Find the time required for an investment of 7,000 dollars to grow to 14,000 dollars at an interest rate of 4% per
year, compounded monthly. Give your answer accurate to 2 decimal places.
Preview
years.

Answers

Answer 1

Answer:

The time required is of 17.53 years.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Find the time required for an investment of 7,000 dollars to grow to 14,000 dollars at an interest rate of 4% per year, compounded monthly.

This is t for which [tex]A(t) = 14000[/tex], considering [tex]P = 7000, r = 0.04, n = 12[/tex]. So

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]14000 = 7000(1 + \frac{0.04}{12})^{12t}[/tex]

[tex](1.0033)^{12t} = 2[/tex]

[tex]\log{(1.0033)^{12t}} = \log{2}[/tex]

[tex]12t\log{1.0033} = \log{2}[/tex]

[tex]t = \frac{\log{2}}{12\log{1.0033}}[/tex]

[tex]t = 17.53[/tex]

The time required is of 17.53 years.


Related Questions

Question 4 of 5
How many solutions does 8 + 6
=
– 4 + have?
A. Two solutions
B. One solution
C. No solutions
D. Infinitely many solutions
SUBMIT

Answers

Your answer would be “One solution”
Explanation:
You can switch what you do with the - 4
You can do
8 + 6 - 4 which is 10
Or
8 - 4 + 6 which would still give us 10

Prove formally. Step by step with statements and reasons.

Answers

Answer:

K

K -> H

H

B -> ~H

H not B (sorry I couldn't type out the symbol)

~B

Step-by-step explanation:

Verbally, what's happening is this:

We have an assertion of K. Since K -> H (K implicates H), and B -> ~H (B implicates a negation of H), a negation of B (~B) is proven. (In this entire process, nothing is given about the symbols except K is true, hence the assertion, which then implicates that H is true and that B is negated since B implicates that negated H is true when in fact it is the opposite.)

Formally, the answer would be the following:

K

K -> H

H

B -> ~H

H not B (sorry I couldn't type out the symbol)

~B

Hope this helped!

Encontrar X..................

Answers

X is 51
Because I did this a few days bakc

a person can type 800 words in 10 minutes.how many words can be type in 1 minute?

Answers

Answer:

Yes they can type about 130 each minute

Step-by-step explanation:

I learned this in a book

Answer:

the person can type

80 wpm

Help me please asap!!​

Answers

Answer:

angle BCA = 45 degree

Step-by-step explanation:

since it is an isosceles triangle , it's one angle is 90 degree whereas other two angles are 45 degree each.

Write the following sentence using mathematical symbols.
The product of 9 and x is less than or equal to - 40.
The answer is

Answers

the answer is 9x ≤ -40

Total employment for sheet metal workers in 2016 is projected to be 201,000. If this is a 6.3% increase from 2006,
approximately what was the tctal employment in 2006?
a. 214,000
b. 187,000
C. 195,000
d. 189,000

Answers

Answer:

D 189,000

Step-by-step explanation:

A right triangle has side lengths 5, 12, and 13 as shown below. Use these lengths to find tanB, sin B, and cos B. (WORK INCLUDED GIVING BRAINLEST TO BEST ANSWER)​

Answers

9514 1404 393

Answer:

tan(B) = 12/5sin(B) = 12/13cos(B) = 5/13

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships.

  Sin = Opposite/Hypotenuse   ⇒   sin(B) = 12/13

  Cos = Adjacent/Hypotenuse   ⇒   cos(B) = 5/13

  Tan = Opposite/Adjacent   ⇒   tan(B) = 12/5

Find the general value of log(1 + i) + log(1 - i)​

Answers

Answer:

the answer would be log 2

Two triangles have the same area. One triangle has a base of 4 cm and a height of 7 cm. If the height of the other triangle is 14 cm, then what is its base length?
3 cm
2 cm
4 cm
5 cm​

Answers

Answer:

x = 2

Step-by-step explanation:

→ Work out the area of the first triangle

0.5 × 4 × 7 = 14

→ Set up an equation for the second base

0.5 × x × 14 = 14

→ Simplify

7x = 14

→ Divide both sides by 7

x = 2

Answer:

option B = 2cm

Step-by-step explanation:

[tex]Area \ of \ first \ triangle = \frac{1}{2} \times base_1 \times height_1 \ [ \where base_1 = 4\cm \ height_1 \ = 7cm \ ][/tex]

                                 [tex]=\frac{1}{2} \times 4 \times 7 \\\\= 14 \ cm^2[/tex]

Given area of second triangle is same as first.

