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Ronch [10]
3 years ago
9

If Free Yer Assets Bank (FYAB) will give you 0.25% compounded quarterly and I.M.A.Q.T.π bank will give you 0.23% interest compou

nded continuously, which is offering the better deal (Hint: Show how long it takes to double an investment).
Mathematics
1 answer:
ivann1987 [24]3 years ago
7 0

Answer:

FYAB gives a better deal.

Step-by-step explanation:

Compound interest:

A = P(1 + \dfrac{r}{n})^{nt}

Continuously compounded interest:

A = Pe^{rt}

For the quarterly compounded interest, r = 0.25%, and n = 4.

2P = P(1 + \dfrac{0.0025}{4})^{4t}

1.000625^{4t} = 2

\log (1.000625^{4t}) = \log 2

4t(\log 1.000625) = \log 2

t = \dfrac{\log 2}{4\log 1.000625}

t = 277

For the continuously compounded interest, r =0.23%

A = Pe^{rt}

2P = Pe^{0.0023t}

2 = e^{0.0023t}

\ln 2 = \ln e^{0.0023t}

\ln 2 = 0.0023t

t = \dfrac {\ln 2}{0.0023}

t = 301

The quarterly compounded doubles in 277 years.

The continuously compounded doubles in 301 years.

Answer: FYAB gives a better deal.

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Philip made a total of 9 bracelets and necklaces from 120 inches of cord. He used 8 inches of cord for each bracelet and 20 inch
Viktor [21]

Answer:

So Philip made 5 bracelets and 4 necklaces.

Step-by-step explanation:

Let x = number of bracelets and y = number of necklaces.

Since we have a total of 9 bracelets and necklaces,

x + y = 9 (1)

Also, we have 8 inches of cord for each bracelet and 20 inches of cord for each necklace, then the total length for the bracelet is 8x and that for the necklace is 20y.

So, the total length for both is 8x + 20y. Since the total length of cord used is 120 inches,

8x + 20y = 120 (2)

Simplifying it we have

2x + 5y = 30  (3).

Writing equations (1) and (3) in matrix form, we have

\left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}9\\30\end{array}\right]

Using Cramer's rule to solve for x and y,

x = det \left[\begin{array}{ccc}9&1\\30&5\end{array}\right] /det \left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \\

x = (9 × 5 - 30 × 1) ÷ (1 × 5 - 1 × 2)

x = (45 - 30) ÷ (5 - 2)

x = 15 ÷ 3

x = 5

y = det \left[\begin{array}{ccc}1&9\\2&30\end{array}\right] /det \left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \\

y = (30 × 1 - 9 × 2) ÷ (1 × 5 - 1 × 2)

y = (30 - 18) ÷ (5 - 2)

y = 12 ÷ 3

y = 4

So Philip made 5 bracelets and 4 necklaces.

3 0
3 years ago
Combine like terms:
mario62 [17]

Answer:

Step-by-step explanation:

6 0
3 years ago
The radius of a cylindrical water tank is 4.5 ft, and its height is 8 ft. What is the volume of the tank?
Brums [2.3K]
The answer is 509 ft^3


Formula:
V = πr^2h
V = 3.14 * 4.5^2 * 8
V = 3.14 * 20.25 * 8
V = 508.68 ft^3

508.68 rounded to the nearest whole number is 509

So the volume of the cylinder is 509 ft^3
5 0
3 years ago
17. The perimeter of rectangle RPQT is 134dm.
Rina8888 [55]

Answer:

\sf 1092 \: dm^2

Refer to the attachment for explication of steps. :)

6 0
2 years ago
Need help with number 6
posledela

Answer:

(3)

Step-by-step explanation:

the sum of n and 5 is (n + 5), then multiply by 3 gives

3(n + 5)

The result is at least 17 which means it must be greater than or equal to 17

3(n + 5) ≥ 17

7 0
3 years ago
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