1. If f(x) = x + 3 and g(x) = x² + 2x - 3, find [gxf](x).

1. If F(x) = X + 3 And G(x) = X + 2x - 3, Find [gxf](x).

Answers

Answer 1

The answer is g(f(x)) =(x+6)(x+2)

From the question, we have

f(x) = x + 3 and g(x) = x² + 2x - 3

g(f(x)) = g(x + 3)

=(x + 3)² + 2(x + 3) - 3

=x² + 9+6x+2x+6-3

=x² + 8x+12

=x² + 6x+2x+12

=(x+6)(x+2)

The answer is g(f(x)) =(x+6)(x+2)

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Related Questions

why will a probability curve always give a probability of zero for a point estimate on a continuous random variable

Answers

Probability curve always give a probability of zero for a point estimate on a continuous random variable.

A probability distribution in which the random variable x can take on any value because there are infinite values that x could assume, the probability of x taking on any one specific value is zero.

we often speak in ranges of values (p(x>0) = .50). The normal distribution is one example of a continuous distribution. The probability that X falls between two values (a and b) equals the integral (area under the curve) from a to b.

Density function:

f(x) = P(a≤x≤b) = ∫f(x).dx ≥ 0.

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TRUE/FALSE. while large groups of individuals work on key oss projects, such as the linux operating system, some widely used efforts have had fewer developers, creating concerns over quality and security.

Answers

The given statement is true. While large groups of individuals work on key OSS projects, such as the Linux operating system, some widely used efforts have had fewer developers, creating concerns over quality and security.

Given,

While large groups of individuals work on key OSS projects, such as the Linux operating system, some widely used efforts have had fewer developers, creating concerns over quality and security.

We have to find whether the given statement is true or false;

OSS;- Open Source Software

Code that is intended to be publicly accessible is known as open source software; anybody can view, alter, and distribute the code as they see appropriate. Peer review and community production are used in the decentralized, collaborative development of open source software.

Here,

The given statement is true.

That is, While large groups of individuals work on key OSS projects, such as the Linux operating system, some widely used efforts have had fewer developers, creating concerns over quality and security.

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What is a system of equations with no solutions called?.

Answers

An inconsistent system of equations.

Consider this equation. if is an angle in quadrant iv, what is the value of ? a. b. c. d.

Answers

Option (a) is correct. The value of sinθ will be [tex]-\frac{5\sqrt{41} }{41}[/tex]

We are given the value of the cosθ  = [tex]\frac{4\sqrt{41} }{41}[/tex] where, θ is in the IV Quadrant.

We know that cosine is the ratio of the adjacent side to the hypotenuse.  Also, we have
hypotenuse = h = 41, And Adjacent Side = b = [tex]4\sqrt{41}[/tex]
So, for the value of the opposite side, we need to use the Pythagorean theorem which is stated as:[tex](Hypotenuse)^{2} = (opposite side)^{2} + (adjacentside)^{2}[/tex]
[tex]h^{2} = a^{2} + b^{2}[/tex]

[tex]a^{2} = h^{2} - b^{2}[/tex]

a = [tex]\sqrt{41^{2} -(4\sqrt{41})^{2} }[/tex] =  [tex]\sqrt{1681 - 656 }[/tex] = [tex]\sqrt{1025}[/tex] = [tex]5\sqrt{41}[/tex]

The opposite side is  [tex]5\sqrt{41}[/tex] , as sine is negative (-) in the IV quadrant so the value will be   [tex]-5\sqrt{41}[/tex].

So we know that Sine is the ratio of the Opposite side to the hypotenuse, which can be written as:

sineθ = [tex]\frac{Opposite}{Hypotenuse}[/tex]

sineθ =  [tex]-\frac{5\sqrt{41} }{41}[/tex]

So, option (a) will be the right option.