[tex]Area \ of \ second \ triangle = \frac{1}{2} \times base_2 \times height_2 \ [ \ where \ height _ 2 = 14cm \ ][/tex]

                           [tex]14 = \frac{1}{2} \times base_2 \times 14\\\\14 = 7 \times base_2\\\\base_2 = 2 \ cm[/tex]

PLEASE HELP ASAP For each expression below, select the letter that corresponds to the equivalent expression from the given list.
(4x^3 – 4 + 7x) – (2x^3- 8)
is equivalent to expression___
(-3x^2 + x^4 + x) + (2x^4 - 7 + 4x) is equivalent to expression ____
(12 – 2x)(2x + 3) is equivalent to expression___

The blanks are for the letters in the picture

Answers

BAnswer:

B-D-A

Step-by-step explanation:

-

Given right triangle ABC with altitude BD drawn to hypotenuse AC

Answers

Given:

In right triangle ABC, BD is the altitude drawn to hypotenuse AC.

[tex]AD=20, DC=45[/tex]

To find:

The length of BD.

Solution:

According to geometric mean theorem of triangles, if an altitude is drawn to the hypotenuse of a triangle, then the altitude is the geometric mean of the segments of the hypotenuse.

Using geometric mean theorem of triangles, we get

[tex]BD^2=AD\times DC[/tex]

[tex]x^2=20\times 45[/tex]

[tex]x^2=900[/tex]

Taking square root on both sides, we get

[tex]x=\dfrac{900}[/tex]

[tex]x=30[/tex]

Therefore, the length of BD is 30 units and the correct option is C.

A bacteria culture is growing at a rate of
r(t) = 7e^0.6t
thousand bacteria per hour after t hours. How much did the bacteria population increase during the first two hours? (Round your answer to three decimal places.)

Answers

Answer:

[tex]{ \bf{r(t) = 7e {}^{0.6t} }} \\ { \tt{r(2) = 7 {e}^{0.6 \times 2} }} \\ = { \tt{7 {e}^{1.2} }} \\ = 23.241 \: thiusand bacteria \: per \: hour[/tex]

23.2 bactéria that is growing I think

What base makes the equation below true?

Note: A number should be entered, not a word.

Answers

Answer:

4

Step-by-step explanation:

in base 4

21 = (2 * 4) + (1 * 1) = 9

Savannah needs to order some new supplies for the restaurant where she works. The
restaurant needs at least 694 knives. There are currently 262 knives. If each set on
sale contains 12 knives, which inequality can be used to determine s, the minimum
number of sets of knives Savannah should buy?

Answers

Answer:

[tex]s\geq 36[/tex]

Step-by-step explanation:

Step 1, how many knives to buy?

The restaurant already has 262 knives. We can subtract this number from their needed 694 knives to find how many they still need:

[tex]694-262=432[/tex] knives.

Step 2, how many sets of knives?

The restaurant needs to buy 432 knives. We know the knives come in sets of 12, so we can divide to find the # of packs she needs to buy, determined by variable s.

Notice how the restaurant needs to buy a minimum of 694 knives, hence we use a greater or equal than symbol:

[tex]\fbox{\frac{432}{12} \geq s}\\[/tex][tex]s\geq \frac{432}{12}[/tex]

[tex]s\geq 36[/tex]

I hope this helps! Let me know if you have any questions :)

The inequality that can be used to determine s, the minimum number of sets of knives Savannah should buy is 694 ≥ 262 + 12s.

Given that;

The restaurant needs at least 694 knives. There are currently 262 knives.

Here, each set on sale contains 12 knives.

