Mathematics College

2.
Find the amount of the annuity.

Amount of Each Deposit: $295

Deposited: Quarterly

Rate per Year: 10%

Number of Years: 6

Type of Annuity: Due


$9,671.28

$9,542.97

$10,076.54

$9,781.54

Answers

Answer 1
To solve this we are going to use the future value of annuity due formula: [tex]FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ][/tex]
where
[tex]FV[/tex] is the future value [tex]P[/tex] is the periodic payment [tex]r[/tex] is the interest rate in decimal form [tex]n[/tex] is the number of times the interest is compounded per year [tex]k[/tex] is the number of payments per year [tex]t[/tex] is the number of years

We know for our problem that [tex]P=295[/tex] and [tex]t=6[/tex]. To convert the interest rate to decimal for, we are going to divide the rate by 100%:
[tex]r= \frac{10}{100} [/tex]
[tex]r=0.1[/tex]
Since the payment is made quarterly, it is made 4 times per year; therefore, [tex]k=4[/tex].
Since the type of the annuity is due, payments are made at the beginning of each period, and we know that we have 4 periods, so [tex]n=4[/tex].
Lets replace those values in our formula:

[tex]FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ][/tex]
[tex]FV=(1+ \frac{0.1}{4} )*295[ \frac{(1+ \frac{0.1}{4} )^{(4)(6)} -1}{ \frac{0.1}{4} } ] [/tex]
[tex]FV=9781.54[/tex]

We can conclude that the amount of the annuity after 10 years is $9,781.54

Related Questions

NEED HELP ASAP ON GEOMETRY!! ONLY 3 QUESTIONS ATTACHED WITH PHOTOS. THANK YOU

Answers

3. Look at the picture.

Use Pythagorean theorem:

[tex]x^2=3.6^2+5.5^2\\\\x^2=12.96+30.25\\\\x^2=43.21\to x=\sqrt{43.21}\\\\\boxed{x\approx6.6}[/tex]


4.
Use Pythagorean theorem:

[tex]3^2+\left(\dfrac{x}{2}\right)^2=6.5^2\\\\9+\dfrac{x^2}{4}=42.25\ \ \ |-9\\\\\dfrac{x^2}{4}=33.25\ \ \ \ |\cdot4\\\\x^2=133\to x=\sqrt{133}\\\\\boxed{x\approx11.5}[/tex]


5.
[tex]\widehat{AB}\ \cong\ \widehat{DE}[/tex]

you have a bottle of water with a leak. after 2 second,there are 28 ounces left in the bottle. after 6 seconds, there are 20 ounces left in the bottle. how fast is the bottle losing water

Answers

In the 6 - 2 = 4 seconds for which we have a report, the bottle lost 28 -20 = 8 ounces.

The bottle is losing water at the rate of (8 oz)/(4 s) = 2 oz/s.

Answer:

rate of losing water =  8 ounce per 4 sec or 2 ounces per sec.

Step-by-step explanation:

Given : after 2 second,there are 28 ounces left in the bottle. after 6 seconds, there are 20 ounces left in the bottle.

To find : how fast is the bottle losing water.

Solution : WE have given that

After 2 second water left in bottle = 28 ounces.

After 6 second water left in bottle  = 20 ounces.

We can see with in ( 6 - 2) ,4 second  bottle lose their  8 ounce water.

Therefore, rate of losing water =  8 ounce per 4 sec or 2 ounces per sec.

A certain drug is made from only two ingredients: compound A and compound B. There are 5 milliliters of compound A used for every 7 milliliters of compound B. If a chemist wants to make 684 milliliters of the drug, how many milliliters of compound A are needed?

Answers

There are 5 milliliters of compound A for every 7 milliliters of compound B.

So the ration between compound A and B will be:

A:B = 5:7

Total amount of drug = 684

Therefore, the amount of drug A needed will be:

[tex] \frac{5}{5+7}*684 \\ \\ = \frac{5}{12}*684 \\ \\ =285[/tex]

Therefore, out of 684 milliliters 285 would be the compound A and the rest would be compound B
A/B = 5/7

Where 5 mm of A per 7mm of B. That should be the equation.

