1=5. 2=10 3=15. 4=10 5=x. what does x equally

You deposit 2000 in account A, which pays 2.25% annual interest compounded monthly. You deposit another 2000 in account b, which

stellarik [79]

To model this situation, we are going to use the compound interest formula: $A=P(1+ \frac{r}{n} )^{nt}$
where
$A$ is the final amount after $t$ years
$P$ is the initial deposit
$r$ is the interest rate in decimal form
$n$ is the number of times the interest is compounded per year
$t$ is the time in years

For account A:
We know for our problem that $P=2000$ and $r= \frac{2.25}{100} =0.0225$ . Since the interest is compounded monthly, it is compounded 12 times per year; therefore, $n=12$ . Lets replace those values in our formula:
$A=2000(1+ \frac{0.0225}{12} )^{12t}$

For account B:
$P=2000$ , $r= \frac{3}{100} =0.03$ , $n=12$ . Lest replace those values in our formula:
$A=2000(1+ \frac{0.03}{12} )^{12t}$

Since we want to find the time, $t$ , when the sum of the balance in both accounts is at least 5000, we need to add both accounts and set that sum equal to 5000:
 $2000(1+ \frac{0.0225}{12} )^{12t}+2000(1+ \frac{0.03}{12} )^{12t}=5000$

Now that we have our equation, we just need to solve for $t$ :
$2000[(1+ \frac{0.0225}{12} )^{12t}+(1+ \frac{0.03}{12} )^{12t}]=5000$
$(1+ \frac{0.0225}{12} )^{12t}+(1+ \frac{0.03}{12} )^{12t}= \frac{5000} {2000}$
$(1.001875)^{12t}+(1.0025 )^{12t}= \frac{5}
{2}$
$ln(1.001875)^{12t}+ln(1.0025 )^{12t}=ln( \frac{5} {2})$
$12tln(1.001875)+12tln(1.0025 )=ln( \frac{5} {2})$
$t[12ln(1.001875)+12ln(1.0025 )]=ln( \frac{5} {2})$
$t= \frac{ln( \frac{5}{2} )}{12ln(1.001875)+12ln(1.0025 )}$
$17.47$

We can conclude that after 17.47 years the sum of the balance in both accounts will be at least 5000.

5 0

3 years ago

Determine the volume of the parallelepiped with one vertex at the origin and the three vertices adjacent to it at (2, â1, â1), (

valentinak56 [21]

Answer:

23

Step-by-step explanation:

Here is the complete question

Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1, 0, -3), (1, 2, 4), and (5, 1, 0).

Solution

We find the volume of the parallelepiped by making a 3 × 3 column matrix whose columns are the corresponding coordinates of the vertices of the parallelepiped.

So, (1, 0, -3), (1, 2, 4) and (5, 1, 0)

$A = \left[\begin{array}{ccc}1&1&5\\0&2&1\\-3&4&0\end{array}\right]$

The determinant of A is the volume of the parallelepiped. So,

detA = 1(2 × 0 - 4 × 1) - 1(0 × 0 - (-3) × 1) + 5(0 × 4 - (-3) × 2)

= 1(0 - 4) - 1(0 + 3) + 5(0 + 6)

= 1(-4) - 1(3) + 5(6)

= -4 - 3 + 30

= 23

So the volume of the parallelepiped is 23

4 0

2 years ago

3. A scuba diver was exploring a reef 32.12 m below sea level. The diver ascended to the surface at a rate of 8.8 m/min. (a) Wri

Mandarinka [93]

A. T= d/r
A good way to remember this is by making a pyramid with 3 parts and putting distance at the top and rate and time in the other two parts. This way you can visibly see the equation and use it if you need to find one for rate.

B. It's reasonable to write distance as a positive number because distance is always positive. You are not able to have a negative distance. Imagine someone standing on a side walk. Even if they are not moving, their distance is 0 which is positive. If they move backwards or forwards, their distance is still positive because it is more than that 0 and they are gaining something.

C. Just plug in the numbers into the formula.
T= d/r
T= 32.12 m /8.8 m/min
T= 3.65 min

4 0

3 years ago

PLZZZ HELP will mark brainliest!

erica [24]

Answer:

(3,8): No, (-1,-11): Yes, (2,7): Yes, (0,-6): No

Step-by-step explanation:

Basically, you just substitute x and y with the numbers given.

18x - 3y = 15

y = 6x - 5

(3,8):

18(3) - 3(8) = 15

54 - 24 = 30 It is not equal to 15, so it does not work.

y = 6x - 5

8 = 6(3) - 5

8 = 13 It is not equal to 8, so it does not work.

Therefore, (3,8) is not a solution.

Try this for every pair and you will find that (-1,-11) and (2,7) are solutions.

I hope this helps!

8 0

2 years ago

X(1+3)= x +3x is an example of which algebraic property?

Dmitry_Shevchenko [17]

Answer:

I think the answer is C.

4 0

2 years ago

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