Let Y1,Y2,....,Y5 be a random sample of size 5 from a normal population with mean 0 and variance 1 and let Y bar=(1/5)sumation from i=1 to 5 Yi. Let Y6 be another independent observation from the same population. What is the distribution ofa) W= sumation from i=1 to 5 of Yi^2 ? Why ?b) U= sumation from i=1 to 5 of ( Yi- Y bar)^2? Why?c) sumation from i=1 to 5 of ( Yi- Y bar)^2 + Y6^2 ? Why?

Answers

Answer 1

a) From the given information, [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

be a random sample of size 5 from a normal population with mean 0 and variance 1. Hence,

[tex]W=(\sum_{i=1}^5 Y_{i}^2)\sim X_{5}^2[/tex]

b) From the given information, the random variable is   [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

and  [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

representing the standard normal variables. Hence,

.[tex]U=(\sum_{i=1}^5 (Y_{i} - \bar{Y})^2) \sim X_{5}^2[/tex]

c) From the given information,[tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

representing the standard normal variables and moreover, [tex]Y_{6}[/tex]

is independent standard normal variable. Hence,  [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2\sim X_{5}^2[/tex]

and

.[tex]Y_{6}^2\sim X_{1}^2[/tex]

What is Chi-square distribution?

Chi-square distribution with k degrees of freedom is defined as the sum of the k standard normal variables. This is also defined as the square of the deviations taken from the mean. Chi-square distribution is used for testing goodness of fit and independence in contingency tables.

• If  [tex]z_{1}, z_{2},...........z_{k}[/tex]

are independent standard normal variables, then

[tex]\sum_{i=1}^k z_{i}^2\sim X_{k}^2[/tex]

• If   [tex]X\sim X_{m}^2[/tex]

and   [tex]Y\sim X_{n}^2[/tex]

, then

[tex](X+Y)\sim X_{m+n}^2[/tex]

Step: 1

(a)

The distribution of    [tex]\sum_{i=1}^5 Y_{i}^2[/tex]

is obtained below:

From the given information, [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

be a random sample of size 5 from a normal population with mean 0 and variance 1. Hence,

[tex]W=(\sum_{i=1}^5 Y_{i}^2)\sim X_{5}^2[/tex]

The random variable,  [tex]W=\sum_{i=1}^5 Y_{i}^2[/tex]

representing the sum of squares of standard normal variables and hence, the distribution of   [tex]W=\sum_{i=1}^5 Y_{i}^2[/tex]

is identified as chi-square distribution.

Hint:

Use chi-square distribution to find the distribution of

.[tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

Step: 2

(b)

From the given information, the random variable is   [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

and  [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

representing the standard normal variables. Hence,

.[tex]U=(\sum_{i=1}^5 (Y_{i} - \bar{Y})^2) \sim X_{5}^2[/tex]

The random variable    [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

representing the sum of squares of deviations taken from the mean for 5 standard normal variables and hence, the distribution of
[tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

is chi-square distribution with 5 degrees of freedom.

Hint:

Use       [tex](X+Y)\sim X_{m+n}^2[/tex]  

to find the distribution of

[tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2+Y_{6}^2[/tex]

Step: 3

(c)

From the given information,[tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

representing the standard normal variables and moreover, [tex]Y_{6}[/tex]

is independent standard normal variable. Hence,  [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2\sim X_{5}^2[/tex]

and

.[tex]Y_{6}^2\sim X_{1}^2[/tex]

Therefore,

[tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2+Y_{6}^2\sim X_{5+1}^2[/tex]

[tex]\sim X_{6}^2[/tex]

The distribution of    [tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2+Y_{6}^2[/tex]

is identified as chi-square distribution with degrees of freedom is obtained by adding the degrees of freedom of[tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

and the degrees of freedom of   [tex]Y_{6}^2[/tex].

The distribution of   [tex]W=\sum_{i=1}^5 Y_{i}^2[/tex]

is chi-square distribution with 5 degrees of freedom.

