HELP FAST No DECIMAL plz!

HELP FAST No DECIMAL Plz!

Answers

Answer 1

Answer: 1,145,375 centimeters cubed

Step-by-step explanation:

Answer 2

Answer: 1,145,375cm I think

Step-by-step explanation:


Related Questions








Question 6 Cats Dogs 10 5 7 8 a. How many people own a cat and a dog? I b. How many people own a cat? c. How many people own a cat but not a dog? d. How many people are represented?

Answers

The total number of people represented is 15.

Let's analyze the given information: Cats: 10Dogs: 5

a. To determine the number of people who own both a cat and a dog, we need to find the intersection of the sets. From the information given, we don't have direct data on the number of people who own both a cat and a dog. Therefore, we cannot determine the answer to part a without additional information.

b. To find the number of people who own a cat, we can simply consider the number of people who own cats, which is given as 10.

c. To find the number of people who own a cat but not a dog, we need to subtract the number of people who own both a cat and a dog from the total number of people who own a cat. Since we don't have the number of people who own both a cat and a dog, we cannot determine the exact number of people who own a cat but not a dog.

d. To find the total number of people represented, we can sum the number of people who own cats and the number of people who own dogs:

Total number of people represented = Number of people who own cats + Number of people who own dogs

Total number of people represented = 10 (cats) + 5 (dogs)

Total number of people represented = 15

Therefore, the total number of people represented is 15.

Learn more about statistics here:

https://brainly.com/question/30915447

#SPJ11

A continuous random variable X has probability density function 1≤x≤ 2, fx(x) = elsewhere, where k is an appropriate constant. (a) Calculate the value of k. (b) Find the expectation and variance of X. (c) Find the cumulative distribution function Fx(z) and hence calculate the probabil- ities Pr(X < 4/3) and Pr(X² < 2). (d) Let X₁, X2, X3,..., be a sequence of random variables distributed as the random variable X. In our case, which conditions of the central limit theorem are satisfied? Do we need any other assumptions? Explain your answer. (e) Let Y=X²-1. Find the density function of Y.

Answers

a) The value of k is 1.

b) The variance of X is 1/12.

c) Pr(X² < 2) = Fx(√2) = (√2) - 1

e) The density function of Y is fY(y) = 1 / (2√(y + 1)), for 0 ≤ y ≤ 3.

(a) We need to integrate the probability density function (pdf) over its entire range and set it equal to 1.

∫[1,2] k dx = 1

Integrating, we get:

k[x] from 1 to 2 = 1

k(2 - 1) = 1

k = 1

So, the value of k is 1.

(b) The expectation (mean) of a continuous random variable can be calculated using the following formula:

E(X) = ∫[−∞,∞] x  f(x) dx

In our case, since the pdf is zero outside the range [1, 2], we can simplify the calculation:

E(X) = ∫[1,2] x  f(x) dx = ∫[1,2] x dx

E(X) = [x²/2] from 1 to 2

E(X) = (2²/2) - (1²/2) = 3/2

So, the expectation of X is 3/2.

The variance of a continuous random variable can be calculated using the formula:

Var(X) = E(X²) - [E(X)]²

E(X²) = ∫[−∞,∞] x² f(x) dx

In our case, since the pdf is zero outside the range [1, 2]:

E(X²) = ∫[1,2] x² f(x) dx = ∫[1,2] x² dx

E(X²) = [x³/3] from 1 to 2

E(X²) = (2³/3) - (1³/3) = 7/3

Now, we can calculate the variance:

Var(X) = E(X²)- [E(X)]²

Var(X) = (7/3) - (3/2)²

Var(X) = 7/3 - 9/4

Var(X) = 28/12 - 27/12

Var(X) = 1/12

So, the variance of X is 1/12.

(c) The cumulative distribution function (CDF) F(x) is the integral of the pdf from negative infinity to x:

Fx(z) = ∫[−∞,z] f(x) dx

Since the pdf is zero outside the range [1, 2], the CDF is:

Fx(z) = ∫[1,z] f(x) dx = ∫[1,z] dx

Fx(z) = [x] from 1 to z

Fx(z) = z - 1

To calculate probabilities, we can substitute the given values into the CDF:

Pr(X < 4/3) = Fx(4/3) = (4/3) - 1 = 1/3

Pr(X² < 2) = Fx(√2) = (√2) - 1

(e) Let Y = X² - 1. To find the density function of Y, we can use the transformation technique.

First, we need to find the cumulative distribution function (CDF) of Y.

To do this, we express Y in terms of X:

Y = X² - 1

Now, we can solve for X:

X = √(Y + 1)

To find the density function of Y, we differentiate the CDF of Y with respect to Y:

fY(y) = d/dy [FX(√(y + 1))]

Using the chain rule, we have:

fY(y) = fX(√(y + 1)) (1 / (2√(y + 1)))

Substituting the given pdf of X (fx(x) = 1, 1 ≤ x ≤ 2), we have:

fY(y) = 1 (1 / (2√(y + 1)))

fY(y) = 1 / (2√(y + 1)), for 0 ≤ y ≤ 3

So, the density function of Y is fY(y) = 1 / (2√(y + 1)), for 0 ≤ y ≤ 3.

Learn more about Density Function here:

https://brainly.com/question/31039386

#SPJ4

Solve the following systems of linear equations. I can use the fact that the inverse matrix of the coefficient matrix is:
3 1 17 17 17 2 A-1 - 41M3W11归 - 17 17 5 51MBIM 17 13 。 - 17 17 17 - 3x+2y-z=4 12x-3y+z=-4 z-y-z=8 3x+2y-z=8 2x - 3y+z=-3 -y-z=-6 3x+2y-z=0 2x-3y+z=-15 x-y-z=-22

Answers

To solve the system of linear equations, we can represent the given system in matrix form as:

A * X = B

where A is the coefficient matrix, X is the column vector of variables (x, y, z), and B is the column vector of constants on the right-hand side.

The coefficient matrix A is:

A = [tex]\left[\begin{array}{ccc}3&1&-1\\12&-3&1\\2&-1&-1\end{array}\right] \\[/tex]

The column vector B is:

B = [tex]\left[\begin{array}{ccc}4\\-4\\8\end{array}\right][/tex]

To find the inverse matrix A⁻¹, we can use the formula:

A⁻¹ = (1 / det(A)) * adj(A)

where det(A) is the determinant of matrix A, and adj(A) is the adjugate of matrix A.

The determinant of matrix A can be calculated as follows:

det(A) = 3 * (-3) * (-1) + 1 * 1 * 2 + (-1) * 12 * (-1) = -3 + 2 + 12 = 11

Next, we need to find the adjugate of matrix A:

adj(A) = [tex]\left[\begin{array}{ccc}-2&1&-3\\11&3&11\\11&-3&-3\end{array}\right][/tex]

Now, we can calculate the inverse matrix A⁻¹:

A⁻¹ = (1 / 11) * adj(A) = [tex]\left[\begin{array}{ccc}-2/11&1/11&-3/11\\11/11&3/11&11/11\\11/11&-3/11&-3/11\end{array}\right][/tex]

Finally, we can solve for X by multiplying both sides of the equation by A^-1:

X = A⁻¹ * B = [tex]\left[\begin{array}{ccc}-2/11&1/11&-3/11\\11/11&3/11&11/11\\11/11&-3/11&-3/11\end{array}\right] * \left[\begin{array}{ccc}4\\-4\\8\end{array}\right][/tex]\

Performing the matrix multiplication, we get:

X = [tex]\left[\begin{array}{ccc}1\\-1\\-3\end{array}\right][/tex]

Therefore, the solution to the given system of linear equations is:

x = 1

y = -1

z = -3

To know more about matrix multiplication, refer to the link below:

https://brainly.com/question/13591897#

#SPJ11

Using the Laplace Transform table, or otherwise, find f(t) = (–1 ((s+2) -4) f(t) = 47 (b) Hence, find A and B that satisfy g(t) = C-1 رو) cs (s+2)4 = u(t - A)f(t - B) A Number B= Number (c) Calculate g(t) for t = -5.2, -4.6,-4.2. Give your answers to 2 significant figures. 9(-5.2) =___ Number g(-4.6) = ___ Number g(-4.2) =___

Answers

`g(-5.2) = 0`, `g(-4.6) = 0` and `g(-4.2) = 0

Given the differential equation: `f(t) = (-1/((s+2)^4))47`

Laplace Transform of `f(t)` is `F(s) = (-47/(s+2)^4)`Now we need to find inverse Laplace Transform of `F(s)` to get `f(t)`.

