Answer:
14.9%
Step-by-step explanation:
Using the compound interest formula;
A = P(1+r)^t
A is the amount = $2000
P is the principal = $1000
r is the rate
T is the time = 5 years
Substitute the given values into the formula;
2000 = 1000(1+r)^5
2000/1000 = (1+r)^5
2 = (1+r)^5
= 1 + r
r = 1.149 - 1
r = 0.149%
Hence the required rate is 14.9%
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Step-by-step answer:
Angle ECF = 110 = angle of intercepted (minor) arc EF.
The inscribed angles (angles EDF and EHF) are equal to half the angle of the inscribed arc, namely 110/2 = 55 degrees.
For your information, an inscribed angle is an angle with its vertex on (circumference of) the circle, formed by two intersecting chords, with a base on the inscribed arc.
A. The expression for the time t it takes to jog 5 miles from the park as a function of r, we shall proceed as follows:
time=(distance)/speed
time=t
distance=5 miles
speed=(r) miles per hour
plugging the values in the formula we get:
t=5/(r)
b. <span> When you run back to the park, your average speed increases by 1 mph. Write an expression representing your new speed.
</span>Given that on the way back, the speed increases by 1 mph, the expression representing new speed will be:
initial speed=r mph
new speed=r+1=(r+1) mph
c. <span> Write an expression for the time t(in hours) it takes to jog 5 miles back to the park.
Here we shall use the formula:
Time taken for the jog 5 miles back to the park will be given by:
time=distance/speed
distance=5 miles
speed=(r+1) mph
thus
time=5/(r+1) hours
d. The expression for total jogging time will be given by:
Total time=5/r+5/(1+r)
=[5(1+r)+5r]/[r(1+r)]
=[5+5r+5r]/[r(1+r)]
=(5+10r)/[r(1+r)]
e] The total time of jogging given that r=4 mph will be:
plugging r=4 in the answer from (d) we get:
(5+10r)/[r(1+r)]
=(5+10*4)/[4(1+4)]
=(5+40)/(4(5))
=45/20
=2.25 hours</span>
Given b equals -3, determine if it is a solution to 4b - 6 = - 18.
So, we have our given which is b = -3, and we are asked to determine if it a solution to the above equation.
To do this, we can plug -3 in for b and see if it works out.
Work:
Plug in -3 for b.
4(-3) - 6 = - 18
-12 - 6 = -18
-12 - 6 = - 18
Thus, b = -3 is a viable solution for the equation of 4b - 6 = -18.