Find out how long it takes a ​$ investment to double if it is invested at compounded . Round to the nearest tenth of a year. Use the formula . A. years B. years C. years D. years

Answers

Answer 1

Answer:

(A) 8.8 years

Step-by-step explanation:

Given that the principal amount = $ 3100

Rate of compound interest = 8% compounded semiannually.

The given formula is

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

Where A is the final amount, P is the principal amount, r is the rate of compound interest, t is the time and n is the number of times per year the interest is compounded.

From the given condition,

P=$3100

r= 8%=0.08 compounded semiannually

n=2

A=2 x 3100=$ 6200.

Put all these in the given formula to get the required time, we have

[tex]6200=3100\left(1+\frac{0.08}{2}\right)^{2t}[/tex]

[tex]\Rightarrow \left(1+0.04\right)^{2t}=6200/3100[/tex]

[tex]\Rightarrow 1.04^{2t}=2\\\\\Rightarrow 2t\log_{10}(1.04)=\log_{10}(2)\\ \\\Rightarrow 2t =\frac{\log_{10}(2)}{\log_{10}(1.04)}\\\\\Rightarrow 2t =17.673\\\\\Rightarrow t = 17.673/2=8.8365\\[/tex]

On rounding to the nearest tenth of a year, t=8.8 years.

So, the invested amount will be double in  8.8 years.

Hence, option (A) is correct.


Related Questions

Here are the first four terms of an arithmetic sequence. 3 10 17 24 Find, in terms of n, an expression for the nth term of this arithmetic sequence.

Answers

Answer:

[tex]a_{n}[/tex] = 7n - 4

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 3 and d = a₂ - a₁ = 10 - 3 = 7 , thus

[tex]a_{n}[/tex] = 3 + 7(n - 1) = 3 + 7n - 7 = 7n - 4

Evaluate: 21x: 8 when x = 4*

Answers

Answer:

10.5

Step-by-step explanation:

21(4) / 8

84 / 8

10.5

Given: AB ∩ CD ∩ GF = O, E ∈ interior of ∠GOB, H ∈ interior of ∠AOF. Without changing the picture indicate: Vertical angle to ∠GOB: ____________

Answers

Answer:

The verticle angle to GOB is AOF.

Step-by-step explanation:

Look at the picture, it's pretty clear

Hey guys, I know this is a lot so I am offering a lot of points. I was stumped on this paper, I just need a little help on how to complete it :)

Answers

So for number one, you would have to divide the number by the one being multiplied. I’ll do the first one and you can do the second one, comment if you need help.
(4)*_=-12 —> -12/4 = -3
Check : -3*4 = -12
The answer would be -3.
For the second one, multiply all the numbers first and find the actual answer.
(4)*(-7)*(-1) —> 4 * -7 = -28 —> -28 * -1 = 28
Then multiply their answers.
Evangelina : (-28)*(-1) = 28
Josh : (4)*(7) = 28

Now check who has the right answer and explain why.

For number three, use the letters and plug in the values that are being given to you.

e —> -e
-e * f = -15
-e * g = 6
f * g = -10

Now solve from there!

I really hope I helped, comment if you have any questions:)

What is the volume of a cylinder with a radius of 1.5 inches and a height of 9 inches round your answer to the nearest hundredthWhat is the volume of a cylinder with a radius of 1.5 inches and a height of 9 inches round your answer to the nearest hundredth

Answers

Answer:

V = 63.62

Step-by-step explanation:

Answer: 63.62 cubic inches

Step-by-step explanation:

REMEMBER :: VOLUME OF CYLINDER = πr^2h

r= 1.5 in.

h= 9 in.

V= π (1.5)^2 (9)

V= π (2.25) (9)

V= π (20.25)

V~63.6172512...

nearest hundredth = 63.62 cubic inches

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what's the missing number? 7/16 = ?/64

a) 4
b) 21
c) 28
d) 55

Answers

Answer: 28

EXPLANATION:
16 ÷ 64 = 4
7 x 4 = 28

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[tex] \frac{7}{16} = \frac{x}{64} \\ [/tex]

[tex] \frac{x}{64} = \frac{7}{16} \\ [/tex]

Multiply sides by 64

[tex]64 \times \frac{x}{64} = 64 \times \frac{7}{16} \\ [/tex]

[tex]x = 4 \times 7[/tex]

[tex]x = 28[/tex]

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The correct answer is (( C )) .