To learn more about the chi-square distribution from the given link

https://brainly.com/question/29012813

#SPJ4


Related Questions

pls help

Given right triangle ABCABC with altitude \overline{BD}
BD
drawn to hypotenuse \overline{AC}
AC
. If AD=7AD=7 and DC=5,DC=5, what is the length of \overline{BD}
BD
in simplest radical form?

Answers

The given assertion states that the length of BD in its simplest radical version is 7/√2.

In arithmetic, what is a triangle?

A triangle is indeed a 3-sided shape that is occasionally (though not frequently) referred to as the trigon. There are three edges and three angles in every triangle, some of which could be the same.

Since BD is an altitude of the right triangle ABC, we can use the Pythagorean Theorem to find the length of BD. First, let's determine the size of AC:

AC² = AD * DC = 7 * 5 = 35

When we square the two edges, we obtain:

AC = √35

Now, we can use the fact that BD is an altitude to write:

BD = (AC * AD) / hypotenuse

where hypotenuse is the length of BC.

Using the Pythagorean Theorem, we can find the length of BC:

BC² = AC² + AB²

Since triangle ABC is a right triangle, we have AB = BC, so we can write:

BC² = AC² + BC²

Simplifying, we get:

BC² / AC² = 2

When we square the two edges, we obtain:

BC / AC = √2

Multiplying both sides by AC, we get:

BC = AC * √2 = √35 * √2 = √70

Now, we can substitute the values of AC, AD, and BC into the formula for BD:

BD = (AC * AD) / BC = (√35 * 7) / √70 = 7 / √2

Therefore, the length of BD in simplest radical form is 7 / √2.

To know more about Triangle visit:

https://brainly.com/question/17335144

#SPJ1

Let g'(x) be constant. Find the fifth derivative of fog(x) for an arbitrary five-times-differentiable function f.

Answers

The derivative of a composite function is given by the chain rule: the fifth derivative of fog(x) depends only on the second and fourth derivatives of f.

d(fog(x))/dx = df/d(g(x)) * d(g(x))/dx

The fifth derivative of fog(x) can be calculated by taking the derivative five times:

d^5(fog(x))/dx^5 = d^5f/d(g(x))^5 * (dg(x)/dx)^5 + 5 * d^4f/d(g(x))^4 * d^2g(x)/dx^2 * (dg(x)/dx)^3 + 10 * d^3f/d(g(x))^3 * (dg(x)/dx)^2 * (d^2g(x)/dx^2)^2 + 10 * d^2f/d(g(x))^2 * (dg(x)/dx) * (d^3g(x)/dx^3) + 5 * df/d(g(x)) * (d^4g(x)/dx^4)

Since g'(x) is constant, dg(x)/dx is also constant, and its derivative is 0. Therefore, all the terms with derivatives of g(x) higher than 1 are 0, leaving us with:

d^5(fog(x))/dx^5 = 5 * d^2f/d(g(x))^2 * (dg(x)/dx)^2 * d^2g(x)/dx^2 + 5 * df/d(g(x)) * d^4g(x)/dx^4

Since g'(x) is constant, dg(x)/dx and d^2g(x)/dx^2 are also constant, and can be replaced by their values. Therefore, the fifth derivative of fog(x) depends only on the second and fourth derivatives of f.

For such more question on derivative

https://brainly.com/question/28376218

#SPJ4

Write a problem about a real-life situation involving temperature or money. The situation should include a number and its opposite that results in an answer of zero

Answers

Therefore , The negative linear equation result indicates that the coffee shop made $56 less from hot coffee drinks than from iced coffee drinks yesterday.

A linear equation is precisely what?

A straightforward regression graph is created using the equation y=mx+b. The y-intercept is m, and the slope is B. Despite the fact that the line before it contains independent parts, it is repeatedly alluded to as a "mathematical formula combining many factors." Only two factors are present in bivariate linear equations. There are no known solutions to application issues concerning linear equations. Y=mx+b.

