A=P (1+r/n)^nt
A= Total amount invested, P=principal amount, r=Interest rate, n=number of time in a year when the interest is earned (for annual, n=1; for semi-annual, n=2, ...), t = time in years
In the current scenario, case 1, n=2; case 2, n=1 and A1=A2, t1=t2
Therefore,
800(1+0.0698/2)^2t = 1000(1+0.0543/1)t
Dividing by 800 on both sides;
(1+0.0349)^2t = 1.25(1+0.02715)^t
(1.0349)^2t = 1.25(1.02715)^t
Taking ln on both sides of the above equation;
2t*ln (1.0349)= ln 1.25 + t*ln (1.02715)
2t*0.0343 = 0.2231+ t*0.0268
0.0686 t = 0.2231+0.0268 t
(0.0686-0.0268)t = 0.2231
0.0418t=0.2231
t=5.337 years
Therefore, after 5.337 years or 5 years and approximately 4 months, their value of investments will be equal.
This value will be,
A=800(1+0.0698/2)^2*5.337 = $1,153.76
$20 a week for 10 weeks is:
20*10 = $200
She spends $6.75 each day for 5 days:
6.75*5 = $33.75.
Lets subtract her spending from her savings to find out how much she has left:
$200-$33.75 = $166.25
Answer:
(-4, 3)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Algebra I</u>
- Solving systems of equations by substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
-3x - 3y = 3
y = -5x - 17
<u>Step 2: Solve for </u><em><u>x</u></em>
<em>Substitution</em>
- Substitute in <em>y</em>: -3x - 3(-5x - 17) = 3
- Distribute -3: -3x + 15x + 51 = 3
- Combine like terms: 12x + 51 = 3
- Isolate <em>x</em> term: 12x = -48
- Isolate <em>x</em>: x = -4
<u>Step 3: Solve for </u><em><u>y</u></em>
- Define equation: y = -5x - 17
- Substitute in <em>x</em>: y = -5(-4) - 17
- Multiply: y = 20 - 17
- Subtract: y = 3
The initial value of a function is the output value of the function when the input value is 0. For example, if your function is tracking how much money you made over a certain amount of time, then the initial value would be however much money you had to begin with on day 0.
HOPE IT HELPED!
<span>P=2,500</span><span>females=f</span><span>males=f+<span>240</span></span>