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If x = 3 and y = 5, work out the value of 4x-2y and 2x² + 3y²

Answers

Answer:

4 × 3 - 2 × 5 = 12 - 10 = 2

2x² + 3y² = 2 × 9 + 3 × 25 = 18 + 75 = 93

Substitute the values for the variables. Since we are given that x=3 and y=5, the new equations will be 4(3)-2(5) and 2(3)^2+ 3(5)^2.

4•3=12
2•5=10

12-10= 2.

Therefore, 4(3)-2(5)=2.

3•3=9

9•2=18

5•5=25

25•3=75.

75+18=93

So, 2(3)^2+ 3(5)^2=93.

The answers will be 2 and 93

Find the 39th term of the following sequence. 17,11, 5, -1

Answers

Answer:

-330

Step-by-step explanation:

a39= 17+ (39-1) * -6

17+ 38 = 55

55*-6 = -330

PLEASE HELP PLEASE I NEED IT TODAY

Answers

Answer:

D

:) Hope this helps.

Step-by-step explanation:

what is the degree measure of f?

Answers

Answer:

98

Step-by-step explanation:

hi there i dont kno but u can ask your mom

can someone help me with this question 2x+3=15 is x

Answers

Answer:

x=6

Step-by-step explanation:

2x+3=15

subtract 3 on both sides

2x=12

x=6

The answer is 6, because 15-3 is 12, and to get 12, you would have to do 2•6, so (2•6)+3=15. So, x=6.

hurry please!!!!!!!!!!!!!!!!

Answers

Answer:

Reflection over the y axis

Step-by-step explanation:

The x's are changing not the y's

Help please!!!!!! And explain ur answer.. I will mark as BRAINLIEST.​

Answers

Answer:

sister it's a picture study Mere question ka pahle aap jawab dijiye aur aapka Jo answer hai vah galat hai samjhe

Help pls help pls help pls help pls help pls

Answers

Answer:

Domain: -2 < x ≤ 3

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)

Step-by-step explanation:

Since domain encompasses x values only, we are looking at the x-values of the graph. We see that our x-values span from -2 to 3. However, since x = -2 is a open dot, it is NOT included in the domain. Since x = 3 is a closed dot, it IS included in the domain:

(-2, 3] or -2 < x ≤ 3

Answer:

ramen is the true answer to lifes problems  

Step-by-step explanation:

Divide (-3x^2 - 9x) ÷ (x + 3)
please explain/show work! <33

Answers

Step-by-step explanation:

[tex]( - 3 {x}^{2} - 9x) \div (x + 3) [/tex]

This is the original equation so you will open the brackets.

[tex] - 3 {x}^{2} - 9x \div x + 3[/tex]

The x will cross the division sign making it times x.

[tex]3 {x}^{2} - 9x \times x = 3[/tex]

So you will proceed to multiply the 9x by x making it;

[tex]3 {x}^{2} - 9 {x}^{2} = 3 [/tex]

So you will subtract 9x² from 3x² which won't be possible so it will be negative.

[tex] - 6 {x}^{2} = 3 [/tex]

Then you will square root both sides making it;

[tex] - \sqrt{6 {x}^{2} } = \sqrt{3} [/tex]

So the ² will cancel the leaving

-6x=3

-6x=1.73(Divide both sides by -6)

x=0.288

That's the final answer.

