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3 years ago

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Robert has $20,000, part or all of which he wants to invest into a combination of government bonds and municipal bonds. He wants

to invest no more than $5,000 into municipal bonds, and at least twice as much into government bonds than into municipal bonds.

1 answer:

stira [4]3 years ago

8 0

Answer:

x + y ≤ 20,000
y ≤ 5,000
x ≥ 2y

Step-by-step explanation:

Given:

Total amount = $20,000

Assume

Government bonds = x

Municipal bonds = y

Computation:

1. Invest total money

x + y ≤ 20,000

2. invest no more than $5,000 into municipal bonds

y ≤ 5,000

3. at least twice as much into government bonds.

x ≥ 2y

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Georgia [21]

Answer: $\dfrac{1}{2\sqrt x}$

<u>Step-by-step explanation:</u>

$\lim_{h \to 0} f(x)=\dfrac{f(x+h)-f(x)}{h}$

f(x) = $\sqrt x\\$

f(x+h) = $\sqrt{x+h}$

$\lim_{h \to 0} f(x)=\dfrac{\sqrt{x+h}-\sqrt x}{h}$

$=\dfrac{\sqrt{x+h}-\sqrt x}{h}\bigg(\dfrac{\sqrt{x+h}+\sqrt x}{\sqrt{x+h}+\sqrt x}\bigg)$

$=\dfrac{(x + h)-(x)}{h(\sqrt{x+h}+\sqrt x)}$

$=\dfrac{h}{h(\sqrt{x+h}+\sqrt x)}$

$=\dfrac{1}{\sqrt{x+h}+\sqrt x}$

$=\dfrac{1}{\sqrt{x+0}+\sqrt x}$

$=\dfrac{1}{2\sqrt x}$

4 0

4 years ago

Jim saw that other bank offered the same rates but compounded the interest more often. Consider if he still put $15,000 into a s

Kazeer [188]

Compound interest is the addition of interest on the interest of the principal amount.

<h3>What is compound interest?</h3>

Compound interest is the addition of interest on the interest of the principal amount. It is given by the formula,

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

As it is given that the principal amount is $15,000; while the rate of interest is 2.8%, and the amount is invested for a period of 5 years.

A.) When the interest is charged weekly,

As we know that there are 52 weeks in a year, therefore, n = 52, substitute the values,

$A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{52})^{52 \times 5}\\\\A = \$17,253.46$

B.) When the interest is charged daily,

As we know that there are 365 days in a year, therefore, n = 365, substitute the values,

$A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{365})^{365 \times 5}\\\\A = \$19,554.55$

C.) When the interest is charged Continuously,

As we know that the formula for continuous compounding is given as,

$A = Pe^{rt}$

Substitute the values, we will get,

$A = 15000 \times (e^{0.024 \times 5})\\\\A= \$16,912.45$

D.) When the interest is charged Monthly,

As we know that there are 12 months in a year, therefore, n = 12, substitute the values,

$A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{12})^{12\times 5}\\\\A = \$15211.23$

E.) When the interest is charged Semi-annually,

As we know that the interest is charged Semi-annually, therefore, n = 2, substitute the values,

$A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{2})^{2\times 5}\\\\A = \$17,237.36$

F.) When the interest is charged Quarterly,

As we know that the interest is charged Quarterly, therefore, n = 4, substitute the values,

$A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{4})^{4\times 5}\\\\A = \$17,245.7$

Learn more about Compound Interest:

brainly.com/question/25857212

4 0

3 years ago

Read 2 more answers

The distance from the ground of a person riding on a Ferris wheel can be modeled by the equation d equals 20 times the sine of t

kodGreya [7K]

We have the function d, representing the distance from the ground of a person riding on a Ferris wheel:

$d(t)=20\sin (\frac{\pi}{30}t)+10$

If we consider the position of the person at t = 0, which is:

$d(0)=20\sin (\frac{\pi}{30}\cdot0)+10=20\cdot0+10=10$

This position, for t = 0, will be the same position as when the argument of the sine function is equal to 2π, which is equivalent to one cycle of the wheel. Then, we can find the value of t:

$\begin{gathered} \sin (\frac{\pi}{30}t)=\sin (2\pi) \\ \frac{\pi}{30}\cdot t=2\pi \\ t=2\pi\cdot\frac{30}{\pi} \\ t=60 \end{gathered}$

Then, the wheel will repeat its position after t = 60 seconds.

Answer: 60 seconds.

7 0

2 years ago

PLEASE HELP!!: 600 raffle tickets were sold for $5 each. There is one $500 first prize and three $200 second prizes. The remaind

sveta [45]

Answer:

$4,100

Step-by-step explanation:

600 x $5 = $3000

$3000 + $500 = $3500

$3500 + $200 + $200 + $200 = $4100

Thanks to

27turekkm

3 0

2 years ago

What is the scientific notation of 3,482,000,000

alisha [4.7K]

The answer Is 3.482 × 10^9

7 0

4 years ago

Read 2 more answers