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Your Question is incomplete, but most probably your full question was

Consider this equation. cosθ  = [tex]\frac{4\sqrt{41} }{41}[/tex] if θ is an angle in quadrant IV, what is the value of sinθ?
(a)       [tex]-\frac{5\sqrt{41} }{41}[/tex]

(b)   [tex]\frac{5\sqrt{41} }{41}[/tex]

(c) [tex]-\frac{5}{4}[/tex]

(d) [tex]\frac{5}{4}[/tex]

Answer: c

Step-by-step explanation:

Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. X y 11 7.31 9 6.56 12 13.36 10 12 7.197.64 14 9.22 5 6.33 4 5.54 13 8.52 8 6.11 5 5.91 Create a scatterplot of the data. Choose the correct graph below. OA OB. OC. O O .............. Lullulilu 5 :50 O CODOO 5f0 OTT 0 5 10 15 20 25 OTT 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 Find the equation of the regression line. ŷ = + x (Round the constant two decimal places as needed. Round the coefficient to three decimal places as needed.) Identify a characteristic of the data that is ignored by the regression line. O A. The data has a pattern that is not a straight line. OB. There is no trend in the data. OC. There is an influential point that strongly affects the graph of the regression line. OD. There is no characteristic of the data that is ignored by the regression line.

Answers

The equation of the regression line is y = 0.430x + 3.59.

A characteristic of the data that is ignored by the regression line is that: A. The data has a pattern that is not a straight line.

How to find an equation of the regression line?

In order to determine a linear equation for the regression line (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatterplot).

In this scenario, the x-values would be plotted on the x-axis of the scatterplot while the y-values would be plotted on the y-axis of the scatterplot.

On the Excel worksheet, you should right click on any of the data point on the scatterplot, select format trend line, and then tick the box to display an equation for the regression line (trend line) on the scatter plot.

By critically observing the scatterplot (see attachment) which models the relationship between the x-values and y-values, a linear equation for the regression line (trend line) is given by:

y = 0.430x + 3.59

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Owen offers to sell his motorcycle to Julian for $5,000. After he makes the offer, Owen has second thoughts. Owen can revoke the offer to sell his motorcycle to Julian: as long as Julian has not yet accepted the offer.

Answers

Owen can revoke the offer to sell his motorcycle to Julian as long as Julian has not yet accepted offer

First Owen offers to sell his motorcycle to Julian for $5000.

Then after makes the offer, Owen has second thoughts and he want to revoke the offer to sell his motorcycle to Julian.

According to revoke of offer to sell an individual who makes an offer have the power to revoke so long as it hasn't yet been accepted by the other party. Therefore he can revoke the price as long as Julian has not yet accepted the offer

Hence, Owen can revoke the offer to sell his motorcycle to Julian as long as Julian has not yet accepted offer

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find the equation of the line passing through the point (3,5) which is perpendicular to the line y=3x+2

Answers

Required equation of line: 3y + x = 18

What is the slope of Straight line?

It is defined as the tangent of the of the angle the line makes with the x-axis.

We know that the when two lines are perpendicular, the product of their slope is -1

slope of given line  = 3  

let slope of required line  = m

3*m = -1

m = -1/3

as the line passes through the point (3,5)

the equation will be: (y-5)/(x-3) = -1/3

3y-15 = 3-x

Equation of Straight line: 3y + x = 18

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What is the intermediate step in the form ( x + a ) 2 = b (x+a) 2 =b as a result of completing the square for the following equation?.

Answers

The intermediate step  in the form ( x + a ) ^2 = b (x+a)  2 =b as a result of completing the square  of x² - 4x = 45 is (x- 2)² = 49

How to determine the intermediate step?

The equation is given as:

x² - 4x = 45

Take the coefficient of x

k = -4

Divide by 2

k/2 = -2

Square both sides

(k/2)^2 = 4

Add 4 to both sides of x² - 4x = 45

x² - 4x + 4= 45 + 4

This gives

x² - 4x + 4= 49

Express as perfect square

(x- 2)² = 49

Hence, the intermediate step of x² - 4x = 45 is (x- 2)² = 49

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3x + 3 = 3(x + 1)
Does this have infinite solutions?

Answers

Answer:

Yes, it has infinite solutions

Step-by-step explanation:

3 ( x + 1 )

= 3 ( x ) + 3 ( 1 )

= 3x + 3

3x + 3 = 3x + 3

Any number can substituted for x.

