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andrezito [222]

2 years ago

5

a car cost $25000 plus $675 for tax, title, and license fees. Ari finances the car by putting down $2,500 in cash and taking out

a 3-year, 4% loan. what will his monthly payments be (if figured across all 3 years rather than annually)?

1 answer:

Sergeu [11.5K]2 years ago

8 0

Answer : .333 percentt per month

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It takes one examiner 36 hours to mark 70 exam papers. How long would it take 6 examiners to mark 70 papers?

Orlov [11]

Answer:

36 divided by 6 is 6

Step-by-step explanation:

idk if im right i j wokeup lol

3 0

2 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

2 years ago

2x+3y is greater than or equal to 500 simplified

madreJ [45]

Its already simplified

3 0

2 years ago

How is adding rational numbers different from adding whole numbers

Luda [366]

Adding rational numbers involves adding decimals and repeating decimals like 4.6666666..... Whole numbers on the other hand involves adding 7+6 which arent exactly decimals

8 0

2 years ago

I really need help with this<br><br> Can someone help me thx<br><br><br> Plsssssss

omeli [17]

Answer:

10x^2 - 4x

Step-by-step explanation:

5x - 2 times 2x will equal the area of 'Potatoes.'

5x times 2x is 10x^2.

2 times 2x is 4x.

I cannot provide an exact value because x hasn't been identified.

I hope this helps.

3 0

2 years ago