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3 years ago

) Would you rather receive $1,500 a year for 12 years, or $1,200 a year for 20 years if the interest rate is 7%?

Mathematics

1 answer:

Umnica [9.8K]3 years ago

6 0

Answer:

$1200 should receive.

Step-by-step explanation:

To check whether to receive $1500 or $1200 just find the present values of each amount.

Present value of annuity $1500:

Present value of annuity = Annuity (P/A, 7%, 12)

Present value of annuity = 1500 (P/A, 7%, 12)

Present value of annuity = 1500 (7.9426)

Present value of annuity = $11913.9

Present value of annuity $1200:

Present value of annuity = Annuity (P/A, 7%, 20)

Present value of annuity = 1500 (P/A, 7%, 20)

Present value of annuity = 1500 (10.5940)

Present value of annuity = $15891

Thus, $1200 should receive.

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A monomial of degree 7 and a leading coefficient of -3

OleMash [197]

Answer:

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Step-by-step explanation:

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3 years ago

How to flip a desk 5 feet long and then flip another desk and it was 10 feet long what would be the answer

-BARSIC- [3]

I think this may be multiplication so 5 times 10 equls50

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3 years ago

Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe

ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for $n\geq 78$

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: $\sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4$

For n=1: $\sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4$

From this point we will assume that $n\geq 2$

As we can see, $\sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4$ and $(4n)^4=256n^4$ . Then,

$\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4$

Now, we will use the formula for the sum of the first 4th powers:

$\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}$

Therefore:

$\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0$

and, because $n \geq 0$ ,

$465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1$

Observe that, because $n \geq 2$ and is an integer,

$n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5$

In concusion, the statement is true if and only if n is a non negative integer such that $n\leq 77$

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute $(4n)^4- \sum^{n}_{i=0} (2i)^4$ for 77 and 78 you will obtain:

$(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064$

$(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992$

7 0

3 years ago

Nachelle goes out to lunch. The bill, before tax and tip, was $8.10. A sales tax of 4% was added on. Nachelle tipped 17% on the

harina [27]

Step-by-step explanation:

Nachelle goes out to lunch. The bill, before tax and tip, was $8.10. A sales tax of 4% was added on. Nachelle tipped 17% on the amount after the sales tax was added. How much was the sales tax? Round to the nearest cent.

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2 years ago

Simplify the square root of 7 divided by square root 27

xxMikexx [17]

Your answer will be 3

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3 years ago