We begin with an unknown initial investment value, which we will call P. This value is what we are solving for.
The amount in the account on January 1st, 2015 before Carol withdraws $1000 is found by the compound interest formula A = P(1+r/n)^(nt) ; where A is the amount in the account after interest, r is the interest rate, t is time (in years), and n is the number of compounding periods per year.
In this problem, the interest compounds annually, so we can simplify the formula to A = P(1+r)^t. We can plug in our values for r and t. r is equal to .025, because that is equal to 2.5%. t is equal to one, so we can just write A = P(1.025).
We then must withdraw 1000 from this amount, and allow it to gain interest for one more year.
The principle in the account at the beginning of 2015 after the withdrawal is equal to 1.025P - 1000. We can plug this into the compound interest formula again, as well as the amount in the account at the beginning of 2016.
23,517.6 = (1.025P - 1000)(1 + .025)^1
23,517.6 = (1.025P - 1000)(1.025)
Divide both sides by 1.025
22,944 = (1.025P - 1000)
Add 1000 to both sides
23,944 = 1.025P
Divide both by 1.025 for the answer
$22,384.39 = P. We now have the value of the initial investment.
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y-intercept )
here m = 
and b = 13, hence
y = x + 13 ← in slope- intercept form
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and AB, C are integers )
multiply all terms in the slope-intercept form by 3
3y = x + 39 ( subtract 3y from both sides )
0 = x - 3y + 39 ( subtract 39 from both sides )
x - 3y = - 39 ← in standard form
Answer:
congruent
Step-by-step explanation:
Answer:
V = 1200π
Step-by-step explanation:
Volume of a cylinder formula:
Let's find the height of the cylinder by multiplying 20 cm by 3/5.
The radius is 1/2 of the diameter, so:
Substitute 12 for h and 10 for r into the volume formula.
Simplify.
- V = π * 100(12)
- V = π * 1200
The volume of a cylinder, in terms of π, is V = 1200π.
Answer:
43,758 different swimmer squad
Step-by-step explanation:
Given;
Total Number of athletes n = 18
Number of athletes needed to be selected r = 8
For this case, the coach need to select 8 players from a total of 18 athletes with no particular order. So, this is a combination case since the order of selection is not relevant.
The number of different swimmer squads the coach could select is;
S = nCr
nCr = n!/(r!×(n-r)!)
Substituting the values of n and r;
S = 18C8
S = 18!÷(8! × (18-8)!)
S = 18! ÷ (8!×10!)
S = 43,758
Therefore, he can select 43,758 possible different squads
