A system of two linear equations in two variables x and y is rewritten as the following augmented matrix:
[ 6 6 | -18 ]
[ -4 -2 | 2 ]
Use the Gauss-Jordan Elimination Method to solve for x and y.
x = _________
y = _________

Answers

Answer 1

Answer:

x = -10

y = 1

Step-by-step explanation:

To use the Gauss-Jordan Elimination Method to solve for x and y, we need to put the augmented matrix in row-echelon form. The first step is to eliminate the x-coefficient in the second row by adding 4 times the first row to the second row. This gives us the following matrix:

[ 6 6 | -18 ]

[ 0 -10 | -10 ]

Next, we need to eliminate the y-coefficient in the second row. We can do this by adding 5 times the second row to the first row, which gives us the following matrix:

[ 1 -10 | -10 ]

[ 0 -10 | -10 ]

Now, the matrix is already in row-echelon form, so we can read the solution directly from the matrix. The solution is x = -10 and y = 1. Therefore, the solutions to the system of linear equations are:

x = -10

y = 1

Note that there may be other solutions to the system of equations, depending on the specific equations that the matrix represents. The Gauss-Jordan Elimination Method will always give us one possible solution, but there may be other solutions as well.


Related Questions

2) If you wish to save up $220,000 using an annuity, what monthly payment is required into the
annuity if the annuity has an APR of 8.0% compounded annually and you wish to reach your
savings goal in 30 years?

Answers

Answer:

$936.91

Step-by-step explanation:

To find the monthly payment required to save up $220,000 using an annuity with an APR of 8.0% compounded annually over 30 years, we can use the following formula:

payment = (goal * rate) / (1 - (1 + rate) ^-n)

In this formula, "goal" is the savings goal, "rate" is the monthly interest rate, and "n" is the number of payments.

To find the monthly payment, we need to first convert the annual interest rate to a monthly rate by dividing it by 12:

rate = 8.0% / 12 = 0.0067

Next, we need to find the number of payments by multiplying the number of years by the number of payments per year:

n = 30 years * 12 payments/year = 360 payments

Substituting these values into the formula, we get:

payment = (goal * rate) / (1 - (1 + rate)^-n)

= (220,000 * 0.0067) / (1 - (1 + 0.0067)^-360)

= $936.91

The monthly payment required to save up $220,000 using an annuity with an APR of 8.0% compounded annually over 30 years is $936.91.

Describe a real-life representation of the following.



12/49 =0.24

Answers

A real-life representation of the following fraction 12/49 =0.24 is that 12kg or rice is to be shared among 49 friends. How many kg will each person get?

How to calculate the fraction?

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

In this case, the real-life representation of the following fraction 12/49 =0.24 is that 12kg or rice is to be shared among 49 friends. How many kg will each person get?

This is illustrated as 12/49.

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400 mg is equal to how many grams

Answers

Since there’s 1000 mg in one gram, divide 400 by 1000, to get 400/1000, which is 4/10, which is 2/5 or 0.4 grams.

LetVbe the vector space of continuous functions defined on the interval[0,1]. Define an inner product onVby the following rule:⟨f,g⟩=∫01f(x)g(x)dx.Use the Gram-Schmidt orthonormalization procedure to produce an orthonormal basis for the subspace spanned by1,x,x2. Use the results to find the closest-point projection ofx3into this subspace.

Answers

The closest projection will have a value of -29/360.

we will follow these steps to use the Gram-Schmidt orthonormalization procedure for producing an orthonormal basis for the subspace spanned by 1, x, and x²,

Set u₁ = 1, a unit vector.

Set v₂ = x and u₂ = v₂ / ||v₂||.

Set v₃ = x² - (x², u₁)u₁ - (x², u₂)u₂, and u₃ = v₃ / ||v₃||.

Thus we get the orthonormal basis for the subspace spanned by 1, x, and x² to be {u₁, u₂, u₃}.

Now we will use the formula for the projection of a vector onto a subspace to find the closest-point projection of x³ into this subspace,

proj_subspace(x³) = (x³, u₁)u₁ + (x³, u₂)u₂ + (x³, u₃)u₃

The inner products will be calculated as follows:

(x³, u₁) = ∫x³ X 1 dx = 1/4

(x³, u₂) = ∫ x³ X x dx = 1/5

(x³, u₃) = ∫ x³ * (x² - (x², u₁)u₁ - (x², u₂)u₂) dx

Here all the integrals will have limits of 0 and 1.

