The amount of money Aria has in the bank after T years is determined by the equation A = 1,000 · 1.0512^T. After how many years will Aria have $2,000 in the bank?
(1) 12.9 (2) 13.9
(3) 14.9
(4) 15.9

Answers

Answer 1

Answer:

Step-by-step explanation:

You are given most of the equation that you need to solve. To find the number of years it will take to have 2000, sub in 2000 for A and solve:

[tex]2000=1000(1.0512)^t[/tex] and begin by dividing away the 1000 on both sides to get

[tex]2=(1.0512)^t[/tex] now we have to take the natural log of both sides:

[tex]ln(2)=ln(1.0512)^t[/tex]. Taking the natural log allows us to bring the t down out front:

ln(2) = t ln(1.0512) and now divide both sides by ln(1.0512):

[tex]\frac{ln(2)}{ln(1.0512)}=t[/tex] and do this on your calculator to get

t = 13.9 years

Answer 2

Answer:

T = 13.9

Step-by-step explanation:

A = 1,000 · 1.0512^T

Let A = 2000

2000 = 1,000 · 1.0512^T

Divide each side by 1000

2000/1000 =  1,000/1000 · 1.0512^T

2 =  1.0512^T

Take the log of each side

log 2 =  log 1.0512^T

We know log a^b = b log a

log 2 =  T log 1.0512

Divide each side by log 1.0512

log 2 / log 1.0512 = T

T=13.88172

Rounding to the nearest tenth

T = 13.9


Related Questions

a microwave oven has a capacity of 1.59ft³. the interior of the microwave of the is 14 in wide and 14 in deep. what is the height of the interior of the microwave, to the nearest tenth of a foot​

Answers

Step-by-step explanation:

The easiest way to do this is to imagine the microwave as a box. Ignore the turntables, whether or not something will spin if it touches an edge, and anything else that would make the fact that we're talking about a microwave confusing. This is a box now. :)

The capacity of our box is 1.59 ft^3, which means it can hold that much of "things" inside it. Instead of a capacity, we'll think of it as the box's total area. A tricky thing to note, is the area is given in ft, where the interior values are given as inches. So we'll need to turn the inches into feet.

To get the area of a box, we do length x width x height.

We're already given the length, 14 (inches), and the width, 14 (inches), so all we need to find now is the height (feet). To turn the lengths into feet, we'll divide them by 12, because there are 12 inches in 1 foot, or Feet = Inches / 12.

To finally turn it into math:

Area (A) = length (L) * width (W) * height (H)

[tex]A = L * W * H[/tex]

Insert known values.

[tex]1.59 = \frac{14}{12} * \frac{14}{12} * H[/tex]

Multiply.

[tex]1.59 = \frac{196H}{144}[/tex]

Simplify.

[tex]1.59 = \frac{49H}{36}[/tex]

Multiply both sides by 36.

[tex]1.59*36 = \frac{49H}{36}*36[/tex]

Simplify.

[tex]57.24 = 49H[/tex]

Divide both sides by 49.

[tex]\frac{57.24}{49} = \frac{49H}{49}[/tex]

Simplify.

[tex]1.16816326... = H[/tex]

To turn make this the nearest Tenth, we round up to the first decimal place.

Answer:

H = 1.2 ft

Plz help me ASAP TwT

Answers

Answer:

Angle CBA

Step-by-step explanation:

It would be CBA because Angle 1 is between those 3 points. Angle 1 is where B is so B would have to go in the middle.

Hope this helps :)

Need help ! Help needed very much !

Answers

Answer:

x/2 > 5

Step-by-step explanation:

Quotient means division

x/2

is more than means greater

x/2 > 5

If the distance between the points (2, -2) and (-1, x) is 5, one of the values of x is

Answers

We know

[tex]\boxed{\sf Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]

ATQ

[tex]\\ \sf\longmapsto \sqrt{(-1-2)^2+(x+2)^2}=5[/tex]

[tex]\\ \sf\longmapsto \sqrt{(-3)^2+x^2+4x+4}=5[/tex]

[tex]\\ \sf\longmapsto \sqrt{9+x^2+4x+4}=5[/tex]

