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mrs_skeptik [129]
3 years ago
9

If you need $3,000 four years from now, how much would you need to deposit into an account that earns 5% interest, compounded an

nually? $_____
Mathematics
1 answer:
Aleks04 [339]3 years ago
6 0

Answer:

2468.11 dollars

Step-by-step explanation:

Amount that should be available after four years =3000 $

Interest rate = 5%

No of years =4

Let P be the principal invested

Then 3000=P(1+0.05)^4\\P=3000(1.05)^{-4} \\=2468.11

Hence 2468.11 dollars should be deposited to get 3000 dollars after 4 years at 5% interest.

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Solve the triangle A = 2 B = 9 C =8
VARVARA [1.3K]

Answer:

\begin{gathered} A=\text{ 12}\degree \\ B=\text{ 114}\degree \\ C=54\degree \end{gathered}

Step-by-step explanation:

To calculate the angles of the given triangle, we can use the law of cosines:

\begin{gathered} \cos (C)=\frac{a^2+b^2-c^2}{2ab} \\ \cos (A)=\frac{b^2+c^2-a^2}{2bc} \\ \cos (B)=\frac{c^2+a^2-b^2}{2ca} \end{gathered}

Then, given the sides a=2, b=9, and c=8.

\begin{gathered} \cos (A)=\frac{9^2+8^2-2^2}{2\cdot9\cdot8} \\ \cos (A)=\frac{141}{144} \\ A=\cos ^{-1}(\frac{141}{144}) \\ A=11.7 \\ \text{ Rounding to the nearest degree:} \\ A=12º \end{gathered}

For B:

\begin{gathered} \cos (B)=\frac{8^2+2^2-9^2}{2\cdot8\cdot2} \\ \cos (B)=\frac{13}{32} \\ B=\cos ^{-1}(\frac{13}{32}) \\ B=113.9\degree \\ \text{Rounding:} \\ B=114\degree \end{gathered}\begin{gathered} \cos (C)=\frac{2^2+9^2-8^2}{2\cdot2\cdot9} \\ \cos (C)=\frac{21}{36} \\ C=\cos ^{-1}(\frac{21}{36}) \\ C=54.3 \\ \text{Rounding:} \\ C=\text{ 54}\degree \end{gathered}

3 0
1 year ago
What is the volume of a sphere having a diameter of 6 cm?
leonid [27]

Answer:

113.1

Step-by-step explanation:

Volume of sphere = \frac{4}{3} × π × r²

Volume of sphere =  \frac{4}{3} × π × 3²

Volume of sphere =  \frac{4}{3} × π × 9

Volume of sphere =  \frac{4}{3} × 9 π

Volume of sphere = 113.1

4 0
2 years ago
Read 2 more answers
Plsssss help me with this angle circle problem what is x
kirza4 [7]

Answer:

x = 3

Step-by-step explanation:

Once again we want to use the relationship stated earlier

Where A * B = C * D

Once again imagine that the segments in the given problem have letters

A = x

B = 12

C = x + 1

D = 9

Now we create an equation using the relationship

12 * x = 9(x+1)

now we solve using basic algebra

step 1 distribute the 9 to the x and the 1

9 * x = 9x

9 * 1 = 9

now we have 12x = 9x + 9

step 2 subtract 9x from each side

12x - 9x = 3x

9x - 9x cancels out

now we have 3x = 9

step 3 divide each side by 3

3x/3=x

9/3=3

we're left with x = 3

4 0
3 years ago
Read 2 more answers
Pumping 25 gallons of gas into a truck in 3 minutes or filling a bathtub with 40 gallons of water in 5 minutes
Eduardwww [97]

Answer:

Step-by-step explanation:

To do this you have to figure each out in gallons per minute.

25/3 = 8 1/3.  This means that the gas is going into the truck at a rate of 8 1/3 gallons per minute.

40/5 = 8.  This means that the water is going into the tub at a rate of 8 gallons per minute.  

The gas is flowing into the truck faster.

5 0
3 years ago
After applying the composition / to 2004-01-04-06-00_files/i0130000.jpg, what are the coordinates of R' and S'? A. R'(–3, 1), S'
Shalnov [3]
Its not A. I got it wrong
5 0
3 years ago
Read 2 more answers
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