Hence we get

= 1/9 - 1/4 X 1/2 - 1/5 X 1/3

= 1/9 - 1/8 - 1/15

= (40 - 45 - 24)/360

= -29/360

Thus, the projection of x³ onto the subspace spanned by 1, x, and x² is:

proj_subspace(x³) = 1/4 X u₁ + 1/5 X u₂ + (1/9 - 1/4 X 1/2 - 1/5 X 1/3) X u₃

This projection is the closest point in the subspace to x³, in the sense that the distance between x³ and proj_subspace(x³) is minimized.

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what is the slope of a equation 2y = 3x + 4

Answers

Answer:

[tex]\textsf{Slope}=\dfrac{3}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]2y=3x+4[/tex]

Rearrange the equation to make y the subject by dividing both sides by 2:

[tex]\implies \dfrac{2y}{2}=\dfrac{3x+4}{2}[/tex]

[tex]\implies y=\dfrac{3x}{2}+\dfrac{4}{2}[/tex]

[tex]\implies y=\dfrac{3}{2}x+2[/tex]

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Compare the rearranged equation with the slope-intercept formula.

Therefore:

[tex]\textsf{Slope}=\dfrac{3}{2}[/tex][tex]\textsf{$y$-intercept}=2[/tex]

1/2% of b is 50 find the quantity b ,if

Answers

Answer: 100

Step-by-step explanation:

You can set up the equation:

50 / (1/2)

Dividing by 1/2 is thhe same as multiplying by 2.

50 / (1/2) = 100

50(2) = 100

Calculate and then write the reciprocal of your answer.


2/43 of the difference of 3 2/15 and 2 5/12

Answers

Step-by-step explanation:

3 2/15 - 2 5/12

4 - 25

1____________ = (60+4) - 25/60

39/60

60

2/43 * 39/60

=78/2580

The value of the reciprocal fraction is A = 30/1 = 30

What is Reciprocal Fraction?

The fraction obtained by swapping or interchanging Numerator and Denominator with each other is known as the Reciprocal of the given fraction. The product of reciprocals is 1.

Given data ,

Let the value of the reciprocal fraction be represented as A

Now , the equation will be

Let the first fraction be represented as p

Now , the value of p = 3 2/15

On simplifying , p = 47/15

Let the second fraction be represented as q

Now , the value of q = 2 5/12

On simplifying , q = 29/12

Now , the equation is B = p - q

Substituting the values in the equation , we get

B = ( 47/15 - 29/12 )

B = 43/60

Now , ( 2/43 ) of the value of A is given as

C = ( 2/43 ) ( 43/60 )

On simplifying the equation , we get

C = ( 2/60 )

C = ( 1/30 )

Now , the reciprocal fraction is given as

A = 30/1

A = 30

Hence , the reciprocal fraction is A = 30/1

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state the distinct ways the number 910 can be written as a product of two positive integer factors. (enter your answer as a comma-separated list of products.)

Answers

Here are different ways to express 910 as the product of two positive integer coefficients:

1 x 910, 2x455, 5x182, 10x91, 13x70, 15x61, 26x35, 30x31

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assuming the roc to be lzl < 113, use long division to determine the values of x[o], x[ -1], and x[ -2].

Answers

Long division can be used to determine the  absolute value of x[0], x[-1], and x[-2] when the roc is known. To do this, divide the roc (113) by the coefficient of the highest power in the polynomial (x2). Then, divide the remainder (3) by the coefficient of the next highest power (x), which gives x[-1] = 3. Finally, divide the remainder (8) by the coefficient of the lowest power (1), which gives x[-2] = 8.

To use long division to determine the values of x[0], x[-1], and x[-2], begin by dividing the roc (113) by the coefficient of the highest power in the polynomial (x2). This gives a result of 113/x2 = 10. This means that x[0] = 10. This number is then used as the divisor for the next step, which is to divide the remainder (3) by the coefficient of the next highest power (x). This gives a result of 3/x = 3, so x[-1] = 3. Finally, divide the remainder (8) by the coefficient of the lowest power (1), which gives 8/1 = 8, so x[-2] = 8. This process can be repeated to determine the values of x[n] for any polynomial.

