If A = C + 3A=C+3, B = 2CB=2C, and C = 4C=4, which is the correct order from least to greatest?
1 answer:
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<span>The correct answer is $1452.50 per year.
Explanation:<span>
We use the formula
</span></span>![P(1+\frac{r}{n})^{nt}+PMT(\frac{[(1+\frac{r}{n})^{nt}-1]}{\frac{r}{n}})\times (1+\frac{r}{n})](https://tex.z-dn.net/?f=P%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D%2BPMT%28%5Cfrac%7B%5B%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D-1%5D%7D%7B%5Cfrac%7Br%7D%7Bn%7D%7D%29%5Ctimes%20%281%2B%5Cfrac%7Br%7D%7Bn%7D%29)
,<span><span>
where P is the amount of principal invested, r is the interest rate as a decimal number, n is the number of times per year the interest is compounded, PMT is the monthly deposit added, and t is the number of years.
Since the amount of principal is not stated, we will assume that Bob is depositing the same amount every following year as he does the first year, so we will let PMT=P.
Our interest rate, r, is 4.2%; 4.2%=4.2/100=0.042.
The number of times the interest is compounded annually, n, is 1.
The amount of time, t, is 7.
We know he wants $50,000. This gives us the equation
50000=P(1+0.042/1)</span></span>⁽¹ˣ⁷⁾<span><span>+P{[(1+0.042/1)</span></span>⁽¹ˣ⁷⁾<span><span>]/(0.042/1)}*(1+0.042/1).
Simplifying this a bit, we have
50000=P(1.042)</span></span>⁷<span><span>+P((1.042</span></span>⁷<span><span>)/0.042)*(1.042).
We can factor out P, giving us
50000=P[1.042</span></span>⁷<span><span>+((1.042</span></span>⁷<span><span>)/0.042)*1.042].
This then gives us
50000=P(34.4234).
Divide both sides:
50000/34.4234 = (P(34.4234))/34.4234,
which gives us P=1452.50.</span></span>
Explanation:<span>
We use the formula
</span></span>
where P is the amount of principal invested, r is the interest rate as a decimal number, n is the number of times per year the interest is compounded, PMT is the monthly deposit added, and t is the number of years.
Since the amount of principal is not stated, we will assume that Bob is depositing the same amount every following year as he does the first year, so we will let PMT=P.
Our interest rate, r, is 4.2%; 4.2%=4.2/100=0.042.
The number of times the interest is compounded annually, n, is 1.
The amount of time, t, is 7.
We know he wants $50,000. This gives us the equation
50000=P(1+0.042/1)</span></span>⁽¹ˣ⁷⁾<span><span>+P{[(1+0.042/1)</span></span>⁽¹ˣ⁷⁾<span><span>]/(0.042/1)}*(1+0.042/1).
Simplifying this a bit, we have
50000=P(1.042)</span></span>⁷<span><span>+P((1.042</span></span>⁷<span><span>)/0.042)*(1.042).
We can factor out P, giving us
50000=P[1.042</span></span>⁷<span><span>+((1.042</span></span>⁷<span><span>)/0.042)*1.042].
This then gives us
50000=P(34.4234).
Divide both sides:
50000/34.4234 = (P(34.4234))/34.4234,
which gives us P=1452.50.</span></span>
Answer:
32, <u>16</u>, <u>8</u>, <u>4</u>, <u>2</u>, 1
Explanation:
The geometric mean can be represented by .
Which is the mean of the product of n numbers, used to find the average of a geometric progression.
Don't get confused by geometric mean, it is only asking you about the next numbers in the geometric sequence given the first and sixth term.
The explicit rule for a geometric sequence can be modeled by:
Where is the nth term,
is the first term in the sequence, n is the term number, and r is the common ratio.
Since we already know the first term, will simply be 32.
Since we know it's geometric, there will be an exponential relationship, which means that we will use the geometric mean to find the common ratio.
There are 6 total terms, r is raised to the n – 1 so 6 – 1 = 5, and that will be the degree of this root.
=
=
.
Therefore: .
Using all the information we have, we can find the explicit rule:
-
= 32
→
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We can test that this works by substituting the number location of the term you want to find.
For instance: