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Mkey [24]
3 years ago
10

if you deposit $8000 into an account paying 9% annual interest compunded semi anually how long will it take for your money to do

uble. round to the nearest hundreth
Mathematics
1 answer:
Anna007 [38]3 years ago
4 0

Answer:

7.87 years

Step-by-step explanation:

#First we determine the effective annual rate based on the 9% compounded semi annual;

i_m=(1+i/m)^m-1\\\\=(1+0.09/2)^2-1\\\\=0.09203

#We then use this effective rate in the compound interest formula to solve for n. Given that the principal doubles after 2 yrs:

A=P(1+i)^n\\\\A=2P, i=i_m\\\\16000=8000(1.09203)^n\\\\2=1.09203^n\\\\n=\frac{log \ 2}{log \ 1.09203}\\\\=7.87324\approx7.87 \ yrs

Hence, it takes 7.87 years for the principal amount to double.

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A plane flew 360km in 3 hrs when flying with the wind.With no change in the wind,the return trip took 4 hrs.Find the speed of th
morpeh [17]
Speed of the plane: 250 mph
Speed of the wind: 50 mph
Explanation:
Let p = the speed of the plane
and w = the speed of the wind
It takes the plane 3 hours to go 600 miles when against the headwind and 2 hours to go 600 miles with the headwind. So we set up a system of equations.
600
m
i
3
h
r
=
p
−
w
600
m
i
2
h
r
=
p
+
w
Solving for the left sides we get:
200mph = p - w
300mph = p + w
Now solve for one variable in either equation. I'll solve for x in the first equation:
200mph = p - w
Add w to both sides:
p = 200mph + w
Now we can substitute the x that we found in the first equation into the second equation so we can solve for w:
300mph = (200mph + w) + w
Combine like terms:
300mph = 200mph + 2w
Subtract 200mph on both sides:
100mph = 2w
Divide by 2:
50mph = w
So the speed of the wind is 50mph.
Now plug the value we just found back in to either equation to find the speed of the plane, I'll plug it into the first equation:
200mph = p - 50mph
Add 50mph on both sides:
250mph = p
So the speed of the plane in still air is 250mph.
6 0
3 years ago
Think about converting 48% to an equivalent fraction in reduced form. If the denominator is 25, what is the numerator?
bulgar [2K]

Answer:

the numerator is 12

Step-by-step explanation:

since 48 is a percent, it would be put as 48/100 as a fraction. since both the numerator and denominator are divisible by 4, you can reduce the fraction into 12/25. Since the question is asking what the numerator was when the denominator was 25, the answer is 12.

8 0
3 years ago
A baseball team won 20 games and lost 10 games. What percent of the games did the team win?
wel

Answer:

66%

Step-by-step explanation:

- First, add 20 + 10 = 30. This will give you the total amount of games.

- Now, make this into a fraction for won games. This should be 20/30.

- Next, take 20/30 and simplify it. You should get 2/3 as a fraction.

- Now, take 2 and divide by 3. (2/3) You should get .66 repeating. This is equal to 66%.

- Therefore 66% is the answer.

- Hope this helps! If you need a further explanation please let me know.

4 0
3 years ago
Read 2 more answers
If two fair dice are rolled, find the probability of a sum of 6 given that the roll
Aliun [14]

Total outcomes of two rolled dice = 6 x 6 = 36

Possibilities for sum of 6 are 3 + 3, 4 + 2, 2 + 4, 5 + 1, 1 + 5. So total possibilities for sum of 6 are five.

<span>Hence the probability for the sum of 6 = 5/36</span>

7 0
3 years ago
2 plus 1 I’m sorry I’m in kindergarten on the way to first grade
natali 33 [55]

The answer is 3

2 + 1 = 3

hoped this helped :) ;)

8 0
3 years ago
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