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Which expression is equivalent to 8x-2y+x+x
A) 4x
B 8x
c) 6x-2y
D) 10x - 2y

Please help will give brainlest!!!

Answers

Answer: D

8x + 1x + 1 x - 2y

The answer is D, because you are adding 2 x's to the 8 x, and there is nothing being added or subtracted to the y value. You are essentially combining like terms.

The two cotton processing companies are producing different products and those are sold out the products one year before. The sold sum of both the two companies salaries are $44,000,000. The sold price of company x is 1000 more than the other. Therefore, find the value of each company's product sold price by framing a linear equation?​

Answers

The value of each company's product sold price is given as follows:

Company x: $22,000,500.Company y: $21,999,500.

How to obtain the values?

The values of each company's product sold price is obtained using a system of equations, for which the variables are defined as follows:

Variable x: Company's x sold price.Variable y: Company's y sold price.

The sold sum of both the two companies salaries are $44,000,000, hence:

x + y = 44000000.

The sold price of company x is 1000 more than the other, hence:

x = 1000 + y.

Then the sold price of company y can be found replacing the second equation into the first, as follows:

1000 + y + y = 44000000

2y = 44000000 - 1000

y = (44000000 - 1000)/2

y = $21,999,500.

The sold price for company x is then calculated as follows:

x = 1000 + y = 1000 + 21999500 = $22,000,500.

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Atoms of element B from HCP lattice and those of the element A occupy 2/3 rd of tetrahedral voids. What is the formula of the compound formed by the elements A and B?

Answers

In a hexagonal-close-pack (HCP) unit cell, the ratio of lattice points to octahedral holes to tetrahedral holes =  1 : 1 : 2 is AB3

let the :

Number of lattice point = 1x.

Number of octahedral points = 1x

Number of tetrahedral  points = 2x

If anions occupy the HCP lattice points and cations occupy half of the octahedral holes.

Number of anions occupying the HCP lattice points, A= 1x

Number of cations occupying the octahedral points, B =  1x

The formula of the compound will be =

If anions occupy the HCP lattice points and cations occupy all of  the octahedral and the tetrahedral holes.

Number of anions occupying the HCP lattice points, A= 1x

Number of cations occupying the octahedral points, B =  x

Number of cations occupying the tetrahedral points, B =  2x

total number of cations = x + 2x = 3x

The formula of the compound will be = AB3

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a positive radial velocity means the object is moving [x] the observer, while a negative velocity means the object is moving [y] the observer.

Answers

a positive radial velocity means the object is moving [x] the observer, while a negative velocity means the object is moving [y] the observer ,x away from, y towards

Radial velocity is the velocity of an object in the direction of an observer. A positive radial velocity means the object is moving away from the observer, while a negative velocity means the object is moving towards the observer.Radial velocity is the speed of an object in a particular direction, as observed from an observer. It is measured in the direction towards or away from the observer. A positive radial velocity means the object is moving away from the observer, in a direction radially outward from the observer. A negative radial velocity means the object is moving towards the observer, in a direction radially inward from the observer.

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Please Help!

You are at a fundraising carnival. You want to play one game and you've narrowed it down to two options, as follows:
OPTION 1: Choose a face card (K, Q, J) from a deck of cards. Then, spin an odd number on an 11-part spinner. $5 per play. Grand prize is $150.
OPTION 2: Roll two dice with a product greater than 4 and less than 12. Then, choose a numbered card from a deck of cards. $15 per play. Grand prize is $200.

Which option will you choose and why? Show your work and explain your thinking.

Answers

To decide which option to choose, we need to consider the probability of winning and the potential payout.

For Option 1, the probability of winning is 3/52 * 5/11 = 15/276 = 5.44%. The potential payout is $150, so the expected value of this option is:

Expected value = Probability of winning * Potential payout = 5.44% * $150 = $8.16

For Option 2, the probability of winning is 6/36 = 16.67%. The potential payout is $200, so the expected value of this option is:

Expected value = Probability of winning * Potential payout = 16.67% * $200 = $33.34

Since the expected value of Option 2 is higher than the expected value of Option 1, it is a better choice. Therefore, I would choose Option 2.

