You deposit $200 every quarter for 12 years into a sinking fund that pays 2.25% interest compounded annually. What is the future
1 answer:
Answer:
$16,974.57
Step-by-step explanation:
The formula for future value is given by
where
FV = future value
PMT = amount deposited each period and is given as 200
i = rate per period = r/m where r is the interest rate and m the frequency of compounding. Here it is mentioned that r = 2.25% and interest is compounded annually ie once per year so m = 1
i = 2.25%/1 = 2.25% = 2.25/100 = 0.0225
The number of payments n = 48 since we make quarterly payments (4 per year) and we are asked to compute for 12 years
Plugging these values into the formula gives
which evaluates to
$16,974.57 which can be rounded up to $16975
depending on the accuracy you desire
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Answer:
the one real zero is in the interval (-1, 0)
Step-by-step explanation:
Descartes' rule of signs tells you there are 0 or 2 positive real zeros. Changing the signs of the odd-degree terms and applying that rule again tells you there is one negative real zero. At the same time, those coefficients (-3, -5, -5, +7) have a negative sum, so you know ...
f(-1) = -6
f(0) = +7
so there is a zero in the interval (-1, 0).
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You can try a few values between x=0 and x=10 to see what the function does in that part of the graph. You find ...
f(1) = 10
f(2) = 21
f(3) = 58
So, it is safe to conclude that there are no real zeros for x > 0.
The only real zero of f(x) is in the interval (-1, 0).
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I like to use a graphing calculator for problems like this.
Answer:
Obese people
Lean People
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, "almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ)".
Solution to the problem
Obese people
Let X the random variable that represent the minutes of a population (obese people), and for this case we know the distribution for X is given by:
Where and
On this case we know that 95% of the data values are within two deviation from the mean using the 68-95-99.7 rule so then we can find the limits liek this:
Lean People
Let X the random variable that represent the minutes of a population (lean people), and for this case we know the distribution for X is given by:
Where and
On this case we know that 95% of the data values are within two deviation from the mean using the 68-95-99.7 rule so then we can find the limits liek this:
The interval for the lean people is significantly higher than the interval for the obese people.