A quantity with an initial value of 6200 decays continuously at a rate of 5.5% per month. What is the value of the quantity after 4 years, to the nearest hundredth?

Answers

Answer 1

Answer:

410.32

Step-by-step explanation:

Given that the initial quantity, Q= 6200

Decay rate, r = 5.5% per month

So, the value of quantity after 1 month, [tex]q_1 = Q- r \times Q[/tex]

[tex]q_1 = Q(1-r)\cdots(i)[/tex]

The value of quantity after 2 months, [tex]q_2 = q_1- r \times q_1[/tex]

[tex]q_2 = q_1(1-r)[/tex]

From equation (i)

[tex]q_2=Q(1-r)(1-r) \\\\q_2=Q(1-r)^2\cdots(ii)[/tex]

The value of quantity after 3 months, [tex]q_3 = q_2- r \times q_2[/tex]

[tex]q_3 = q_2(1-r)[/tex]

From equation (ii)

[tex]q_3=Q(1-r)^2(1-r)[/tex]

[tex]q_3=Q(1-r)^3[/tex]

Similarly, the value of quantity after n months,

[tex]q_n= Q(1- r)^n[/tex]

As 4 years = 48 months, so puttion n=48 to get the value of quantity after 4 years, we have,

[tex]q_{48}=Q(1-r)^{48}[/tex]

Putting Q=6200 and r=5.5%=0.055, we have

[tex]q_{48}=6200(1-0.055)^{48} \\\\q_{48}=410.32[/tex]

Hence, the value of quantity after 4 years is 410.32.

Answer 2

Answer:

442.44

Step-by-step explanation:


Related Questions

the price of a computer was decreased by 20% to £136. what was the price before it was decreased

Answers

Answer:

170

Step-by-step explanation:

Let x be the original price

x* .20 is the decrease

x - .20x = new price

.80x = new price

.8x = 136

Divide each side by .8

.8x/.8 = 136/.8

x =170

Answer:

7

Step-by-step explanation:

Determine whether the graphs of y=1/2x-8 and y=-2x-6 are parallel, perpendicular, coincident, or none of these.

Answers

Answer:

They are parallels

Step-by-step explanation:

100) Reflect the point in (a) the x-axis and (b) the y-axis.
36. (4,1)
37. (-2,3)
38. (2, -5
39. (-3.5, -2.5) ​

Answers

Answer:

Step-by-step explanation:

36. (4,1)

x-axis(4,-1)

y-axis(-4,1)

37.(-2,3)

x-axis(2,-3)

y-axis(-2,3)

38.(2,-5)

x-axis(-2,5)

y-axis(2,-5)

39.(-3.5, -2.5)

x-axis(-3.5,2.5)

y-axis(3.5,-2.5)

Please correct me I am wrong

Here is the y-axis formula (-x,y)

Here is the x-axis formula(x,-y)

Determine of 10% of 300.

using a double number line

Answers

Answer:

100%     -     300

------------------------

10%      -      x

[tex]100x=300*10\\100x=3000\\x=\frac{3000}{100}\\x=30[/tex]

Answer:

may I try it can be

Step-by-step explanation:

10% of 300

10÷100x300

0.1×300

30

I need help plz! If anyone knows, I would truly appreciate it! Thank uuu!!!!^^
(5 screenshots included)

Answers

Answer:

pic1 a pic2 d

Step-by-step explanation:

i did this

1 : D 2 : A

i hade this paper earlier

Three (3) movie tickets cost $36. At this rate, what is the cost per
ticket?
O $18
$33
O $12
O $108

Answers

$12 have a good day!! make sure u eat something!

Answer: 12$

Step-by-step explanation:

12X3 =36 , or 12 +12 +12 = 36

PLEASE HELP .!!! ILL GIVE BRAINLIEST.. *EXRTA POINTS* .. DONT SKIP :(( !
ILL GIVE 40 POINTS .

Answers

Answer:

7 / 12

Step-by-step explanation:

(0 + 1/2 + 1/2 + 1/2 + 1 + 1) / 6 = 7 / 12 or 0.58

brainliest to who ever answers correctly

Answers

Answer:

it’s either no slope or 0, I dont exactly know which one you would put in to be correct

Step-by-step explanation:

no slope i’m pretty sure let me know what the answer is if i’m wrong

NEED HELP FAST PLEASE!