[tex]\\ \sf\longmapsto \sqrt{x^2+4x+13}=5[/tex]

[tex]\\ \sf\longmapsto x^2+4x+13=5^2=25[/tex]

[tex]\\ \sf\longmapsto x^2+4x+13-25=0[/tex]

[tex]\\ \sf\longmapsto x^2+4x-12=0[/tex]

[tex]\\ \sf\longmapsto x^2+6x-2x-12=0[/tex]

[tex]\\ \sf\longmapsto x(x+6)-2(x+6)=0[/tex]

[tex]\\ \sf\longmapsto (x-2)(x+6)=0[/tex]

[tex]\\ \sf\longmapsto x=2\:or\:x=-6[/tex]

The curved part of this figure is a semicircle.

What is the best approximation for the area of this figure?

18+24.25π units²

18+12.125π units²

36+24.25π units²

36+12.125π units²

Answers

Answer:

carna estralia con frema es 36+12.125tt ernits es answeana

Step-by-step explanation:

Answer:

18+12.125π units²

Is it possible to build a triangle with side lengths of 3, 3, and 9?

Answers

Answer:

N0

Step-by-step explanation:

The sides of a triangle must be

a-b< c< a+b  where a and b are the two smaller sides and c is the larger side

3-3 <9< 3+3

0<9<6

This is not true so it cannot make a triangle

answer:

no

step-by-step explanation:

each side must be smaller than the sum of other sides

so

9+3>3-right

3+3<9-wrong

adebook
Homework:
Homework 1
Save
Question 11, 1.1.87
HW Score: 76.92%, 10 of 13 points
Score: 0 of 3
>
cents
Shannon, who is paid time-and-a-half for hours worked in excess of 40 hours, had gross weekly wages of $551 for 52 hours worked. What is her regular hourly rate?

Answers

Answer:

frnddcchdddssjegtgeeusiss ehejsbdvbsjwjgebee e e e e r ytjrbehww

Answer:

$9.5

Step-by-step explanation:

40x+12*1.5x=551

40x+18x=551

58x=551

58x/58=551/58

x=9.5

I put 40x to represent her normal rate when she isnt working overtime which is over 40 hours. And then I put 12*1.5x which is broken down into two parts, 12 represent the amount of overtime hours worked 12 hours overtime (52-40=12) and 1.5x represents the time-and-a-half (which if you didnt know is where you get paid 1.5 times your hourly wage each hour worked overtime). And when you solve this equation you get 9.5 hours an hour as her regular hourly rate

Sarah has 27
27 feet of wire to make bead necklaces. If each necklace
requires 12 feet of wire, how many necklaces can she make?
1

Answers

Sarah can make 2, however she will have 3 feet leftover

Answer:

= 2 R 3

= 2 3/12

= 2 1/4

Step-by-step explanation:

  0 2

1 2 2 7

 − 0  

   2 7

 − 2 4

     3

1-2. Roel earns P 8,000 per month as basic salary. In addition, he earned P 5,725.50 as commission and P 852.50 as overtime pay in January. How much did he earn that month?

3-4. A biscuit factory originally packaged 0.65kg of crackers. To increase profitability, the company reduced the weight by 0.035 kg with a more affordable price. What is the new weight per pack of crackers?

Answers

Answer:

a. he earn 14578.00 in that month.

What is the value of x in the figure below? In this diagram, AABD ~ ACAD.
15
B
х
20

Answers

Answer:

E

Step-by-step explanation:

(leg of big triangle)² = (part of hypotenuse below it) × (whole hypotenuse)

15² = x × 20

225 = 20x ( divide both sides by 20 )

[tex]\frac{225}{20}[/tex] = x , that is

x = [tex]\frac{45}{4}[/tex] → E

The value of the x in the given triangle is 45/4.

What are similar triangles?

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Given is right triangle ABC, divided into two more right triangles, ADC and ADB, also, triangle ABD ~ triangle CAD.

Therefore, according to the definition of similar triangles, the corresponding sides are in proportion.

we have,

CA / CB = CD / CA

15/20 = x/15

x = 15²/20

x = 225/20

x = 45/4

Hence, the value of the x in the given triangle is 45/4.