47. Find the value of x

Answers

4755245666322257799764

refers to meeting the needs of the present generation without compromising the ability of future generations to meet their own needs​

Answers

The term that refers to meeting the needs of the present generation without compromising the ability of future generations has been sustainability.

¿What is sustainability?

This has been a development that focuses on meeting the needs that arise today without compromising the resources of the following generations.

Sustainability is of paramount importance because:

It enables and contributes to economic growth. Contribute to environmental care and conservation.

¡Hope this helped!

Consider the dot plots which show the distribution of data collected on two high school basketball players. Which statement BEST describes the center of the data collected for the two players? Responses A mean score for player 1 is greatermean score for player 1 is greater B range is greater for player 1range is greater for player 1 C median score for player 2 is greatermedian score for player 2 is greater D mean score for player 2 is greatermean score for player 2 is greater E mean scores are the same for both players

Answers

The best description of the dot plot is;  median scores are the same for both players

How to interpret dot plots?

A dot plot is defined as a simple plot that displays data values as dots above a number line. Now, dot plots show the frequency with which a specific item appears in a data set. Dot plots shows the distribution of the data.

The median of a data set is simply defined as the value in the middle of that same data set when arranged in ascending order.

From player 1, the data set when arranged in ascending order are;

8, 10, 10, 10, 12, 12, 14, 16, 16

In this case, the exact middle term is 12 which will be the median

For player 2, the data set when arranged in ascending order are;

0, 2, 6, 10, 12, 16, 18, 22, 22

In this case, the exact middle term is 12 which will be the median.

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which of the following initial values of the variable y would result in the variable z being set to 2 after the code segment is executed?

Answers

When the following code section runs, the value of the variable y will be -2.

Given that,

We have to find when the following code section runs, what value will the variable y have? Assume the following input values:

The code mentioned above is explained in the section below.

Here, x=5, n=0, and the input values are 1–6.

So, x>3 is true.

Control will go to second if block and input y and z.

Now y=1 and z=2 and n=1

Next control goes to if(x) since x>0 which is true.

Now z=3 and x=4 and y=0 and n=0

Her n==0 so r=z- ++x => 3- (5) =>-2.

Hence r=-2

Therefore, the variable r=-2 is the output for the code.

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Which, if any, is not a characteristic necessary for obtained values of chi-square to be distributed according to the tabled values of the chi-square distribution?
a. expected frequencies must be equal for all groups
b. the null hypothesis must be true
c. sampling must be random
d. all of the above must be true

Answers

Expected frequencies must be equal for all groups is correct option.

Expected frequency of all groups in chi square test should not be equal initially to perform the test.To help establish whether observed results are consistent with expected outcomes and to rule out the possibility that observations are the result of chance, a chi-square test is utilized. When data are being evaluated from a random sample and the variable in issue is a categorical variable, a chi-square test is applicable.Chi-square distributions are helpful for testing hypotheses because of how closely they resemble the conventional normal distribution. Many significant statistical tests and theories revolve around the standard normal distribution, which is a normal distribution with a mean of zero and a variance of one.

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What is the role of galaxies, planets, satellites, comets, and asteroids in shaping the universe?​

Answers

We can say that the role of galaxies, planets, satellites, comets and asteroids, in the conformation of the universe, is based on being elements to structure it.

¿What is the universe and what are its components?

In physics, it is mentioned that the universe is all physical existence that exists, this goes from our planet to what is found abroad.

Within the universe, as an entity, how to find different elements that structure it, for example, we have:

GalaxiesPlanetsSatellitesKitesAsteroids

¡Hope this helped!

Describe what is meant by the statement “Renting can restrict ones lifestyle.”

Answers

I believe this means that if you rent you will always have money to pay back, restricting how much money you have in life

(this may not be correct this is just how i interpreted this secentence)

Which of the following is not a solution for x < 8?
O x = -3
OX= 7.95
Ox=9
OX= 4.3

Answers

Answer:

x=9

Step-by-step explanation:

x=9

To find out what is a solution for x<8  you have to plug in all the answer choices for x.

