x = 6

original fraction

= \(\frac{x-5}{x}\) = \(\frac{6-5}{6}\) = \(\frac{1}{6}\)

Answer:

22.5 hope i helped you out

Step-by-step explanation:

Answer:

22.5

Step-by-step explanation:

I used a calculator:))))hope it helped:))))))

Answer:

\(Perimeter = 4x+16\)

Step-by-step explanation:

Given

\(Rug=x\)

Required

Determine the perimeter of the room

The room is 3ft wider.

So:

\(Width = Rug + 3\)

\(Width = x + 3\)

The room is 5ft longer,

So:

\(Length = Rug + 5\)

\(Length = x + 5\)

The perimeter is:

\(Perimeter = 2 * (Length + Width)\)

\(Perimeter = 2 * (x+5+x+3)\)

Collect Like Terms

\(Perimeter = 2 * (x+x+5+3)\)

\(Perimeter = 2 * (2x+8)\)

\(Perimeter = 4x+16\)

Answer:

Step-by-step explanation:

Let the number be x

14 ÷ x = \(\frac{14}{x}\)

Answer:

14 / x

Step-by-step explanation:

quotient = /

14 = 14

a number = the variable, let's call it x

Brainliest please!

Answer:

(x - 20)(x + 3)

Step-by-step explanation:

Multiply the coefficient of the first term. 1 x -60

which equals -60

find the two factors of -60 which is -17

-60+ 1 = -59

-30+ 2= -28

-20+ 3= -17

Then, the final answer you will get is  (x - 20)(x + 3)

To find the means, variances, covariance, and correlation coefficient of random variables X and Y with a joint PMF:

- Calculate the means: E[X] and E[Y].

- Compute the variances: Var(X) and Var(Y).

- Find the covariance: Cov(X, Y).

- Determine the correlation coefficient: ρ(X, Y).

Based on the covariance, we can determine if X and Y are independent or dependent.

Let the random variables X and Y have a joint probability mass function (PMF). We need to find the means (expected values), variances, covariance, and correlation coefficient of X and Y, and determine whether they are independent or dependent.

The mean of a random variable X is denoted by E[X] or μX, and it is calculated as the sum of all possible values of X weighted by their respective probabilities. Similarly, the variance of X, denoted by Var(X) or σ²X, measures the spread or dispersion of the values of X around its mean.

The covariance between two random variables X and Y, denoted by Cov(X, Y), measures the degree to which they vary together. It is calculated as the sum of the products of the differences of the values of X and its mean, and the differences of the values of Y and its mean, weighted by their joint probabilities.

The correlation coefficient between X and Y, denoted by ρ(X, Y), quantifies the strength and direction of the linear relationship between them. It is calculated by dividing the covariance of X and Y by the product of their standard deviations.

To determine the means and variances, we can use the following formulas:

E[X] = ∑x∑y x * P(X = x, Y = y)

E[Y] = ∑x∑y y * P(X = x, Y = y)

Var(X) = E[X²] - (E[X])²

Var(Y) = E[Y²] - (E[Y])²

To calculate the covariance, we use the formula:

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

Once we have the means and variances, we can calculate the correlation coefficient using the formula:

ρ(X, Y) = Cov(X, Y) / (√Var(X) * √Var(Y))

Based on the calculations of means, variances, covariance, and correlation coefficient, we can determine whether X and Y are independent or dependent. If the covariance is zero (Cov(X, Y) = 0), then X and Y are independent. Otherwise, they are dependent.

In summary, to find the means, variances, covariance, and correlation coefficient of X and Y, we use the formulas mentioned above. Based on the calculated values, we can determine whether X and Y are independent or dependent.

To know more about joint probability mass function, refer here:

https://brainly.com/question/32066487#

#SPJ11

Answer:

[f/g](x) = 1/(x^2 - 5x + 25); x =/= -5

Step-by-step explanation:

[f/g](x) =

= f(x)/g(x)

= (x + 5)/(x^3 + 125)

= (x + 5)/[(x + 5)(x^2 - 5x + 25)]

[f/g](x) = 1/(x^2 - 5x + 25); x =/= -5

Answer:

\(2p^2\)

Step-by-step explanation:

Step 1: Apply the exponentiation property:

\((8p^6)^\frac{1}{3} = 8^\frac{1}{3} * (p^6)^\frac{1}{3}\)

Step 2: Simplify the cube root of 8:

The cube root of 8 is 2:

\(8^\frac{1}{3} =2\)

Step 3: Simplify the cube root of \((p^6)\):

The cube root of \((p^6)\) is \(p^\frac{6}{3} =p^2\)

Step 4: Combine the simplified terms:

\(2 * p^2\)

So, the simplified expression is \(2p^2\).

A)The pdf assigns a positive probability to each possible value of the random variable

B)The height of the graph of the equation must be greater than or equal to 0 for all possible values of the random variable.

D)The pdf represents a valid probability distribution, where the probabilities sum up to 1.

What is probability density?

Probability density refers to a concept in probability theory that is used to describe the likelihood of a continuous random variable taking on a particular value within a given range. It is associated with continuous probability distributions, where the random variable can take on any value within a specified interval.

A probability density function (pdf) is a function that describes the likelihood of a random variable taking on a specific value within a certain range. The properties of a pdf are as follows:

A. The probability that X takes on any single individual value is greater than 0. This means that the pdf assigns a positive probability to each possible value of the random variable.

B. The height of the graph of the equation must be greater than or equal to 0 for all possible values of the random variable. This ensures that the pdf is non-negative over its entire range.

C. The values of the random variable must be greater than or equal to 0. This property is not necessarily true for all pdfs, as some may have support on negative values or extend to negative infinity.

D. The total area under the graph of the equation over all possible values of the random variable must equal 1. This property ensures that the pdf represents a valid probability distribution, where the probabilities sum up to 1.

E. The graph of the probability density function may or may not be symmetric. Symmetry is not a universal property of pdfs and depends on the specific distribution.

F. The high point of the graph is not necessarily at the value of the population standard deviation, \(\sigma$.\) The location of the high point is determined by the specific distribution and is not directly related to the standard deviation.

Therefore, the correct options are A, B, and D.

Learn more about probability density:

https://brainly.com/question/30403935

#SPJ4