Let us assume that;

The minimum number of sets of knives Savannah should buy = s

Hence the inequality for the given condition is,

694 ≥ 262 + 12s

To learn more about inequality visit:

https://brainly.com/question/25944814

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The table contains the lengths of the sides of different triangles. Do the given side lengths form a right triangle?

Drag and drop Yes or No into the box next to the side lengths.


5 cm, 12 cm, 13 cm

8 cm, 9 cm, 10 cm

3 cm, 4 cm, 4 cm

7 cm, 24 cm, 25 cm

1 cm, 4 cm, 9 cm

Answers

Answer:

ans: it's order wise

a) yes

b) no

c) no

d) no

Step-by-step explanation:

use pythagoras theorem

h² = p² + b²

data given satisfying the theorem form right angled triangle

The perimeter of a rectangle 6 5/7 ft and 2 5/6 ft

Answers

Perimeter is the sum of all the lengths of the sides of the rectangle. Rectangles have two sets of parallel sides, each pair being the same length.
So to find the perimeter: 2(6 5/7) + 2(2 5/6) can be used

Since the question is in fraction form, I will work through the problem and provide an answer in fraction form as well.

6 and 5/7 as an improper fraction is 47/7. 2 and 5/6 as an improper fraction is 17/6. So our new equation is:

2(47/7) + 2(17/6)

After multiplying both fractions by 2, we get:

94/7 + 34/6

In order to add we must find the least common denominator, which is 42

After converting our fractions and using the LCD, the equation is:

564/42 + 238/42

Adding these together results in 802/42

Simplifying the fraction results in 19 4/42, or 19 2/21

escribe un acto bueno de las personas y explica por qué es bueno​

Answers

Answer:

Un buen acto o acción podría ser el donar dinero a la caridad, o contribuir con alimentos a comedores sociales. Estas serían buenas acciones porque, sin ninguna duda, ayudarían a contribuir con el bienestar de la sociedad, a través de la realización de medidas efectivas para luchar contra la pobreza, el hambre y la desigualdad de la población.

Graph the set on a number line. {-1/2, -1 3/4}

Answers

Answer:

D

Step-by-step explanation:

Each dot is 1/4 and we are going from 0 to -2

х
9) -5 +
-6
-16
please help!

Answers

Answer:

x = 16

Step-by-step explanation:

[tex]-5+\frac{x}{-16} =-6[/tex]

[tex]-5+\frac{16}{-16} =-6[/tex]

[tex]-5-1=-6[/tex]

[tex]-6=-6[/tex]

Answer:

101

Step-by-step explanation:

-5 + ×/-16=-6

-5+x=96

x= 101

PLEASE HELP ME ASAP!​

Answers

Answer:

A

Step-by-step explanation:

A


This is the correct answer

Please help! Which interval describes where the graph of the function is positive?

Answers

Answer:

c. -oo < x < -1

Step-by-step explanation:

according to the graph the function possitive

=> y > 0 , and x < -1

What is the exponential regression equation that fits these data? x у 1 4 2 9 3 27 4 90 5 250 6 580 O A. y = 39.16x2 - 169.38x+ 158.9 O B. y = 1.31(2.804) O C. y = 2.80(1.31") O D. y = 104.74x - 206.6​

Answers

Answer:

1.31(2.80)^x

Step-by-step explanation:

Given the data :

x : 1 2 3 4 5 6

y : 4 9 27 90 250 580

Using technology, the exponential regression data obtained by fitting the data is :

y = 1.31(2.80)^x

Where, y = predicted value

1.31 = Initial value

2.80 = growth fractor

x = period

Answer:

1.31(2.80)^x

trust me i just did the cst

Step-by-step explanation:

Fran swims at a speed of 2.1 ​km/h in still water. The Lazy River flows at a speed of 0.7 ​km/h. How long will it take Fran to swim 10 km​ upstream?
What is​ Fran's speed while swimming​ upstream?

Answers

Answer: Fran's speed while swimming​ upstream = 1.4 km/h

Step-by-step explanation:

Given: Fran's swimming speed = 2.1 ​km/h

Speed of river = 0.7 km/h

The direction against the stream is called upstream.