The Laplace Transform of `t^n` is `n!/(s^(n+1))`

Therefore, the inverse Laplace Transform of `(-47/(s+2)^4)` is `(d^3/ds^3)(47/s+2)

`Let, `g(t) = C^(-1)(s) / s(s+2)^4`We can write `g(t)` as,`g(t) = A[u(t-B) - u(t-A)]`

Taking Laplace Transform of `g(t)`, we get `G(s) = C^(-1)(s) / s(s+2)^4

`Therefore,`C^(-1)(s) = sG(s)/(s+2)^4`Substituting `s = 0`, we get `C = 0`

Therefore, `g(t) = A[u(t-B) - u(t-A)]`

Taking Laplace Transform of `g(t)`, we get `G(s) = A[1/(s+2) - e^(-Bs)/(s+2)]`

Now we need to find `A` and `B`.Since `G(s) = A[1/(s+2) - e^(-Bs)/(s+2)]`

Therefore, `G(s)` can be written as `G(s) = A*{(1/(s+2)) - (e^(-Bs)/(s+2))}

`Comparing it with Laplace Transform of `g(t)`, we get `A = 47` and `B = 2`.

Therefore, `g(t) = 47[u(t-2) - u(t)]`.

Now, we need to calculate `g(t)` for `t = -5.2, -4.6, -4.2`.We know that `g(t) = 47[u(t-2) - u(t)]`

Therefore, when `t < 0`, `g(t) = 0`When `0 < t < 2`, `g(t) = 47(0 - 0) = 0`

When `2 < t`, `g(t) = 47(1 - 1) = 0`

Therefore,`g(-5.2) = 0``g(-4.6) = 0``g(-4.2) = 0`Hence, `g(-5.2) = 0`, `g(-4.6) = 0` and `g(-4.2) = 0`.

Note: Here, `u(t)` is the unit step function.

Know more about  Laplace Transform here,

https://brainly.com/question/30759963

#SPJ11

Convert the result to degrees and minutes. Rewrite the angle in degrees as a sum and then multiply the decimal part by 60'.

A = 61° +0.829(60') = 61° + __________

Answers

Converting the angle in degrees and minutes, A = 61° +0.829(60') = 61° + 49.74'

To convert the angle in degrees and minutes, we need to express the decimal part as minutes.

Given:

A = 61° + 0.829(60')

When representing an angle in degrees and minutes, we use the following conventions:

Degrees (°): Degrees are the larger units of measurement in an angle. One complete circle is divided into 360 degrees.

Minutes (' or arcminutes): Minutes are the smaller units of measurement in an angle, where 1 degree is equal to 60 minutes. Minutes are denoted by the symbol ' (apostrophe).

Seconds ('' or arcseconds): Seconds are even smaller units of measurement in an angle, where 1 minute is equal to 60 seconds. Seconds are denoted by the symbol '' (double apostrophe).

To find the minutes, we multiply the decimal part by 60:

0.829(60') = 49.74'

Therefore, the angle A can be rewritten as:

A = 61° + 49.74'

To know more about angle, refer here:

https://brainly.com/question/31912194

#SPJ4

An airline has 81% of its flights depart on schedule. It has 69% of its flights depart and arrive on schedule. Find the probability that a flight that departs on schedule also arrives on schedule. Round the answer to two decimal places. a. 1.25 b. 0.85 c. 0.45 d. 0.43

Answers

The answer is option b) 0.85.

The probability that a flight that departs on schedule also arrives on schedule is 0.85.

Let's denote the event of a flight departing on schedule as D and the event of a flight arriving on schedule as A.

We are given that P(D) = 0.81, which represents the probability of a flight departing on schedule. We are also given that P(D ∩ A) = 0.69, which represents the probability of a flight both departing and arriving on schedule.

We want to find P(A|D), which represents the probability of a flight arriving on schedule given that it has departed on schedule.

P(A|D) = 0.69 / 0.81 ≈ 0.85

To learn more about probability

brainly.com/question/31828911

#SPJ11

what are the focus and directrix of the parabola with equation y=1/12x^2

Answers

The focus and directrix of the parabola with equation y = (1/12)x^2 can be determined using the properties of parabolas. The focus is located at the point (0, p), where p is the coefficient of the squared term.

For the given equation y = (1/12)x^2, the coefficient of the squared term is 1/12. Therefore, the focus is located at the point (0, 1/4). The focus is the point on the parabola that is equidistant to both the vertex and the directrix. In this case, since the parabola opens upwards, the focus is above the vertex.

The directrix, on the other hand, is a horizontal line located at a distance of -p from the vertex. In this case, the directrix is located at y = -1/4. It is a line parallel to the x-axis and acts as a mirror for the parabolic curve.

To learn more about parabola click here :

brainly.com/question/11911877

#SPJ11


asap
25. A class of 150 students took a final examination in mathematics. The mean score was 72% and the standard deviation was 14%. Determine the percentile rank of a score of 79%, assuming that the marks

Answers

The percentile rank of a score of 79% ≈ 69.15%.

To determine the percentile rank of a score of 79%, we need to find the proportion of scores that fall below 79% in a normal distribution with a mean of 72% and a standard deviation of 14%.

We can use the Z-score formula to standardize the score and then find the corresponding percentile rank.

Z = (X - μ) / σ

Where:

Z is the standardized score (Z-score)

X is the raw score

μ is the mean

σ is the standard deviation

Calculating the Z-score for a score of 79%:

Z = (79 - 72) / 14

Z = 0.5

Using a Z-table or a statistical calculator, we can find the percentile corresponding to a Z-score of 0.5.

Hence the percentile rank of a score of 79% is approximately 69.15%. This means that the score of 79% is higher than approximately 69.15% of the scores in the class.

To know more about percentile refer here:

https://brainly.com/question/1594020#

#SPJ11







Solve the following problems. 1. Calculate the area of the segment cut from the curve y=x(3-x) by the line y=x. 2. Find the area between the line y=x and the curve y=x2. 3. Find the area contained bet

Answers

1. the area of the segment cut from the curve y = x(3 - x) by the line y = x is 4/3 square units.

2. the area between the line y = x and the curve y = x^2 is 1/6 square units.

1. To calculate the area of the segment cut from the curve y = x(3 - x) by the line y = x, we need to find the points of intersection between the curve and the line. Setting the equations equal to each other, we have:

x(3 - x) = x

Expanding the left side, we get:

3x - x² = x

Rearranging the equation, we have:

3x - x²  - x = 0

Combining like terms, we get:

-x² + 2x = 0

Factoring out an x, we have:

x(-x + 2) = 0

This equation is satisfied when x = 0 or x = 2. So, the curve and the line intersect at x = 0 and x = 2.

To find the corresponding y-values, we substitute these x-values into the equation y = x(3 - x):

For x = 0:

y = 0(3 - 0) = 0

For x = 2:

y = 2(3 - 2) = 2

So, the points of intersection are (0, 0) and (2, 2).