Here,

Let H be the number of hot coffee drinks sold yesterday, and I be the number of iced coffee drinks sold yesterday. We know that:

H + I = 100 (since a total of 100 cups were sold)

We also know that the average price of a hot coffee drink was $3.50 and the average price of an iced coffee drink was $2.00. Therefore, the total revenue from hot coffee drinks is:

3.50H

And the total revenue from iced coffee drinks is:

2.00I

To find the difference in revenue between the hot and iced coffee drinks sold yesterday, we need to subtract the revenue from iced coffee drinks from the revenue from hot coffee drinks:

3.50H - 2.00I

We want this expression to equal zero, so we can set it equal to zero and solve for H:

3.50H - 2.00I = 0

3.50H = 2.00I

H = (2/3.50)I

H ≈ 0.57I

Since H + I = 100, we can substitute 0.57I for H in the equation:

0.57I + I = 100

1.57I = 100

I ≈ 63.7

Rounding to the nearest whole number, we get:

I = 64

Therefore, H = 100 - I = 36

So the difference in revenue between the hot and iced coffee drinks sold yesterday is:

3.50H - 2.00I = 3.50(36) - 2.00(64) = $72 - $128 = -$56

The negative result indicates that the coffee shop made $56 less from hot coffee drinks than from iced coffee drinks yesterday.

To know more about linear equation visit:

https://brainly.com/question/11897796

#SPJ1

The complete question is "Write a problem about a real-life situation involving temperature or money. The situation should include a number and its opposite that results in an answer of zero

A local coffee shop sells iced and hot coffee drinks. Yesterday, the shop sold a total of 100 cups of coffee. The average price of a hot coffee drink was $3.50 and the average price of an iced coffee drink was $2.00.

What is the difference in revenue between the hot and iced coffee drinks sold yesterday?"

Como se hace este problema? X+4x=235

Answers

Respuesta:

x = 47

Explicación paso a paso:

Necesitamos resolver x en este problema.

[tex]x+4x=235[/tex]

Combinar los términos x juntos
[tex]5x=235[/tex]

Divide 5 en ambos lados

[tex]x=47[/tex]

Nuestra respuesta es 47

a bad contains pennies nickels dimes and quarters they're 50 coins and all of the coins 12% of pennies and 44 dimes there are eight more nickels than pennies how much money does a bag contain​

Answers

The total amount of money in the bag is M = $ 2.98

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as M

Now , the value of M is

Let the total amount of money in the bag be M

The number of coins in the bag = 50 coins

The number of pennies = 12 % of coins

So , the number of pennies = ( 12/100 ) x 50 = 6 pennies

The number of dimes in the bag = 44 % of the coins

The number of dimes in the bag = ( 44/100 ) x 50 = 22 dimes

The number of nickels = 8 + number of pennies = 8 + 6

The number of nickels = 14 nickels

The remaining number of coins are quarters

On simplifying the equation , we get

So , the number of quarters = 50 - 6 - 22 - 14 = 8 quarters

And , the value of 6 pennies = $ 0.06

The value of 22 dimes = $ 0.22

The value of 14 nickels = $ 0.70

The value of 8 quarters = $ 2.00

Therefore , the total amount in the bag = $ 2.00 + $ 0.70 + $ 0.22 + $ 0.06

The total amount of money in the bag = $ 2.98

Hence , the total money in the bag is $ 2.98

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ9

Hide Assignment Information
Instructions
In this module we learned about statistical inference. The idea in this type of analysis is to use samples that are selected randomly to extract knowledge related to a larger population group that is the focus of the study question.
A normally distributed blood test results has a mean of 79 and a standard deviation of 8.2. According to the central limit theorem, if a large number of samples are taken from a population with a variance, the mean of the samples will eventually be equal to the population mean.
Discuss the below points in the assignment:
This is a normally distributed dataset for blood test results, Explain the range [mean - one standard deviation , mean + one standard deviation]? After identifying the limits (start/end) of the range discuss the percentage of the blood test results that will be included in this range. (Sixty eight percent of the dataset area is within one standard deviation of the mean in a normal distribution, ninety five percent of the data values will be within 2 standard deviation o the mean, and ninety nine point seven percent of the data values will be within 3 standard deviation of the mean).
Find the percentage of scores that are between 75 and 85.

