9589+5319 simplified using decimal form​

Answers

Answer 1

Answer:

149.08

Step-by-step explanation:

9,589+5,319= 14,908

14,908 in decimal form is 149.08

therefore, your answer is 149.08


Related Questions

Please help me with this question!

Please help me with this question!

Answers

It’s C,
Hope it helps,
Message me if you want explanation,
Can I get brainliest answer

URGENT!! I have 12 minutes left!!
Question: Which words have horizontal reflection symmetry? Select all that apply.
A. MOM
B. BOB
C. BIB
D. TOOT

Answers

Answer:

c

Step-by-step explanation:

Answer:

MOM

TOOT

Step-by-step explanation:

A triangular prism has a height of 11 meters and a base with the following measurements. All dimensions are in meters. What is the value of B?​

A triangular prism has a height of 11 meters and a base with the following measurements. All dimensions

Answers

Answer:

The answer is 14 meters

Step-by-step explanation:

duhhhhhhhhhhhhhhh

Answer:

the answer is 7m2

Step-by-step explanation:

4/2 = 2

2* 3.5 = 7m2

I hope this will help you!!

From the last question I had sorry

From the last question I had sorry

Answers

Answer: 1/2

Step-by-step explanation: Rises 1 and goes to the right 2.

9514 1404 393

Answer:

  1/2

Step-by-step explanation:

The line goes up 1 unit for each 2 units to the right. The slope is ...

  rise/run = 1/2

Could someone please help. please help asap I need it. see picture...
find the​ x- and​ y-intercepts
and write The equation in standard form with integer coefficients

Could someone please help. please help asap I need it. see picture...find the x- and y-interceptsand

Answers

The x-intercept is 5 and the y-intercept is 2.

The standard form of the line is 2x + 5y = 10.

How to find the x-intercept, y-intercept and equation in standard form?

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis. In other words, the x -intercept is the value of x when y = 0 and the y-intercept is the value of y when x = 0.

Hence, the x-intercept is 5 and the y-intercept is 2.

Let's find the equation in standard form.

Ax + By = C

where

A, B and C are constant

Using slope intercept form,

y = mx + b

where

m = slopeb = y-intercept

Hence, using (5, 0) and (0, 2)

m = 2 - 0 / 0 - 5

m = - 2 / 5

Therefore.

y = - 2 / 5x + 2

Hence, let's multiply through by 5 to eliminate the fraction

5y = -2x + 10

Therefore, the standard form is as follows:

2x + 5y = 10

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Supposed you want to buy a used car but your savings is not enough. To do this, you borrow P60,000 to be amortized in four equal payments at the end of each of the next four years, and the interest rate is paid 15 percent on the outstanding loan. What is the loan outstanding balance at the end of 2nd year?

Answers

The outstanding balance on the loan at the end of the 2nd year would be P54,000.

The loan of P60,000 is being amortized in four equal payments over four years. Each payment includes both the principal amount and the interest. The interest rate on the outstanding loan is 15 percent.

To calculate the loan outstanding balance at the end of the 2nd year, we need to determine the amount of principal repaid and subtract it from the original loan amount.

Each year, the borrower makes equal payments, so each payment would be P60,000 divided by 4, which is P15,000. However, each payment also includes interest. The interest on the outstanding loan balance at the beginning of the 2nd year is 15 percent of P60,000, which is P9,000.

The amount of principal repaid in the 2nd year is the total payment of P15,000 minus the interest of P9,000, which is P6,000.

Therefore, at the end of the 2nd year, the outstanding loan balance would be the original loan amount of P60,000 minus the principal repaid in the 2nd year, which is P60,000 - P6,000 = P54,000.

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Nate accelerates his skateboard uniformly along a straight path frim rest to 12.625 m/s in 1.968 s. What is Nates average velocity (in m/s) during this time interval?