To find the area of the segment, we integrate the curve y = x(3 - x) from x = 0 to x = 2 and subtract the integral of the line y = x over the same interval:

Area = ∫[0, 2] (x(3 - x)) dx - ∫[0, 2] x dx

Integrating the first term:

∫(x(3 - x)) dx = ∫(3x - x²) dx = (3/2)x² - (1/3)x³

Integrating the second term:

∫x dx = (1/2)x²

Now, we evaluate the definite integrals:

Area = [(3/2)x² - (1/3)x³] [0, 2] - [(1/2)x²] [0, 2]

    = [(3/2)(2)² - (1/3)(2)³] - [(1/2)(2)² - (1/2)(0)²]

    = [6 - (8/3)] - [2 - 0]

    = (18/3 - 8/3) - 2

    = 10/3 - 2

    = 4/3

Therefore, the area of the segment cut from the curve y = x(3 - x) by the line y = x is 4/3 square units.

2. To find the area between the line y = x and the curve y = x² we need to find the points of intersection between the two curves. Setting the equations equal to each other, we have:

x = x²

Rearranging the equation, we get:

x² - x = 0

Factoring out an x, we have:

x(x - 1) = 0

This equation is satisfied when x = 0 or x = 1. So, the line and the curve intersect at x = 0 and x = 1.

To find the corresponding y-values, we substitute these x-values into the equations:

For x = 0:

y = 0

For x = 1:

y = 1

So, the points of intersection are (0, 0) and (1, 1).

To find the area between the line and the curve, we integrate the difference of the two functions from x = 0 to x = 1:

Area = ∫[0, 1] (x - x²) dx

Integrating the function:

∫(x - x²) dx = (1/2)x² - (1/3)x³

Now, we evaluate the definite integral:

Area = [(1/2)x² - (1/3)x³] [0, 1]

    = [(1/2)(1)² - (1/3)(1)³] - [(1/2)(0)² - (1/3)(0)³]

    = (1/2 - 1/3) - (0 - 0)

    = 1/6

Therefore, the area between the line y = x and the curve y = x^2 is 1/6 square units.

Learn more about Integration here

https://brainly.com/question/31585464

#SPJ4

what type of function is f(x) = 2x3 – 4x2 5? exponential logarithmic polynomial radical

Answers

The type of function f(x) = 2x^3 – 4x^2 + 5 is a polynomial function.

A polynomial function is a mathematical function consisting of one or more terms, each term being a product of a constant and a variable raised to a non-negative integer exponent. In this case, the function f(x) = 2x^3 – 4x^2 + 5 satisfies this definition.

The function f(x) is a polynomial of degree 3, indicated by the highest exponent in the function, which is 3. The terms in the function are multiplied by constants (2, -4, and 5) and powers of the variable x (x^3, x^2, and x^0). The coefficients and exponents involved are all integers.

Therefore, based on the given function f(x) = 2x^3 – 4x^2 + 5, we can conclude that it is a polynomial function.

To learn more about exponential logarithmic polynomial radical

brainly.com/question/32035390

#SPJ11

For a cach of the following draw the probability distribution a) A spinner with equal sector is to be spus. Determine the probability of each different outcome and then graph the results on a single Cartese plase (Uniform) b) The probability of Simon hitting a home is 0:34 Simon is expected to boto times. (Binomial)

Answers

a) For a spinner with equally sized sectors, the probability distribution is uniform, meaning each outcome has an equal probability. This can be represented graphically with a flat line.

b) Given Simon's probability of hitting a home run is 0.34 and assuming each attempt is independent, Simon's expected number of home runs can be calculated using the binomial distribution.

a) For a spinner with equal sectors, the probability distribution is uniform. Since each sector has an equal chance of being landed upon, the probability of each outcome is the same.

Let's assume there are n sectors on the spinner. The probability of each outcome is 1/n. To graph the results on a Cartesian plane, we can plot the outcomes on the x-axis and their corresponding probabilities on the y-axis.

Each outcome will have a height of 1/n, resulting in a constant horizontal line at that height across all outcomes.

b) If the probability of Simon hitting a home run is 0.34, and he is expected to bat n times, we can use the binomial distribution to determine the probability of Simon hitting a certain number of home runs.

The probability mass function (PMF) of the binomial distribution can be used to calculate these probabilities. Each outcome represents the number of successful home runs (k) out of the total number of trials (n). We can calculate the probability of each outcome using the formula

P(k) = (n choose k) [tex]* p^k * (1-p)^{n-k},[/tex]

where p is the probability of success (0.34) and (n choose k) is the binomial coefficient. We can plot the outcomes on the x-axis and their corresponding probabilities on the y-axis to graph the binomial distribution.

The resulting graph will show the probabilities of different numbers of home runs for Simon.

To learn more about probability distribution visit:

brainly.com/question/795909

#SPJ11

Find the Laplace Transform of f(t):

f(t) 0, π-t, 0, = fx = t< π π ≤ t < 2π t> 2π

Answers

The Laplace transform of f(t) is given by: F(s) = (-2π/s) * e^(-2πs) + (π/s) * e^(-πs) - (1/s^2) * (∞)

To find the Laplace transform of the function f(t), we need to evaluate the integral of f(t) times e^(-st) from 0 to infinity, where s is the complex frequency parameter. Let's consider the different intervals for t and calculate the Laplace transform accordingly.

For 0 ≤ t < π:

f(t) = 0 in this interval, so the integral for this part is also 0.

For π ≤ t < 2π:

f(t) = t in this interval. So we have:

∫[π to 2π] t * e^(-st) dt

To evaluate this integral, we can use integration by parts. Let's choose u = t and dv = e^(-st) dt.

Then, du = dt and v = (-1/s) * e^(-st).

Using the integration by parts formula:

∫ u dv = uv - ∫ v du

We get:

∫[π to 2π] t * e^(-st) dt = (-t/s) * e^(-st) | [π to 2π] - ∫[π to 2π] (-1/s) * e^(-st) dt

Simplifying, we have:

= (-t/s) * e^(-st) | [π to 2π] - (1/s^2) * e^(-st) | [π to 2π]

Evaluating this expression at t = 2π and t = π, we get:

= (-(2π)/s) * e^(-2πs) + (π/s) * e^(-πs) - ((1/s^2) * e^(-2πs) - (1/s^2) * e^(-πs))

For t > 2π:

f(t) = t in this interval. So we have:

∫[2π to ∞] t * e^(-st) dt

To evaluate this integral, we can use the Laplace transform property for t^n * e^(-st), which is n! / (s^(n+1)).

In this case, n = 1, so the Laplace transform of t * e^(-st) is 1 / (s^2).

Using this property, we get:

= ∫[2π to ∞] 1 / (s^2) dt = (-1/s^2) * t | [2π to ∞]

Evaluating this expression at t = ∞ and t = 2π, we get:

= (-1/s^2) * (∞ - 2π) = (-1/s^2) * (∞)

Therefore, the Laplace transform of f(t) is given by:

F(s) = (-2π/s) * e^(-2πs) + (π/s) * e^(-πs) - (1/s^2) * (∞)

To learn more about Laplace transform

https://brainly.com/question/32625910

#SPJ11

A study measured the weights of a sample of 30 rats under experiment controls. Suppose that 12 rats were underweight.
1. Calculate a 95% confidence interval on the true proportion of underweight rats from this experiment._____...______
2. Using the point estimate of p obtained from the preliminary sample, what is the minimum sample size needed to be 95% confident that the error in estimating the true value of p is less than 0.02?__________
3. How large must the sample be if you wish to be 95% confident that the error in estimating p is less than 0.02, regardless of the true value of
p?__________

Answers

The 95% confidence interval on the true proportion of underweight rats from this experiment is (0.189, 0.611), the minimum sample size required to be 95% confident that the error in estimating the true value of p is less than 0.02 is 576 and,  the sample size required to be 95% confident that the error in estimating p is less than 0.02, regardless of the true value of p, is 9604.

1. Calculation of a 95% confidence interval on the true proportion of underweight rats:

Here, n = 30, and p = 12/30 = 0.4 (12 rats out of 30 were underweight).

We will use the following formula to calculate the 95% confidence interval on the true proportion of underweight rats: (p - E, p + E),

where E = zα/2 * √[p (1 - p) / n]We know that α = 0.05 (since the confidence level is 95%).

Therefore, zα/2 = z0.025 = 1.96 (from the standard normal table).

E = 1.96 * √[(0.4)(0.6) / 30] = 0.211(p - E, p + E) = (0.4 - 0.211, 0.4 + 0.211) = (0.189, 0.611)

Therefore, a 95% confidence interval on the true proportion of underweight rats from this experiment is (0.189, 0.611).

2. Calculation of the minimum sample size required to be 95% confident that the error in estimating the true value of p is less than 0.02:

Here, we will use the following formula to calculate the minimum sample size required:n = [zα/2 / E]² * p * (1 - p)

We know that α = 0.05 (since the confidence level is 95%). T

herefore, zα/2 = z0.025 = 1.96 (from the standard normal table).

E = 0.02 (since we want the error to be less than 0.02).p = 0.4 (using the point estimate of p obtained from the preliminary sample).n = [1.96 / 0.02]² * 0.4 * 0.6 = 576

Therefore, the minimum sample size required to be 95% confident that the error in estimating the true value of p is less than 0.02 is 576.

3. Calculation of the sample size required to be 95% confidence that the error in estimating p is less than 0.02, regardless of the true value of p:

We will use the following formula to calculate the sample size required:

n = [zα/2 / E]²We know that α = 0.05 (since the confidence level is 95%).

Therefore, zα/2 = z0.025 = 1.96 (from the standard normal table).

E = 0.02 (since we want the error to be less than 0.02).n = [1.96 / 0.02]² = 9604

Therefore, the sample size required to be 95% confident that the error in estimating p is less than 0.02, regardless of the true value of p, is 9604.

To know more about 95% confidence interval visit:

https://brainly.in/question/35949101

#SPJ11

A fast-food restaurant manager believes that 27% of customers who order Double Whopper Cheeseburgers (1,000 calories, if you are counting ) also order a Diet Coke along with their meal. A recent survey of 325 customers revealed that 32% of customers that ordered a Double Whopper Cheeseburger also ordered a Diet Coke. The test statistic calculated to determine whether or not the actual proportion of 27% has changed based on this sample is closest to: 2.03 2.70 O 1.645 2.57 QUESTION 20 The total rejection region for a two-tailed test for a mean, that has a test statistic, of 2.16 has an area or probability closest to about 48% about 1.5% about 98% about 3%?

Answers

The test statistic calculated to determine whether or not the actual proportion of 27% has changed based on this sample is closest to A. 2.03 .

The total rejection region for a two-tailed test for a mean, that has a test statistic, of 2.16 has an area or probability closest to D. 3 %.

How to find the test statistic?

To find the test statistic, we need to use the formula for a hypothesis test for a proportion:

Z = (sample proportion - population proportion ) / √ [ ( p ( 1 - p ) / n )]

The test statistic would be  :

Z  = (0.32 - 0.27) / √ [(0.27 x 0.73) / 325]

Z = 0.05 / √ [0.1971 / 325]

Z = 0.05 / √ [0.0006064615]

Z = 0.05 / 0.024626

Z = 2.03

If we look at a standard normal distribution table or use a statistical software, a Z score of 2.16 (or -2.16 for the two-tailed test) corresponds approximately to a p-value of 0.031 or 3. 1%.

The closes total rejection region is therefore about 3 %.

Find out more on test statistic at https://brainly.com/question/15110538

#SPJ4

Alice decides to set up an RSA public key encryption using the two primes p = 31 and q = 41 and the encryption key e = 11. You must show all calculations, including MOD-calculations using the division algorithm! (1) Bob decides to send the message M = 30 to her using this encryption. What is the code C that he will send her? (2) What is Alice's decryption key d? Remember that you have to show all your work using the Euclidean algorithm. (3) Alice also receives the message C = 101 from Carla. What was her original message M?

Answers

(1) The code C that Bob will send to Alice is 779.

To find the code C that Bob will send to Alice using RSA encryption, we follow these steps:

1: Calculate n, the modulus:

n = p × q = 31 × 41 = 1271

2: Calculate φ(n), Euler's totient function:

φ(n) = (p - 1) × (q - 1) = 30 × 40 = 1200

3: Find the decryption key d using the Euclidean algorithm:

We need to find a value for d such that (e × d) ≡ 1 (mod φ(n)).

Using the Euclidean algorithm:

φ(n) = 1200, e = 11

1200 = 109 × 11 + 1

11 = 11 × 1 + 0

From the Euclidean algorithm, we have:

1 = 1200 - 109 × 11

Therefore, d = -109

4: Adjust d to be a positive value:

Since d = -109, we add φ(n) to d to get a positive value:

d = -109 + 1200 = 1091

5: Encrypt the message M:

C ≡ M^e (mod n)

C ≡ 30^11 (mod 1271)

To calculate this, we can use repeated squaring:

30² ≡ 900 (mod 1271)

30⁴ ≡ (30²)² ≡ (900)² ≡ 810000 (mod 1271) ≡ 60 (mod 1271)

30⁸ ≡ (30⁴)² ≡ (60)² ≡ 3600 (mod 1271) ≡ 1089 (mod 1271)

30¹¹ ≡ 30⁸ × 30² × 30 (mod 1271) ≡ 1089 × 900 × 30 (mod 1271) ≡ 11691000 (mod 1271) ≡ 779 (mod 1271)

Therefore, the code C that will be sent is 779.

(2) To find Alice's decryption key d, we already calculated it in Step 4 as d = 1091.

(3) To find Alice's original message M from the received code C, we can use the decryption formula:

M ≡[tex]C^d (mod \ n)[/tex]

M ≡ [tex]101^1091 (mod \ 1271)[/tex]

To calculate this, we can use repeated squaring:

101² ≡ 10201 (mod 1271) ≡ 789 (mod 1271)

101⁴ ≡ (101²)² ≡ (789)² ≡ 622521 (mod 1271) ≡ 1146 (mod 1271)

101⁸ ≡ (101⁴)² ≡ (1146)² ≡ 1313316 (mod 1271) ≡ 961 (mod 1271)

101¹⁶ ≡ (101⁸)² ≡ (961)² ≡ 923521 (mod 1271) ≡ 579 (mod 1271)

101³² ≡ (101¹⁶)² ≡ (579)² ≡ 335241 (mod 1271) ≡ 30 (mod 1271)

101⁶⁴ ≡ (101³²)² ≡ (30)² ≡ 900 (mod 1271)

101¹²⁸ ≡ (101⁶⁴)² ≡ (900)² ≡ 810000 (mod 1271) ≡ 60 (mod 1271)

101²⁵⁶ ≡ (101¹²⁸)² ≡ (60)² ≡ 3600 (mod 1271) ≡ 1089 (mod 1271)

To know more about Bob refer here:

https://brainly.com/question/30362091

#SPJ11

Consider the quasi-linear PDE given by u + (u* − 1)ur = 0, - where and t represent space and time, with initial conditions x < 0, 1, 1 - x, u(x,0) = 0 < x < 1, 0, 1 < x. (i) Show that the characteristic curves are given by x = t(f³(C) − 1) + C. (ii) Give the solution u(x, t) in implicit form. (iii) What geometric property of the characteristic curves indicate the presence of a shock? Explain why shocks occur for all x ≤ 0. (iv) Find the time, t = ts, and place x = x, when the system has its first shock. (v) Sketch the characteristic curves for this system of partial differential equation and initial condition, including the position of the first shock.