Answers

The Inferential statistics is given below.

What is statistics?

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

Given is to discuss the statistical inference.

Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability.Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population.Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population

Therefore, the Inferential statistics is given above.

To solve more questions on Inferential statistics, visit the link-

brainly.com/question/29014197

#SPJ1

QUICK!! 50 POINTS PLUS BRAINLIEST AND THANKS
Which programs were parts of FDR's New Deal?

Choose all answers that are correct.

Responses

Works Progress Administration

Civil Rights Act

Federal Deposit Insurance Corporation

Fair Labor Standards Act

Answers

Federal Deposit Insurance Corporation, programs were parts of FDR's New Deal.

What is Social Security?

Social security is the protection that a society provides to individuals and households to ensure access to health care and to guarantee income security, particularly in cases of old age, unemployment, sickness, invalidity, work injury, maternity or loss of a breadwinner.

here, we have,

One of Franklin D. Roosevelt's most well-known and widespread programmers, Social Security was first introduced in 1935. One of the New Deal initiatives that helped the nation emerge from the Great Depression and recover its assets and wealth as well as give the economy new life was Social Security.

In order to help the aged and disabled better support themselves while they were unable to work, Social Security established safety net protections.

The Social Security programmed and Fannie Mae, or The Federal National Mortgage Association, both still exist today, despite the fact that the majority of the New Deal policies were abandoned when the United States entered World War II. After World War II, Fannie Mae contributed to funding and fueling the housing boom for soldiers coming home.

To learn more about Social Security

brainly.com/question/23913541

#SPJ1

The scores on a standardized test are normally distributed with a mean of 105 and standard deviation of 15. What test score is 1.2 standard deviations above the mean?

Answers

87 is the test score is 1.2 standard deviations above the mean.

What is Statistics?

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that scores on a standardized test are normally distributed with a mean of 105 and standard deviation of 15.

We need to find the test score is 1.2 standard deviations above the mean

1.2 standard deviations is 1.2×15 =18

So 105-18=87

87 is the score that is 1.2 standard deviations from the mean.

Hence, 87 is the test score is 1.2 standard deviations above the mean.

To learn more on Statistics click:

https://brainly.com/question/29093686

#SPJ1

2 wholes 4 by 5 minus 4 wholes 1 by 3

Answers

ANSWER -

To solve this expression, we first need to multiply each whole number by its corresponding length and width to get the area. Then, we can subtract the areas as indicated in the expression:

2 wholes * 4 * 5 = 40

4 wholes * 1 * 3 = 12

So the expression becomes:

40 - 12 = 28

So the final answer is 28.

Pablo's is a popular Mexican restaurant, known especially for its homemade salsa. During dinner last night at Pablo's, 7 tables of people ordered chips and salsa for every 2 tables that did not. Pick the diagram that models the ratio in the story. A total of 108 tables of people dined at Pablo's last night. How many of the tables ordered chips and salsa?

Answers

Answer: Let X be the number of tables that ordered chips and salsa. Then, 7X tables did not order chips and salsa. So, X + 7X = 108, which simplifies to 8X = 108. Dividing both sides by 8, we have X = 13.5.

Since X must be a whole number, we round down to get X = 13 tables ordered chips and salsa.

Step-by-step explanation:

The slope line below is:

Answers

Answer: 4/3

Step-by-step explanation:

Look at the points (0,-4) (3,0)

Formula: y2-y1/x2-x1

Substitute: 0-(-4)/3-0 = 4/3

Please make me brainliest, I would also add you as friend if you make me brainliest!