Learn more about similar triangles click;

https://brainly.com/question/14926756

#SPJ7

please help me please i will give brainliest

Answers

Answer:

I think It would be A

Step-by-step explanation:

Answer:

i think its A

Step-by-step explanation:

(if its not im sorry :( )

Find the value of x.

Answers

r h==ptgggggggggggggggggggggggggggggggggggggggggggggggggggtnnnnnnn

Can someone help please

Answers

Answer:

[tex]10^{-3}[/tex]

Step-by-step explanation:

Answer:

https://tex.z-dn.net/?f=10%5E%7B-3%7D

Step-by-step explanation:

Is (3,8) a solution to the inequality 14x + 12y = 12?

Answers

Answer:

No

Step-by-step explanation:

14x + 12y = 12

(3, 8)

14(3) + 12(8) = 12

42 + 96 = 12

138 = 12

trigonometric identities

Answers

With 180° < θ < 270°, we know that both cos(θ) < 0 and sin(θ) < 0.

Then from the Pythagorean identity, it follows that

sin²(θ) + cos²(θ) = 1   ==>   sin(θ) = -√(1 - cos²(θ))

and so

sin(θ) = -√(1 - (-8/13)²) = -√105/13

Recall the double angle identity for sine:

sin(2θ) = 2 sin(θ) cos(θ) = 2 (-√105/13) (-8/13) = 16√105/169

If the fourth term in a geometric sequence is –1 and the common ratio is –1, find the explicit formula of the sequence.

A)

an = (1) ⋅ (–1)n – 1 for n ≥ 1

B)

an = (– 1) ⋅ (1)n – 1 for n ≥ 1

C)

an = (–1) ⋅ (–1)n – 1 for n < 1

D)

an = (1) ⋅ (1)n – 1 for n ≥ 2

Answers

Answer:

Hello,

Answer A

Step-by-step explanation:

[tex]a_4=-1\\q=-1\ common\ ratio\\\\a_4=a_1*q^3\ -1=a_1*(-1)^3 \Longrightarrow\ a_1=1\\\\\\\boxed{a_n=1*(-1)^{n-1}}\\\\\\Since \ all \ formula\ are\ so\ bad\ written,\ I\ suppose\ that\ the\ answer \ is \ A\\[/tex]

Answer:

 

an = (1) ⋅ (–1)n – 1 for n ≥ 1

Step-by-step explanation:

took the test and got it right

hope this helps

I am a 4 digit number all my digits are different they add up to 20 the hundred's digit is double than the one's digit

Answers

Answer:

- 2864

Step-by-step explanation:

Given that,

The number is of 4 digits

All are different

The sum of the 4 digits = 20

Hundred's digit is twice than one's digit

A.T.Q.

Let the unit digit be 4. So, the hundred's digit would be 4 * 2 = 8

Now, we have

_8_4

We know that the sum of four digits is 20. Thus,

_ + 8 + _ + 4 = 20

∵ _ + _ = 20 - 12 = 8

The possible numbers must make a sum of 8. Thus, one possibility can be 2 and 6.

Therefore, the number can be

2864  

( 2 + 8 + 6 + 4 = 20)

SHOW YOUR STEPS PLEASE. SOMEONE PLEASE HELP ME I NEED THE ANSWER ASAP!!!

The cost, c(x), in dollars per hour of running a certain steamboat is modelled by the function c(x)=1.7x^2-13.6+166.4, where x is the speed in kilometres per hour. At what approximate speed should the boat travel to achieve minimum cost? what is the minimum cost?​

Answers

Answer:

x = 4

139.2

Step-by-step explanation:

Given the Cost function :

C(x) = 1.7x² - 13.6x + 166.4

To achieve minimum cost ;

dc/dx = 0

dc/dx = 2(1.7)x - 13.6

3.4x - 13.6 = 0

3.4x = 13.6

x = 13.6 / 3.4

x = 4

To achieve minimum cost, speed = 4 ;

Minimum cost will be :

C(x) = 1.7x² - 13.6x + 166.4

Put x = 4

C(4) = 1.7(4)² - 13.6(4) + 166.4

C(4) = 27.2 - 54.4 + 166.4 = 139.2

Minimum cost = 139.2

1. Find the ratio of of 25cm and 1m .
2. Find the product of (a + 4)(a − 4).

Answers

Answer:

1..

solution....

here given

25cm

1m=100cm

now,

25/100=1/4

1:4

2....