Answer: Yes

Step-by-step explanation: First, distribute 3(x+1), which is 3x+3. Then we have 3x+3=3x+3, which is the same thing.

hope this helps!

please give brainliest!

1. Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) g(t) = |4t − 5| 2.
2.Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) h(t) = t3/4 − 3t1/4 3.
3.Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = x5e−8x 4.
4.Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 − 27x2 − 72x + 1, [−2, 5]

Answers

2. Critical numbers of a function h(t) = t^(3/4) - 3t^(1/4) are (1/16 , -1/16).

A number is critical if it makes the derivative of the expression equal 0.

Critical numbers are values of a function where the function's tangent lines are either horizontal or vertical.

Given function is,

h(t) = t^(3/4) - 3t(1/4)

We have to find critical points.

For this we will take derivative and set it with 0

Therefore

h'(t) = (3/4)t^(-1/4) - 3(1/4)t^(-3/4) = 0

3/4[t^(1/4)] = 3/4[t^(3/4)]

4t^(3/4) = t^(1/4)

4 = 1/√t

t = 1/16 and t= -1/16.

Therefore critical points are (1/16 , -1/16).

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Please help me do my math revision. I just need an explanation. You will get all my points.

Answers

it is translation because there is no change in size of shape just direction is changed both are opposite sided

If you are solving this problem, which list or table is the best way to organize the given information? sydney is buying fruit. Strawberries are priced at $1. 68 per pound, and raspberries are priced at $2. 98 per pound. If she selects 8. 4 pounds of strawberries and 1. 8 pounds of raspberries, how much will she spend on the fruit?.

Answers

Sydney will spend $19.48 on fruit.

Price of strawberries = $1.68 per pound

Price of raspberries = $2.98 per pound

Sydney wants to buy 8.4 pounds of strawberries and 1.8 pounds of raspberries.

Therefore,

Price of 8.4 pounds strawberries = 8.4*Price per pound

Price of 8.4 pounds strawberries = 8.4*1.68 = $14.112

Price of 1.8 pounds raspberries = 1.8*price per pound

Price of 1.8 pounds raspberries = 1.8*2.98 = $5.364

Total spent on fruit = Price of 8.4 pounds strawberries + Price of 1.8 pounds raspberries

Total spent on fruit = $14.112 + 5.364 = 19.48

Rounding off to nearest hundredth;

Total spent on fruit = $19.48

Therefore, Sydney will spend $19.48 on fruit.

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Find the closed formula or a recursive definition for each of the following sequences. Assume the first term given is a1. (16 pts) (a) 2,6,12,20,30,42,…(b) 1,5,23,119,719,…(c) 2,4,6,10,16,26,42,…(d) 8,12,17,23,30,…

Answers

In mathematics, a closed-formula is a mathematical expression that uses a finite number of standard operations. It may contain constants, variables, and operations etc.

A closed formula is an expression that can be computed by applying a fixed or finite number of standard opertions.

Example; Assume that the first term is a1(16 pts)

(a) 2,6,12,20,30,42,....

(b) 1,5,23,119,719,…

(c) 2,4,6,10,16,26,42,…

(d) 8,12,17,23,30,…

hence the closed formula will be a1=(1+1,1+5,1+11,1+29,1+24)

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In 2011, telemundo paid $600 million for spanish-language u. S. Rights to the 2018 and 2022 fifa men’s world cup. How many viewers watched the 2018 fifa men’s world cup on telemundo?.

Answers

Across all broadcast and streaming channels, Telemundo claimed an average of 2.5 million viewers for the 2018 FIFA Men's World Cup.

What is telemundo?

The company that owns Telemundo is NBCUniversal Telemundo Enterprises, a unit of NBCUniversal, which is in turn owned by Comcast. Telemundo is an American Spanish-language terrestrial television network. With programmes syndicated globally to more than 100 nations in more than 35 languages, it offers content on a national level.