Let's consider what the question asks for:

--> slope of line

The slope of the line is calculated by:

  [tex]\text{Slope}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

  --> where:

      [tex](x_1,y_1)-- > \text{any one point on the line}\\\\(x_2,y_2)-- > \text{another point on the line}[/tex]

Let's find our points

  [tex](x_1,y_1)-- > (3,0)\\\\(x_2,y_2)-- > (0,-4)[/tex]

Let's plug these points into our equation:

 [tex]\text{Slope}=\dfrac{y_2-y_1}{x_2-x_1} =\dfrac{-4-0}{0-3}=\dfrac{-4}{-3} =\dfrac{4}{3}[/tex]

Answer: 4/3

Ann is 24 years older than Denny. In 10 years, Ann will be 3 times as old as Denny. How old is Ann now?

Answers

Answer I think Ann is 36 and Denny is 12 Im not for sure but thats what i got

Step-by-step explanation:

What is the area, in square feet, of the
isosceles trapezoid below?
8 ft
6.2 ft
15.4 ft

Answers

Answer:

86.4 ft^2

Step-by-step explanation:

I need to find the slope of the graph at x= -1
And the answer for A, B, C, D (I really need help)

Answers

Answer:

See below

Step-by-step explanation:

The derivative function f' is the slope of the function at any given 'x'

A) f ' = 8 x^3 - 24 x^2

B ) put in x = -1 and compute   8 ( -1)^3 -24(-1)^2 = -8 - 24 = - 32 slope

C)  we know the slope (-32) and the x coordinate (-1)   put this value of x into the original equation to find y = 2(1^4) - 8(-1)^3 + 6 = 16

   so point slope form of the line is

       y - 16 = -32 (x - -1)    re-arrange:

       y = -32x -16

D) where slope (f ') = 0 the slope is 0 and thus the tangent line is horizontal      8x^3 - 24x^2 = 0    

                         8x^3 = 24x^2

                           8x = 24

                             x = 3  

Maria kept a log of the number of miles she jogged each time she went for a run as she trained for an upcoming marathon. She displayed the logged runs in the histogram below.

A histogram titled Maria's Monthly Jogging has miles run on the x-axis and number of runs on the y-axis. 1 to 1.99 miles is 2 runs; 2 to 2.99 miles is 5 runs; 3 to 3.99 miles is 5 runs; 4 to 4.99 miles is 3 runs; 5 to 5.99 miles is 4 runs; 6 to 6.99 miles is 7 runs; 7 to 7.99 miles is 4 runs.

What is the range of the number of miles Maria jogged?
0 to 7
0 to 7.99
1 to 7.99
1 to 8

Answers

Answer:

1 to 7.99 miles

Step-by-step explanation:

According to the given histogram, Maria logged runs for 1 to 7.99 miles, and the number of runs for each mile range is also given. Therefore, the range of the number of miles Maria jogged is 1 to 7.99 miles.

Note that the histogram shows that there were no recorded runs for exactly 8 miles, so the range does not include 8.

Carly has 2.85 pounds of cat food she uses 0.19 pound of cat food to feed one cats. How many cats can Carly feed

Answers

Answer:

To find the number of cats Carly can feed, divide the total weight of cat food by the weight of cat food used per cat.

2.85 lbs ÷ 0.19 lbs/cat = 15 cats

Therefore, Carly can feed 15 cats.

PLEASE HELP I DONT UNDERSTAND!

Write the following polynomial in descending powers of the variable and with no missing powers

3x^3 -70


3x^3 -70=?

Answers

with no missing powers, meaning including any "stepping down" values, anyhow, let's do so

[tex]3x^3-70\implies \boxed{\begin{array}{llll} 3x^3+0x^2+0x^1 + 0x^0 - 7 \\\\\\ 3x^3+0x^2+0x^1 - 7 \end{array}}[/tex]

now, notice, the others were there all along, however their coefficient is 0, thus anything times 0 goes poof, however they were there all along.

some folks like to use the 1st form there, I usually use the 2nd form, but both are acceptable.

13. ABCD is
a. Congruent
b. Similar
c. Neither
to A'B'C'D'.

Answers

i’m pretty sure it’s a

Sorry I cant do this for much points, But i need help asap pleaseeee!

Answers

The perimeter of the figure is given by the sum of the perimeter of rectangle and a semicircle P = 20.28

What is the Perimeter of a Rectangle?