Given that the total mm is 684
A + B = 684
A = 5/7 * B

5/7 B + B = 684
B=400
A = 5/7 * 400 = 285mm

A = 285mm

Write parametric equations of the line 2x-y=3

Answers

In this item we are given with the equation, 2x - y = 3. The equation contains two variables, x and y. We assume in this item that the value of x is independent of the value of y; however, y values depends on the given values of x. In parametric form, the equation would take the form,

    f(x) = y = ax + b

where a is the numerical coefficient of x and b is constant. Transforming the given equation to this form,

   f(x)  = y = 2x - 3

Answer: The required parametric equation is y=2t-3.

Step-by-step explanation:

Since we have given that

2x+-y=3

We need to rewrite in parametric equation:

The parametric equation is written as

[tex]f(x)=y=at+b[/tex]

So, Arranging the given equation in the above equation, we get

[tex]2x-y=3\\\\2x-3=y\\\\f(x)=y=2x-3[/tex]

And then put x = t, to get the exact parametric form.

Hence, the required parametric equation is y=2t-3.

Find a function that models the population after t years

Answers

a) You have:

[tex]f(0) = 270000\\
f(1) = 1.04f(0), \\
f(2) = 1.04f(1) = 1.04(1.04f(0)), \\
f(t) = 1.04f(t-1) = 1.04(1.04f(t-2)) ... = 1.04^{t}f(0) = 1.04^{t}*270000 [/tex]

b) [tex]f(2004-1998) = 1.04^{2004-1998} * 270000 = 341636[/tex]

c)
[tex]1.04^{x-1998} * 270000 \geq 534094 \\ x - 1998 \geq {ln( \frac{534094}{270000} )}/{ln(1.04)} x \geq 2015.4 x = 2016[/tex]

You planted 488 acres of corn last season. you sold all your corn: 8,120 bushels in August and 64,100 bushels in September. what is your yield pet acre, rounded to the nearest bushel per acre

Answers

The yield per acre will be given by:
[total amount of bushels sold]/[area of the field]
Total amount sold=64100+8120=72220
area=488 acres
thus
72220/488
=147.992~148 bushels per acre

Answer:

There will be approx 148 bushels in per acre.

Step-by-step explanation:

You planted 488 acres of corn last season.

you sold all your corn: 8,120 bushels in August and 64,100 bushels in September.

Total bushels = [tex]8120+64100=72220[/tex]

Now, this amount of bushels were in 488 acres of land.

So, per acre will contain = [tex]72220/488=147.99[/tex]≈ 148 bushels

Hence, there will be approx 148 bushels in per acre.

5y^2 - 2y - 7 are (5y - 7) and ( )

Answers

You have the following expression given in the problem above, which is a quadratic equation:

 5y^2 - 2y - 7=0

 When you factor the quadratic equation, you obtain the following form of it:
 (5y - 7)(y +1)=0

 Therefore, as you can see the answer is: (5y - 7)(y +1)=0
 

what is the poorest country in the world

Answers

According to the data of December 2017, the most poorest countries in the world are in Africa (Guinea, Somali, Mozambique, Burundi, Malawi, Liberia, Central African Republic, Niger), the most poorest is Central African Republic.
Its economic basically is dependent on diamonds export, the most of the diamonds is soled on the 'black' market, which allow to pass the taxes of government...
Final answer:

The poorest countries in the world are primarily in Africa and Asia, according to the World Bank's 2020 report. These countries struggle with governance issues, economic struggles, conflict, and other socio-economic problems, inhibiting their growth. The Democratic Republic of Congo, despite its wealth in resources, significantly exemplifies this due to political instability.

Explanation:

According to the World Bank rankings, many of the poorest countries globally share common traits such as governance failures, economic struggles, and conflicts. These factors, among others, inhibit economic growth and improvement across sectors such as healthcare, education, and infrastructure.

As detailed in the World Bank's 2020 report, the ten lowest income countries include nations primarily located in Africa and Asia. Due to various socioeconomic issues, these countries have low gross national income (GNI) per capita, with notable examples including Afghanistan, Ethiopia, and Zimbabwe.

Learn more about World's poorest countries here:

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Let P(2, 3) be a point on a figure. The figure is dilated by a scale factor of 4.

What are the coordinates of P′?

Write the ordered pair.

Answers

Hi there!

If (2,3) is a point and 4 is the scale factor, we need to multiply both x and y by 4 to dilate the figure. Doing this gives us (8,12).

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

The blades on a wind turbine trace a circular path with radius 100 feet. Suppose the turbine spins at 20 revolutions per minute. What is the linear velocity, in miles per hour (1 mile equals 5,280 feet), of a point on the tip of a blade? Round the answer to the nearest tenth.

