Annual interest is P*r^t, r is 0.05 here, t is 9/12=3/4=0.75
P*0.05^0.75=120
use your calculaor: P= 120÷ (0.05)^0.75=1135
so he invested about 1135 dollars
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Answer:
150 degrees
Step-by-step explanation:
Let's start off by looking at what we are working with in this specific problem:
We can see that we are looking at 2 angles, angle L and angle M, that add up to a total of 180 degrees (aka a straight line)
Now that we know that, we also have to keep is mind that angle L + angle M = 180 degrees.
Now that we've got all of that out of the way, let's set up a simple algebraic equation:
angle L + angle M = 180
We also know that angle L is 30 degrees so let's add it into the equation we have just created:
30 + angle M = 180
We now know that 30 plus angle M (whatever it might be) is equal to 180 so in order to solve this problem we have to do some simple subtraction.
180 - 30 = angle M
Now we are left with:
150 degrees = angle M
A=number of seats in section A
B=number of seats in section B
C=number of seats in section C
We can suggest this system of equations:
A+B+C=55,000
A=B+C ⇒A-B-C=0
28A+16B+12C=1,158,000
We solve this system of equations by Gauss Method.
1 1 1 55,000
1 -1 -1 0
28 16 12 1,158,000
1 1 1 55,000
0 -2 -2 -55,000 (R₂-R₁)
0 12 16 382,000 (28R₁-R₂)
1 1 1 55,000
0 -2 -2 -55,000
0 0 4 52,000 (6R₂+R₃)
Therefore:
4C=52,000
C=52,000/4
C=13,000
-2B-2(13,000)=-55,000
-2B-26,000=-55,000
-2B=-55,000+26,000
-2B=-29,000
B=-29,000 / -2
B=14,500.
A + 14,500+13,000=55,000
A+27,500=55,000
A=55,000-27,500
A=27,500.
Answer: there are 27,500 seats in section A, 14,500 seats in section B and 13,000 seats in section C.
