Factor 14x2+6x-7x-3 by grouping

A certain company recently sold five-year $1000 bonds with an annual yield of 9.75%. After how much time could they be sold for

Brut [27]

Answer:

After 7 years and 5 months.

Step-by-step explanation:

Let x represent number of years.

We have been given that a certain company recently sold five-year $1000 bonds with an annual yield of 9.75%.

We can see that the value of bond is increasing exponentially, so we will use exponential growth formula to solve our given problem.

$y=a\cdot (1+r)^x$ , where,

y = Final value,

a = Initial value,

r = Rate in decimal form,

x = Time

$9.75\%=\frac{9.75}{100}=0.0975$

Substituting given values:

$y=1000\cdot (1+0.0975)^x$

$y=1000\cdot (1.0975)^x$

Since we need the selling price to be twice the original price, so we will substitute $y=2000$ in above equation as:

$2000=1000\cdot (1.0975)^x$

$\frac{2000}{1000}=\frac{1000\cdot (1.0975)^x}{1000}$

$2=1.0975^x$

Switch sides:

$1.0975^x=2$

Take natural log of both sides:

$\text{ln}(1.0975^x)=\text{ln}(2)$

Applying rule $\text{ln}(a^b)=b\cdot \text{ln}(a)$ :

$x\cdot \text{ln}(1.0975)=\text{ln}(2)$

$\frac{x\cdot \text{ln}(1.0975)}{\text{ln}(1.0975)}=\frac{\text{ln}(2)}{\text{ln}(1.0975)}$

$x=\frac{0.6931471805599453}{0.0930348659671894}$

$x=7.45040231265$

$x\approx 7.4504$

Since x represents time in years, so we need to convert decimal part into months by multiplying .4504 by 12 as 1 year equals 12 months.

7 years and 12*0.4504023 months = 7 years 5.4 months = 7 years 5 months

Therefore, after 7 years and 5 months the company could sold the bonds for twice their original price.

8 0

3 years ago

EQUATIONS ON BOTH SIDES solve for -3 + 4x =37

miss Akunina [59]

The answer to this equation would be 10!

Steps:
Add 3 to both sides of the equation this would add 3 to 37 making it 40 and when you add 3 to -3 it cancel out so the new equation should look like this!

4x=40

The next step is to divide both sides by four and you get the answer!

X=10

3 0

3 years ago

Read 2 more answers

For a ride on a rental scooter, Charlie paid a $3 fee to start the scooter plus 11 cents per minute of the ride. The total bill

Sever21 [200]

Answer: Charlie travelled for 96 minutes . <h2>Explanations : </h2>

Given

• A ride on a rental scooter cost $3 plus 11 cents per minute for a ride ,

,

• Total bill for Charlies ride = $13.56

,

• Let Charlies ride be equal to ,t minutes, long

,

• This is a linear function representing the total bill for Charlies ride as follows :

$3\text{ + }0.11t=13.56\text{ }$ <h2>Therefore , solving for t , we get that t = </h2> $\begin{gathered} 0.11t\text{ = 13.56 - 3 } \\ 0.11t\text{ = 10.56 } \\ \frac{0.11t}{0.11\text{ }}=\text{ }\frac{10.56}{0.11} \\ \therefore\text{ t = 96 minutes} \end{gathered}$

• t = 96 minutes ,

• This means that Charlie travelled for, 96 minutes ,.

,

• With a total bill of $13.56 , Charlies ride was 96 minutes long.

4 0

2 years ago

(201)3 is equivalente to: (11)10; (10010)2; (11)16; (23)8

sashaice [31]

$(201)_3=2\cdot3^2+0\cdot3^1+1\cdot3^0=2\cdot9+0\cdot3+1\cdot1=18+1=\boxed{(19)_{10}}$

Answers:

A) No

$(11)_{10}\neq(19)_{10}$

B) No

$(10010)_2=1\cdot2^4+0\cdot2^3+0\cdot2^2+1\cdot2^1+0\cdot2^0=16+0+0+2+0=\\\\=\boxed{(18)_{10}\neq(19)_{10}}$

C) No

$(11)_{16}=1\cdot16^1+1\cdot16^0=16+1=\boxed{(17)_{10}\neq(19)_{10}}$

D) Yes

$(23)_8=2\cdot8^1+3\cdot8^0=16+3=\boxed{(19)_{10}}$

7 0

3 years ago

Need help asap

vlabodo [156]

Answer:

7680

Step-by-step explanation:

16(24)20

7680

8 0

3 years ago

Read 2 more answers