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P of rectangle = 2 ( Length + Width )

Given data ,

Let the perimeter of the figure be represented as P

Let the width of the rectangle W = 4

So , the radius of the circle = 4 / 2 = 2

Now , the length of the rectangle = 5

And , the perimeter of the figure = 5 + 5 + 4 + ( perimeter of semicircle )

where the perimeter of semicircle = πr

On simplifying , we get

The perimeter of the figure P = 14 + 2π

The perimeter of the figure P = 14 + 6.28

The perimeter of the figure P = 20.28

Hence , the perimeter of the figure is 20.28

To learn more about perimeter of rectangle click :

https://brainly.com/question/15725265

#SPJ1

would someone be able to help me out with this problem? thank you so much if u can! been stuck on it for 20 minutes now​

Answers

Answer:

Form W-2 is completed by an employer and contains important information that you need to complete your tax return. It reports your total wages for the year and the amount of federal, state, and other taxes withheld from your paycheck.

Form 1040 is used by U.S. taxpayers to file an annual income tax return.

Head of household offers wider tax brackets, a bigger standard deduction and faster eligibility for other write-offs.

Step-by-step explanation:

We bow down before Your divine presence and bring You our deepest worship as we experience Your tender love, Father!

What is the equation of Shrödinger?​

Answers

Answer:

see attached

Step-by-step explanation:

The Schrödinger equation, sometimes called the Schrödinger wave equation, is a partial differential equation. It uses the concept of energy conservation (Kinetic Energy + Potential Energy = Total Energy) to obtain information about the behavior of an electron bound to a nucleus.

see attached

Answer:

[tex]\hat{H} \Psi=E \Psi[/tex]

Step-by-step explanation:

[tex]\hat{H}[/tex]= the total energy of a system in all aspects. this includes both potential and kinetic energy.

[tex]\Psi[/tex]= wave function. if I remember right the wave function is exactly that, the function in which the wave is behaving, reflected on a graph.

[tex]E[/tex]= energy

Find and identify the traces of the quadric surface
x2 + y2 − z2 = 4
given the plane.
x = k
Find the trace.
Identify the trace.
circle ellipse hyperbola parabola
y = k
Find the trace.
Identify the trace.
circle ellipse hyperbola parabola
z = k
Find the trace.
Identify the trace.
circle ellipse hyperbola parabola
Describe the surface from one of the graphs in the table.
ellipsoid elliptic paraboloid hyperbolic paraboloid cone hyperboloid of one sheet hyperboloid of two sheets
(b) If we change the equation in part (a) to
x2 − y2 + z2 = 4,
how is the graph affected?
The graph is rotated so that its axis is the x-axis.
The graph is rotated so that its axis is the y-axis.
The graph is rotated so that its axis is the z-axis
The graph is shifted one unit in the negative y-direction.
The graph is shifted one unit in the positive y-direction.
(c) What if we change the equation in part (a) to
x2 + y2 + 2y − z2 = 3?
The graph is rotated so that its axis is the x-axis.
The graph is rotated so that its axis is the y-axis.
The graph is rotated so that its axis is the z-axis
The graph is shifted one unit in the negative y-direction.
The graph is shifted one unit in the positive y-direction.

Answers

The answer of the questions:

a) The surface is an ellipsoid,

(b) If the equation is changed to x² - y² + z² = 4, the graph is still an ellipsoid, and

(c) If the equation is changed to x² + y² + 2y - z² = 3, the graph is not an ellipsoid anymore,

What is an ellipsoid?

An Ellipsoid is a closed surface on which all plane cross sections are either ellipses or circles. An ellipsoid is symmetrical about three mutually perpendicular axes that intersect at the center.

(a)

x = k:

Trace: Circle in the x-z plane

Identification: Circle

y = k:

Trace: Circle in the y-z plane

Identification: Circle

z = k:

Trace: Circle in the x-y plane

Identification: Circle

The surface is an ellipsoid, which is a 3-dimensional surface that is the result of stretching or compressing a sphere along different axes.