Answers

The quasi-linear partial differential equation (PDE) u + (u* − 1)ur = 0 is considered, along with the initial conditions. The characteristic curves are found to be x = t(f³(C) − 1) + C, and the solution u(x, t) is obtained in implicit form.

(i) To find the characteristic curves, we can rewrite the given PDE as dx/dt = f(u), where f(u) = (u* − 1)ur. Applying the method of characteristics, we have dx/f(u) = dt. Integrating this expression, we get x = t(f³(C) − 1) + C, where C is a constant of integration.

(ii) The solution u(x, t) can be obtained in implicit form by considering the initial conditions. Using the characteristic curves x = t(f³(C) − 1) + C, we can express u(x, t) as u(x, t) = u(x, 0) = 0 for x < 0, u(x, t) = u(x, 0) = 1 for 0 < x < 1, and u(x, t) = u(x, 0) = 0 for x > 1.

(iii) The geometric property of the characteristic curves that indicates the presence of a shock is the crossing of characteristics. Shocks occur when two characteristics intersect, causing a discontinuity in the solution. In this case, shocks occur for all x ≤ 0 because the characteristic curves with C < 0 cross the x-axis, resulting in a shock.

(iv) To find the time t = ts and place x = x of the first shock, we need to determine the value of C at which two characteristics intersect. By setting the expressions for x in terms of C equal to each other and solving for C, we can find the constant of integration corresponding to the first shock.

(v) A sketch of the characteristic curves can be made using the equation x = t(f³(C) − 1) + C. The position of the first shock can be determined by finding the intersection of two characteristic curves. By plotting the characteristic curves for various values of C, we can visualize the location of the shock.

Learn more about discontinuity here:

https://brainly.com/question/28914808

#SPJ11

By using the e- definition of limits, prove that lim,- (2.x2 – 1 + 1) = 7. 2 0

Answers

To prove that limₓ→0 (2x² - 1 + 1) = 7, we can use the ε-δ definition of limits.

Let ε > 0 be given. We need to find a δ > 0 such that if 0 < |x - 0| < δ, then |(2x² - 1 + 1) - 7| < ε.

Simplifying the expression inside the absolute value, we have |2x² - 1 + 1 - 7| = |2x² - 7|.

To find a suitable δ, we can bound the expression |2x² - 7| using a known value. We observe that |2x² - 7| = 2|x|² - 7.

Since we want to find a δ such that |(2x² - 7) - 0| < ε, we can choose δ such that 2|x|² < ε/2 + 7.

Now, let's consider the term 2|x|². We know that |x| < δ, so we have |x|² < δ².

Choosing δ ≤ 1 ensures that |x| < 1, and hence |x|² < δ².

Setting δ = min(1, √((ε/2 + 7)/2)), we can ensure that if 0 < |x - 0| < δ, then |(2x² - 7) - 0| < ε.

Therefore, we have shown that limₓ→0 (2x² - 1 + 1) = 7 using the ε-δ definition of limits.

To know more about the ε-δ definition of limits, refer here: https://brainly.com/question/27322217#

#SPJ11

You may need to use the appropriate appendix table or technology to answer this question Automobiles manufactured by the Efficiency Company have been averaging 43 miles per gation of gasoline in highway driving. It is believed that its new automobiles average more than 43 miles per gallon. An independent testing service road-tested 36 of the automobiles. The sample showed an average of 44.5 miles per galian with a standard deviation of 1 miles per gaten. (a) With a 0.05 level of significance using the critical value approach, test to determine whether or not the new automobiles actually do average more than 43 miles per ga State the null and alternative hypotheses (in miles per gation). (Enter te for as needed.) H₂² H₂ Compute the test statistic 3 x Determine the critical value(s) for this test. (Round your answer(s) to three decimal places. If the test is one-tated, enter NONE for the unusta) test statistics a test statistic 23 State your conclusion O Reject H There is sufficient evidence to conclude that the new automobiles actually do average more than 43 miles per gallon Do not reject He. There is insufficient evidence to conclude that the new automobiles actually do average meve than 43 miles per gallon Reject H. There is insufficient evidence to conclude that the new automobiles actually do average more than 43 miles per gan Do not reject H There is sufficient evidence to conclude that the new automobiles actually do average more than 43 mis per gan (b) What is the p-value associated with the sample results? (Round your answer to four decimal places) p-value- ion based on the p-value?

Answers

(a) Reject H₀; There is sufficient evidence to conclude that the new automobiles actually do average more than 43 miles per gallon.

(b) p-value ≈ 0.0000; Strong evidence against H₀; The new automobiles actually do average more than 43 miles per gallon with a very high level of confidence.

(a) The null hypothesis, H₀: μ ≤ 43 (miles per gallon)

The alternative hypothesis, H₁: μ > 43 (miles per gallon)

Computing the test statistic:

Test statistic, t = (X' - μ₀) / (s / √n) = (44.5 - 43) / (1 / √36) = 4.5

Determining the critical value:

Since the alternative hypothesis is one-tailed (greater than), we need to find the critical value at α = 0.05 with degrees of freedom (df) = n - 1 = 36 - 1 = 35.

Using a t-table or software, the critical value at α = 0.05 and df = 35 is approximately 1.690.

State your conclusion:

Since the test statistic (4.5) is greater than the critical value (1.690), we reject the null hypothesis.

There is sufficient evidence to conclude that the new automobiles actually do average more than 43 miles per gallon.

(b) To find the p-value associated with the sample results, we compare the test statistic to the t-distribution with df = 35.

Using a t-table or software, we find that the p-value is less than 0.0001 (approximately).

Interpretation based on the p-value:

The p-value is extremely small, indicating strong evidence against the null hypothesis.

We can conclude that the new automobiles actually do average more than 43 miles per gallon with a very high level of confidence.

To know more about level of confidence, refer here:

https://brainly.com/question/31508283

#SPJ4

Given that f(0) = 1+ 2?, and g(x) = 10 – 2, find a) (gof) (c) = g(f(x)) b) The domain of (gºf)(x) = g(f(x)) a)g (f(x)) = 9+ b) Domain: All real numbers O a) 9 (f()) = 11 -2, (11 minus x) b) Domain: All real numbers. O a)g (f (x)) = 9-32 (the square root of 9 minus x squared) b) Domain: [-3.3] a)g (f(x)) = 9 - 2? (the square root of 9 minus x squared) b) Domain: (- 0,3]U[3,-)

Answers

a) (g∘f)(x) = 9 - 2√(9 - x)

b) Domain: [-3, 3]

c) g(f(x)) = 9 - 2(x^2)

d) Domain: All real numbers

In part (a), the composition (g∘f)(x) represents the function g applied to the output of f. It is obtained by substituting the expression for f(x) into g(x). The resulting function is 9 - 2 times the square root of (9 - x).

In part (b), the domain of (g∘f)(x) is determined by considering the restrictions on the square root function. The expression inside the square root must be non-negative, so 9 - x ≥ 0. Solving this inequality gives x ≤ 9. Therefore, the domain is the interval [-3, 3].

In part (c), g(f(x)) is obtained by substituting the expression for f(x) into g(x). The resulting function is 9 - 2 times x squared.

In part (d), the domain of g(f(x)) is all real numbers since there are no restrictions on the square root function.

Overall, the compositions involve substituting the expression for f(x) into g(x) and analyzing the domain based on the restrictions of the involved functions.

Learn more about inequality:

https://brainly.com/question/30238989

#SPJ11

Problem 9-23 Using the Student t distribution, find the critical upper-tail values for the following tail areas: (a) alpha-,1 df 6 (b) alpha-.0005 df-30

Answers

The critical upper-tail values are:

(a) For alpha = 0.01 and df = 6, the important t-fee is about 2.447.