Answers

Answer:

is c because i had that problem already

Solve the inequality *
5< -2x + 5 < 25

Answers

Answer:

[tex]\huge\boxed{-10<x<0\to x\in(-10;\ 0)}[/tex]

Step-by-step explanation:

[tex]5<-2x+5<25\qquad|\text{subtract 5 from all sides}\\\\0<-2x<20\qquad|\text{change all signs}\\\\0>2x>-20\to -20<2x<0\qquad|\text{divide all sides by 2}\\\\-\dfrac{20}{2}<\dfrac{2x}{2}<\dfrac{0}{2}\\\\-10<x<0[/tex]

Fill in the missing terms of the arithmetic sequence.
-7, __, 1, 5, __, 13
A. 4, 10
B. -3, 9
C. -3, 10
D.-4, 9

Answers

Answer:

B

Step-by-step explanation:

using the back to back numbers 1 and 5, you can tell that each number goes up by 4. ex: -7+4=-3+4=1+4=5+4=9+4=13 and so on

can someone help me understand how to do this?

Answers

Answer:

1/3

Step-by-step explanation:

To get no solution, you want to get rid of x and leave an incorrect equation.

In this case, we will use 1/3x.

1/3x + 2 = 1/3x - 3

We subtract 1/3x on both sides. This will cause the 1/3x's to cancel out.

1/3x - 1/3x + 2 = 1/3x - 1/3x - 3

2 ≠ -3

As we know, 2 is not 3. Therefore, there is no solution if 1/3x is used.

????????????????????

A teacher is writing an exam with 60
questions. If she has finished writing 70% of
the questions, how many questions does she
still need to write?


A) 18

B) 20

C) 30

D) 42


Can smb yk..

Answers

20 is the answer your welcome you will get it right don’t worry

ILL GIVE BRAINLIEST ! Choose all the expressions that are equivalent to 3(2 + 11) *

32 + 311
3(2) + 3(11)
3(2) + 11
6 + 11
6 + 33
3 + 22

Answers

Answer:

6+33 and 3(2)+3(11) are the correct answers.

Step-by-step explanation:

Plz help its really urgent!!

Answers

Answer:

3)0.4 and 1.8

Step-by-step explanation:

:):):):):):):);):):)

BRAINLESS




don't answer if you don't know the answer to the question



The triangle is rotated 90° clockwise around the point (0,0). What will be the coordinates of the image of point L after the rotation?

Answers

Answer:

B

Step-by-step explanation:

You see the long side is right on the x axis so the L point will be the same length from itd rotation. Its rotation will have the long side laying along the Y axis and making it (2, 6)

Which points are on the graph of g(x) = (1/5)x?
Select each correct answer.
(3, 125) (-2,5) (1, 0) (-1, 5)?

Answers

Given:

The function is

[tex]g(x)=(\dfrac{1}{5})^x[/tex]

To find:

The correct ordered pairs.

Solution:

We have,

[tex]g(x)=(\dfrac{1}{5})^x[/tex]

For x=3,

[tex]g(3)=(\dfrac{1}{5})^3[/tex]

[tex]g(3)=\dfrac{1}{125}[/tex]

So, the ordered pair is [tex](3,\dfrac{1}{125})[/tex].

For x=-2,

[tex]g(-2)=(\dfrac{1}{5})^{-2}[/tex]

[tex]g(-2)=(5)^2[/tex]             [tex][\because (\dfrac{a}{b})^{-n}=(\dfrac{b}{a})^n][/tex]

[tex]g(-2)=25[/tex]

So, the ordered pair is [tex](-2,25)[/tex].

For x=1,

[tex]g(1)=(\dfrac{1}{5})^1[/tex]

[tex]g(1)=\dfrac{1}{5}[/tex]

So, the ordered pair is [tex](1,\dfrac{1}{5})[/tex].

For x=-1,

[tex]g(-1)=(\dfrac{1}{5})^{-1}[/tex]

[tex]g(-1)=(5)^1[/tex]             [tex][\because (\dfrac{a}{b})^{-n}=(\dfrac{b}{a})^n][/tex]

[tex]g(-1)=5[/tex]

So, the ordered pair is (-1,5). This is the correct answer.

Therefore, the correct option is D.