Answers

Answer:

  6.3125 m/s

Step-by-step explanation:

When acceleration is uniform, the average velocity over the interval is the average of the starting and ending velocities:

  (0 +12.625 m/s)/2 = 6.3125 m/s

Please give me the correct answer

Please give me the correct answer

Answers

Answer:

4, 5, 6, 7, 8

and

k≥4

hope this helps! :)

Please help i give 36 points please help and i only have three questions

name the 10 native american cultural groups found in north america.

why did each native american cultural group develop a distinct culture?

choose any two of these groups and provide a brief description of their cultures.

be certain to include an example or explanation telling how and why the cultures developed as they did.

Answers

Navajo, Lakota Sioux, Iroquois, Cherokee, Apache, Hopi, Ojibwe, Mohawk, Inuit and Nez Perce.

Native American cultural groups found in North America

1. Navajo: The Navajo people are the largest Native American group in the United States, primarily residing in the Southwest. They have a rich culture centered around their language, art, weaving, and traditional ceremonies.

2. Lakota Sioux: The Lakota Sioux are a Plains Native American group known for their nomadic lifestyle and deep connection to the land. They were skilled hunters, relied on buffalo for sustenance and materials, and developed a warrior-based society.

3. Iroquois (Haudenosaunee): The Iroquois Confederacy, or Haudenosaunee, is a group of Native American tribes located in the northeastern United States and southeastern Canada. They are known for their longhouses, matrilineal kinship system, political governance, and the creation of the Great Law of Peace.

4. Cherokee: The Cherokee Nation is located primarily in the southeastern United States. They developed an agricultural society with advanced farming techniques and were known for their sophisticated government structure, written language (Cherokee syllabary), and cultural resilience.

5. Apache: The Apache tribes, including the Chiricahua, Jicarilla, and Western Apache, inhabited the southwestern United States. They were skilled warriors and hunters, adapting to their environment by utilizing guerrilla warfare tactics and developing deep spiritual beliefs.

6. Hopi: The Hopi people are located in northeastern Arizona. They are known for their religious ceremonies, intricate pottery, and architectural structures, including their adobe dwellings called pueblos. The Hopi have a strong spiritual connection to the land and maintain a communal lifestyle.

7. Ojibwe (Chippewa): The Ojibwe tribes reside primarily in the northern Great Lakes region. They have a rich cultural heritage rooted in storytelling, traditional crafts such as birch bark canoe building and beadwork, and the Midewiwin society, which is a spiritual and healing tradition.

8. Mohawk: The Mohawk Nation is part of the Iroquois Confederacy and resides in the northeastern United States and eastern Canada. They were historically agriculturalists, known for their farming techniques such as the Three Sisters (corn, beans, and squash) and were also skilled warriors.

9. Inuit: The Inuit people inhabit the Arctic regions of North America, including Alaska, Canada, and Greenland. They have a unique culture adapted to the harsh Arctic environment, relying on hunting, fishing, and the use of igloos and other snow shelters for survival.

10. Nez Perce: The Nez Perce Tribe traditionally resided in the Pacific Northwest. They were skilled horse breeders, hunters, and gatherers. They had a complex social structure and were known for their artistic expressions, including intricate beadwork and basketry.

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The North American continent is home to numerous Native American cultural groups, each with its distinct history, traditions, and cultural practices. While it is challenging to encompass all of them, here are ten Native American cultural groups found in North America:

1. Navajo (Diné)

2. Cherokee (Tsalagi)

3. Lakota (Sioux)

4. Apache (Ndee)

5. Iroquois (Haudenosaunee)

6. Hopi (Hopituh Shi-nu-mu)

7. Ojibwe (Anishinaabe)

8. Cheyenne (Tsitsistas)

9. Choctaw (Chahta)

10. Mohawk (Kanien'kehá:ka)

Each Native American cultural group developed a distinct culture due to a combination of geographical factors, historical experiences, available resources, and interactions with neighboring tribes. Factors such as climate, landforms, flora, fauna, and proximity to water sources played significant roles in shaping their lifestyles, economies, and social structures. Additionally, migration patterns, trade networks, and intertribal conflicts influenced cultural exchange and differentiation.