(b) For alpha = 0.0005 and df = 30, the critical t-price is approximately 3.809.

To locate the essential upper-tail values using the Student t distribution, we want to determine the t-price that corresponds to a given tail place and ranges of freedom.

(a) For alpha = 0.01 (1% significance level) and levels of freedom df = 6:

Using a t-table or statistical software, we are able to find the vital t-value for an top-tail vicinity of zero.01 and levels of freedom df = 6.

The critical t-cost for alpha = 0.01, df = 6 is approximately 2.447.

(b) For alpha = 0.0005 (0.05% importance stage) and tiers of freedom df = 30:

Again, using a t-table or statistical software, we will discover the crucial t-fee for an top-tail region of zero.0005 and stages of freedom df = 30.

The crucial t-price for alpha = 0.0005, df = 30 is about 3.809.

Therefore, the critical upper-tail values are:

(a) For alpha = 0.01 and df = 6, the important t-fee is about 2.447.

(b) For alpha = 0.0005 and df = 30, the critical t-price is approximately 3.809.

To know more about critical upper-tail values,

https://brainly.com/question/30654453

#SPJ4


Let
S be the annual sales (in millons) for a particlular electronic
item. The value of S is 54.8 for 2007. What does S=54.8 mean in
this Situation

Answers

S = 54.8 in this situation means that the annual sales of the particular electronic item were 54.8 million in the year 2007.

Given, Let S be the annual sales (in millions) for a particular electronic item. The value of S is 54.8 for 2007.Annual refers to a yearly basis and, in this situation, S refers to the annual sales of the electronic item that is mentioned. "Particular" refers to a specific electronic item that is mentioned in the given question. So, S = 54.8 in this situation means that the annual sales of the particular electronic item were 54.8 million in the year 2007.

To know more on value visit:

https://brainly.com/question/11546044

$SPJ11

The given S = 54.8 for 2007 means that the annual sales (in millions) of a particular electronic item was 54.8 million dollars for the year 2007.What is annual sales?Annual sales refer to the total amount of revenue generated by a company or a product in a year.

It is an important metric used to determine the financial performance of a company. Annual sales are calculated by multiplying the number of units sold by the price per unit.To calculate annual sales, the following formula can be used:Annual Sales = Number of Units Sold × Price per UnitWhere,Number of Units Sold refers to the total number of units sold in a yearPrice per Unit refers to the selling price of one unit of the product.

To know more about sales, visit:

https://brainly.com/question/29436143

#SPJ11

A famous commercial for Tootsie Pops once asked, "How many licks to the center of a Tootsie Pop?" A student asked 81 volunteers to count the number of licks before reaching the center. The mean number of licks was 356.1 with a standard deviation of 185.7. a. Construct a 70% confidence interval for the population mean. b. Interpret the interval.

Answers

a. The 70% confidence interval for the population mean number of licks to the center of a Tootsie Pop is (304.8, 407.4).

b. This interval suggests that we can be 70% confident that the true population mean number of licks falls within the range of 304.8 to 407.4. In other words, based on the sample data, we estimate that the average number of licks to reach the center of a Tootsie Pop is somewhere between 304.8 and 407.4.

To construct the confidence interval, we use the formula:

Confidence Interval = x ± (t * (s / √n))

where x is the sample mean, s is the sample standard deviation, n is the sample size, and t is the critical value from the t-distribution corresponding to the desired confidence level.

For a 70% confidence level, the critical value is approximately 1.296, which can be obtained from the t-distribution table or using statistical software.

Plugging in the values:

Confidence Interval = 356.1 ± (1.296 * (185.7 / √81)) = (304.8, 407.4)

Therefore, based on the sample data, we can be 70% confident that the true population mean number of licks to the center of a Tootsie Pop falls within the range of 304.8 to 407.4.

To know more about confidence intervals, refer here:

https://brainly.com/question/32546207#

#SPJ11

Let V be a vector space with inner product (,). Let T be a linear operator on V. Suppose W is a T invariant subspace. Let Tw be the restriction of T to W. Prove that (i) Wt is T* invariant. (ii) If W is both T,T* invariant, then (Tw)* = (T*)w. (iii) If W is both T, T* invariant and T is normal, then Tw is normal.

Answers

If W is both T, T* invariant, and T is normal, then Tw is normal.

(i) To prove that Wₜ is T* invariant, we need to show that for any w ∈ Wₜ, T*w ∈ Wₜ.

Let w ∈ Wₜ, which means w = Tw for some v ∈ V.

Now consider T*w. Since W is T-invariant, we have T*w ∈ W. Since W is a subspace, it follows that T*w ∈ Wₜ.

Therefore, Wₜ is T* invariant.

(ii) If W is both T and T* invariant, we want to show that (Tₜ)* = (T*)w for any w ∈ Wₜ.

Let w ∈ Wₜ, which means w = Tw for some v ∈ V.

To find (Tₜ)*, we need to consider the adjoint of the operator Tw. Using the property of adjoints, we have:

⟨(Tₜ)*w, v⟩ = ⟨w, Tw⟩ for all v ∈ V.

Substituting w = Tw, we get:

⟨(Tₜ)*w, v⟩ = ⟨Tw, T(v)⟩ for all v ∈ V.

Since W is T-invariant, we have T(v) ∈ W for all v ∈ V. Therefore:

⟨(Tₜ)*w, v⟩ = ⟨Tw, T(v)⟩ = ⟨w, T(v)⟩ for all v ∈ V.

This implies that (Tₜ)*w = Tw for all v ∈ V, which is equal to w. Hence, (Tₜ)*w = w.

Therefore, (Tₜ)* = (T*)w.

(iii) If W is both T and T* invariant, and T is normal, we want to show that Tw is normal.

To prove that Tw is normal, we need to show that TT*w = (T*w)T* for any w ∈ Wₜ.

Let w ∈ Wₜ, which means w = Tw for some v ∈ V.

Consider TT*w:

TT*w = T(Tw) = T²w.

And (T*w)T*:

(T*w)T* = (Tw)T* = T(wT*) = TwT*.

Since W is T-invariant, we have T*w ∈ Wₜ. Therefore:

TT*w = T²w = T(Tw) = T(T*w).

Also, we have:

(T*w)T* = TwT* = T(wT*) = T(Tw).

Hence, TT*w = (T*w)T*, which implies that Tw is normal.

Therefore, if W is both T, T* invariant, and T is normal, then Tw is normal.

To know more about T-invariant subspaces , refer here:

https://brainly.com/question/31976742#

#SPJ11

Use the random sample data to test the claim that the mean travel distance to work in California is less than 35 miles. Use 1% level of significance. • Sample data: = 32.4 mi s = 8.3 mi n = 35 1. Identify the tail of the test. [ Select] 2. Find the P-value [Select] 3. Will the null hypothesis be rejected?

Answers

The tail of the test will be the left tail because we are testing whether the mean travel distance to work in California is less than 35 miles.

How to calculate the value

In order to find the p-value, we can use a one-sample t-test. We will calculate the t-value and then find the corresponding p-value.

Sample mean  = 32.4 mi

Sample standard deviation (s) = 8.3 mi

Sample size (n) = 35

Hypothesized mean (μ) = 35 mi

Substituting these values into the formula, we have:

t = (32.4 - 35) / (8.3 / √35)

Calculating the value, we find:

t ≈ -1.770

To find the p-value, we need to consult a t-distribution table or use statistical software. For a one-tailed test with a significance level of 1% and 34 degrees of freedom (n - 1), the p-value is approximately 0.045.

Since the p-value (0.045) is less than the significance level of 1%, we reject the null hypothesis.

Learn more about hypothesis on

https://brainly.com/question/11555274

#SPJ4

What is an assumption of a Spearman's rho test? a) Residuals are equal across predictor variables along the criterion variable. b) Data must be ordinal. c) Independent variables must be independent of each other. d) Data is linear.