What does a,b,c,d,e equal to

Answers

Well it all determines on whatt the Equation is

Step-by-step explanation:

360÷60=6 one angle

a=18

b=36

c=84

d=108

e=114

the graph of a linear function f passes through the point (-1,9) and has a slope of -3. what is the zero of f?
answer choices:
-6
4
2
-2

Answers

Answer:

Answer: x=2 (third option)

Step-by-step explanation:

Equation of a line

Being m is the slope and (h,k) is a point through which the line passes, the point-slope form of the equation of a line is:

y - k = m ( x - h )

We have the function f passes through the point (-1,9) and has a slope of m=-3. The point-slope equation of the line is:

y - 9 = -3 ( x - (-1) )

Operating:

y - 9 = -3 ( x + 1 )

y - 9 = -3x - 3

Adding 9:

y = -3x + 6

To calculate the zero of the function we set y=0 and solve for x:

-3x + 6 = 0

Subtracting 6:

-3x = - 6

Dividing by -3

x = - 6 / ( - 3 )

x = 2

Answer: x=2 (third option)

Which of the following mixtures will have a stronger coffee flavor? explain please thank you!!
A) Mixture B
B) Mixture A
C) Both the mixtures are equally strong.

Answers

Mixture B because there’s a higher ratio of coffee to milk than in Mixture A (1:3 vs. 1:2)

Choose scales for the coordinate plane shown so that you can graph the points J(10, 5), K(20, 4), L(5, −5), M(−15, 2), and N(−15, −4). PLEASE QUICK I HAVE 15 mins

Answers

Answer:

x axis use 5 and y axis use 1

Step-by-step explanation:

5 on the x axis would make it big enough to fit up to 30 on both positive and negative sides. 1 on the y axis would fit 6 on both sides. this makes it big enough to fit all the coordinates

help!!
3x+6x+14=41
Solving Multi-Step Equations by Combining Like Terms

Answers

Answer:

x = 3

Step-by-step explanation:

Given

3x + 6x + 14 = 41, that is

9x + 14 = 41 ( subtract 14 from both sides )

9x = 27 ( divide both sides by 9 )

x = 3

Answer:

x=3

Step-by-step explanation:

3x+6x+14=41

9x + 14 = 41

    - 14 = - 14

9x = 27

x=3

16. Find the value of x*
8. 2x-6

A 10
B 7
C -7
D -10

Answers

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[tex]2x - 6 = 8[/tex]

Add sides 6

[tex]2x - 6 + 6 = 8 + 6[/tex]

[tex]2x = 14[/tex]

Divide sides by 2

[tex] \frac{2x}{2} = \frac{14}{2} \\ [/tex]

[tex]x = 7[/tex]

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The correct answer is (( B )) .

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The answer to this is an

If f(x) = x2 + 2x + 3, what is the average rate of change of Rx) over the interval (-4, 6]?

Answers

Answer:

Step-by-step explanation:

The average rate of change of a function over an interval is simply the slope over the interval because:

[tex]let \: g(x)=f'(x)\\\frac{\int\limits^b_a {g(x)} \, dx }{b-a}(the\:average\:value\:of\:g)=\frac{f(b)-f(a)}{b-a}[/tex]

We have to know f(6) and f(-4)

[tex]f(x) = x^2 + 2x + 3\\f(6) = 6^2 + 2(6) + 3\\f(6) = 36 + 12 + 3\\f(6) = 51\\\\f(-4) = (-4)^2 + 2(-4) + 3\\f(-4) = 16 - 8 + 3\\f(-4) = 11\\\\\frac{f(6)-f(-4)}{6-(-4)} = \frac{51-11}{10} = \frac{40}{10} = 4[/tex]

riddle
What runs around the whole yard without moving?

Answers

Answer:

a yard stick, maybe I'm right

Answer:

a fence

Step-by-step explanation:

HAHAHA LOL

ABC is congruent to EDC, BC = 5 units and DE = 12 units. What is the length of AE?

Answers

Answer:

AE = 26 units

Step-by-step explanation:

Given that ABC is congruent to EDC, therefore, the corresponding angles and corresponding lengths of ∆ABC and ∆EDC are equal to each other in measure.

AE = 2(AC) = 2(CE) or

AE = AC + CE

Let's find the AC using Pythagorean Theorem, since the ∆s are both right triangles.

BA is congruent to DE.

Since DE = 12 units, therefore, BA = 12 units.