Let's explore the cultures of the Cherokee and the Hopi as examples:

1. Cherokee (Tsalagi):

The Cherokee people were historically concentrated in the southeastern region of the United States. They developed an agricultural society, cultivating crops such as corn, beans, and squash. The Cherokee had a matrilineal kinship system, where descent and inheritance were traced through the mother's line. They had a complex political structure with a chiefdom, council, and clan system. The Cherokee are renowned for their unique syllabary, invented by Sequoyah, which enabled the written expression of their language. Despite facing significant challenges during European colonization, including forced removal on the Trail of Tears, the Cherokee managed to preserve their language, cultural practices, and sense of community.

2. Hopi (Hopituh Shi-nu-mu):

The Hopi people reside primarily in northeastern Arizona. Their culture is deeply rooted in agriculture and is centered around the cultivation of corn, beans, and squash, known as the Three Sisters. The Hopi developed an intricate system of terraced farming to optimize water usage in their arid environment. They have a matrilineal social structure, where property and clan membership are passed down through the female line. The Hopi are known for their religious ceremonies and ceremonial katsina dances, which reflect their spiritual beliefs and the cycles of the agricultural calendar. Their culture places great emphasis on community cooperation, harmony, and maintaining a balanced relationship with nature.

The Cherokee and Hopi cultures developed as they did due to their unique geographical locations and historical experiences. The Cherokee's agrarian society emerged in the fertile lands of the southeastern United States, while the Hopi's agricultural practices evolved to adapt to the arid conditions of northeastern Arizona. Both groups incorporated cultural practices and values that were essential for their survival and provided a framework for their social cohesion and identity. The resilience and determination of these cultures allowed them to withstand external pressures and maintain their distinct traditions throughout history.

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Consider the three mutually exclusive projects that follow. The firm's MARR is 10% per year.
EOY Project 1 Project 2 Project
3 0−$10,000−$8,500−$11,000
1−3$5,125$4,450$5,400
1. Calculate each project's PW.
2. Which project would you recommend?
3. Determine the IRR of each project
4. Why might one project have the highest PW while a different project has the largest IRR?

Answers

The present worth (PW) of each project is calculated based on the given cash flows and the firm's minimum attractive rate of return (MARR) of 10% per year.

To calculate the PW of each project, we discount the cash flows at the MARR of 10% per year. The PW for each project is determined as follows:

Project 1: EOY 0: -\(10,000 + (5,125 / (1 + 0.10)^1) + (5,125 / (1 + 0.10)^2) + (5,125 / (1 + 0.10)^3) = $10,682.13\)

Project 2: EOY 0: -\(8,500 + (4,450 / (1 + 0.10)^1) + (4,450 / (1 + 0.10)^2) + (4,450 / (1 + 0.10)^3) = $9,202.79\)

Project 3: EOY 0: \(11,000 + (5,400 / (1 + 0.10)^1) + (5,400 / (1 + 0.10)^2) + (5,400 / (1 + 0.10)^3) = $9,834.71\)

The project with the highest PW is recommended. In this case, Project 1 has the highest PW of $10,682.13, so it would be the recommended project.

The IRR for each project can be determined by finding the discount rate that makes the PW equal to zero. Using the cash flows provided, the IRR for each project can be calculated using a trial-and-error approach or financial software. Let's assume the IRRs are as follows:

Project 1: IRR ≈ 17.5%

Project 2: IRR ≈ 15.3%

Project 3: IRR ≈ 13.8%

The project with the highest PW may differ from the project with the largest IRR due to the timing and magnitude of cash flows. The PW takes into account the timing of cash flows and discounts them to the present value. It represents the total value created by the project over its lifetime. On the other hand, the IRR considers the rate of return that equates the present value of cash inflows to the initial investment. It represents the project's internal rate of return.

Therefore, a project with a higher PW indicates higher overall value, while a project with a larger IRR implies a higher rate of return. These measures can lead to different rankings depending on the cash flow patterns and the MARR.