Answers

The assumption of Spearman's rho test is that the data must be ordinal. The correct option is b.

Spearman's rho test is a nonparametric measure of correlation between two variables. It is used when the variables are measured on an ordinal scale, meaning that the data can be ranked but not necessarily measured with equal intervals.

The test is based on the ranks of the observations rather than their actual values. Therefore, the assumption of Spearman's rho test is that the data being analyzed should possess an ordinal level of measurement.

The test does not require the assumption of linearity, as it can capture monotonic relationships between variables. It also does not assume equal residuals across predictor variables along the criterion variable (option a) or the independence of the predictor variables (option c).

However, it is important to note that Spearman's rho test is not appropriate for analyzing data that is strictly nominal or interval/ratio in nature.

To know more about Spearman's rho, refer here:

https://brainly.com/question/9000085#

#SPJ11

What relationship do the ratios of sin x° and cos yº share?
a. The ratios are both identical (12/13 and 12/13)
b. The ratios are opposites (-12/13 and 12/13)
c. The ratios are reciprocals. (12/13 and 13/12)
d. The ratios are both negative. (-12/13 and -13/12)

Answers

The relationship between the ratios of sin x° and cos yº is that they are reciprocals. The correct answer is option c. The ratios of sin x° and cos yº are reciprocals of each other.

In trigonometry, sin x° represents the ratio of the length of the side opposite the angle x° to the length of the hypotenuse in a right triangle. Similarly, cos yº represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

Since the hypotenuse is the same in both cases, the ratios sin x° and cos yº are related as reciprocals. This means that if sin x° is equal to 12/13, then cos yº will be equal to 13/12. The reciprocals of the ratios have an inverse relationship, where the numerator of one ratio becomes the denominator of the other and vice versa.

It's important to note that the signs of the ratios can vary depending on the quadrant in which the angles x° and yº are located. However, the reciprocal relationship remains the same regardless of the signs.

Learn more about hypotenuse here:

https://brainly.com/question/16893462

#SPJ11

Carefully sketch (and shade) the (finite) region R in the first quadrant which is bounded above by the (inverted) parabola y +(6 -x ), bounded on the right by the straight line r = 3, and is bounded below by the horizontal straight line y=5.

Answers

The finite region R in the first quadrant is bounded above by the inverted parabola y = -(x^2 - 6x), bounded on the right by the straight line r = 3, and bounded below by the horizontal straight line y=5.

To find the finite region R in the first quadrant, we need to plot the given curves and find their intersection points.

First, let's plot the horizontal straight line y=5. This line passes through the point (0,5) and is parallel to the x-axis.

Next, let's plot the straight line r=3. This is a vertical line that passes through the point (3,0) and is parallel to the y-axis.

Finally, let's plot the inverted parabola y = -(x^2 - 6x). We can rewrite this equation as y = -[(x-3)^2 - 9]. This parabola opens downwards and its vertex is at (3,9).

To find the intersection points of these curves, we need to solve their equations simultaneously.

The horizontal line y=5 intersects the parabola when:

5 = -(x^2 - 6x)

x^2 - 6x - 5 = 0

(x-1)(x-5) = 0

So the line intersects the parabola at x=1 and x=5.

The vertical line r=3 intersects the parabola when:

r = 3

y = -(x^2 - 6x)

y = -(9 - 6x)

y = 6x - 9

So the line intersects the parabola at (3,-3) and (3,9).

Now we can find the finite region R in the first quadrant. It is bounded above by the inverted parabola y = -(x^2 - 6x), bounded on the right by the straight line r = 3, and bounded below by the horizontal straight line y=5.

Thus, the horizontal straight line y=5 and the inverted parabola y = -(x2 - 6x) are the upper, right, and lower boundaries of the finite region R in the first quadrant, respectively.

To know more about inverted parabola refer here:

https://brainly.com/question/16974521#

#SPJ11

Report the following: (a). At what value does the CDF of a N(0,1) take on the value of 0.3? (b). At what value does the CDF of a N(0, 1) take on the value of 0.75? (c). What is the value of the CDF of a N(-2,5) at 0.8? (d). What is the value of the PDF of a N(-2,5) at 0.8? (e). What is the value of the CDF of a N(-2,5) at -1.2?

Answers

The values are as follows: (a) -0.52, (b) 0.68, (c) 0.7764, (d) the value of the PDF at 0.8 using the given parameters, and (e) 0.3300.

(a) The value at which the cumulative distribution function (CDF) of a standard normal distribution (N(0,1)) takes on the value of 0.3 is approximately -0.52.

(b) The value at which the CDF of a standard normal distribution (N(0,1)) takes on the value of 0.75 is approximately 0.68.

(c) The value of the CDF of a normal distribution N(-2,5) at 0.8 can be calculated by standardizing the value using the formula Z = (X - μ) / σ, where X is the given value, μ is the mean, and σ is the standard deviation. After standardizing, we find that Z ≈ 0.76. Using a standard normal distribution table or calculator, we can determine that the CDF value at Z = 0.76 is approximately 0.7764.

(d) The value of the probability density function (PDF) of a normal distribution N(-2,5) at 0.8 can be calculated using the formula f(x) = (1 / (σ * √(2π[tex]^(-(x -[/tex] μ)))) * e² / (2σ²)), where x is the given value, μ is the mean, σ is the standard deviation, and e is Euler's number (approximately 2.71828). Plugging in the values, we can compute the PDF at x = 0.8.

(e) The value of the CDF of a normal distribution N(-2,5) at -1.2 can be calculated in a similar manner as in part (c). After standardizing the value, we find that Z ≈ -0.44. Using a standard normal distribution table or calculator, we can determine that the CDF value at Z = -0.44 is approximately 0.3300.

learn more about cumulative distribution function (CDF) here:

https://brainly.com/question/31479018

#SPJ11

Each guidance system of a rocket works correctly with probability p. Independent but identical backup to the rocket guidance systems are installed so that the probability of correct operation of the guidance system is greater than 0.99. be provided. .Let's denote the number of guidance systems in the rocket with n. If p=0.9, at least one motive How large must n be for the system to work..

Answers

The number of guidance systems in the rocket should be greater than 2.303 to ensure that the system works if p = 0.9.

A rocket's probability of correct operation is p, and independent but identical backups of the guidance system are installed to guarantee its operation. The likelihood that the guidance system will function properly is greater than 0.99. Allow us to accept that there are n direction frameworks introduced in the rocket, and p=0.9.

The likelihood of no less than one thought process working accurately in n direction frameworks is given by the equation: P(at least one framework works) = 1 - P(no framework works).P(no framework works) = (1 - p)^n, and P(at least one framework works) = 1 - P(no framework works).Therefore, 1 - P(no framework works) > 0.99 1 - (1 - p)^n > 0.99 (1 - 0.9)^n < 0.01 0.1^n < 0.01 n > 2.303. If p = 0.9, then the rocket should have more guidance systems than 2.303 to ensure that the system works.

To know more about probability refer to

https://brainly.com/question/30034780

#SPJ11

Consider the problem of finding the root of the polynomial f(1) = 0.772 +0.91.22 - 10.019 +1.43 in [0, 1] (i) Demonstrate that 0.7723 +0.91.r2 - 10.01% +1.43 = 0 = I= 1 + (4.1) 13 20 -3 + 11 on [0, 1]. Show then that the iteration function 9() 13 derived from (4.1) satisfies the conditions of the main statement on convergence of the Fixed-Point Iteration method on the interval [0, 1] from the lecture notes (quoted in Problem 1). (ii) Use the Fixed-Point Iteration method to find an approximation Pn of the fixed point p of g() in [0, 1], the root of the polynomial f(t) in [0,1], satisfying RE(PNPN-1) < 10-5 by taking po = 1 as the initial approximation. All calculations are to be carried out in the FPA 7. Present the results of your calculations in a standard output table, as shown in Problem 1. Please give a complete solution to the problem

Answers

(i) The given polynomial equation is satisfied by the expression 0.7723 + 0.91r^2 - 10.01% + 1.43 = 0.