Answers

Radius = r = 100 feet
Angular velocity = w= 20 revolutions per minute = 20 x 2π radians per minute
Angular velocity = w = 40π radians per minute

Linear velocity = v = r w

So,

Linear velocity = v = 100 x 40π = 4000π feet per minute
v = 4000π x 60/5280 miles per hour
v = 142.8 miles per hour

Thus the Linear Velocity of the turbine will be 142.8 miles per hour
Final answer:

The linear velocity of a point on the tip of a blade on a wind turbine is approximately 0.05 miles per hour.

Explanation:

To find the linear velocity of a point on the tip of a blade on a wind turbine, we need to convert the rotational speed to linear speed. The formula to do this is linear speed = radius × angular speed. In this case, the radius is 100 feet and the turbine spins at 20 revolutions per minute. First, we convert the revolutions per minute to radians per second by multiplying by 2π/60. Then, we multiply the angular speed by the radius to find the linear speed.

Angular speed = 20 revolutions per minute × 2π/60 = 20π/60 = π/3 radians per second

Linear velocity = 100 feet × π/3 = 100π/3 feet per second

Finally, to convert the linear velocity to miles per hour, we divide by 5280 (since 1 mile equals 5280 feet).

Linear velocity = (100π/3) / 5280 ≈ 0.05 miles per hour

Learn more about Linear velocity here:

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Anwar says that the shape below is a parallelogram. is he correct that a kite is a parallelogram explain

Answers

Short answer: No afraid not.

Opposite sides of a parallelogram must be equal and parallel. The opposite sides of a kit are neither. To make sure you understand, measure the upper left side and the lower right side. The upper left is shorter than the  lower right (even though these sides are opposite one another).

It you extend the upper left line upward and do the same thing to the lower right,  you will get two lines that meet. No parallelogram will do that. 

A shop sells 200 chocolate vanilla and strawberry ice creams 45% of the ice cream sold are vanilla and 30% are strawberry how many chocolate ice creams are sold

Answers

Ice creams:
(1) Chocolate
(2) Vanilla
(3) Strawberry

There are three types of flavors.

45% of the ice creams are vanilla
30% of the ice creams are strawberry
x percent of the ice creams are chocolate

The total amount of ice creams is 200 that corresponds to 100%. Therefore:

45% + 30% + x = 100%

Solving for x:
x = 25%

Then the number of chocolate ice creams are:

[tex]25\%(200) = 50 [/tex]

Finally:
50 chocolate ice creams are sold

Final answer:

The answer explains how to calculate the number of chocolate ice creams sold in a situation where vanilla and strawberry ice creams are already accounted for.

Explanation:

The total number of ice creams sold is 200.

45% are vanilla ice creams. 45% of 200 is 90.

30% are strawberry ice creams. 30% of 200 is 60.

To find the number of chocolate ice creams sold:

Chocolate ice creams = Total ice creams - (Vanilla ice creams + Strawberry ice creams)

Chocolate ice creams = 200 - (90 + 60)

Chocolate ice creams = 200 - 150 = 50

Therefore, 50 chocolate ice creams are sold.

The standard guidelines for fluid intake recommend that a 10dash​20-kg child should have 1000 mL of fluid plus 50 mL for each full kilogram of body weight over 10 kg per day. How many​ 8-ounce glasses of fluid should a 43​-pound child have each​ day? The 43​-pound child should drink about nothing ​8-ounce glasses of fluid each day.

Answers

Given that the standard guidelines for fluid intake recommend that a 10 - 20 kg child should have 1000 mL of fluid plus 50 mL for each full kilogram of body weight over 10 kg per day.

1 ounce contains 29.57 mL of fluid, thus an 8-ounce glass contains 8(29.57) = 236.56 mL of fluid.

1 pound is equivalent to 0.45 kg, thus, 43 pound is equivalent to 43(0.45) = 19.35 kg

Thus, the standard guidelines for fluid intake recommend for a 43 pounds (19.35 kg) child is given by 1000 + 9(50) = 1000 + 450 = 1450 mL of fluid per day.