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I need help with these questions. 1

I need help with these questions. 1
I need help with these questions. 1
I need help with these questions. 1
I need help with these questions. 1
I need help with these questions. 1

Answers

Answer:

first question : I think it's corresponding angle

second question : is lines AD and GH ,b/c skew means two lines that are not parallel and don't intersect

Step-by-step explanation:

HOPE THIS HELPS

Solve for x
5(x + 1) = 6x+2

Answers

Answer:

X = 3

Step-by-step explanation:


Step 1:

Expand brackets

5x + 5 = 6x + 2

Step 2:

Get 5x on other side by subtracting

5 = 1x + 2

Step 3 :

Get 2 on other side by subtracting

3 = 1x

X = 3 or - 3

2O POINTS + BRAINLIEST || Which of these scale factors will result in an Enlargement?
A. 0
B. 1/2
C. 1
D.5

Answers

Answer:

D 5

Step-by-step explanation:

Answer:

B. 1/2?

Step-by-step explanation:

Help please, easy math i just need to double check!

Help please, easy math i just need to double check!

Answers

Answer:

48

Step-by-step explanation:

a = bh

a = 6x 8 = 48

They throw the hypotenuse or the long side which in this case is 10in to try to throw people off. You don't need it in this problem.

Write the equation of a line perpendicular to 3x-8y = -7 that passes through the point (-3,6).

(please help! Thanks!)

Answers

y=−8x/3−2. is the equation of line perpendicular to 3x - 8y = -7

What is perpendicular line ?

In elementary geometry, two geometric objects are perpendicular if they cross at a right angle. The perpendicular sign can be used to graphically express the state of perpendicularity. It is described as the intersection of two lines, two planes, or two planes and a line.

Calculation

The equation of the line in the slope-intercept form is y=3x/8+7/8.

The slope of the perpendicular line is negative inverse: m=−8/3.

So, the equation of the perpendicular line is y=−8x/3+a.

To find a, we use the fact that the line should pass through the given point: 6=(−8/3)⋅(−3)+a.

Thus, a=−2.

Therefore, the equation of the line is y=−8x/3−2.

y=−8x/3−2. is the equation of line perpendicular to 3x - 8y = -7

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Write the equation of a line perpendicular to 3x-8y = -7 that passes through the point (-3,6).(please

I NEED HELP ON THIS ASAP!!!!

I NEED HELP ON THIS ASAP!!!!

Answers

In the two functions as the value of V(x) increases, the value of W(x) also increases.

What is the value of the functions?

The value of functions, V(x) and W(x) is determined as follows;

for h(-2, 1/4); the value of the functions is calculated as follows;

v(x) = 2ˣ ⁺ ³ = 2⁻²⁺³ = 2¹ = 2

w(x) = 2ˣ ⁻ ³ = 2⁻²⁻³ = 2⁻⁵ = 1/32

for h(-1, 1/2); the value of the functions is calculated as follows;

v(x) = 2ˣ ⁺ ³ = 2² = 4

w(x) = 2ˣ ⁻ ³ = 2⁻⁴ = 1/16

for h(0, 1); the value of the functions is calculated as follows;

v(x) = 2ˣ ⁺ ³ = 2³ = 8

w(x) = 2ˣ ⁻ ³ = 2⁻³ = 1/8

for h(1, 2); the value of the functions is calculated as follows;

v(x) = 2ˣ ⁺ ³ = 2⁴ = 16

w(x) = 2ˣ ⁻ ³ = 2⁻² = 1/4

for h(2, 4); the value of the functions is calculated as follows;

v(x) = 2ˣ ⁺ ³ = 2⁵ = 32

w(x) = 2ˣ ⁻ ³ = 2⁻¹ = 1/2

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What is the value of x?

What is the value of x?

Answers

X of the graph is sum

NEED HELP AND FAST IM ONLINE WITH MY TEACHER
Daniel worked for 2 1/3 hours and earned $18.20.

How much would he make if he worked for 5 1/4 hours?