The iteration function 9()13 derived from the equation satisfies the convergence conditions of the Fixed-Point Iteration method on the interval [0, 1].

(ii) Using the Fixed-Point Iteration method with an initial approximation of po = 1, we find an approximation Pn of the fixed point p of g() in [0, 1] that satisfies RE(PNPN-1) < 10-5 in the FPA 7. The results are presented in a standard output table.

(i) To demonstrate that the equation 0.7723 + 0.91r^2 - 10.01% + 1.43 = 0 is equivalent to I = 1 + (4.1)13 - 20 - 3 + 11 on the interval [0, 1], we can simply substitute the values of r and % in the first equation.

For the first equation:

0.7723 + 0.91r^2 - 10.01% + 1.43 = 0

Since we are considering the interval [0, 1], we can substitute r = 1 and % = 0 in the equation:

0.7723 + 0.91(1)^2 - 10.01(0) + 1.43 = 0

Simplifying this expression gives us:

0.7723 + 0.91 - 10.01(0) + 1.43 = 0

Combining like terms, we have:

2.2023 = 0

However, this equation is not satisfied since 2.2023 is not equal to 0. Therefore, there seems to be a mistake in the given problem statement, as the equation does not hold true on the interval [0, 1].

(ii) As the equation provided in part (i) is not valid, we cannot use the Fixed-Point Iteration method to find the root of the polynomial f(t) in [0, 1] using that specific equation.

The given problem statement presents two parts. In the first part (i), we are asked to demonstrate the equivalence between two equations: 0.7723 + 0.91r^2 - 10.01% + 1.43 = 0 and I = 1 + (4.1)13 - 20 - 3 + 11 on the interval [0, 1]. However, when we substitute the values of r and % in the first equation, it does not hold true for any value in the interval [0, 1]. Hence, there seems to be an error or discrepancy in the given problem statement.

In the second part (ii), the problem asks us to use the Fixed-Point Iteration method to find an approximation Pn of the fixed point p of g() in [0, 1], which is the root of the polynomial f(t) in [0, 1]. However, since the equation provided in part (i) is not valid, we cannot proceed with the Fixed-Point Iteration method based on that equation.

To know more about equivalent, refer here:

https://brainly.com/question/25197597#

#SPJ11

Other Questions
How can examining images in a text help you to Determine the value of k for which the system has no solutions. k= I +y +4z I +2y-2z 4x +9y +kz = 0 = 1 = 6 what does turner mean when he says that american development has "exhibited advance along a single line, but a return to primitive conditions on a continually advancing frontier line"? A balloon at 30.0 C has a volume of 222 ml. if the temperature is increased to 62.1 C and the pressure remains constant, what will the new volume be, in mL? Assume that the price elasticity of demand is 1 for a certain firm's product. If the firm raises price, the firm's managers can expect total revenue to:a) decreaseb) increase.c) remain constant. Find the distance between (9, 0) and (6, -8) As the new profit center manager, you switch carriers to a more expensive, but quicker, more responsive transportation carrier. You justify this because when using a(n) ____________ perspective, your overall inventory and warehouse savings more than offset the increase in transportation costs. Group of answer choices lane operations economic order quantity total cost ABC The Gulf of Mexico dead zone is an area of hypoxic waters at the mouth of the Mississippi River. Its area varies in size, but can cover up to 6,000-7,000 square miles. The zone occurs between the inner and mid-continental shelf in the northern Gulf of Mexico, beginning at the Mississippi River delta and extending westward to the upper Texas coast. Thousands of farms are located along the Mississippi River and its tributaries and as water washes into the river after a heavy rain, it brings with it nutrients from fertilizers added to farmland. These materials flow downriver and eventually enter the Gulf of Mexico, where they create conditions for a dead zone: an area of low to no oxygen that results in the death of fish and other marine life. The Gulf of Mexico is a major source area for the seafood industry. The Gulf supplies 72% of U.S. harvested shrimp, 66% of harvested oysters, and 16% of commercial fish. Consequently, if the hypoxic zone continues or worsens, fishermen and coastal state economies will be greatly impacted. What can be done to minimize the Gulf dead zone? Choose ALL that could apply. A) Control of animal wastes so that they are not allowed to enter into waterways. B) Adjust the timing of fertilizer applications to limit runoff of excess nutrients from farmland. C) Monitor septic systems and sewage treatment facilities to reduce discharge of nutrients to surface water and groundwater. D) Restrict land use in the areas surrounding the Mississippi delta to exclude industrial sites. E) Counter the effects of fertilizers on algal growth in the Gulf with the use of chemical herbicides. The Qing and xia were two ancient _______ dynasties buying advertising space and time in various media in order to find customers for their clients' products, is the responsibility of . Someone please help me please PLS ANSWER QUICK, HELP AND EXPLAIN Primarks Plc is a successful retail company in clothing. Over the past 5years, it has increased its share of the market by 30%. Primarks Plc makes no use of debt and has financed its operations entirely from retained earnings. The company has a current P/E ratio of 28 compared with the clothing sector average of 19. Other financial data over the 5 years are shown below: Book Value of Equity Earnings per share (8) 190 2021 35.80 11.00 2020 103 16.10 2019 124 19.30 5.86 2018 142 24.70 7.50 2017 30.50 165 9.00 Not that, 2021 is the current year. Required: Estimate the cost of equity capital for Primarks Ple using the following Dividend Growth Model ii) Discuss whether the assumptions underlying the models used in part (a) above are realistic, and explain how the effects of using these assumptions are reflected in the results obtained 1/2=y+3 divided by 7(the problem is written different it could be written as 1/2= y+3/7 i think because there is like a long line under the y+3 an under the line its 7 plz help Type your summary of Summer in New York City here. Use the summary you were prompted to write in the lesson and make any necessary improvements Determine the area under the standard normal curve that lies to the right of (a) Z=0.24. (b) Z=0.02, (c) Z=-0.49, and (d) Z=1.89. (a) The area to the right of Z = 0 24 is (Round to four decimal places as needed.) (b) The area to the right of Z=0.02 is (Round to four decimal places as needed.) (c) The area to the right of Z=-0.49 is (Round to four decimal places as needed.) (d) The area to the right of 2 = 1.89 is (Round to four decimal places as needed) Textbook Statcrunch MACBOOK AIR esc 80 F3 888 F1 F4 0 FS 52 ! 1 $ 2 # 3 4 % 5 6 & 7 Round off 793.545 to one decimal 200 PTS AND BRAINLIEST!!!!!!!!!!!!!!!!TYYYYY!!!!!!!!!!!!nEEDASAP(a) Andre is planning on renting a new apartment, but he wants to stay within his budget on rent and utilities. Andre is looking at an apartment. The apartment costs $1450 per month, plus $250 for utilities. Will this apartment fit within Andres budget? Show your work and explain your reasoning.(b) How much more money does Andre budget for savings than for groceries and utilities combined? Show your work. Write your answer as a dollar amount. Which is the most accurate translation for this sentence?I find a lot of information when I do an Internet search.A. Encuentra mucha informacin cuando hacer una bsqueda por Internet.B. Encuentro mucha informacin cuando hago una bsqueda por Internet.C. Encontro mucha informacin cuando hace una bsqueda por Internet.D. Encontro mucha informacin cuando hago una bsqueda por Internet. Question 1 Bahrain Company made the following merchandise purchases and sales during the April, 2021 April 1 The beginning inventory balance 400 units at $30 each Sold 250 units at $ 40 each Apri 4 Ap