When you plug in -3, you get -3<8 and 8 is bigger than -3, so then that makes it a solution because -3 is less than 8 and when you plug it in it sets the equation right.

When you plug in 7.95, you get 7.95<8 and 8 is bigger than 7.95 by a few but it still is bigger so then it's a solution because 7.95 is less than 8 making it a solution.

When you plug in 4.3, you get 4.3<8 and 8 is bigger than 4.3 so then it's  a solution because it sets the equation right.

When you plug in 9, you get 9<8 and that's not right because 8 isn't bigger than 9, setting this answer choice as a non-solution to the inequality.

(Hope you understand this..)

price was $80 yesterday and $104 today whats the percentage increase​

Answers

Answer:

30%

Step-by-step explanation:

The price of the item increased by $24 from yesterday to today, which represents a 30% increase. To calculate this, divide the increase in price by the original price and multiply the result by 100%:

$24 / $80 x 100% = 30%

Therefore, the percentage increase in the price of the item from yesterday to today is 30%.

-5xy² + 7x²y+3y³ - 8x³

Answers

11

According to question

-5xy²+7x²y+3y³-8x³

putting x=2 and y=3

⇒ -5(2)(3)²+7(2)²(3)+3(3)³-8(2)³

⇒-5(18)+7(12)+3(27)-8(8)

⇒-90+84+81-64

∴  11

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The correct question is find the value of equation if x=2 and y=3 , -5xy² + 7x²y+3y³ - 8x³

Universal Electric manufactures sell two models of lamps X and Whose profit being $ 15 and $ 10 respectively. The Process involves two workers A and B who are available for this kind of work with 100 and 80 hours per month respectively. A assembles X in 20 minutes and Y in 30 minutes. B paints X in 20 minutes and Y in 10 minutes. Assuming that all lamps made can be sold without difficulty, determine production figures that maximize profit.
y

Answers

The production figure to maximize the profit is is Z = 15x + 10y  subject to

2x + 3y ≤ 600 ; 2x + y ≤ 480  ; x,y≥ 0 .

In the question ,

it is given that ,

a company named Universal Electric manufactures sell two models of lamps that is Lamp X and Lamp Y  and

Whose profit is  $ 15 and $ 10 respectively.

let the number units the company manufactures of lamp X be = x units

let the number units the company manufactures of lamp Y be = y units

let the total profit be = Z ,

So , the profit to maximize be Z = 15x + 10y

worker A assembles Lamp X in 20/60 hours and Lamp Y in 20/60 hours ; and that he is available for 100 hours per month;

So , the inequality is

(20/60)x + (30/60)y ≤ 100.

20x + 30y ≤ 6000

2x + 3y ≤ 600

Similarly , worker B assembles Lamp X in 20/60 hours and Lamp Y in 10/60 hours ; and that he is available for 80 hours per month;

the inequality will be ,

(20/60)x + (10/60)y ≤ 80.

20x + 10y ≤ 4800

2x + y ≤ 480  .

Therefore , the LPP to maximize the profit is Z = 15x + 10y  subject to

2x + 3y ≤ 600 ; 2x + y ≤ 480  ; x,y≥ 0 .

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- GIVING 50 POINTS - !!!PLEASE I BEG OF YOU HELP ME!!! What is the probability that a given student is on financial aid, given that he or she is a graduate? P(Financial Aid | Graduate)=[?]

Answers

The probability that a given student is on financial aid, given that he or she is a graduate is 0.72

How to determine the probability that a graduate student is on financial aid?

Probability is the measure of the likelihood of an event occurring. In other words, it is a numerical representation of the chance that a particular event will happen.

Probability (graduate student is on financial aid) = number of (graduate student is on financial aid / total number of graduate students

Tota number of graduate students = 1879+ 731 =  2610

P(Financial Aid | Graduate) = 1879 / 2610 = 0.72

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The multiple instruments on the spacecraft-Cassini observed a giant storm erupted in December 2010 on Saturn. Which one of the following descriptions is NOT correct for the giant storm?
A. The storm developed in the northern hemisphere.
B. Lightning was not detected in the giant storm.
C. The storm generated very bright clouds on Saturn.
D. The storm affected the radiant energy budget of Saturn

Answers

The correct answer is option B.