Answers

Answer:

2 1/3hrs→ $18.20

1 hr→ $7.80

5 1/4hrs→ $7.80x5 1/4= $40.95

Step-by-step explanation:

here u go pls make me brainliest

Answer:

just above 41 dollars but since there is only two decimals $41.00

Step-by-step explanation:

The actual width of a dual carriageway is 24m. If the plane in which you are drawing is at a scale of 1: 200, how many millimeters will the drawing be wide?

Answers

Answer:

8 cm

Step-by-step explanation:

24 ÷ 3

Anna's babysitter charges $4.50 per hour. anna doesn't want to pay any more than $27. which inequality represents the number of hours, h, anna can have a babysitter?

Answers

6 hours. 4.50 x 6 is 27. found it by dividing 4.50 by 27.

Lexie opened a cheesecake store right beside St. Joachim School. At recess, Angelo bought some slices of cheesecake. Nick bought twice as many slices as Angelo. Sabrina bought four less than three times as many slices as Angelo. Carmine bought twice the sum of what Angelo bought and five more. Siobhan bought three times the sum of what Angelo and Sabrina bought. Lexie sold a total of 57 slices of cheesecake at recess. How many slices of cheesecake did each person buy?

Answers

Angelo bought 3 slices, Nick bought 6 slices, Sabrina bought 7 slices, Carmine bought 13 slices, and Siobhan bought 33 slices.

We should call the quantity of cuts Angelo purchased "A".

Scratch purchased two times as numerous as Angelo, so Scratch purchased 2A cuts.

Sabrina purchased four under three fold the number of as Angelo, so Sabrina purchased 3A - 4 cuts.

Carmine purchased two times the amount of what Angelo purchased and five more, so Carmine purchased 2(A + 5) cuts.

Siobhan purchased multiple times the amount of what Angelo and Sabrina purchased, so Siobhan purchased 3(A + (3A - 4)) cuts, which streamlines to 9A - 12 cuts.

We realize that the all out number of cuts sold was 57, so we can set up a situation:

A + 2A + (3A - 4) + 2(A + 5) + (9A - 12) = 57

Streamlining and settling for A:

A = 3

So Angelo purchased 3 cuts, Scratch purchased 2A = 6 cuts, Sabrina purchased 3A - 4 = 5 cuts, Carmine purchased 2(A + 5) = 16 cuts, and Siobhan purchased 9A - 12 = 15 cuts

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what is the proportional relationship between x 2 6 8 10 and y 6 18 24 30

Answers

The proportional relationship is y = 3x.

What is the proportional relationship?

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

Here, we have

Given:

x:  2, 6, 8, 10

y:  6, 18, 24, 30

We have to find the proportional relationship between x and y.

So, we can see from inspection and visual observation that there is a proportional relationship between x and y.

6 = 3  2,  18 = 3  6, 24 = 3  8, 30 = 3  10.

Hence, The proportional relationship is y = 3x.

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Write the equation of the line, in point-slope form. Identify (x1 y2) as slope (-2,2). Use the box provided to submit all of your calculations and final answers.

Write the equation of the line, in point-slope form. Identify (x1 y2) as slope (-2,2). Use the box provided

Answers

Answer:

y + 2 = -1(x - 2)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Point-Slope Form: y - y₁ = m(x - x₁)  

x₁ - x coordinate y₁ - y coordinate m - slope

Step-by-step explanation:

Step 1: Define

Point (-2, 2)

Point (2, -2)

Step 2: Find slope m

Substitute:                    \(m=\frac{-2-2}{2+2}\)Subtract/Add:               \(m=\frac{-4}{4}\)Divide:                          \(m=-1\)

Step 3: Write equation

Point-Slope Form:   y + 2 = -1(x - 2)

And we have our final answer!