Speed in Upstream = Fran's swimming speed - Speed of river

= 2.1-0.7  km/h

= 1.4 km/h

hence, Fran's speed while swimming​ upstream = 1.4 km/h

If y= 5x- 2 were changed to y = x-2, how would the graph of the new
function compare with the first one?
O A. It would be less steep.
O B. It would be steeper.
O C. It would be shifted down.
OD. It would be shifted left.

Answers

The correct answer is a d

Find the difference of (4.2x10^3)-(2.7x10^3)
Show work!

Answers

Step-by-step explanation:

Is it helpful ?

plz let me know

3x + 1 over 4y2

What is the value of the expression above when x = 3 and y = 4? You must show all work and calculations to receive full credit.

Answers

Answer:

5/32

Step-by-step explanation:

(3x+1)/4y^2

(3(3)+1)/[4(4)^2]

(3*3+1)/[4(4)(4)]

(9+1)/[4*16]

10/64

simplify

5/32

The value of the expression at x = 3 and y = 4 is  [tex]\frac{5}{32}[/tex]   .

Concept:Firstly we will convert the expression into numerical form.Then, we will substitute the value of x & y respectively in the expression and simplify it.

How to solve the given question?Converting the expression into numerical form.
∴ Let [tex]F(x,y) = \frac{3x+1}{4y^2}[/tex]
Substituting x = 3 and y = 4 in the given expression.
∴[tex]F(x = 3,y =4) = \frac{3(3)+1}{4(4)^2} = \frac{10}{64}[/tex]
∴ [tex]F(3,4) = \frac{5}{32}[/tex]

Thus, the value of the expression at x = 3 and y = 4 is  [tex]\frac{5}{32}[/tex]   .

Learn more about expressions here:

https://brainly.com/question/723406

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Eighty members of a bike club were asked whether they like touring bikes and whether they like mountain bikes. A total of 70 like touring bikes, 47 like mountain bikes, and 5 do not like either.

A 4-column table with 3 rows. The first column has no label with entries likes mountain bikes, does not like mountain bikes, total. The second column is labeled liking touring bikes with entries a, c, 70. The third column is labeled does not like touring bikes with entries b, 5, e. The fourth column is labeled total with entries 47, d, 80.

What are the correct values of a, b, c, d, and e?

a = 42, b = 28, c = 33, d = 5, e = 10
a = 42, b = 5, c = 28, d = 33, e = 10
a = 5, b = 42, c = 28, d = 10, e = 33
a = 5, b = 10, c = 28, d = 33, e = 42

Answers

Answer: Choice B

a = 42, b = 5, c = 28, d = 33, e = 10

====================================================

Explanation:

Refer to the diagram below. We have a table of values in which some values (if not most) are unknown. We have variables as placeholders until we can figure out which numbers replace them.

Along the bottom row, we see that 70+e = 80, which solves to e = 10. I subtracted 70 from both sides.

That must mean the answer is between choice A or choice B.

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

Since e = 10, and b+5 = e (third column), we can replace the 'e' with 10 to get the equation b+5 = 10. That solves to b = 5. This rules out choice A.

The final answer is choice B

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

If you want to keep going to find a, c and d, then let's solve a+b = 47 which is the same as a+5 = 47 after replacing letter b with 5.

a+5 = 47 solves to a = 42 after subtracting both sides by 5.

Then along the first column, we see that a+c = 70 which is the same as 42+c = 70. Isolating c gets us c = 28

Lastly, c+5 = d is shown along the second row. Plug in c = 28 to find that d = c+5 = 28+5 = 33

So overall we have:

a = 42, b = 5, c = 28, d = 33, e = 10

Answer:

b is correct

Step-by-step explanation:

Which of the data sets below has a mean of 48? Select all that apply.

A) 51, 53, 43
B) 24, 91, 18, 65, 52
C) 65, 18, 72, 33, 52
D) 72, 18, 56, 46

Answers

C) 65, 18, 72, 33 and D) 72, 18, 56, 46

Answer this math gods

Answers

Answer:

y = 4x^2

Hope that this helps!

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