The observation of a giant storm on Saturn from spacecraft Cassini indicates that lightning was not detected in the giant storm.

Usually Mega storms on Saturn happen on every 20 to 30 years.

Through the Cassini spacecraft, scientists could see a massive storm in December 2010. They saw that the storm waves were spreading from the planet's centre and that it was seen as a ringed globe.

The storm waves covered the whole surface of Saturn and had a diameter of around 190,000 miles or 300,000 kilometres.

Simply said, this enormous storm is also known as the Great Northern Storm or the Great White Spot.

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How to find the length of a line segment in a circle?
Additional Topics in Math
Calculator: Not Permitted
Circle Geometry
The semicircle above has a radius of r inches, and chord CD is parallel to the diameter AB. If the length of CD is 2/3 of the length of AB, what is the distance between the chord and the diameter in terms of r?

Answers

The semicircle above has a radius of r inches, The distance between the chord and the diameter in terms of r is √5 r/3 inches.

What is chord of Circle ?

A chord of a circle can be defined as a line segment connecting any two points on the circumference. It should be noted that the diameter is the longest chord of a circle which passes through the center of the circle.

To find the distance required one can use either the Pythagorean theorem or the trigonometric ratios. Let the semicircle have center O. The diameter AB has length 2r. Because chord CD is 2/3 of the length of the diameter,

CD=2/3(2r) = 4r/3

let the distance between diameter AB and chord CD be x inches. To find x draw a right triangle connecting center O, the midpoint, E of chord CD, and point C . Using Pythagorean theorem here,

r² = x² + (CD/2)²

=> r² = x² + (2r/3)²

=> r² = x² + 4r²/9

=> x² = r² - 4r²/9 = 5r²/9

=> x = √5 r/3

Hence, the distance between the chord and the diameter in terms of r is √5r/3..

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NEED HELP ASAP ALSO I’M GIVING A TON OF POINTS AND THANKS! :)

Answers

Answer:

Compounded Semiannually: [tex](1.03454)^t[/tex] and APR = 3.454%

Compounded Quarterly: [tex](1.03469)^t[/tex] and APR = 3.469%

Step-by-step explanation:

Compound Interest Formula:

The Compound Interest Formula is as follows: [tex]A = P(1 + \frac{r}{n})^{nt}[/tex], which can also be written as: [tex]A = P((1 + \frac{r}{n})^n)^t[/tex], using properties of exponents. This is crucial since we want one value inside the parenthesis to calculate the APR (Annual Percentage Rate). Since we want the APR, the only thing we really care about is the [tex](1 + \frac{r}{n})^n[/tex], but this is going to be our APR + 1.

In the question, it's formatted as: [tex]b^t[/tex], and this inside part is going to be our b, so: [tex]b = (1 + \frac{r}{n})^n[/tex], and to calculate the APR we simply subtract 1.

Calculating APR:

Compounded semiannually means the interest is compounded twice a year, so n = 2. We are also given the interest to be 3.425% which in decimal form is 0.03425

Plugging this into the formula stated above we get: [tex]b = (1 + \frac{0.03425}{2})^2 \approx 1.03454[/tex]

So we have the form:

[tex](1.03454)^t[/tex]

With our APR simply being the base - 1:

[tex]APR \approx 0.03454[/tex]

We multiply this by 100 to get it in percentage form:

[tex]APR\approx 3.454\%[/tex]

Compounded quarterly means the interest is compounded four times a year, so n = 4. Plugging in known values we get:

[tex]b = (1 + \frac{0.03425}{4})^4 \approx 1.03469[/tex]

So we have the form:

[tex](1.03469)^t[/tex]

With our APR simply being the base - 1

[tex]APR \approx 0.03469[/tex]

Multiply this by 100 to get it in percentage form:

[tex]APR \approx 3.469\%[/tex]

Answer:

[tex]\begin{array}{|c|c|c|}\cline{1-3} \vphantom{\dfrac12} \sf koooAccount& b^t& \sf Annual\;Percentage\;rate \\\cline{1-3} \vphantom{\dfrac12} \sf compounded\;annually& (1.03425)^t& 3.425\%\\\cline{1-3} \vphantom{\dfrac12} \sf compounded\;semiannually & \left(1.03454\right)^t &3.454\% \\\cline{1-3} \vphantom{\dfrac12} \sf compounded\;quarterly & \left(1.03469\right)^t& 3.469\%\\\cline{1-3} \vphantom{\dfrac12} \sf compounded\; daily& \left(1.03484\right)^t& 3.484\%\\\cline{1-3} \end{array}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