Choose the equation in slope-intercept form of a line with the following qualities:

slope: -4

y-intercept: -10

A. y = -10x + 4
B. y = -10x + - 4
C. y= -4x - 10
D. -4x - 10y = 1

Answers

Answer:

C. y=-4x-10

Step-by-step explanation:

The equation for a line in slope-intercept form is:

y=mx + b

m: slope

b: y-intercept

x,y: x and y coordinate pair

So the answer would be...

y=-4x-10

C: y= -4x - 10

Slope intercept form is using the format, y=mx+b. The slope being m, (-4 in this scenario), and the y intercept being b, (-10 in this scenario).

Use definition (3), Sec. 19, to give a direct proof that dw = 2z when w = z2. dz 4. Suppose that f (zo) = g(20) = 0 and that f' (zo) and g' (zo) exist, where g' (zo) + 0. Use definition (1), Sec. 19, of derivative to show that f(z) lim ? z~20 g(z) f'(zo) g'(zo)

Answers

f(z)/g(z) → f'(zo)/g'(zo) as z → zo  of derivative to show that f(z) lim.

Let us use definition (3), Sec. 19, to give a direct proof that dw = 2z when w = z².

We know that dw/dz = 2z by the definition of derivative; thus, we can write that dw = 2z dz.

We are given w = z², which means we can write dw/dz = 2z.

The definition of derivative is given as follows:

If f(z) is defined on some open interval containing z₀, then f(z) is differentiable at z₀ if the limit:

lim_(z->z₀)[f(z) - f(z₀)]/[z - z₀]exists.

The derivative of f(z) at z₀ is defined as f'(z₀) = lim_(z->z₀)[f(z) - f(z₀)]/[z - z₀].

Let f(z) = g(z) = 0 at z = zo and f'(zo) and g'(zo) exist, where g'(zo) ≠ 0.

Using definition (1), Sec. 19, of the derivative, we need to show that f(z) lim ?

z~20 g(z) f'(zo) g'(zo).

By definition, we have:

f'(zo) = lim_(z->zo)[f(z) - f(zo)]/[z - zo]and g'(zo) =

lim_(z->zo)[g(z) - g(zo)]/[z - zo].

Since f(zo) = g(zo) = 0, we can write:

f'(zo) = lim_(z->zo)[f(z)]/[z - zo]and g'(zo) = lim_(z->zo)[g(z)]/[z - zo].

Therefore,f(z) = f'(zo)(z - zo) + ε(z)(z - zo) and g(z) = g'(zo)(z - zo) + δ(z)(z - zo),

where lim_(z->zo)ε(z) = 0 and lim_(z->zo)δ(z) = 0.

Thus,f(z)/g(z) = [f'(zo)(z - zo) + ε(z)(z - zo)]/[g'(zo)(z - zo) + δ(z)(z - zo)].

Multiplying and dividing by (z - zo), we get:

f(z)/g(z) = [f'(zo) + ε(z)]/[g'(zo) + δ(z)].

Taking the limit as z → zo on both sides, we get the desired result

:f(z)/g(z) → f'(zo)/g'(zo) as z → zo.

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Please show work for my understanding

Please show work for my understanding

Answers

Answer:

(x-10)

Step-by-step explanation:

Hopefully my work is legible--if not, feel free to ask me to clarify!

I did synthetic division on the righthand side to make sure the answer was correct. Hope this helps :)

Please show work for my understanding

Answer:

\(\displaystyle x - 10\)

Step-by-step explanation:

Since the divisor is in the form of \(\displaystyle x - c,\)use what is called Synthetic Division. Remember, in this formula, -c gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so do not forget it. Anyway, here is how it is done:

−1| 1 −9 10

↓ −1 10

________

1 −10 0 \(\displaystyle \hookrightarrow x - 10\)

You start by placing the c in the top left corner, then list all the coefficients of your dividend [x² - 9x - 10]. You bring down the original term closest to c then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient will be an \(\displaystyle x,\)then you end it off with \(\displaystyle 10,\)giving you the quotient of \(\displaystyle x - 10.\)

I am joyous to assist you at any time.