191 million people watched the 64 live games of the 2018 World Cup in Russia, according to FIFA World Cup. With approximately 100 million viewers in the US this year and an estimated 30 million to 50 million viewers worldwide, this greatly outpaces the predicted TV audience for the Super Bowl. How many individuals tuned in to the 2022 World Cup? Utilizing information from Nielsen and Adobe Analytics, the number of views is calculated. 24 matches were played during the first seven days of the 2022 FIFA World Cup QatarTM, with an average audience (TAD) of 57 million across Telemundo, Peacock, and Telemundo streaming platforms—an increase of 24%. A year is equivalent to one year.

Hence, across all broadcast and streaming channels, Telemundo claimed an average of 2.5 million viewers for the 2018 FIFA Men's World Cup.

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What is the solution QR to this system of linear equations 12q 3r 15?.

Answers

(-2, 13) is the solution (q, r) to this system of linear equations. 12q + 3r = 15 - 4q - 4r = - 44.

What is Linear Equation ?

Linear equation is defined as the equation in which the greatest power of the variable is always one. Linear equation is also known as one-degree equation. In linear equation the standard form is

Ax + B = 0

where,

A = coefficient

B = constant

x = variable

The given equations are

12q + 3r = 15      ….. (1)

- 4q - 4r = - 44   ……. (2)

Multiply equation (2) by 3, we get

- 12q - 12r = - 132 ….. (3)

Now by adding the equations (1) and (3), we get

3r - 12r = 15 - 132

- 9r = - 117

r = 117/9 = 13

By Substituting the value of r in equation (2), we get

- 4q - 4 (13) = - 44

- 4q - 52 = - 44

- 4q = - 44 + 52

- 4q = 8

q = - 2

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NOTE: The given question is incomplete on the portal. Here is the complete question.

QUESTION: What is the solution (q, r) to this system of linear equations? 12q + 3r = 15 - 4q - 4r = - 44.

1. consider the linear transformation t r3r3 defined by 0 (1). find the matrix representation of t with respect to the standard basis of r3. (2). find the nullspace of t and determine the nullity. (3). find the range of t and determine its rank (4). find the matrix representation of t with respect to the basis 11.0 01

Answers

The matrix representation of t with respect to the basis is {(1,0,0), (1,1,0), (1,1,1).

T: 1R^3 -> IR^3 activated by

T(x1 y1 z1) = (x+y+z, y+z, 0)

(1,0,0), (0,1,0), (0,0,1) be standard basis of IR^3

Therefore T(1,0,0) = (1,0,0)

(1,0,0) is 1st column of matrix of T

T(0,1,0) = (1,1,0)

(1,1,0) is 2nd column of matrix of T

T(0,0,1) = (1,1,0)

(1,1,0) is 3rd column of matrix of T

Therefore Matrix representation of T with respect to standard basis of IR^3 is

A = 1,1,1    0,1,1    0,0,0

2. Nullspace of T = kennel T

KerT = {(x,y,z)E IR^3/T(x,y,z,) = (0,0,0)}

KerT = {(x,y,z)E IR^3/(x+y+z, y+z,0) = (0,0,0)}

KerT = {(x,y,z)E IR^3/(x+y+z = 0, y+z,0)

KerT = {(x,y,x) EIR^3/x = 0, y = -2}

KerT = {(0,-z,z)}

KerT = {z(0,-1,1)} = Multiple of T

As it contains only one linear independent rectors = nullity = 1

3. Range T = {T(x,y,z)/(x,y,x) EIR^3}

= {(x+y+z, y+z,0)}

Range T = {(x+y+z)(1,0,0) + (y+z)(0,1,0)}

As range contains only two linear independent rectors = Rank = 2

4. T(x,y,z) = (x+y+z, y+z,0)

consider basis, B = {(1,0,0), (1,1,0), (1,1,1)}

T(1,0,0) = (1,0,0)

(1,0,0) = a(1,0,0) + b(1,1,0) + c(1,1,1)

(1,0,0) = (a+b+c, b+c, c)

a+b+c = 1, b+c = 0, c = 0

b = 0, a = 1

Therefore above of a,b,c gives first column matrix

Now,

T(1,1,0) = (2,1,0)

consider (2,1,0) = a(1,0,0) + b(1,1,0) + c(1,1,1)

(2,1,0) =  (a+b+c, b+c, c)

a+b+c = 2, b+c = 1, c = 0

b = 1, a = 1

Therefore above values of a,b,c gives 2nd column of matrix

Now,

T(1,1,1) = (3,2,0)

(3,2,0) = a(1,0,0) + b(1,1,0) + c(1,1,1)

(3,2,0) = (a+b+c, b+c, c)

a+b+c = 3, b+c = 2, c = 0

b = 2, a = 1

Therefore above values of a,b,c gives 3rd column of matrix

Hence the answer is the matrix representation of t with respect to the basis is {(1,0,0), (1,1,0), (1,1,1).