From inspection of the compound interest formula:

[tex]\implies b^t=\left[\left(1+\dfrac{r}{n}\right)^n\right]^t[/tex]

To find the annual percentage rate:

[tex]\implies APR=(b-1)\times 100[/tex]

Compounded annually

Given:

r = 3.425% = 0.03425n = 1

Substitute the values into the formula for [tex]b^t[/tex]:

[tex]\implies b^t=\left[\left(1+\dfrac{0.03425}{1}\right)^1\right]^t[/tex]

[tex]\implies b^t=\left(1.03425\right)^t[/tex]

Therefore, the annual percentage rate is:

[tex]\implies APR=(1-1.03425) \times 100[/tex]

[tex]\implies APR=0.03425 \times 100[/tex]

[tex]\implies APR=3.425\%[/tex]

Compounded semi-annually

Given:

r = 3.425% = 0.03425n = 2

Substitute the values into the formula for [tex]b^t[/tex]:

[tex]\implies b^t=\left[\left(1+\dfrac{0.03425}{2}\right)^2\right]^t[/tex]

[tex]\implies b^t=\left(1.03454326...\right)^t[/tex]

[tex]\implies b^t=\left(1.03454\right)^t[/tex]

Therefore, the annual percentage rate is:

[tex]\implies APR=(1-1.03454) \times 100[/tex]

[tex]\implies APR=0.03454 \times 100[/tex]

[tex]\implies APR=3.454\%[/tex]

Compounded quarterly

Given:

r = 3.425% = 0.03425n = 4

Substitute the values into the formula for [tex]b^t[/tex]:

[tex]\implies b^t=\left[\left(1+\dfrac{0.03425}{4}\right)^4\right]^t[/tex]

[tex]\implies b^t=\left(1.03469241...\right)^t[/tex]

[tex]\implies b^t=\left(1.03469\right)^t[/tex]

Therefore, the annual percentage rate is:

[tex]\implies APR=(1-1.03469) \times 100[/tex]

[tex]\implies APR=0.03469 \times 100[/tex]

[tex]\implies APR=3.469\%[/tex]

Compounded daily

Given:

r = 3.425% = 0.03425n = 365

Substitute the values into the formula for [tex]b^t[/tex]:

[tex]\implies b^t=\left[\left(1+\dfrac{0.03425}{365}\right)^{365}\right]^t[/tex]

[tex]\implies b^t=\left(1.03484162...\right)^t[/tex]

[tex]\implies b^t=\left(1.03484\right)^t[/tex]

Therefore, the annual percentage rate is:

[tex]\implies APR=(1-1.03484) \times 100[/tex]

[tex]\implies APR=0.03484 \times 100[/tex]

[tex]\implies APR=3.484\%[/tex]

Note: There is an error in the given table:  the given "compounded daily" rate is incorrect.

According to the graph of H(w) below, what happens when the width
approaches zero?
Height
25-
(4,25)
(5,20)
(10,10)
(20,5)
25
Width
50
OA. The height gets very large.
OB. The height equals zero.
OC. The height approaches a horizontal asymptote.
OD. The height gets very small.

Answers

As per the graph of H(w) when w draws near to no the worth of H(w) gets extremely high.

Explain bit about graph of the function?

The graph of a function f  is the arrangement of all places in the plane of the structure (x, f(x)). We could likewise characterize the diagram of f to be the chart of the situation y = f(x). In this way, the chart of a capability if an exceptional instance of the diagram of a situation.

According to question:

Think about the gave diagram of H(w)

If we observer the diagram of the function H(w) we reasoned that as the worth of w pushes toward 0 the worth of H(w) increments quickly.

The worth of H(W) is getting increasingly high when we are moving towards 0.

So, we can say that

When W → 0, H(w) → ∞

Thus, As per the chart of H(w) when w draws near to no the worth of H(w) gets extremely enormous.

To know more about graph of the function visit:

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