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2 years ago

If $300 is invested at a rate of 5% per year and is compounded quarterly, how much will the investment be worth in 15 years?

1 answer:

5 0

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$300\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &15 \end{cases} \\\\\\ A=300\left(1+\frac{0.05}{4}\right)^{4\cdot 15}\implies A=300(1.0125)^{60}\implies A\approx 632.15$

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Find the increasing functions. Then arrange the increasing functions in order from least to greatest rate of change. (not all of

Aleksandr [31]

Answer:

to a function is increasing we have to find the slope of the function

the higher the slope the faster the growth

Step-by-step explanation:

slope = 5/2. which is 2.5
slope 2 = -1/2 which is -0.5
slope 3 = 3/2 which is 1.5
slope 4 = 1/2 which is 0.5
slope 5= 4/3 which is 1.33
slope 6 = 3/4 which is 0.75

so the function in increasing order

y= -1/2x + 1/2

y= 1/2x - 2

y=3/4x - 10

y=4/3x -7/3

y=3/2x-11/2

y=5/2x +10

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3 years ago

What is the domain and range of f(x)= |x+6|

andreev551 [17]

as the function is polynomial domain exist for all real number ie (-infinity to + infinity) but range exist (0 to +infinity ) due to modulus negetive range do not exist

4 0

3 years ago

Read 2 more answers

How do you do these questions?

algol [13]

Answer:

-x¹⁴ / 5040

-½ < x < ½

Step-by-step explanation:

f(x) = e^(-x²)

The Taylor series for eˣ centered at 0 is:

eˣ = ∑ (1/n!) xⁿ

Substitute -x²:

e^(-x²) = ∑ (1/n!) (-x²)ⁿ

e^(-x²) = ∑ (1/n!) (-1)ⁿ x²ⁿ

The 14th degree term occurs at n=7.

(1/7!) (-1)⁷ x¹⁴

-x¹⁴ / 5040

ln(1 + x) = ∑ₙ₌₁°° (-1)ⁿ⁺¹ xⁿ / n

If we substitute 4x²:

ln(1 + 4x²) = ∑ₙ₌₁°° (-1)ⁿ⁺¹ (4x²)ⁿ / n

Using ratio test:

lim(n→∞)│aₙ₊₁ / aₙ│< 1

lim(n→∞)│[(-1)ⁿ⁺² (4x²)ⁿ⁺¹ / (n+1)] / [(-1)ⁿ⁺¹ (4x²)ⁿ / n]│< 1

lim(n→∞)│-1 (4x²) n / (n+1)│< 1

4x² < 1

x² < ¼

-½ < x < ½

7 0

3 years ago

Plz helppp Use Distributive Property to Solve for x 4 (x + 3)=8

11Alexandr11 [23.1K]

Answer:

x=-1...

have a great day

mark me brainliest

4 0

3 years ago

Read 2 more answers

Brainliest pls help

Airida [17]

<h3>Volume:</h3>

With this prism, first separate it into a rectangular prism and a right triangle prism.

First, with the rectangular prism, it would have the units 5 * 5 * 6.3. Then with the right triangle prism, it would take the rest of the remaining space of it, being 3 * 5 * 6.3

The equation for the volume of a rectangular prism is L*W*H and the equation for the volume of a right triangle prism is (L*W*H) / 2.

With this, plug the numbers in for both prisms to get the volume of each of them:

Rectangular prism Volume

5*5*6.3

157.5

Right triangle prism Volume

(3*5*6.3) / 2

94.5 / 2

47.25

Lastly, combine these two values to get the total volume:

157.5 + 47.25 = 204.75 (Round Up) -->

204.8 cm^3 = Total Volume

<h3>Surface Area:</h3>

Next, with the surface area of the prism. For this, lets combine all of the faces of the prism then add them all up.

First, lets do the bottom of the prism, or the base. It uses the lengths 8 cm and 6.3 cm. Lets do L * W to get the area of this face:

8 * 6.3 = 50.4

Next, lets do the slant side of it, which has the lengths 5.8 and 6.3.

5.8 * 6.3 = 36.54

Then, the top side with the lengths 5cm and 6.3 cm.

5.3 * 6.3 = 33.39

After that, the left side face that opposite to the slantly one:

5 * 6.3 = 31.5

Saving the most tedious part of it for last, the right trapezoids. Luckily, there is an equation for this:

1/2 x (Sum of parallel sides) x (perpendicular distance between the parallel sides).

So, within each of these right trapezoids, there's the parallel sides of 5 and 8. There's also a perpendicular side of 5cm. With this, we can plug this into the equation to solve for this part:

1/2 x (5+8) * (5)

1/2 x (13) * (5)

1/2 x (65)

32.5

Since there's two of them, times this by 2:

32.5 * 2 ---> 65.

Now, with the area of all of the faces, these can be added up for the total surface area:

50.4 + 36.54 + 33.39 + 31.5 + 65 ---> 216.83 (Round Down)-->

216.8 cm^2 = Total Surface Area

8 0

3 years ago