(a+4)(a-4)

a^2-4^2

a^2-16

Step-by-step explanation:

hope it will help you

determine the general term of this sequence -15:-11;-7;,,173

Answers

Answer:

UWUNOE BRO HUUZEM HIHUDHS

Step-by-step explanation:

A ladder that is 17 feet long is 8 feet from the base of a wall. How far up the wall does the ladder reach?

Answers

H=17ftB=8ft

Using Pythagoras theorem

[tex]\\ \Large\sf\longmapsto P^2=H^2-B^2[/tex]

[tex]\\ \Large\sf\longmapsto P^2=17^2-8^2[/tex]

[tex]\\ \Large\sf\longmapsto P^2=289-64[/tex]

[tex]\\ \Large\sf\longmapsto P^2=225[/tex]

[tex]\\ \Large\sf\longmapsto P=\sqrt{225}[/tex]

[tex]\\ \Large\sf\longmapsto P=15ft[/tex]

Answer:

Applying the Pythagorean theorem we have :wall length is : a²-b²=c²⇒17²-8²=c²⇒c=15(c>=0)

Step-by-step explanation:

we have : the length of the ladder is the hypotenuse of the triangle ; the length of the ladder, which is far from the wall, is the right angle side of the triangle (draw your own illustration)

Can SOMEONE PLEASE HELP ME? I really need to get this work done by tonight. PLEASE

Answers

All triangles add up to 180 degrees so you’ll need to figure out what the two numbers you already have add up to then figure out the leftover and that’ll be your answer xx

HELP PLEASE !! REAL ANSWER ONLY

find the surface area of the cylinder round to the nearest tenth ​

Answers

Answer:

CSA is 12.57

TSA is 18.85 .. i dont know what the question is asking..

I will recommend you to use TSA

Answer:

19ft

Step-by-step explanation:

Formula for surface area of the cylinder=2πr(r+h)

We have,

h=2ft

d=2ft

r=d/2=2/2=1ft

Now,

2πr(r+h)=2π*1(1+2)=2π*1*3=6π=18.8495559215

Rounding to the nearest tenth,

We get Surface area of the cylinder=19 ft

Which is a y-intercept of the continuous function in the
table?
х
-2.
-1
0
1
2.
3
f(x)
15
10
5
0
-5
-10
O (5,0)
O (0, 1)
O (0,5)
O (1,0)

Answers

Answer:

(0,5) --> 5 is the y intercept

Step-by-step explanation:

Give 6 x,y pairs you look for the pair with x=0 to find the y intercept,

SO that would be the 3rd set or (0,5)

The y-intercept of the function is A = ( 0 , 5 )

What is a function rule?

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

Now , the value of A is

Now , the x values of the function are

x = { -2 , -1 , 0 , 1 , 2 , 3 }

And , the y values of the function are

y = { 15 , 10 , 5 , 0 , -5 , -10 }

And , the y intercept of the function is when the value of x = 0

So , when x = 0

y = 5

Hence , the y-intercept is ( 0 , 5 )

To learn more about function rule click :

https://brainly.com/question/3760195

#SPJ7

Mrs. Helton is making gift bags as prizes for her math classes.  She has 30 little bags of Hershey Kisses and 15 Blow Pops.  What is the greatest number of gift bags she can make if all gift bags are the same, and she does not want any left over?​

Answers

Answer:

3

Step-by-step explanation:

I LOVE CANDY hope it helps 45/3 is hte gretaets factor the answer is 3.. i think

Answer:

45 gift bags.

Step-by-step explanation:

take 30 and divide it by 15. your answer is 2. 2 hk bags and 1 blow pop is equal to 3. so you would multiply 3 by 15 to get your conclusion

hi pls help. pls explain a bit:) thank you

Answers

Answer:

i think this is right i’m sorry if not :)

hello pls help it has to do with shapes and volume. thank u :D

Answers

Hi there!

[tex]\large\boxed{r\approx 10.6 cm}[/tex]

Solve for the radius using the pythagorean theorem:

a² + b² = c²

We know the lengths of the hypotenuse and one leg, so:

a = 12

b = ?

c = 16

Plug these into the equation:

12² + b² = 16²

Simplify:

144 + b² = 256

Subtract both sides by 144:

b² = 112

Take the square root:

b ≈ 10.6

Thus the radius is about 10.6 cm.

suppose the function g(x) doubles the square of the input and then subtracts 13. what is g(3)?

Answers

Given:

The function [tex]g(x)[/tex] doubles the square of the input and then subtracts 13.

To find:

The value of [tex]g(3)[/tex].

Solution:

Let [tex]x[/tex] be the input value.

The square of the input is [tex]x^2[/tex].

Doubles the square of the input [tex]2x^2[/tex].

Doubles the square of the input and then subtracts 13, i.e., [tex]2x^2-13[/tex].

So, the function is:

[tex]g(x)=2x^2-13[/tex]

Putting [tex]x=3[/tex] in the above function, we get

[tex]g(3)=2(3)^2-13[/tex]

[tex]g(3)=2(9)-13[/tex]

[tex]g(3)=18-13[/tex]

[tex]g(3)=5[/tex]

Therefore, the value of [tex]g(3)[/tex] is 5.

A rectangular hockey field is 50m long and 35m wide calculate the length of it's diagonal​

Answers

Answer:

length=50m

width=35m

diagonal=?

using Pythagoras theorem

where c=diagonal,a=length(50m),b=width(35)

c² =a² + b²

c² =(50)² + (35)²

c² =2500+1225=3725

Taking square root on both sides

c=61m

Therefore the diagonal is 61m

Solve the equation step by step

Answers

Let x be the amount of salt in the solution.

At day's end, the concentration of salt in the beaker is

x / (4 L) = 0.08 = 8%

Solve for x to get

x = 0.08 (4 L) = 0.32 L

So at the beginning, the concentration of salt in the beaker was

(0.32 L) / (5 L) = 0.064 = 6.4%

Other Questions
In a paragraph, explain why would you recommend the readers to read The house on mango street. If the prism has 3 layers, what would the volume of theprism be in cubic centimeters?OA) 4 cubic centimetersOB) 8 cubic centimetersOC) 12 cubic centimetersOD) 16 cubic centimeters This year, more girls __ _______ on courses in art and design. (ENROLLMENT) Help meeeeeeeee pleaseeeeeeee A self-fulfilling prophecy occurs when a youth receives negative feedback from significant others, the youth interprets this feedback as accurate, and his or her behavior conforms to this negative expectation.a. Trueb. False A father is now twice as old as his son. If the sum of their ages ten years ago was fifty two, how old are they today? What the answer please thank you so much is kinetic energy the same as energy? or is it a type of energy? A carnot engine has an efficiency of 50% when its sink temperature is 27C. The temperature of source is: a) 300C b) 327C c) 273C d) 373C In ABC, mA=a, mB=, mC=y. AB = c, AC = b, BC = a. Find the remaining parts of each triangle if the following parts are given.a=6.00, b=7.56, y = 54 There are 3200 students at Lake High School and 2/5 of these students are sophomores. If 3/8 of the sophomores are opposed to the school forming a crew team and 1/8 of the remaining students (not sophomores) are also opposed to forming a crew team, how many students are in favor of this idea? help me to solve tan^3 2x-3tan2x+2=0 How do you measure your own ability? What have you done in the past classes that encourage you to keep working to develop your skills and imagination? Have you done independent work that friends or family liked and complimented you on? A fruits seller bought some lemon for Re 1 for 15 lemon. if he sold all lemons at 25% profit, how many lemons were sold for Rs 1. define environmental science Instructions: Determine if the two triangles inthe image are congruent. If they are, state howyou know by identifying the postulate.th The DNA sequence ATC AGC GCT GGC CCG is part of a gene.How many proteins are coded for by this message?15145 Anyone here who can help me with this? What is the slope of the points (-2,7) and (2,-5)?4-3-123 A diameter of a circle is 12 inches. What's the distance when rotate 3 circle ?