Therefore, the number of 8-ounce glasses a 43 pound child should have is given by:

[tex] \frac{1450}{236.56} =6.13\approx6\ glasses[/tex]

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Hazel covered a box with felt. The dimensions of the box are shown in the figure below: A rectangular prism is shown. The length of the rectangular prism is labeled as 11 inches, the height is labeled as 6 inches, and the width is labeled as 8 inches. The felt costs 9¢ per square inch. She will only pay for the felt used to cover the box, even if there is waste or extra. How much money did Hazel spend on the felt? $18.18 $27.72 $36.36 $45.54

Answers

i think the answer to this question is (C) $36.36.
Hello, 

The surface area of a rectangular prism is:
A=2(xy+xz+yz), where x,y, and z are the dimenisions
We are told that she will spend .09 per in^2, x=11, y=6, and z=8 so we can say cost is:
C=2(9/100)(11*6+11*8+6*8)
C=(18/100)(66+88+48)
C=$36.36


In a class of 147 students, 95 are taking math(m), 75 are taking science (s), 52 are taking both math and science. What is the probability of randomly choosing a student who is taking neither math nor science? Round your answer to the nearest tenth

Answers

Subtract 52 from m, s, and the total amount of students.. 52 is the amount of students that would take both math and science. m now equals 43, s now equals 23, and the total students remaining is 95.

Since the criteria wants you to exclude students that take math or science, add m and s together. 

[tex]43 + 23 = 66[/tex]

This is the total amount of students that take math or science.

To find the probability of picking a student that doesn't take math or science, subtract 66 from the total amount of students. 

[tex]95 - 66 = 29[/tex]

Take this amount and divide by the total amount of students again.

[tex] \frac{29}{95} = 0.3052[/tex]

Convert the decimal into a percentage.

[tex]0.3052 = 30.52[/tex] %

There is a 30.52% chance of picking a student that doesn't take math nor science.

Answer:

31/147

Step-by-step explanation:

good luck babes <3

Explain what is a Fungi?

Answers

A single-cellular living organism.
A fungi is any member of the group of eukaryotic organisms that includes microorganisms such as yeasts and molds, as well as the more familiar mushrooms.

Use the quadratic formula to solve the equation. If necessary, round answers to the nearest hundredth. 5x2 + 16x – 84 = 0

Answers

Hello!!

x + 6 = 0 or 5x - 14 = 0

x = -6 or 5x - 14 = 0

x = -6 or 5x = 14

Therefore, x = -6 or x = 14/5 (Two solutions found)

Good luck :)

If g(x)= 2x^4+3x^3-x^2, find g(-1)

Answers

When you have a function of g(-1) you first plug in -1 to all x's then you solve it.

Answer: x=0

hey can you please help me posted picture of question

Answers

The inverse functions have a property that the composition of two inverse functions always results is x. 

From the given options, only the pair given in option B result in the composition equal to x.

[tex]F(x)= \frac{12}{x}-18 \\ \\ G(x)= \frac{12}{x+18} \\ \\ F(G(x))= \frac{12}{ \frac{12}{x+18} }-18 \\ \\ F(G(x))= \frac{12(x+18)}{12}-18 \\ \\ F(G(x))=x+18-18=x [/tex]

This proves, F(x) and G(x) are inverse of each other.

So the answer to this question is Option B

The hyperbola with center at (4, 5), with vertices at (0, 5) and (8, 5), with b = 2.

Answers

The standard form of hyperbola is:
(x-h)²/a²-(y-k)²/b²=1
center:(4,5)
Length of the horizontal transverse axis: 8-5=3=2a
thus
a=3/2
a²=9/4
b=2
b²=4

Hence the equation will be:
(x-4)²/(9/4)-(y-5)²/4=1
simplifying this we get:
[4(x-4)²]/9-(y-5)²/4=1

Answer:

Step-by-step explanation:

The correct answer is (x-4)^2/16 - (y-5)^2/4 = 1

plz help ill give u brainlist

Answers

Okay, so the ratio from yellow balls to white balls:
2:3
Let's represent it with n
5n = 50
n = 10
3 * 10 is 30
There are 30 white golf balls.

PLZ HELP NOOOWWWW!!!! 15 points!

A sewing pattern calls for 1/2 meter of red ribbon and 1/5 meter of blue ribbon. What is the unit rate in meters of red ribbon per meter of blue ribbon?

Answers

Hello!

First you have to find how many sections of blue ribbon makes 1 meter

1/5 * 5 = 1

It takes 5 sections of blue ribbon to make one meter of blue ribbon

Multiply this by the sections of red ribbon

1/2 * 5 = 2.5

The answer is 2.5 meters of red ribbon for every meter of blue ribbon

Hope this helps!
Hello!

