Y divided by 4, if y =3.6

If your invest $150 at 7% interest compounded annually,in how many years will you have $400?. Give your answer of the nearest te

taurus [48]

Answer:

14.5 years.

Step-by-step explanation:

Given that you invest $150 at 7% interest compounded annually. Now we need to find about in how many years will you have $400. Then round the answer ot the nearest tenth of a year.

So plug the given values into compound interest formula.

$A=P\left(1+r\right)^t$

$400=150\left(1+0.07\right)^t$

$\frac{400}{150}=\left(1+0.07\right)^t$

$\ln\left(\frac{400}{150}\right)=\ln\left(1+0.07\right)^t$

$\ln\left(\frac{400}{150}\right)=\ln\left(1.07\right)^t$

$\ln\left(\frac{400}{150}\right)=t\cdot\ln\left(1.07\right)$

$\frac{\ln\left(\frac{400}{150}\right)}{\ln\left(1.07\right)}=t$

$14.4967313882=t$

Which is approx 14.5 years.

8 0

4 years ago

Skyler is 104 miles away from Marcus. They are traveling towards each other. If Marcus travels 8 mph faster than skyler and they

Nina [5.8K]

Speed of skyler is 204 mph and speed of marcus is 212 mph

Solution:

Skyler is 104 miles away from Marcus

Therefore,

Distance = 104 miles

They meet after 4 hours

Time taken = 4 hours

Let "x" be the speed of sklyer

Marcus travels 8 mph faster than skyler

Therefore,

Speed of marcus = 8 + x

They are traveling towards each other

Since they are traveling towards each other, we can add up their speeds

Speed = x + 8 + x = 2x + 8

The distance is given by formula:

$distance = \frac{speed}{time\ taken}\\\\104 = \frac{8+2x}{4}\\\\104 \times 4 = 8 + 2x\\\\8 + 2x = 416\\\\2x = 416-8\\\\2x = 408\\\\x = 204$

Thus speed of skyler = x = 204 mph

Speed of marcus = 8 + x = 8 + 204 = 212 mph

Thus speed of skyler is 204 mph and speed of marcus is 212 mph

6 0

3 years ago

Which is the equation of a hyperbola with directrices at x = ±3 and foci at (4, 0) and (−4, 0)?

photoshop1234 [79]

Answer:A. x squared over 16 minus y squared over 4 ...

Step-by-step explanation:

4 0

2 years ago

3x-15>48 on a number line

Nana76 [90]

Answer:

x>21

Step-by-step explanation:

3x-15>48

Add 15 to each side

3x-15+15>48+15

3x > 63

Divide by 3

3x/3 >63/3

x > 21

Open circle at 21 since there is no equals sign, line to the right

3 0

3 years ago

find a homogeneous linear system of two equations in three unknowns whose solution space consists of those vectors in R3 that ar

Leona [35]

$\mathbf a=(1,1,1)^\top=1\,\mathbf i+1\,\mathbf j+1\,\mathbf k$
$\mathbf b=(-2,3,0)^\top=-2\,\mathbf i+3\,\mathbf j$
$\mathbf a\times\mathbf b=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\1&1&1\\-2&3&0\end{vmatrix}=-3\,\mathbf i-2\,\mathbf j+5\,\mathbf k=(-3,-2,5)^\top$

Basically, you're looking for a matrix $\mathbf A$ such that

$\mathbf A(\mathbf a\times\mathbf b)=\mathbf 0$

i.e. a matrix $\mathbf A$ whose nullspace with basis vector $\mathbf a\times\mathbf b$ .

By the rank-nullity theorem, the rank of $\mathbf A$ and the dimension of its nullspace must add up to the number of columns, so

$\mathrm{rank}\mathbf A+\underbrace{\mathrm{null}\mathbf A}_1=3\implies\mathrm{rank}\mathbf A=2$

One easy choice for a row would be $\begin{bmatrix}1&1&1\end{bmatrix}$ , since

$(1,1,1)(-3,-2,5)^\top=0$

Now you only need to find another combination such that the second row of $\mathbf A$ is independent of the first. An easy choice for this is to let the first element be 0, and the next be 1. Then the last element must be $\dfrac25$ , as

$\left(0,1,\dfrac25\right)(-3,-2,5)^\top=0$

So,

$\underbrace{\begin{bmatrix}1&1&1\\0&1&\frac25\end{bmatrix}}_{\mathbf A}\begin{bmatrix}-3\\-2\\5\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix}$

is one possible solution.

3 0

3 years ago