Side lengths: 24 in, 30 in, and 36 in

Answers

Volume of this is 25920 inches cubed

Find the values of b such that the function has the given maximum value [tex]f(x) = -x^2+bx-65[/tex]. I already have it in vertex form as [tex]-(x+\frac{b}{2})^2-65+\frac{b^2}{4}[/tex] but I don't know what to do from here

Answers

Answer:

b = {20, -20}

Step-by-step explanation:

Given function:

f(x) = -x² + bx - 65 with maximum value of 35

To find

The value of b

Solution:

Maximum value is obtained at vertex as a < 0

Vertex coordinate of x is:

x = -b/2a = -b / -2 = 1/2b

Solving for b:

35 = - (1/2b)² + b(1/2b) - 65- 1/4b² + 1/2b² = 1001/4b² = 100b² = 400b = √400b = ± 20

See attached

The sum of two numbers is 4. The larger number is 12 more than three times the smaller number. What are the numbers?

Answers

Step-by-step explanation:

So, we will take one of the numbers = x

And the other is 12 more than 3 times it, so = 3x + 12

So they said if we add them, we will get 4

So x + (3x + 12) = 4

4x + 12 = 4

4x = 4 - 12

4x = - 8

x = - 8 ÷4

x = - 2

So one of the numbers x = - 2

The other is 3x + 12

So x = - 2

3x +12 = 3(-2) + 12

= 6

So the 2 numbers = 6 and - 2

Lets check!

6 + (-2) = 4

So it's right!

I'LL GIVE BRAINLIEST TO WHOEVER ANSWERS THE QUESTION CORRECTLY!!!

A.) 6 units
B.) 10.7 units
C.) 5.5 units
D.) 3 units

Answers

Answer:

A

Step-by-step explanation:

Δ NLP and Δ NMO are similar, thus the ratios of corresponding sides are equal, that is

[tex]\frac{NL}{NM}[/tex] = [tex]\frac{NP}{NO}[/tex] , substitute values

[tex]\frac{15+x}{15}[/tex] = [tex]\frac{28}{20}[/tex] ( cross- multiply )

20(15 + x) = 420 ( divide both sides by 20 )

15 + x = 21 ( subtract 15 from both sides )

x = 6

Last Tuesday was silly hat day at Wesley's school. 33 students wore a silly hat and 517 students did not. What percentage of the students wore a silly hat?

Answers

Answer: 6%

Step-by-step explanation:

Number of students that wore a silly hat = 33

Number of students that students that did not = 517

Total number of students = 33 + 517 = 550

The percentage of the students that wore a silly hat

= 33/550 × 100

= 6%

amelia needs to buy some dog food at the nearest store, 3 bags of dog food cost $10.50 how much would amelia spend on 5 bags

Answers

Answer:

15.25

Step-by-step explanation:

Answer:

First  you would have  to find the unit  price for the dog food so you would do 10.50 ÷ 3 to get 3.5, so for one bag it costs $3.50, next you would multiply 3.50 by 5 to get 17.5, so your answer would be $17.50

Write a equivalent expression for (4n + 14) + (5 + 8n)

Answers

Answer:

= 12n + 19

Step-by-step explanation:

can yall explain me what is PSAT please i need to know :)​

Answers

Answer:

g o o g l e states, "The PSAT/NMSQT stands for the National Merit Scholarship Qualifying Test, which students take as a sophomore or junior."

Step-by-step explanation:

Answer:

The PSAT stands for Practice Standardized Aptitude Test.

Step-by-step explanation:

This test is meant to evaluate a student's college-specific skills.

which graph is correct for the equation

Answers

Answer:

I think the answer is C.

Step-by-step explanation:

graph it on demos and it should show you

Please help it’s geometry! I’ll make brainliest

Answers

GX is the angle bisector. Answer is C
The second should be correct sorry if I’m wrong

I need help solving this practice question ​

Answers

[tex]3x-9=45\\3x=45+9\\3x=54\\x=18[/tex]

Fun fact

Bananas are curved because they grow towards the sun ☀️

Answer: the answer is 18

Step-by-step explanation:

ANSWER ME 2 QUESTION.....URGENT....SO PLZZ FASTLY SND ME THE ANSWER....​
FAST
FAST
FAST
FAST
FAST
FAST
FAST
FAST
FAST
FAST
FAST

Answers

Answer:

whats up , whats the question ?

Step-by-step explanation:

Can you please help me!

Answers

Answer:

16

Step-by-step explanation:

Pythagoras theorem was used

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