The unit rate would be 2.5.

Because you take the 2 out of 1/2 and get the unit rate.

Hope this helped. :)

300 minutes equals how many hours

Answers

300 minutes equals five hours.
We know that there are 60 minutes in an hour. To find the total number of hours, we can divide the total minutes by 60 minutes.

300 minutes / 60 minutes = 5 hours 

Suppose that an open box is to be made from a square sheet of cardboard by cutting out squares from each corner as shown and then folding along the dotted lines. If the box is to have a volume of 576 cubic inches, find the original dimensions of the sheet of cardboard.

Answers

Here this may help, it gives the answer too



Given the following functions f(x) and g(x), solve (f ⋅ g)(2) and select the correct answer below: (1 point)

f(x) = 2x2 − 10

g(x) = x + 9



−22


22


−66


66

Answers

For this case we have the following functions:
 f (x) = 2x2 - 10
 g (x) = x + 9
 Evaluating both functions for x = 2 we have:
 f (2) = 2 (2) ^ 2 - 10 = 8 - 10 = -2
 g (2) = (2) + 9 = 2 + 9 = 11
 Then, multiplying both functions we have:
 (f ⋅ g) (2) = (-2) (11)
 (f ⋅ g) (2) = -22
 Answer:
 the correct answer below is:
 -22

Answer:

-22

Step-by-step explanation:

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Calculate the slope of a line that intersects points (6,2) and (-4,-3).

A. 1/2
B. 2/3
C. 4/5
D. 7/8

Answers

Difference in y: -3 - 2 = -5
Difference in x: -4 - 6 = -10

slope = (difference in y)/(difference in x)

slope = (-5)/(-10) = 5/10 = 1/2

Answer: A. 1/2

The slope of the line passing through the points (6,2) and (-4,-3) is calculated using the slope formula (y2 - y1) / (x2 - x1), resulting in a slope of 1/2.

To calculate the slope of a line that intersects points (6,2) and (-4,-3), we use the slope formula, which is (change in y) / (change in x), or (y2 - y1) / (x2 - x1). Here, we consider point 1 to be (6,2) and point 2 to be (-4,-3).

Using the formula:

y2 = -3y1 = 2x2 = -4x1 = 6

Substituting the values into the formula gives us the following calculation:

Slope = (-3 - 2) / (-4 - 6)

Slope = (-5) / (-10)

Slope = 1/2

Therefore, the correct answer is A. 1/2.

The sales of lawn mowers t years after a particular model is introduced is given by the function y = 5500 In(9t+4), where y is the number of lawn mowers sold. How many mowers will be sold 4.5 years after a model is introduced? Round your answer to the nearest whole number. Show your work to find the number of mowers for credit.

Answers

20875.2 All you have to do is plug in the numbers to the equation.

A cat and a dog have a race. The cat’s strides are 30% shorter than the dog’s but it makes 30% more strides than the dog. Which of them will win the race?

Answers

Asked and answered elsewhere.
https://brainly.com/question/9994969

Chris Shopper received a $1,000 discount loan to purchase a washer and dryer. The loan was offered at 12% for 120 days. What are the proceeds? $40.00 $144.00 $960.00 $1,440.00

Answers

The loan proceeds will be given as follows:
A=P(1+r/100)^n
Plugging the values we obtain
n=4 months=
A=1000(1+12/3*100)^1
A=$1040
hence the proceeds will be:
1040-1000=$40

Answer:

The correct answer is 960.

Step-by-step explanation:

120/360=0.333

Remember to use 360 because a bank year is 360 days.

Then you use the interest formula:

I= P×R×T

I=1000×0.12×0.333

39.99=I

Now take 1000 because your principal is 1000, and subtract that from 1000

1000-39.99=960

The pyramid shown has a square base that is 14 centimeters on each side. The slant height is 15 centimeters. What is the surface area of the pyramid?