(b)

If the equation is changed to x² - y² + z² = 4, the graph is still an ellipsoid, but it is rotated so that its axis is the x-axis.

(c)

If the equation is changed to x² + y² + 2y - z² = 3, the graph is not an ellipsoid anymore, and its shape cannot be determined from the equation alone.

This is because the equation contains a linear term (2y) that makes it non-quadratic.

To find the shape of the surface, a more in-depth analysis would be required.

Hence, the answer of the questions:

a) The surface is an ellipsoid,

(b) If the equation is changed to x² - y² + z² = 4, the graph is still an ellipsoid, and

(c) If the equation is changed to x² + y² + 2y - z² = 3, the graph is not an ellipsoid anymore,

To learn more about an ellipsoid visit,

https://brainly.com/question/29853961

#SPJ4

Write each rate as a unit rate. $ 46 for 5 toys.

Answers

Answer:

$9.20 per toy or $9.20/1

Step-by-step explanation:

$46/5 hours=9.2

The length of a rectangle is 4 in longer than its width.
If the perimeter of the rectangle is 40 in, find its area.

Answers

Answer:

Step-by-step explanation:

Let, width = x

length = x+4

perimeter, 2(x+4+x) = 40

4x+8 = 40

4x = 32

x = 8

so, (x+4) = 8+4 = 12

so, the area would be,

= 12 * 8 = 96 in²

Please help due tonight!!!!!!

Answers

Answer: -4,9 I AM PRETTY SURE FROM ALL OF MY RESEARCH SIORRY IF I AM WRONG I WISH YOU GOODLUCK

Step-by-step explanation:

The missing number that goes under the radical is 17

translate then solve:five times the difference of twice and number and three decreased by the sum of the number and 8 equals 13

Answers

Answer: x = 4

Step-by-step explanation:

Translating the problem into mathematical terms:

Let's call the number x. Then the problem can be written as:

5 * (2x - 3) - (x + 8) = 13

Expanding the left side of the equation:

5 * 2x - 5 * 3 - x - 8 = 13

Simplifying the left side of the equation:

10x - 23 - x - 8 = 13

Combining like terms:

9x - 31 = 13

Adding 31 to both sides of the equation:

9x = 44

Dividing both sides of the equation by 9:

x = 4.88888...

Since x has to be a whole number, we round down to the nearest whole number:

x = 4

Therefore, the number that satisfies the equation is 4.

Which objective function models the total profit from neck-
laces and wristbands?
Let x = the number of necklaces Mack makes.
Let y = the number of wristbands Mack makes.
A P(x, y) = 25x+40y
B P(x, y)=40x + 25y
c P(x, y) = 3x + 2y
D P(x, y) = 2x + 3y

Answers

The answer js D
Hope this helps

In 2009, a laptop computer was purchased for $800. Each year since, the resale value has decreased by 27%.
Let t be the number of years since 2009. Let y be the value of the laptop computer, in dollars.
Write an exponential function showing the relationship between y and t.

Answers

On solving the provided question we can say that by percentage y = $1900(77/100)t

What is percentage?

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

In 2005, a laptop computer was purchased for 81900. Each year since, the resale value has decreased by 23%. Let t be the number of years since Let Y be the value of the laptop computer, in dollars. Write an exponential function showing the relationship between Y and

t. value of laptop in 2005 81900 decrease in resale \/aIUe each year

23 77% resale value of laptop after each year = 100

resale value after one x $1,900

Now, Hence relation between value of the laptop computer and time is

y = $1900(77/100)t

To know more about percentage visit:

https://brainly.com/question/28269290

#SPJ1

The Wilson family's back yard is a rectangular plot that has a length of 100 feet and a width of 80 feet. The family planted a garden with a length and width of 60 feet. The family planted a lawn in the remaining area of the back yard, as shown.What is the area, in square feet, of the lawn in the Wilson family's back yard?

Answers

The area of the lawn in the Wilson family's back yard is 4400 square feet.

The Wilson family's back yard is a rectangular plot that has a length of 100 feet and a width of 80 feet.