Express as a trinomial
(3x+1)(3x+8)

Answers

Answer:

9x^2+24x+3x+8

9x^2+27x+8

Step-by-step explanation:

Answer:

9x^2 + 27x + 8

Step-by-step explanation:

well you have to break this down and simplify it so that'll give us

9x^2 + 24x + 3x + 8

9x^2 + 27x + 8

there's ur answer

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Last year, Kaitlin opened an investment account with $8600. At the end of the year, the amount in the account had decreased by 28%. (a) Fill in the blank to write the year-end amount in terms of the original amount. Write your answer as a decimal. Year-end amount = 1 x Original amount​

Answers

Answer:

Kaitlin's account will have 72% of the money initially invested, that is, about $ 6,192.

Step-by-step explanation:

Given that last year Kaitlin opened an investment account with $ 8,600, and at the end of the year, the amount in the account had decreased by 28%, to determine the year-end amount in terms of the original amount both in whole numbers and in decimals, the following calculation must be performed:

100 - 28 = 72

8,600 x 0.72 = X

6.192 = X

Thus, Kaitlin's account will have 72% of the money initially invested, that is, about $ 6,192.

The partial sum 1 + 10 + 19 +.... 199 equals :___________

Answers

The partial sum of the given sequence, 1 + 10 + 19 + ... + 199, can be found by identifying the pattern and using the formula for the sum of an arithmetic series.  Hence, the partial sum of the sequence 1 + 10 + 19 + ... + 199 equals 4497.

To find the partial sum of the given sequence, we can observe the pattern in the terms. Each term is obtained by adding 9 to the previous term. This indicates that the common difference between consecutive terms is 9.

The formula for the sum of an arithmetic series is Sₙ = (n/2)(a + l), where Sₙ is the sum of the first n terms, a is the first term, and l is the last term.

In this case, the first term a is 1, and we need to find the value of l. Since each term is obtained by adding 9 to the previous term, we can determine l by solving the equation 1 + (n-1) * 9 = 199.

By solving this equation, we find that n = 23, and the last term l = 199.

Substituting the values into the formula for the partial sum, we have:

S₂₃ = (23/2)(1 + 199),

= 23 * 200,

= 4600.

However, this sum includes the terms beyond 199. Since we are interested in the partial sum up to 199, we need to subtract the excess terms.

The excess terms can be calculated by finding the sum of the terms beyond 199, which is (23/2)(9) = 103.5.

Therefore, the partial sum of the given sequence is 4600 - 103.5 = 4496.5, or approximately 4497 when rounded.

Hence, the partial sum of the sequence 1 + 10 + 19 + ... + 199 equals 4497.

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An algal bloom covers 50m² of the surface of an isolated lake. The bloom grows at the rate of 80% every day. If the bloom covers the entire surface of the lake all plant and animal life in the lake will die. The Environmental Protection Agency can only get a team to the lake over land, a journey of 3 days. If the surface of the lake has a total area of 550m², will the team arrive in time to save the lake? How long would it take for the bloom to cover 500m² of the lake surface?

Answers

An algal bloom covers 50m² of a lake's surface and grows at a rate of 80% every day. The lake has a total surface area of 550m², and the Environmental Protection Agency team takes 3 days to reach the lake. We need to determine if the team will arrive in time to save the lake and find out how long it would take for the bloom to cover 500m² of the lake's surface.

To determine if the team will arrive in time to save the lake, we need to calculate how much the bloom will grow in 3 days. Starting with an initial area of 50m², the growth rate of 80% means the bloom will increase to 80% of its current size each day.

After the first day, the bloom will cover (50 + 0.8 * 50) = 90m².

After the second day, it will cover (90 + 0.8 * 90) = 162m².

After the third day, it will cover (162 + 0.8 * 162) = 291.6m².

Since the bloom's coverage after 3 days is still less than the total lake surface area of 550m², the team will arrive in time to save the lake.

To determine how long it would take for the bloom to cover 500m² of the lake's surface, we can set up an equation:

50 * (1 + 0.8)^n = 500,

where n represents the number of days. Solving this equation, we find that it would take approximately 6.57 days (or approximately 7 days) for the bloom to cover 500m² of the lake's surface.

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