Answers

we know that

surface area=area of the base+4*[area of one lateral triangle side]

area of the base=b²
b is the side length of the square
b=14 cm
area of the base=14²-----> 196 cm²

area of one lateral triangle side=b*h/2
b is the side length of the square
b=14 cm
h is the height of the lateral triangle side
h is equal to the slant height 
h=15 cm

area of one lateral triangle side=14*15/2----> 105 cm²

surface area=196+4*[105]------> 616 cm²

the answer is
the surface area is 616 cm²
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The function f(x)=2^x and g(x)=f(x)+k.If k=-5,what can be concluded about the graph of g(x)? the graph of g(x) is shifted horizontally a.5 units to the left of the graph of f(x)b. 5 units to the right of the graph of f(x)c.the graph is not shifted horizontally from the graph of f(x) Is the underlined verb in the present progressive or past progressive tense? I was cooking dinner when the phone rang. A. present progressive B. past progressive Daniel gets a weekly $10 allowance. He has swimming class once a week and pays a $1.50 pool fee. After class, he sometimes goes out to eat with friends and spends $5 to $10. He is saving up for new swim trunks and sets aside $2.50 per week. Every few weeks, he goes to a swim meet in another town and spends $3 to $9 on bus fare. This month, Daniel went out with friends and spent $8.50 for lunch. He went to 2 swim meets and spent $7 on bus fare each time. What are this months totals of his fixed and variable expenses?fixed expenses total: $ ___variable expenses total: $ ___ Does a rough draft have to be as long as the final paper what is the volume of the right prism? ______ft3 3+4(z+5)=31 please show the correct step by step and correct answer _____ was a wealthy businessman, whose execution caused riots in Saint-Domingue. One of the greatest examples of islamic architecture is located in india and is called the Cameroon corp. manufactures and sells electric staplers for $15.90 each. if 10,000 units were sold in december, and management forecasts 5% growth in sales each month, the dollar amount of electric stapler sales budgeted for february should be: Which term applies to the process by which our political attitudes are formed by our environment? political diversity political socialization political demography random factors? What is the following product of sqrt 10 times sqrt 10 Who in the crucible does Joseph McCarthy represent? How would I write #3 _____ is any condition of unusual deposits of black pigment in body tissues or organs.a. melanosisb. ileumc. iliumd. leukocyte PLEASE HELP: Question above WILL MARK BRAINLIEST!!!Which action would be prevented by the underlined portion of the First Amendment? A)Newspapers cannot criticize the President. B)Citizens cannot attend a rally against war. C)Methodism is declared the national religion. D)People are prevented from worshiping on Saturday. Jen makes necklaces by stringing different color beads each necklace is 18 in Long Jen has an 86 inch length of beaded string how many necklaces can she make How has the history and understanding of african art been influenced by colonialism? Select the equations that are equivalent to the equation y 2 = 3(x + 6). Select all that apply.y = 3x + 20y = 3x + 62x - y = -33x - y = -20 *98 POINTS*The Fall of the House of UsherBy Edgar Allan PoeNoticing these things, I rode over a short causeway to the house. A servant in waiting took my horse, and I entered the Gothic archway of the hall. A valet, of stealthy step, thence conducted me, in silence, through many dark and intricate passages in my progress to the studio of his master. Much that I encountered on the way contributed, I know not how, to heighten the vague sentiments of which I have already spoken. While the objects around mewhile the carvings of the ceilings, the sombre tapestries of the walls, the ebon blackness of the floors, and the phantasmagoric armorial trophies which rattled as I strode, were but matters to which, or to such as which, I had been accustomed from my infancywhile I hesitated not to acknowledge how familiar was all thisI still wondered to find how unfamiliar were the fancies which ordinary images were stirring up. On one of the staircases, I met the physician of the family. His countenance, I thought, wore a mingled expression of low cunning and perplexity. He accosted me with trepidation and passed on. The valet now threw open a door and ushered me into the presence of his master.Roderick Usher's poemBy Edgar Allan PoeIn the greenest of our valleys,By good angels tenanted,Once a fair and stately palaceRadiant palacereared its head.In the monarch Thought's dominionIt stood there!Never seraph spread a pinionOver fabric half so fair.Banners yellow, glorious, golden,On its roof did float and flow;(Thisall thiswas in the oldenTime long ago);And every gentle air that dallied,In that sweet day,Along the ramparts plumed and pallid,A winged odor went away. ...And, round about his home, the gloryThat blushed and bloomedIs but a dim-remembered storyOf the old time entombed.And travellers now within that valley,Through the red-litten windows seeVast forms that move fantasticallyTo a discordant melody;While, like a rapid ghastly river,Through the pale door,A hideous throng rush out forever,And laughbut smile no more.Which theme is represented in both the paragraph and the poem? Change is for the better. Change is for the worse. Love is always everlasting. Health and happiness always win out.