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
Answer:
(a) x = -1.10 and x = 1.10
Step-by-step explanation:
A straightforward square root will give the value of x.
<h3>Solution</h3>
Divide by the coefficient of x^2:
x^2 -30/25 = 0
x^2 -1.20 = 0
Add 1.20, and take the square root.
x^2 = 1.20
x = ±√1.20 ≈ ±1.0954
x ≈ -1.10 and 1.10 . . . . . round to hundredths
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<em>Additional comment</em>
For small values of x, the root of (1+x) is approximately 1+x/2. For a root accuracy to the nearest hundredth, x < 0.21 (as here). For accuracy to the nearest thousandth, x < 0.064.
Answer:
$80.73
Step-by-step explanation:
115 * 0.35 = $40.25 off
115 - 40.25 = $74.75 after sale
add tax (0.08)
74.75 * 0.08 = $5.98 tax
74.75 + 5.98 = $80.73 in total
The inequality should be
The sign on the right is only a 'smaller than' sign because he spent less than 180.
On the left, assuming that even if Calvin took nobody (poor Calvin), we should assume that he at least went himself, hence he spent a minimum of $12.