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let h be a subgroup of g. and suppose h is the only subgroup of g of order(h). show that h is normal in g

Answers

To prove that  h be a subgroup of g. and suppose h is the only subgroup of g of order(h) h is normal in g is that it is proven by homomorphism .

This is a small contribution, however in reaction to a remark above, you may additionally clear up this with out the use of any homomorphism properties. Assume the subgroup H has order n and select out g∈g. Then, for any [tex]h∈H: = (ghg^-1)^n ghg^-1.ghg^1/n time.\\= gh^n g^-1 = geg ^-1 = geg ^-1 = gg ^-1 = e[/tex]

Since H has order n. The above holds for all h∈H, so the subgroup gHg−1 has order n, so it's miles identical to H through assumption. Then each h∈H has a few h∈H such that ghg−1=h′, implying gh=h′g, so gH=H

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write a while loop to read integers from input until -1 is read. for each integer read before -1, add the integer times two to vector integervector. ex: if the input is 9 8 5 2 -1, then the output is: 18 16 10 4

Answers

While loop is a condition based loop which run till condition is true. So by giving condition that value is not equal to -1 while will run till -1 is entered.

→vectorname.push_back(value) function is used to add elements to a vector.

→vectorname.at(index) function is used to access element present at index.

The following is how the algorithm and program code will be written:

ALGORITHM :

Input value

while loop run till value is not equal to -1

Inside loop add value to vector

Input value

End loop

Output vector elements

PROGRAM CODE :

// C++ Program

#include

#include using namespace std;

// Main

int main()

{

   // Vector declaration

   vector dataVect; // Variable declaration

   int value; int i;

   // Input value cin >> value;

   // While value is not equal to -1

   while(value!=-1){

           // Add that value to vector

   dataVect.push_back(value);

   // Input value cin >> value;

   }

   // Output vector elements one by one

   for (i=0; i

   cout<<< dataVect.at(i) << endl;

    }

    return 0;

}

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Sally can paint a room in 5 hour while it take teve 7 hour to paint the ame room. How long would it take them to paint the room if they worked together?

Answers

Sally and Steve approximately 2.9 hours to paint the room together.

What is the time and work concept?

The fundamental concept of Time and Work is the same as it is in all Arithmetic topics, namely the concept of Proportionality. When the amount of work done remains constant, efficiency is inversely proportional to time.

What is the relationship between time, work done, and work rate?

Work Done = Time Spent Work Rate

Work Rate = [tex]\frac{1}{time taken}[/tex].

Time Spent = [tex]\frac{1}{rate of work}[/tex].

If a piece of work is completed in x days, then the work completed in one day = [tex]\frac{1}{x}[/tex].

There are two kinds of questions about time and work. Individuals working alone or in groups with different individuals can be a problem.

efficiencies or there may be issues with combined group efficiency. Now, if a person 'A' completes a specific task in X days, the work completed by 'A' in one day is = [tex]\frac{1}{x}[/tex].

Similarly, if a person 'B' completes a specific task in Y days, then his work completed in one day is =[tex]\frac{1}{y}[/tex].

So, if A and B work collaboratively, their combined work done in one day will be [tex]\frac{1}{x} +\frac{1}{y}[/tex], and they will be able to complete the work in [tex]\frac{xy}{x+y}[/tex] days.

Given:

Sally spends 5 hours painting one room.

Steve spends 7 hours painting one room.