Let us assume that A₁ be the area of the reactangular plot.

Using the formula for the area of rectangle,

A₁ = 100 × 80

A₁ = 8000 sq. ft.

The family planted a garden with a length and width of 60 feet.

This means, the shape of the garden must be square.

Using the formula for the area of square,

A₂ = 60 × 60

A₂ = 3600 sq. ft.

The family planted a lawn in the remaining area of the back yard, as shown.

Let us assume that A represents the area of the lawn in the Wilson family's back yard.

A = A₁ - A₂

A = 8000 - 3600

A = 4400 sq. ft.

Therefore, the required area is: 4400 sq.ft.

Learn more about tha area of rectangle here:

https://brainly.com/question/27431338

#SPJ4

Been stuck on this question please help me.

Answers

Answer:

Step-by-step explanation:

Using the Pythagorean Theorem, we know the hypotenuse is 2[tex]\sqrt{26}[/tex]

sin = Opp/hyp ----> [tex]\frac{5}{2\sqrt26}[/tex]

csc = hyp/opp -----> [tex]\frac{2\sqrt{26} }{5}[/tex]

cot = adj/opp -------> [tex]\frac{7}{5}[/tex]

Other Questions
what are the differences between unitary, federal and confederal arrangements., and do you think federalism is best suited for the united states? why or why not? a= (6,7) and b= (1,2) if a-b =(x,y) work out values of x and y Anna compra helado y naranjas en la tienda. Ella paga un total de $59.53. Ella paga un total de $6.49 por el helado. Ella compra 8 bolsas de naranjas que cuestan la misma cantidad cada una.Escribe y resuelve una ecuacin que se pueda usar para determinar X, cunto cuestacada bolsa de naranjas.Ecuacin:Respuesta: X= 1. What number am I?I have four digits.My tens and tenths are the same value.My hundredths is the difference of 5 and 1.My tens is double my hundredths.My ones is the other factor of 4 besides 1 and itself. President Eisenhower used domino theory to argue that the United States had to prevent the spread of Communism no nation could win a nuclear war because both nations would be destroyed the threat of a nuclear war was enough to prevent an enemy attack you want to compare the bacterial density in 3 different water sources. you dilute each sample 1:1,000 and plate on a petri dish. after 24h, the plates contain 500, 750, and 270 colonies, respectively. what do you do? a patient is to receive medications through a small-bore nasogastric feeding tube. which nursing actions are appropriate? (select all that apply) a patient is to receive medications through a small-bore nasogastric feeding tube. which nursing actions are appropriate? (select all that apply) verifying tube placement after medications given. lay the patient flat prior to medication administration. use an enteral tube syringe to administer medications. flush tube with 30 to 60 ml of water after the last dose of medication. check for gastric residual before giving the medications. keep the head of the bed elevated for 60 minutes after the medications are given. What might a peasized gland within the skull be?salivary glandpituitary glandmammary glandsebaceous glandB Path to food thru the digestive system from a grasshopper What quadrant will the complex number (2i-10) be in? When testing a patient for streptococcal pharyngitis, a phlebotomy technician should implement which of the following types of transmission-based precautions? b) By what factor does the fundamental frequency change when the mass per unit length of a guitar string increases by a factor of 3.50? which is true? question 4 options: a program with multiple classes is contained in a single file a programmer must decide what a class contains and does class data are normally public a programmer should sketch a class while writing the code the viral structure responsible for recognizing specific host cells is? a nurse assesses a client with crackles. what medical condition should the nurse suspect? select all that apply. Leonard is known for being very intelligent. He can figure out almost any problem, and his friends are always coming to him for advice. Which of the following statements about Leonard's brain is MOST accurate? What are the example of a bloodborne pathogen engineering control? what challenges do european host countries face as they determine how to allocate limited resources to their citizens and refugee populations? The population of town X was 220,000 in 2000, and 252,000 in 2010. Project the population in 2020. A woman who is heterozygous for the recessive hemophilia gene dose not exhibit the disease. Her sons but not her daughters inherit the disease called?