Answer: the value of the account after 6 years is $101559.96
Step-by-step explanation:
If $64,000 is invested in an IRA account, then
Principal = $64,000
So P = 64,000
The rate at which $64000 was compounded is 8%
So r = 8/100 = 0.08
If it is compounded once in a year, this means that it is compounded annually (and not semi annually, quarterly or others). So
n = 1
We want to determine the value of the account after 6 years, this means
time, t = 6
Applying the compound interest formula,
A = P(1 + r/n)^nt
A = amount after n number of years
A = 64000( 1 + 0.08/1)^1×6
A = 64000(1.08)^6
A= 64000×1.58687432294
A= 101559.956668416
Approximately $101559.96 to 2 decimal places
ANSWER
1.2 hours
EXPLANATION
Let x represent the number of hours it takes to complete the paint job.
The fraction of a job done per hour with both of them working is 1/x.
Lyle does 1/3 of the painting in one hour
(For example, if it took 3 hours to paint the room, then in one hour, only 1/3 of the room will be painted. In two hours, 1/3 + 1/3 = 2/3 of the room will be painted. In three hours, 1/3+1/3+1/3=3/3=1 of the room will be painted---completed)
Selena does 1/2 of the painting in one hour.
Therefore, for one hour, the fraction of the Job that Lyle does added with the fraction of the Job that Selena does is equal to 1/x, which is the fraction of the job done with both of them working
1/3 + 1/2 = 1/x
Multiply both sides of the equation by x
x/3 + x/2 = 1
Factor out x from the left side
x(1/3 + 1/2) = 1
Combine fractions. Get a common denominator for 1/3 and 1/2.
LCD of 1/3 and 1/2 is 6. 1/3 is equivalent to 2/6 and 1/2 is equivalent to 3/6.
x(2/6 + 3/6) = 1
x (5/6) = 1
x = 1 * 6/5
x = 6/5
x = 1.2 hours
ALTERNATIVE EXPLANTION:
job = rate · time ⇔ rate = job/time ⇔ time = job/rate
Lyle can do 1 paintjob of the room in 3 hours. Therefore, Lyle's rate is 1/3 paintjob per hour.
Selena can do 1 paintjob of the room in 2 hours. Therefore, Selena's rate is 1/2 paintjob per hour.
Their rate when working together is combined:
rate = 1/3 + 1/2 = 2/6 + 3/6 = 5/6
Since time = job/rate and we are interested in 1 paintjob, then job = 1 and
time = 1 / (5/6) = 6/5 = 1.2 hours
The lines are perpendicular to each other because the graph of y = –6 is a horizontal line with a slope that is undefined, and the graph of x = 1/6 is a vertical line with a slope of 0.
The lines are perpendicular to each other because the graph of y = –6 is a vertical line with a slope that is undefined, and the graph of x =1/6 is a horizontal line with a slope of 0.
The lines are perpendicular to each other because the graph of y = –6 is a vertical line with a slope of 0, and the graph of x =1/6 is a horizontal line with a slope that is undefined.
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The lines are perpendicular to each other because the graph of y = –6 is a horizontal line with a slope of 0, and the graph of x =1/6 is a vertical line with a slope that is undefined.
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The 3 is in the one-thousandths place.
You can call this number "zero point zero zero three."
Since the 3 is in the thousandths place, this number can also be called "three thousandths."
Use the name of the number to find the ratio.
"three thousandths" means 3 out of 1000.
The ratio is 3:1000 or 3/1000.