In response to the question

Sally will paint part of the room in one hour = [tex]\frac{1}{5}[/tex] part

Steeve will paint part of the room in one hour = [tex]\frac{1}{7}[/tex] part

Together they will paint =[tex]\frac{5*7}{5+7}[/tex] = [tex]\frac{35}{12}[/tex]part

∴ then the complete room will be pained by them = [tex]\frac{35}{12}[/tex]

     = 2.916666… hours

Sally and Steve approximately 2.9 hours to paint the room together.

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melody realizes she'll need to buy more eggs than necessary, since she needs to buy eggs by the dozen. now she wants to calculate how many eggs will be leftover in the final carton of eggs. that will help her decide whether to make extra icing. which line of code successfully calculates and stores the number of leftover eggs in the final carton? choose 1 answer:

Answers

The number of leftover eggs line of code is given by:

leftoverEggs ← 12 - (neededEggs MOD 12)

Melody is putting together a program to assist her in planning the items for a bake sale. Three eggs are needed for each batch of cookies, and she plans to make nine. This program determines the total number of eggs needed:

eggsInBatch ← 3

numBatches ← 9

neededEggs ← eggsInBatch * numBatches

Melody understands she'll need to purchase more eggs than required since she must purchase them in 12-egg packages. She is now attempting to determine how many eggs will remain in the last carton of eggs. She can then decide whether to prepare additional icing.

Because the number of needed eggs mod 12 gives us the remainder, that is the leftover eggs that can't be put in the carton, they are the leftover eggs, Since, each carton has 12 eggs, we have to subtract 12 - the needed eggs to obtain the number of leftover eggs.

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What is the domain of a square root?.

Answers

The domain of the square root function is x≥0.

What is a function?

Any relation in which each input has exactly one output is referred to as a function. To put it another way, the function outputs one value exactly for each input value. Because one is mapped to two different values, the graph above depicts a relation rather than a function. But if one were instead mapped to a single value, the relation above would become a function. Furthermore, output values could be identical to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

The square root function's purpose must now be considered. The positive number that results in the input after being squared is returned as the principal root or output. Since y will be bigger than or equal to 0, we may be certain of that.

To find out a perfect square we need to find out square root is an integer.

Hence, The domain of the square root function is x≥0.

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Which phrase correctly represents the algebraic expression for 22-n?

Answers

Using Algebraic expression, Twenty-two decreased by a number say n is phrase form of Algebraic expression (22 - n) . So, The correct option is option (D).

Algebraic expression :

An algebraic expression is a mathematical expression containing variables, constants, coefficients, and algebraic operations. For example, 5x - 5y + 5 is an algebraic expression.

There are several kinds of algebraic expressions. A monomial is a unary algebraic expression whose exponent and variables are non-negative integers.

We have given an algebraic expression (22 - n)

where n is an integer, 22 is a constant term, and subtraction is an algebraic operator.

So, the correct phrase for the algebraic expression in ( 22-n ) is 22 minus the number.

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Complete question:

Which phrase correctly represents the algebraic expression for 22-n?

A.) A number decreased by twenty-two

B.) The total of twenty two and a number

C.) The difference of two and a number

D.)Twenty-two decreased by a number

Salaries of entry-level computer engineers have Normal distribution with unknown mean and variance. Three randomly selected computer engineers have salaries (in $1000s): 30, 50, 70 (a) Construct a 90% confidence interval for the average salary of an entry-level computer engineer. 302 Probability and Statistics for Computer Scientists (b) Does this sample provide a significant evidence, at a 10% level of significance, that the average salary of all entry-level computer engineers is different from $80,000? Explain. (c) Looking at this sample, one may think that the starting salaries have a great deal of variability. Construct a 90% confidence interval for the standard deviation of entrylevel salaries.

Answers

a) The 90% confidence interval for the average salary of an entry-level computer engineer is of: (16.28, 83.72).

b) The sample contains the value 80, hence it does not give sufficient evidence that the average salary of all entry-level computer engineers is different from $80,000.

c) The 90% confidence interval for the standard deviation of entry level salaries is of: (6.67, 389.86).

What is the confidence interval for the population mean?

The bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.

The sample in this problem is given as follows:

30, 50, 70.

Hence the values of the parameters are given as follows:

[tex]\overline{x} = 50, s = 20, n = 3[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 3 - 1 = 2 df, is t = 2.92.