BC = 5 units (given)

Using Pythagorean Theorem:

AC² = BA² + BC²

AC² = 12² + 5² (substitution)

AC² = 144 + 25 = 169

AC = √169

AC = 13 units

Since ∆ABC = ∆EDC, therefore:

AE = 2(AC)

AE = 2(13)

AE = 26 units

Which expression is equivalent to – (4-3)?

A. -2(to the power of 2) + 3
B. -2(to the power of 2)– 3
C. -3 - 2(to the power of 2)
D. -3 +2(to the power of 2)

Answers

Answer:

answer is really hard and small, but I can't help because I don't know,

sorry not sorry

lol

regards,

Rosemary

Bernard says “When you halve a whole number that ends in 8, you always
get a number that ends in 4”

Write down an example to show that Bernard is wrong.

is this a trick question?

Answers

Answer:

Bernad is WRONG.

Step-by-step explanation:

Let us take the number '18' (ends with 8)

The half of 18 is '9' (doesn't end with 4)

Let us take the number '38' (ends with 8)

The half of 38 is '19' (doesn't end with 4)

Therefore, Bernard is wrong.

Bernard is wrong because When you halve a whole number that ends in 8, you always cannot get a number that ends in 4

What is an arithmetic operation?

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

Bernard says “When you halve a whole number that ends in 8, you always get a number that ends in 4”

It can be written mathematically:

Let's suppose the number is '18' (ends with 8)

The half of 18 =  9 (doesn't end with 4)

Let's suppose the number is '38' (ends with 8)

The half of 38 = 19 (doesn't end with 4)

Thus, Bernard is wrong because When you halve a whole number that ends in 8, you always cannot get a number that ends in 4

Learn more about the arithmetic operation here:

brainly.com/question/20595275

#SPJ2

Suppose that 2000 is placed in an account that pays 13% interest compounded each year. Assume that no withdrawals are made from the account. Do not do any rounding.
A:Find the amount in the account at the end of 1 year.
B: Find the amount in the account at the end of 2 years.

Answers

After one year there will be $2260 and after two years there will be $2553.80

The amount will be $2260 in the account at the end of 1 year. The amount will be $2553.8 in the account at the end of 2 years.

What is Compound interest?

Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.

A = P(1+r/100)ⁿ

Where:

A = the future value of the investment or loan

P = the principal investment or loan amount

r = the interest rate (decimal)

n = the number of compound periods

As per the question, the given data will be:

p = $2000

r = 13%

t = 1 year

To calculate the amount in the account at the end of 1 year.

A = P(1+r/100)ⁿ

Substitute the values of p,r, and t in the formula,

A = 2000(1 + 13/100)¹

A = 2000(1 + 0.13)¹

A = 2000(1.13)

A = $2260

To calculate the amount in the account at the end of 2 years.

A = 2000(1 + 13/100)²

A = 2000(1 + 0.13)²

A = 2000(1.13)²

A = $2553.8

Thus, the amount will be $2260 in the account at the end of 1 year. The amount will be $2553.8 in the account at the end of 2 years.

To learn more about Compound interest click here:

brainly.com/question/25857212

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what is 2 over 5 simplafied

Answers

Answer:

2/5 simplified is 1/2.5 or .4

Step-by-step explanation:

You simplify by dividing the numerator by the denominator. Thus 2/5 is

.40.

Hope this helps!

Due in 3 mins !! 3 questions Triangle ABC, is rotated 90° counter clockwise about the origin to make triangle A'B'C. Drag and drop the coordinates to describe the transformation !! ( picture!)

Answers

Answer:

A'=(3,-2) B'=(-1,-4) C'=(-5,-3)

Step-by-step explanation:

90 degrees counterclockwise uses (-y,x) so you just plug in the negative y value in the x spot and the x value in the y spot

so can someone of u say the answer becoz I couldn't find the answer I am new here the question is given​

Answers

Answer: The first one is 9/49 and in decimal form it's 0.18367... the second one in fraction form is 16807/161051 and in decimal form is 0.10435824...

Step-by-step explanation: hope this helped

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