If the Alexanders completed the 735 mi. trip in 15 hr., what was their average rate of travel?

If an investment of $3000 grows to $4432.37 in eight years with interest compounded annually , what is the interest rate?

melamori03 [73]

$\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\to &\$4432.37\\
P=\textit{original amount deposited}\to &\$3000\\
r=rate\to r\%\to \frac{r}{100}\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annually, thus once}
\end{array}\to &1\\
t=years\to &8
\end{cases}$

$\bf 4432.37=3000\left(1+\frac{r}{1}\right)^{1\cdot 8}\implies \cfrac{4432.37}{3000}=(1+r)^8
\\\\\\
\sqrt[8]{\cfrac{4432.37}{3000}}=1+r\implies \sqrt[8]{\cfrac{4432.37}{3000}}-1=r
\\\\\\
0.0500001086\approx r\qquad\qquad\cfrac{r\%}{100}\approx 0.0500001086
\\\\\\
r\%\approx 100\cdot 0.0500001086\implies r=\stackrel{\%}{5}$

6 0

3 years ago

at noon joice drove to the lake at 30 mi. per hour, but she made a long walk back at 4 mi. per hour. how long did she walk ifshe

Kryger [21]

Distance = 30 mph * time
distance = 4 mph * time

distance = 30 mph * t
distance = 4 mph * (17-t)

Since distance is equal then
30 mph * t = 4 mph * (17-t)

30t = -4t + 68

34t = 68

t = 2 hours

We see the return trip time is (17 -t ) which is 15 hours.
The beginning trip time is 2 hours.

Double Check
Beginning trip = 30 miles * 2 = 60 miles
Return trip = 4 miles * 15 = 60 miles.

3 0

3 years ago

Simplify 4+1/2(24)=x^2

olga nikolaevna [1]

Answer x1 =-4 and x2=4

7 0

3 years ago

Read 2 more answers

Rachel has a box in the shape of a prism with a square base. The capacity of the box is 150 cubic inches. The height of the box

Alex777 [14]

Answer:

Step-by-step explanation:

What do we know about that prism?

It's a rectangular prism with a square base.

Height: y (from question)

base length: x (from question)

base width: x (from question, since it's a square base).

Total volume: 150 cu inches

The question lacks a relationship between x and y the "is __ times", but we can see from the answer choices that they all show a constant relationship:

y = 1.5 x

The volume of a prism is obtained by multiplying the lengths of its 3 dimensions: V = length * width * height. In our case, we then have

150 = x * x * y

then we replace y by its x-expressed equivalent:

150 = x * x * (1.5x) = 1.5x³

then we isolate x³ by dividing each side by 1.5

x³ = 100, we do the cubic root on each side

x = 4.64

So, answer is D. x = 4.6 and y = 6.9

If you you 4.64 * 4.64 * 6.96 = you get 149.8, which is very close to 150.

8 0

3 years ago

Next door to me lives a man with his son. They both work in the same factory. I watch them going to work through my window. The

kirza4 [7]

9514 1404 393

Answer:

k = 5

Step-by-step explanation:

Suppose the distance to the factory is 1 unit. Then the speed the father walks is ...

speed = distance/time = 1 / 30 . . . . units per minute

When the father leaves 10 minutes earlier than the son, his position t minutes after the son starts walking is ...

d = 1/30(t +10)

Similarly, when the father starts 5 minutes earlier than the son, his position t minutes after the son starts walking is ...

d = (1/30)(t +5)

We want that to be the same as the distance the son covers t minutes after he starts walking. The son's progress is ...

d = 1/20t

To find the value of k such that the distance covered is the same 2k minutes after the son starts, we will use t=2k and d=d, so ...

(1/30)(2k +5) = (1/20)(2k)

4k +10 = 6k . . . . . multiply by 60

10 = 2k . . . . . . . . . subtract 4k

5 = k . . . . . . . . . . . divide by 2

__

The attached graph shows the different scenarios, where the blue line is the son's progress. When the father starts 5 minutes earlier, the son meets him half-way to the factory after 10 minutes, so k = 10/2 = 5.

5 0

2 years ago