Then the lower bound of the interval is of:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 50 - 2.92\frac{20}{\sqrt{3}} = 16.28[/tex]

The upper bound of the interval is of:

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 50 + 2.92\frac{20}{\sqrt{3}} = 83.72[/tex]

What is the confidence interval for the standard deviation?

The bounds of the confidence interval for the standard deviation are given as follows:

[tex]\frac{(n - 1)s^2}{\chi^2_\frac{\alpha}{2}} \leq \sigma \leq \frac{(n - 1)s^2}{\chi^2_{1 - \frac{\alpha}{2}}}[/tex]

The critical values of the chi-square distribution with a confidence level of 90% and 2 df are given as follows:

[tex]\chi^2 = 0.1026, \chi^2 = 5.9915[/tex]

Hence the lower bound of the interval is of:

2 x 20/5.9915 = 6.67.

The upper bound of the interval is of:

2 x 20/0.1026 = 389.86.

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How does Hamlet's view of death change throughout the play?.

Answers

Being afraid of the unknown prevents Hamlet from using death as a solution to end his difficulties.

Hamlet's perspective on death changes as he comes to terms with the fact that it is inevitable and he isn't sure he wants to experience it since death might not be preferable to life. Hamlet repeatedly longs for death to put an end to his suffering due to his sadness and agony, but he hesitates since death is forbidden in the Christian religion for fear of being sentenced to eternal torment in hell.We also learn that since another factor contributing to Hamlet's terrible demise was his inability to "do" rather than just "be." His speech, which is primarily about death, demonstrates his propensity to reflect rather than act.

This is how Hamlet's view of death changes throughout the play.

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If X1 , X2 , X3 and X4 are (pairwise) uncorrelated randomvariables, each having mean 0 and variance 1, compute thecorrelations coefficient of(a) X1 + X2 and X2 + X3 ;(b) X1 + X2 and X3 + X4

Answers

The correlation coefficient of

(a) X1 + X2 and X2 + X3  would be 1/2.

(b) X1 + X2 and X3 + X4 would be 0.

What is the correlation in statistics?

Correlation is a statistical measure (a number) that describes the magnitude and direction of a relationship between two or more variables. A correlation between variables, on the other hand, does not imply that a change in one variable is the cause of a change in the values of the other variable.

(a) X1 + X2 and X2 + X3.

We have

Cov(X1 + X2, X2 + X3) = Cov(X1, X2) + Cov(X1, X3) + Cov(X2, X2) + Cov(X2, X3)

                                    = 0 + 0 + Var(X2) + 0

                                    = 1.

We know that

Var(X1 + X2) = Var(X1) + Var(X2) + 2 Cov(X1, X2) = 1 + 1 + 2 · 0 = 2.

Similarly, Var(X2 + X3) = 0. So the correlation between X1 + X2 and X2 + X3 is

                        [tex]=\frac{Cov(X1+X2, X2+X3)}{\sqrt{Var(X1 + X2) Var(X2 + X3)} }\\\\=\frac{1}{\sqrt{2.2} }\\\\=\frac{1}{2}[/tex]

(b) X1 + X2 and X3 + X4.

Since

Cov(X1 + X2, X3 + X4) = Cov(X1, X3) + Cov(X1, X4) + Cov(X2, X3) + Cov(X2, X4)

                                   = 0 + 0 + 0 + 0

                                   = 0,

the correlation between X1 + X2 and X3 + X4 is 0.

Hence, the correlation coefficient of X1 + X2 and X2 + X3  would be 1/2

and X1 + X2 and X3 + X4 would be 0.

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There is a line through the origin that divides the region bounded by the parabola and the x-axis into two regions with equal area. What is the slope of that line?.

Answers

Using the slope line formula,

The slope of line y = mx is 1.0315.

We have given that,

parabola equation is y = 5x - 3x²

line passing through origin is in the form of y = mx

==> mx = 5x - 3x²

==> 3x²+ mx - 5x = 0

==> 3x² + x(m -5) = 0

==> x(3x + (m -5)) = 0

==> x = 0 , x = (5 -m)/3

The total area of the bounded region is then the integral of 5x - 3x² from x = 0 to x = (5-m)/3

Area under y = 5x - 3x2 and y = mx is (125/54)/2 = 125/108

==> [0 to (5 -m)/3] ∫(5x - 3x²-mx )dx = 125/108

==> [0 to (5 -m)/3]∫( (5 - m)x - 3x2 )dx = 125/108

==> [0 to (5 -m)/3] ((5 - m)x²/2 - x³ )= 125/108

==> (5 - m)[(5 -m)/3]²/2 - ((5 -m)/3)³ = 125/108

==> (5 -m)³/18 - (5 -m)³/27 = 125/108

==> (5 -m)³/54 = 125/108

==> (5 -m)³ = 125/2

==> (5 -m) = 3.9685

==> m = 5 - 3.9685

==> m = 1.0315

Hence slope of line = 1.0315

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Question 6 (2 points) Match each assumption of inference in linear regression on the left with how that assumption is checked. 1. Normality Dots align with the diagonal of a normal probability plot. 2. Linearity Dots align on a scatterplot 3. Equal variance Question 7 (2 points) Indicate whether the symbols on the left refer to the population or sample. V My, ßo, ß1 1. Population r 2. Sample V

Answers

1)Normal dots are the set of data that has a normal distribution and a graph of your data can help to decide whether or not the data is normal. Making a histogram of the data can help to decide whether or not a set of data is normal, but a normal probability plot is more specialized: it graphs z-scores (normal scores) against the data set.

2)A scatterplot displays an association between two sets of data. A scatterplot can also be named a scattergram or a scatter diagram.

3)Equal variances are when the variances are roundabout the same across the samples. Unequal variances can change the error rate and lead to false positives.

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Mazie supply company uses the percent of accounts receivable method. On december 31, it has outstanding accounts receivable of $55,000, and it estimates that 2% will be uncollectible. Prepare the year-end adjusting entry to record bad debts expense under the assumption that the allowance for doubtful accounts has: (a) a $415 credit balance before the adjustment. (b) a $291 debit balance before the adjustment.

Answers

Assuming that the provision for doubtful accounts has been recorded, the year-end adjusting statement to record bad debts expenditure

Define the term doubtful accounts?A receivable that may eventually turn into a bad debt is known as a questionable account or doubtful debt. Establishing a provision for doubtful accounts is crucial for your income statement if consumers make purchases on credit.

1. The $415 will be subtracted since allowance for dubious debts has a credit balance.

Bad debt expenses = (Outstanding accounts receivable  ×  Uncollectible rate) - Credit balance

Bad debt expenses = (2%  × $55,000) - $415

Bad debt expenses = $1,100 - $415

Bad debt expenses = $685

The journal entries are -

Date  Particulars                                 Debit      Credit

Bad debt expense A/c                      $685

Allowance (Doubtful Accounts)        $685

As Bad debt expenses are the, bad debt expense plotted.

2. There is a debit balance in the allowance for dubious debts, thus $291 will be added.

Bad debt expenses = (Outstanding accounts receivable   × Uncollectible rate) + Debit balance

Bad debt expenses = (2%  × $55,000) + $291

Bad debt expenses = $1,100 - (-$291)

Bad debt expenses = $1,391

The journal entries are -

Date  Particulars                                 Debit      Credit

Bad debt expense A/c                    $1,391

Allowance (Doubtful Accounts)   $1,391

As Bad debt expenses are the, bad debt expense plotted.

Thus, assuming that the provision for doubtful accounts has been recorded, the year-end adjusting statement to record bad debts expenditure.

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What is the outlier in a data set 5th grade?.

Answers

the outlier is the furthest number from the rest of the numbers
example: in the set of numbers containing 6, 4, 3, 8, 2, 23 the outlier is 23

 Simplify 355/1000.

Answers

Answer: [tex]\frac{71}{200}[/tex]

Step-by-step explanation: All you have to do is divide both numbers by 5.

hope this helps!

please give brainliest!

Answer:

71/200

Step-by-step explanation:

The gcf of 355 and 1000 is 5

divide each side by 5

you get 71/200

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